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United States Patent Application 
20170118717

Kind Code

A1

Rawlins; Gregory S.
; et al.

April 27, 2017

Method, Apparatus and System for Rendering an Information Bearing Function
of Time
Abstract
An embodiment of the present invention is directed to a method for
partitioning an energy or power source. The energy source may be, for
example, a battery or batteries or other power supply or power supplies
for an electronic device, such as a cell phone, or mobile device. The
energy source (battery for example), or power supply, provides power to a
cell phone, or mobile device or any other load or power consuming device.
Partitioning this energy source is a technique for controlling its
operation so that power is provided to the power consuming device, such
as a cell phone more efficiently, thereby extending the length of time
the phone can be used between recharging.
Inventors: 
Rawlins; Gregory S.; (Chuluota, FL)
; Sorrells; David F.; (Middleburg, FL)

Applicant:  Name  City  State  Country  Type  ParkerVision, Inc.  Jacksonville  FL  US
  
Assignee: 
ParkerVision, Inc.
Jacksonville
FL

Family ID:

1000002408399

Appl. No.:

15/401066

Filed:

January 8, 2017 
Related U.S. Patent Documents
        
 Application Number  Filing Date  Patent Number 

 14489121  Sep 17, 2014  
 15401066   
 61878867  Sep 17, 2013  

Current U.S. Class: 
1/1 
Current CPC Class: 
H04W 52/0261 20130101 
International Class: 
H04W 52/02 20060101 H04W052/02 
Claims
1.68. (canceled)
69. A nontransitory computer readable medium storing a series of steps
to execute a method adapted to generate an information bearing function
of time comprising: utilizing a mathematical description of modulation;
generating a functional description of an original data set that is to
modulated; generating an estimation function (D.epsilon..sub.R) with
differential quantities; calculating one or more values for the
information bearing function of time based on realtime input samples and
the estimation function; and generating the information bearing of
function of time based on the calculating step.
70. The method as claimed in claim 69, wherein the mathematical
description of modulation includes real and imaginary components and/or
numbers.
71. The method as claimed in claim 69, wherein the mathematical
description includes digital I and Q components.
72. The method as claimed in claim 69, wherein the information bearing
function of time is a modulated RF carrier waveform.
73. The method as claimed in claim 72, wherein dynamic range of the
modulated RF carrier waveform is approximately between 10 dB and 174 dB.
74. The method as claimed in claim 72, wherein the modulated RF carrier
signal is at two or more power levels.
75.118. (canceled)
119. A nontransitory computer readable medium that stores a series of
steps to execute a method comprising: accounting for a number of desired
degrees of freedom in a system; accounting for a number of undesired
degrees of freedom in the system; exciting one or more of the desired
degrees of freedom with energy; and assessing a response by one or more
of the undesired degrees of freedom and one or more of the desired
degrees of freedom.
120. The method as claimed in claim 119, further comprising: utilizing
apriori information to identify desired degrees of freedom and undesired
degrees of freedom.
121. The method as claimed in claim 119, further comprising:
characterizing the desired degrees of freedom and the undesired degrees
of freedom for the system.
122. The method as claimed in claim 119, wherein the undesired degrees of
freedom include rotational, translational, vibrational and other forms of
spurious energy.
123. The method as claimed in claim 119, further comprising: identifying
a total number of degrees of freedom by accounting for a number of
desired degrees of freedom and a number of undesired degrees of freedom.
124. The method as claimed in claim 119, further comprising: estimating a
probability that one or more of the undesired degrees of freedom will be
in an unexcited state; and controlling one or more of the undesired
degrees of freedom utilizing the probability.
125. The method as claimed in claim 124, further comprising: identifying
one or more thermal characteristics to estimate the probability that one
or more of the undesired degrees of freedom will be in an unexcited
state.
126. The method as claimed in claim 119, further comprising: estimating a
probability that one or more of the desired degrees of freedom will be in
an unexcited state; and controlling one or more of the desired degrees of
freedom utilizing the probability.
Description
CROSS REFERENCE TO RELATED APPLICATION
[0001] This application claims the benefit of U.S. Provisional Patent
Application No. 61/878,867 (Atty. Docket No. 1744.2370000), filed Sep.
17, 2013, titled "Method, Apparatus and System for Rendering an
Information Bearing Function of Time," which is incorporated herein by
reference in its entirety.
BACKGROUND
[0002] Field
[0003] Embodiments of the present invention relate generally to a method,
apparatus and system for rendering an information bearing function of
time based on input signals. Embodiments of the present invention present
a novel solution to increasing operational battery life and reduced
thermal footprint of a cell phone or other communications device,
apparatus, module, subsystem or component by using enhanced information
distribution and power supply control techniques. More particularly,
embodiments of the present invention are directed to rendering the
information bearing function of time based on efficient information
distribution and without requiring feedback loops or predistortion
techniques.
[0004] Background Discussion
[0005] Currently, cell phones and other mobile communications platforms
use an integral battery as a power source. The power source has limited
storage capacity and users are increasingly demanding better performance
from their cell phones. Generally, the cell phone transmitter, and
particularly the power amplifier (PA), consumes a significant amount of
battery power and generates the most heat when compared with other phone
functions. The relative battery power demand of the PA is driven by the
RF link budget and PA efficiency. The PA is not efficient because it
transmits signals while operating in a substantially linear mode of
operation. Both high power output and linearity are required to ensure
that the transmissions from the cell phone conform to currently defined
industry standards, and to overcome communication link budget deficits.
Unwanted heat is generated by the PA because of inefficiencies in PA
operation.
[0006] Generally, PAs operating in a linear mode, are not particularly
efficient, and so, currently, a compromise must be made between battery
life and conformance to the defined industry standards. Since the defined
industry standards are mandatory and inflexible, the reduced battery life
due to the PAs higher power consumption has been expected as a necessary
impact.
[0007] Several conventional PA techniques have been developed in an
attempt to improve operational efficiency of cell phones. Some examples
of these conventional techniques include: envelope tracking;
predistortion; feedback loops; and polar modulation. Other conventional
approaches include amplification techniques, which include: Class AB
power amplifiers; stage switching amplifiers, or Doherty amplifiers;
envelope elimination and restoration amplifiers (EER); and outphasing and
linear amplification with nonlinear components (LINC) amplifiers. Each of
these conventional techniques has drawbacks that make it inadequate.
Thus, embodiments of the present invention have innovated in a different
direction to overcome the inadequacies of the conventional approaches.
Some conventional approaches are described below.
[0008] Envelope Tracking
[0009] An objective of envelope tracking is to improve the efficiency of
power amplifiers (PA) carrying high peakto averagepowerratio (PAPR)
signals. The need to achieve high data throughput within limited spectrum
resources requires the use of linear modulation with high peak to average
power. Unfortunately, traditional fixedsupply power amplifiers operating
under these conditions have low efficiency. One approach to improve the
efficiency of a power amplifier is to vary the amplifier's supply voltage
in synchronism with the amplitude envelope of the RF signal. This is
known as envelope tracking.
[0010] Some types of envelope tracking may include: using direct current
(DC) to direct current (DC) converters; power DAC (digital analog
converter); and Class "AB" push pull video amplifiers. These are some of
the methods used to amplify the amplitude signal. A single amplifier
could also be used with Class "A" operation to transfer amplitude
information to the carrier envelope. Unfortunately, this is a very
inefficient method to transfer envelope energy to the radio frequency
(RF) amplifier. Often envelope tracking is used to make slow adjustments
to the DC supply only when envelope fluctuations are of relatively low
bandwidth. Such an apparatus is not stable or competitively efficient if
modulated at a higher rate as needed in presentday cell phones.
[0011] Another approach is envelope tracking through adjustment of an
amplifier power supply using DC to DC converters. The DC to DC converter
output is varied by its output duty cycle in proportion to a desired
energy so that the resultant filtered voltage level reproduces an
amplitude modulation signal. Unfortunately, a drawback to this approach
is that a high modulation rate may not be achieved without distortion
and/or stability problems.
[0012] In some DC to DC tracking converters the efficiency falls as the
load current decreases. This drop is unsatisfactory for optimal
modulation restoration techniques since it usually causes performance to
fall outside industry specification requirements. Also, another
disadvantage to this approach is that such DC converters often require a
large, ferrite core inductor to convert the switched energy to envelop
power. This undesirably adds to the complexity and cost of the DC
converter. Other semiconductor tradeoffs force the issue of reduced
efficiency versus power output and bandwidth.
[0013] PreDistortion
[0014] Typically, predistortion techniques apply a predistorted power
amplifier (PA) input signal to a PA. This predistorted PA input signal
is used to cancel or compensate for inherent distortion of the PA and
attempts to improve linearization of the PA. Unfortunately, most digital
implementations of predistortion utilize digital signal processing (DSP)
and software, which can cause resource challenges and consume significant
power associated with the management of current PAs, which follow rapid
changes in power levels. Moreover, digital implementations of
predistortion require significant investment of integrated circuit
silicon area.
[0015] Yet another drawback to predistortion techniques is the need to
insert a nonlinear module (typically known as a "predistorter" module)
before the RF power amplifier. This predistorter module counters the
nonlinear portion of the PA transfer characteristic. Thus the overall
system response from input to the output of the PA is linear when
compensated by the predistortion module. The philosophy of this approach
identifies the PA nonlinearity as an undesirable design limitation or
weakness which must be removed. Efficiency is not a primary optimization
parameter for such schemes.
[0016] Adaptive digital predistortion is a technique that involves
digital implementation of the predistorter module and a feedback loop
that adapts to changes in the response of the PA due to varying operating
conditions. The major drawbacks to this technique are increased power
consumption, complexity, size and cost of the system due to the adaptive
feedback architecture.
[0017] Feedback Loops
[0018] As mentioned with respect to predistortion above, a feedback loop
is a circuit configuration that adapts to changes in the response of the
PA due to varying operating conditions. For example, there is a specific
type of feedback loop known as a "regenerative feedback loop".
[0019] Typically, any RF (radio frequency, which possesses a rate of
oscillation in the range of about 3 kHz to 300 GHz, which corresponds to
the frequency of radio waves, and the alternating currents, which carry
radio signals) feedback oscillator can be operated as a regenerative
receiver if modified to provide a controllable reduction in the feedback
loop. It also requires coupling the feedback loop to an incoming signal
source, and coupling audio frequencies out of the feedback loop to a
subsequent audio amplification stage.
[0020] Unfortunately, feedback loops, including regenerative feedback
loops, require additional components and therefore, increase the power
consumption, complexity, size and cost of the circuit. Also, feedback
loops introduce a number of waveform distortions that must be addressed.
Thus, the feedback loops can actually introduce additional noise and
errors into the system. These unwanted imperfections introduced by the
feedback loop result in various waveform contaminations which often
offset the benefits.
[0021] Polar Modulation
[0022] Polar modulation is a modulation technique that uses a modulated
signal that is both phase modulated (PM) and amplitude modulated (AM). In
one example of polar modulation, the low power modulated signal is split
into two components: a phase component; and a magnitude component. The
phase and increased magnitude components are then combined using an
amplifier.
[0023] Unfortunately, polar modulation is an inadequate solution because
it requires a relatively large sample rate compared to the signal Nyquist
bandwidth and often requires the use of predistortion in the phase and
magnitude. Feedback loops are often employed further complicating
solutions at a significant cost in efficiency.
[0024] In addition to the conventional techniques described above, the
field of power amplification also includes the use of amplifiers such as:
Class "AB" Power Amplifiers; Stage Switching and Doherty Amplifiers;
Envelope Elimination and Restoration (EER) Amplifiers; and Outphasing and
Linear Amplification with Nonlinear Components (LINC) Amplifiers. Each of
these amplification techniques suffers drawbacks that make them
unsuitable for use with cell phones.
[0025] Class "AB" Power Amplifiers
[0026] While Class "AB" Power Amplifiers are a mature and popular
technology for high production volume RF amplification circuits, such
amplifiers suffer numerous drawbacks. For instance, Class "AB" amplifiers
achieve only incremental efficiency gains by adaptive bias control,
envelope tracking control, and power supply control. There is a
detrimental tradeoff between linearity and efficiency. "OvertheAir"
specifications impose minimum linearity requirements such that precise
input power backoff is required to balance linearity and efficiency.
("Input power backoff" is a reduction of the output power when reducing
the input power. The efficiency of the power amplifier is reduced due to
backoff of the output power, because the amplifier operates in a linear
region.) Since input power backoff is waveform dependent, the input power
backoff must be increased for higher peak to average waveforms, which
reduces efficiency making Class "AB" amplifiers less than ideal for many
applications.
[0027] Stage Switching Amplifiers and Doherty Amplifiers
[0028] Another conventional approach is to use either stage switching
amplifiers or Doherty amplifiers.
[0029] Stage switching amplifiers are typically implemented with switches
or staggered bias control, which can be optimized for efficiency at
multiple operating points. Stage switching amplifiers have higher average
efficiencies than traditional class "AB" power amplifiers when the output
power range traverses the operating points and such amplifiers can also
be integrated in various semiconductor processes.
[0030] Stage switching amplifiers have a number of undesirable drawbacks.
For example, stage switching amplifiers are normally constructed using
Class "AB" stages and therefore, have all of the limitations of Class
"AB" power amplifiers, some of which were described above. These
drawbacks include a tradeoff of linearity versus efficiency and heat
dissipation.
[0031] Doherty amplifiers are another conventional technique. These
amplifiers have increased efficiency for higher peak to average ratio
waveforms and the carrier power amplifier PA is biased Class "B"
amplification. Typically, with Doherty amplifiers, the carrier PA alone
supplies the output power over most of the output power dynamic range.
The peaking PA is biased as Class "C" amplification and the peaking PA is
"off" during most of the output power dynamic range. The peaking PA and
carrier PA of Doherty amplifiers both supply output power during waveform
peaks.
[0032] Doherty amplifiers suffer numerous undesirable performance
drawbacks. For example, they require precise control of the input drive
and bias of the carrier and peaking PAs (power amplifiers). They also
require precise impedance values to ensure minimum distortion crossover
performance as well as having all of the limitations of linear Class "B"
power amplifiers. As with the case of stage switching amplifiers, Doherty
amplifiers also suffer from linearity versus efficiency tradeoff
problems. Additionally, Doherty amplifiers have inadequacies due to input
backoff considerations, heat dissipation versus linearity tradeoff.
[0033] Thus, both stage switching amplifiers and Doherty amplifiers suffer
from numerous drawbacks, some of which have been discussed above. These
numerous drawbacks result in less than desired performance for many
applications.
[0034] Envelope Elimination and Restoration (EER) Amplifiers
[0035] EER amplifiers separate the phase and amplitude components from a
modulated signal. This type of nonlinear power amplifier technology is
employed in the phase signal path, which has no amplitude component. The
amplitude signal path has no phase component. EER amplifiers can utilize
Class "C", "D", "E", "F" and other nonlinear amplifiers.
[0036] EER amplifiers are also referred to as Kahn and/or polar amplifiers
and are more efficient than Class "AB" power amplifiers at lower output
power levels. The EER amplifier permits the bias and power supply
voltages to be controlled so as to optimize power consumption at
different power levels. Theses amplifiers can be largely integrated in
various semiconductor technologies.
[0037] However, EER amplifiers (Kahn and/or polar amplifiers) have
numerous undesirable characteristics. For example, EER amplifiers have
extreme difficulty maintaining phase signal path and amplitude signal
path alignment. Furthermore, small alignment errors will result in the
failure to pass most ACPR/ACLR requirements. Additionally, EER amplifiers
generally require feedback to achieve linearity requirements. These
feedback mechanisms typically involve polar feedback with separate
amplitude correction and phase correction loops or Cartesian feedback
loops. As discussed above herein, feedback loops greatly reduce amplifier
efficiency. The EER amplifiers which utilize DC to DC converter also
require the DC/DC converter bandwidth to be greater than the signal
bandwidth and are dependent on input waveform linearity. This is a
serious drawback since input waveforms must significantly exceed the
output linearity requirements.
[0038] Another conventional approach has been to use polar amplifiers with
Cartesian feedback. It requires a complex demodulator (I/Q
(InPhase/Quadrature) Receiver) for the feedback path. Furthermore, using
this approach can cause errors in the complex demodulator such as
Quadrature and Amplitude imbalance that will be present on the output
signal. Other drawbacks of this approach include: difficulty maintaining
feedback loop stability due to path delays from the baseband to the RF
output; the complex demodulator reduces the efficiency; and the
requirement that the amplitude envelope reconstruction bandwidth must be
much greater than the desired output signal bandwidth.
[0039] Outphasing and Linear Amplification with Nonlinear Components
(LINC) Amplifiers
[0040] Outphasing was first proposed by H. Chireix, ("High Power
Outphasing Modulation," Proc. IRE, Vol. 23, No. 11, November 1935, pp.
13701392 as a method of Generating High Power/High Quality AM Signals
with vacuum tubes. Starting around 1975, the term "Outphasing" was
supplemented with LINC (Linear Amplification with Nonlinear Components)
as the technology was adopted for use in microwave applications.
Outphasing, or LINC, is a technique that provides InPhase and Quadrature
Phase Baseband Inputs and incorporates transmitter function. It
eliminates the traditional RF transmitter to PA (power amplifier) input
interface impedance match, filter, and backoff requirements. LINC is
able to utilize multiple nonlinear amplifiers in an attempt to increase
amplifier efficiency, favorable thermal characteristics and higher
available output power. Indeed LINC does not have any amplitude and phase
alignment issues that EER architectures do and LINC also has a simple
transfer function. Another advantage of LINC techniques is that InPhase
and Quadrature inputs are transformed into two or more constant envelope
signal components.
[0041] While LINC has some advantages, as discussed above, the technique
suffers serious drawbacks. For example, LINC requires power combiner
technology with the accompanying large physical size (quarter wave
elements are 3.75 cm (1.5 inches) at 2 GHz and 7.5 cm (3.0 inches) at 1
GHz). Secondly, LINC cannot be integrated without large losses, which
causes it to be impractical due to semiconductor die size. LINC also
suffers from a relatively narrow practical application bandwidth.
Moreover, parametric and temperature variations adversely affect
performance. LINC has a limited operational temperature range for optimal
performance.
[0042] Another significant drawback to LINC techniques is a requirement
for isolation between branch power amplifiers. While lossless combiners
(reactive elements only) have been used, this creates output waveform
distortions. Simple Pinetworks have also been used and create undesired
output waveform distortions.
[0043] Referring back to outphasing, the phase accuracy requirements and
physical size are significant drawbacks. For example, at any given power
level, to produce quality waveforms, 40 dB of output power dynamic range
is desirable. Therefore, two sinusoids with perfect amplitude and phase
balance need to vary between 0 degrees phase and 178.86 degrees phase to
achieve a 40 dB dynamic power output range. The accuracy required to
achieve 40 dB challenges the tolerance of practical circuits in a high
volume application. Thus, this technique is not desirable for current
cell phone applications.
[0044] With respect to the large physical size required by outphasing, as
mentioned previously, quarter wave elements are 3.75 cm (.about.1.5
inches) at 2 GHz and 7.5 cm (.about.3.0 inches) at 1 GHz. With such large
size requirements, this approach currently cannot be integrated without
large losses, whenever quarter wave combiner techniques are used even on
a silicon based substrate. Furthermore, it is impractical due to
semiconductor die size. Other drawbacks, similar to those mentioned above
include: narrow bandwidth; having real losses that adversely affect
efficiency; parametric and temperature variations that adversely affect
performance; unittounit performance variations that unexpectedly vary
loss, isolation, and center frequency. Additionally, outphasing has a
limited temperature range for optimal performance and requires isolation
between power amplifiers. Similar to LINC described above, lossless
combiners (reactive elements only) have been used and create undesired
output waveform distortions. Yet another drawback is that outphasing
requires significant branch phase accuracy and branch amplitude accuracy
to generate waveforms of acceptable quality.
BRIEF SUMMARY
[0045] Embodiments of the present invention are directed to methods,
apparatus and systems, as well as components of the methods, apparatus
and systems that provide blended control, (also known as BLENDED CONTROL
BY PARKERVISION.TM., BLENDED CONTROL BY PARKERVISION.TM. is a registered
trademark of ParkerVision, Inc., Jacksonville, Fla.) that enhances power
efficiency or energy efficiency or thermodynamic efficiency (hereafter
simply efficiency unless otherwise stated) for base band and RF
modulation processes. This BLENDED CONTROL BY PARKERVISION.TM. utilizes a
process of distributing domains of information to various apparatus
modulation and encoding functions as well as one or more than one energy
source to improve efficiency of communications systems, devices, and
components including transmitters. This involves the process of
information and energy partitioning, associated with a FLUTTER.TM.
algorithm, (FLUTTER.TM. is a registered trademark of ParkerVision, Inc.,
Jacksonville, Fla.).
[0046] FLUTTER.TM. organizes input control signals, derived from the
information source, into domains, which when processed and reintegrated,
efficiently reconstitute a desired modulation and/or encoding.
FLUTTER.TM. dynamically manipulates multiple degrees of freedom (.nu.+i)
in hardware and/or software, which control the magnitudes and phases of
partitions, whilst allocating quantities of information per partition.
[0047] One novel embodiment of the present invention includes utilizing
FLUTTER.TM. to render an information bearing function of time, which
includes waveforms and/or signals and/or a combination of waveforms and
signals, an RF modulated waveform, and/or an RF modulated carrier signal.
The FLUTTER.TM. process includes compositing multiple signals, for
example, three or more signals, to render the information bearing
function of time, or a representation, or facsimile thereof, such as
electronic data representing the information bearing function of time.
These signals may include one or more phase functions and two or more
amplitude functions. The compositing process includes processing
constituent signals substantially simultaneously (or concurrently or in
parallel), with each constituent signal assigned a weighting factor
dependent on the information distributed by the constituent signal, the
efficiency associated with the constituent signal statistical
distribution and the efficiency for reintegrating constituent signals to
form a desired information bearing function of time. Compositing may also
include mapping of one or more signals or portions of one or more signals
to ranges or domains of functions and their subordinate values according
to a dynamic covariance or crosscorrelation of the functions
distributed within blended controls to an apparatus that generates a
desired output signal or signals. The composite statistic of the blended
controls is determined by at least one information source with
information entropy of H(x), the number of the available degrees of
freedom for the apparatus, the efficiency of each degree of freedom, and
the corresponding potential to reliably distribute a specific signal rate
and information in each degree of freedom. Compositing includes a
dynamically and statistically weighted calculation of a desired complex
signal in terms of the encoded information, complex crosscorrelations of
subordinate functions, compositing signals and minimized waste energy per
unit time. Furthermore, the compositing signals may have different
bandwidths, and spectral distributions. The desired output composited
signal may be an RF carrier signal or a base band signal. The desired
output RF carrier or baseband signal may also exist at variable power
levels.
[0048] A communications platform transmitter based on FLUTTER.TM. and
BLENDED CONTROL BY PARKERVISION.TM. generates a desired communications
signal at the proper signal level and frequency. The results of employing
FLUTTER.TM. and BLENDED CONTROL BY PARKERVISION.TM. algorithms and
architectures are increased efficiency, lower thermal footprint and
universal signal construction. For example, using these algorithms and
architectures, mobile communications devices can operate longer per
battery charge cycle while running cooler. In addition, modern digital
communications standards as well as Legacy modulation standards are
accommodated.
[0049] FLUTTER.TM. significantly reduces the effective sampling rates
and/or bandwidths as well as agile power source resolution critical to
certain aspects of signal envelope reconstruction when compared to Legacy
technologies. FLUTTER.TM. greatly relieves the specification of agile
power supply design used in complex signal envelope construction. While
current technology approaches seek to increase sample rates and
resolution of switched power supplies to increase envelope reconstruction
bandwidths and quality, FLUTTER.TM. enables the minimum information
distributed to one or more agile power sources utilized as part of a
desired complex signal reconstruction process. Unlike legacy
technologies, average complex envelope sample rates in the power source
path may be tailored to fall below the Nyquist reconstruction sample rate
using FLUTTER.TM., if so desired. Compliant signals may be created by the
composite of sparsely sampled power sources with (I) degrees of freedom
and additional (.nu.) degrees of freedom within various encoding and
modulation functions of the transmitter. Given a certain information
entropy allocated to agile power source utilization, FLUTTER.TM. is the
most efficient approach. The FLUTTER.TM. algorithm selects from a minimum
number of specifically tailored power source metrics, distributed at
irregular sample intervals of time dependent on envelope statistics,
whilst assisting the other degrees of freedom in the transmitter in the
process of signal envelope construction. Furthermore, this can be
accomplished with an open loop feed forward (OLFF) algorithm if so
desired. The feed forward approach can also be accompanied by a maximum
pursuit of nonlinearity in a plurality of parallel algorithm paths to
further enhance efficiency whilst preserving ultimate output signal
integrity. Legacy approaches such as envelope tracking, Kahn's technique
and envelope restoration, utilize Nyquist or greater sampling rates,
distributing samples at regular intervals of time, in the power supply
path to construct signal envelopes. Often these techniques utilize
feedback algorithms to enhance quality and compensate for nonlinearities,
in contrast to FLUTTER.TM.. The sampled power supply values are not
optimal, like values determined through FLUTTER.TM.. Rather, they are
determined through standard sampling approaches to follow the magnitude
of a desired envelope at specific regular sample instants (sample
instants are independent of signal envelope statistics) while
interpolating between these sampled values, primarily using filtering
technologies.
[0050] FLUTTER.TM., provides the maximum practical efficiency for signal
envelope construction given finite energy or power supply resources and
the desire to minimize energy or power supply resource performance
requirements when those resources are dynamic.
One Embodiment: Partitioning an Energy Source
[0051] One embodiment of the present invention is directed to a method for
partitioning an energy or power source. The energy source may be, for
example, a battery or batteries or other power supply or power supplies
for an electronic device, such as a cell phone, or mobile device. The
energy source (battery for example), or power supply, provides power to a
cell phone, or mobile device or any other load or power consuming device.
Partitioning this energy source is a technique for controlling its
operation so that power is provided to the power consuming device, such
as a cell phone more efficiently, thereby extending the length of time
the phone can be used between recharging. Each energy partition has one
or more associated sample regions. A sample region corresponds to a range
of voltage and current, from which metered quantities may be extracted,
acquired, generated or sampled and allocated to power the electronic
device, including circuits used for transmission and reception of
information bearing functions of time. A sample region includes one or
more samples that can be used to render a representation of a signal
(information bearing function of time). This representation may be a
reconstruction or rendering. The number of partitions and their
associated metrics are a function of a desired efficiency to render the
desired signal.
[0052] In one embodiment of the present invention, the number of
partitions is bounded by a desired resolution i.ltoreq.2.sup.K where;
[0053] i=number of partitions; and [0054] K=desired resolution for
rendering the signal [0055] (information bearing function of time).
[0056] Thus, the number of partitions (i) is less than or equal to 2
raised to the K.sup.th power.
[0057] A desired signal typically includes information, such as data that
is encoded on a waveform.
[0058] The signal (information bearing function of time) that is rendered,
using the partitioning method described herein, can have an information
entropy value from zero to a maximum value determined by the dynamic
range and ability to access or create resolution of the signal. The
entropy value represents the degree of signal uncertainty; the greater
the entropy the greater the uncertainty and information content.
[0059] The partitioning method described above can also utilize auxiliary
degrees of freedom to determine one or more rendering parameters of a
particular partition. The auxiliary degrees of freedom possess the
quality of, for example, a dimension, or dimensions, or subset of a
dimension, associated with a conceptual mathematical space known as phase
space into which energy and/or information can individually or jointly be
imparted and represented. Such a phase space may be multidimensional and
sponsor multiple degrees of freedom. A single dimension may also support
multiple degrees of freedom. There may be a number, up to and including
.nu., of auxiliary degrees of freedom associated with each one of the 1
partitions. i is typically a number of power source partitions in a
FLUTTER.TM. algorithm. Thus the .nu. degrees of freedom are associated
with other aspects of information encoding functions. Hereafter .nu., i
and auxiliary degrees of freedom will be referred to as desired degrees
of freedom unless otherwise stated.
[0060] Another embodiment of the present invention is directed toward the
partitioning method described above wherein the partitioning method has
parameters for rendering (i.e. rendering parameters) the signal (i.e.,
the information bearing function of time). The rendering parameters or
rendering functions may be expressed as, for example, an amplitude
function, a phase function, a frequency function, or combinations and
permutations of amplitude functions, phase functions and frequency
functions. The amplitude function may be, for example, a voltage or
current versus time or a discrete set of sample values versus sample
number or discrete time increment. The phase function may be for example
a phase angle versus time or a discrete set of sample values versus
sample number or discrete time increment. The frequency function may be,
for example, a frequency versus time or a discrete set of sample values
versus sample number or discrete time increment. Also, amplitude, phase,
and frequency may be interrelated by functions. In addition, rendering
parameters may also consist of operational constants along with some
number of rendering functions. Rendering parameters can be obtained and
assigned from knowledge of the signal and characterization of the
apparatus used for signal construction. Rendering parameters are
coordinated by and distributed by blended controls, which manipulate one
or more degrees of freedom within the apparatus.
[0061] Yet another embodiment of the present invention is directed to the
partitioning method described above in which the energy source (for
example, one or more batteries) may be associated with a plurality of
domains. Domains include a range of values or functions of values
relevant to mathematical and/or logical operation or calculation within
the FLUTTER.TM. algorithm. Domains may apply to multiple dimensions and
therefore bound hypergeometric quantities or objects and they may
include real and imaginary numbers or sets of mathematical and/or logical
functions or objects. Domains may be identified using subsets of the
values from (.nu., i) indices the desirable degrees of freedom for the
system or apparatus. (.nu., i) may be used to specify blended controls
and associated functions. Domains may be associated with sub spaces of
the phase space.
[0062] Yet another embodiment of the present invention is directed to the
partitioning method described above and also utilizes current
differentials. These current differentials provide energy to each
partition in charge increments. In this case differential refers to a
difference between some desired value and some preferred reference value.
[0063] Yet another embodiment of the present invention is directed to the
partitioning method described above and also utilizes electromagnetic
(EM) field differentials. These EM field differentials provide energy to
each partition. In this case differential refers to a difference between
some desired value and some preferred reference value.
[0064] Yet another embodiment of the present invention is directed toward
the partitioning method described above wherein the energy source is
either a fixed energy source or a variable energy source. A fixed energy
source provides access to a fixed potential or rate of charge from one or
more sources. A variable energy source provides access to a variable
potential or rate of charge from one or more sources.
[0065] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes defining a voltage
domain as a function of V.sub..xi.V.sub..xi.1=.DELTA.V.sub.i where .xi.
is a sample increment number. The voltage domain may be fixed or
adjustable. A fixed voltage domain does not change. An adjustable voltage
domain is adjustable over a range of .DELTA.V.sub.i, or a multiplicity
thereof. The adjustment may also be based on H(x).sub..nu.,i or
H(x).sub..nu..sub.i, a set of entropy functions dependent on a number of
transmitter degrees of freedom and power source degrees of freedom. In
this instance, .nu..sub.i is an index for blended controls for one or
more degrees of freedom within a regulator apparatus, where .nu. is a
number of degrees of freedom and i is a power source partition number.
[0066] Yet another embodiment of the present invention is directed to the
partitioning method described above and includes using at least a portion
of prior knowledge to construct a complex signal envelope. The prior
knowledge is information about the desired signal (information bearing
function of time) that is known prior to the rendering of the signal.
This prior knowledge is used in the partitioning procedure to determine
partition metrics, and may include statistical characterization.
[0067] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes parsing the system
input information H(x) into constituent information functions
H(x).sub..nu.,i and/or H(x).sub..nu..sub.i to form domains. Domains may
possess jointlystatistically dependent functions of the constituent
entropy sets H(x).sub..nu.,i, H(x).sub..nu..sub.i.
[0068] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes adjusting .nu., i
and/or .nu..sub.i based on, signal statistics and apparatus
characterization, where .nu. is an index for blended controls for one or
more degrees of freedom.
[0069] Yet another embodiment of the present invention is directed to the
partitioning method described above, wherein the partitioning step
described above also includes generating a blended control function. The
blended control function can be expressed as function {tilde over
(I)}{H(x).sub..nu..sub.i} and/or {tilde over (I)}{H(x).sub..nu.,i} where
.nu.=1, 2, 3 . . . , and i=1, 2, 3, . . . . The blended control function
is used to construct signals via the control of apparatus degrees of
freedom. The blended control function may use a plurality of paths,
including parallel paths, and may also include at least a partial
crosscorrelation between related domains.
[0070] Yet another embodiment of the present invention is directed to the
partitioning method described above, wherein the blended control function
excludes crosscorrelation between domains. In this embodiment, the
blended control function operates independent of crosscorrelation.
[0071] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes calculating and/or
approximating a statistical dependence for the correlations and creating
a composite statistic from the blended controls.
[0072] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes establishing one or
more paths for the partitioning procedure. FLUTTER.TM. can manipulate
partitions which are based on any relevant dynamic operational parameter.
For example, FLUTTER.TM. can manipulate energy, momentum, voltage,
current, and entropy partitions. Manipulations of these quantities
contain portions of the information of a desired signal distributed in
blended controls to parallel segments of a transmitter apparatus.
Information may be encoded in complex values (magnitude and phase) for
each blended control path.
[0073] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes switching a power
source or other partition resource at a rate less than a sampling rate.
This may also include switching the power source or other partition
resource at a rate less than or equal to the Nyquist rate associated with
a rendered output signal. This may also include switching a power supply
or other energy partition resource at a rate greater than the Nyquist
rate. This may include switching a power supply at irregular intervals.
This may also include switching a power supply or other partition
resource at a rate different than the rate used to reconstruct an output
signal.
[0074] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes establishing
sampling rates related to domains. In this embodiment information entropy
and entropy rate within the domain may be used to determine the domain
sampling rate.
[0075] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes establishing domain
bandwidths. Bandwidths associated with processing domains may be less
than a rendering bandwidth for a desired output signal.
[0076] Yet another embodiment of the present invention is directed to the
partitioning method described above wherein one or more blended control
paths manipulate energy partitions. The blended control paths can adjust
the relative weight and access to degrees of freedom of any partition.
The blended control paths, being dynamic, can vary as the information
bearing function of time evolves.
[0077] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes coordinating at
least two partition paths based on one or more parameters of the
information bearing function of time. Thus, partition paths may be
structured depending on parameter(s) of the information bearing function
of time (signal). The parameters of the information bearing function of
time include, for example, functions of phase, and/or functions of
amplitude, entropy, and efficiency.
[0078] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes utilizing one or
more partitions based on one or more energy sources.
[0079] Yet another embodiment of the present invention is directed to the
partitioning method described above and also utilizes a prior
characterization of a system response. The prior characterization can be
used to determine the number of partitions, their associated metrics and
associated sample rates. As described herein, the prior characterization
of the system response is information about the signal that is known
prior to the rendering of the signal.
[0080] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes coordinating one or
more FLUTTER.TM. algorithm parameters. These FLUTTER.TM. algorithm
parameters may include, for example, statistics, ranges, domains, logic
functions and/or metrics. The coordinating is a function of one or more
transmitter parameters. The transmitter parameters may include, for
example, power control states, temperature, power supply levels, antenna
interface circuit impedance, waveform statistics, data rate, channel
frequency, GPS coordinates, accelerometer data, compass information, and
spatial orientation.
[0081] Yet another embodiment of the present invention is directed to the
partitioning method described above, wherein one or more of the energy
partitions are statistically allocated. The one or more of the energy
partitions are allocated to transition between constellation points
within a phase space. The energy partitions are allocated based on a
radial difference of an average of a particular portion of phase space
relative to the phase space center, where a radial value of zero is
designated as the center position of the phase space. Different energy
partitions possess different radial values.
[0082] Yet another embodiment of the present invention is directed to the
partitioning method described above, wherein one or more of the energy
partitions are allocated based on Peak to Average Power Ratio (PAPR)
statistics of the rendered information bearing function of time.
[0083] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes imparting
information embedded within the functions {tilde over
(I)}{H(x).sub..nu..sub.i} and/or {tilde over (I)}{H(x).sub..nu.,i} to one
or more information domains from one or more information sources to
interface to an RF signal modulation architecture. This information
includes any data suitable for application.
[0084] Yet another embodiment of the present invention is directed to the
partitioning method described above and also includes modifying an
operational state of a power supply during the partitioning procedure.
This modification may be for example, turning the power supply "on" or
"off". This modification may also include switching between two or more
power sources during the partitioning procedure. This modification may
also include adjustment of two or more power sources during the
partitioning procedure.
[0085] Yet another embodiment of the present invention is directed to the
partitioning method described above in which one or more partitions are
allocated based on efficiency of operation. Efficiency of operation may
be determined by apparatus characterization, rendered signal statistics
(such as PAPR), by a process of associating volumes of phase space with
associated domain functions, in part based on rendered parameters. This
process is used to develop blended controls. The blended controls can be
used to coordinate partitions.
Another Embodiment: Generating an Information Bearing Function of Time
[0086] Yet another embodiment of the present invention is directed to a
method to generate an information bearing function of time. The
information bearing function of time may be, for example, a signal or
waveform, RF modulated signal, representation of a signal, such as
electronic data stored on a computerreadable medium, an information
bearing energetic function of time and space that enables communication,
or a modulated RF carrier waveform, having a dynamic range of
approximately between 20 dB to 174 dB. The modulated RF carrier waveform
may have one or more power levels. This method may be facilitated by
storage on a computerreadable medium, such as software, or RAM (Random
Access Memory) ROM (Read Only Memory), PROM (Programmable Read Only
Memory), EEPROM (Electrically Erasable Programmable Read Only Memory),
nonvolatile memory, flash memory, memory stick, or other suitable
electronic storage medium.
[0087] This method includes utilizing a mathematical description of
modulation and characterization of apparatus based on prior knowledge of
the apparatus. This mathematical description or substantially equivalent
functional representation provides a model suitable for describing the
modulation and/or information encoding process of the apparatus. A
functional description of an original data set is generated and an
estimation is also generated. The estimation function represents an
approximation of a deviation from an expected, or desired, function of a
signal compared to a signal at the output of the apparatus model. One or
more values for the output information bearing function of time (signal)
are calculated based on realtime input samples, apparatus
characterization and/or real time measurements, and used to develop the
estimation function. The realtime input samples are signals or other
inputs received by the system.
[0088] Yet another embodiment of the present invention is directed to the
method to generate an information bearing function of time in which the
mathematical description of modulation includes real and imaginary
components. The mathematical description includes digital I and Q
components. The Icomponents include "Inphase" and the Qcomponents
include "Quadraturephase".
Another Embodiment: Rendering a Representation of an Information Bearing
Function of Time
[0089] Yet another embodiment of the present invention is directed to a
method for rendering a representation of an information bearing function
of time. The information bearing function of time may be a signal or a
waveform, or an RF carrier signal or a modulated RF carrier waveform.
[0090] The method includes accessing parameters of a desired information
bearing function of time. These parameters include, for example,
amplitude, phase, frequency or functions thereof and may be based on
prior system knowledge. Multiple signals are composited to form a desired
output signal. Compositing includes, for example, mapping one or more
signals or portions of one or more signals to ranges or domains of
functions and their subordinate values. Mapping is accomplished according
to the FLUTTER.TM. algorithm. FLUTTER.TM. manages the apparatus functions
which generate the constituent signals of the blended controls. The
composite statistic of the blended controls is determined by an
information source with source entropy of H(x), the number of the
available degrees of freedom for the apparatus, the efficiency of each
degree of freedom, and the corresponding potential to distribute a
specific signal rate as well as information rate in each degree of
freedom. A representation of the desired information bearing function of
time is rendered based on the compositing step. The rendering may be an
output signal or waveform, or an electronic representation stored on an
electronic medium, such as a computerreadable medium.
[0091] Yet another embodiment of the present invention is directed to the
method for rendering a representation of an information bearing function
of time, as described above, wherein the compositing step includes
managing a covariance of statistical parameters of constituent signals.
Functions of the constituent signals are reintegrated in the compositing
process to form a desired output signal.
[0092] Yet another embodiment of the present invention is directed to the
method for rendering a representation of an information bearing function
of time, as described above, wherein the compositing step includes
crosscorrelations. The crosscorrelations are measurements or
calculations of similarity between two or more waveforms and/or signals.
[0093] Yet another embodiment of the present invention is directed to the
method for rendering a representation of an information bearing function
of time, as described above, wherein the compositing step includes
calculations or measurements of statistical dependencies. The statistical
dependencies include, for example, a condition in which two or more
random variables are not statistically independent.
[0094] Yet another embodiment of the present invention is directed to the
method for rendering a representation of an information bearing function
of time, as described above, wherein the composited signals include one
or more subsets of signals.
[0095] Yet another embodiment of the present invention is directed to the
method for rendering a representation of an information bearing function
of time, as described above, wherein compositing consists of a function
of three or more signals. This set of signals may include, for example,
two or more amplitude functions and one or more phase functions. Indeed,
each of the two or more amplitude functions may have an associated
spectral distribution and respective bandwidths. For example; the first
amplitude function has a first spectral distribution and the second
amplitude function has a second spectral distribution; the first spectral
distribution and bandwidth being different than the second spectral
distribution and bandwidth. In a like manner the multiplicity of phase
functions may possess unique spectral distributions and bandwidths.
[0096] Yet another embodiment of the present invention is directed to the
method for rendering a representation of an information bearing function
of time, as described above, wherein two or more functions (amplitude
and/or phase) have an associated spectral density. Indeed, a first
function has a first spectral density and a second function has a second
spectral density; these first and second spectral densities being at
least partially statistically independent of one another or partially
uncorrelated.
[0097] Yet another embodiment of the present is directed to the method for
rendering a representation of an information bearing function of time, as
described above, wherein the parameters of a desired information bearing
function of time are based, at least in part, on prior knowledge obtained
by apparatus characterization.
Another Embodiment: Generating an Information Bearing Function of Time
Using a Synthesizing Step
[0098] Yet another embodiment of the present invention is directed to a
method for generating an information bearing function of time, or a
representation thereof, that includes identifying one or more
characteristics of an information bearing function of time. The
information bearing function of time may be, for example, a signal,
waveform, RF modulated signal, an RF carrier signal, or wave
representation or composite waveforms. A representation, such as a
waveform, signal, data set, electronic rendering or other manifestation,
of the information bearing function of time may be synthesized based upon
a composition or compositing of multiple signals.
[0099] The composition or compositing includes mapping of one or more
signals or portions of one or more signals to ranges or domains of
functions and their subordinate values according to a dynamic covariance
or crosscorrelation of the functions that distribute blended controls to
an apparatus which generates signals. A composite statistic of the
blended controls can be determined by an information source with source
entropy of H(x), the number of the available degrees of freedom for the
apparatus, the efficiency of each degree of freedom, and the
corresponding potential to distribute a specific signal rate in and
information each degree of freedom. The composition may include, for
example: examining covariance of statistical parameters of a signal of
interest; and crosscorrelations and/or calculated and/or measured
dependencies.
[0100] Yet another embodiment of the present invention is directed toward
the method for generating an information bearing function of time,
described above wherein the multiple signals include three or more
signals. The three or more signals include two or more amplitude
functions and one or more phase functions. Indeed, each of the two or
more amplitude functions has a spectral distribution. For example, a
first amplitude function has a first spectral distribution and bandwidth
and a second amplitude function has a second spectral distribution and
bandwidth; the first spectral distribution does not necessarily equal the
second spectral distribution, or the two spectral distributions may be at
least partially correlated.
[0101] Yet another embodiment of the present invention is directed to the
method for generating an information bearing function of time, described
above wherein parameters of a desired information bearing function of
time are based, at least in part, on prior characterization (prior
knowledge) of the apparatus. The prior knowledge may include, for
example, prior known information about the desired information bearing
function of time, as well as characteristics of an apparatus such as
modulator, encoder or transmitter.
Another Embodiment: Generating an Information Bearing Function of
TimeAccessing Parameters
[0102] Yet another embodiment of the present invention is directed to a
method for generating an information bearing function of time. This
method includes accessing parameters of a desired information bearing
function of time. These parameters include, for example, amplitude,
phase, frequency, or functions thereof. A first subset representation of
the desired information bearing function of time is generated based on
one or more input signals and a first function. The first subset
representation of the desired information bearing function of time is
compared to the parameters of a desired information bearing function of
time and a differential quantity is identified based on the comparison.
The input signals are composited with additional one or more input
signals when the differential quantity exceeds a predetermined threshold
and a second subset representation of the desired information bearing
function of time is generated based on the compositing step. In this case
differential refers to a difference between some desired value and some
preferred reference value.
[0103] Yet another embodiment of the present invention is directed to the
method described above, wherein the differential quantity is a function
of desirable characteristics of the information bearing function of time.
Indeed, the desirable characteristics of the information bearing function
of time include one or more of function of amplitude, function of
frequency and/or function of phase.
[0104] Yet another embodiment of the present invention is directed to the
method described above and also includes identifying one or more
statistics of amplitude, frequency and/or phase.
[0105] Yet another embodiment of the present invention is directed to the
method described above, wherein the parameters of a desired information
bearing function of time are based on prior characterization (prior
knowledge) of the apparatus. This apriori or a priori or prior knowledge
includes information that was known, or identified, prior to the
rendering of the information bearing function of time.
[0106] Yet another embodiment of the present invention is directed to the
method described above, wherein the first subset representation and the
second subset representation are based on nonlinear functions. Thus, the
subset representations are not linear.
[0107] Yet another embodiment of the present invention is directed to the
method described above, wherein the parameters of a desired information
bearing function of time include real and imaginary components that are
established prior to generating a first subset representation of the
desired information bearing function of time.
Another Embodiment: Optimizing a Power Source
[0108] Yet another embodiment of the present invention is directed to a
method for optimizing the relevant metrics of one or more power sources.
This method includes accessing characterizations of an information
bearing function of time. The information bearing function of time may
be, for example, a signal, waveform, RF modulated signal, an RF carrier
signal, or representation or composite waveforms or electronic
replication thereof. A plurality of input sources providing power are
accessed. These input power sources also serve as constituent input
signals, which may be nonlinear and/or switched. Two or more of the input
signals are composited to generate a representation of the desired output
information bearing function of time. This representation may be a
waveform, signal, or electronic representation. An operational state of
at least one of the power sources is controlled based on the compositing
step.
Another Embodiment: Apparatus to Control an Energy Source
[0109] Yet another embodiment of the present invention is directed to an
apparatus to control one or more energy sources. The apparatus includes a
storage module adapted to store one or more functions of the
characteristics of a desired information bearing function of time. These
functions may include, for example, one or more of function of amplitude,
function of frequency and/or function of phase. The information bearing
function of time may be, for example, a signal, waveform, RF modulated
signal, an RF carrier signal, or representation of composite waveforms.
[0110] The apparatus also includes a first module adapted to receive one
or more input signals and provide a first subset of output signals. A
second module, which is operatively coupled to the first module, is
adapted to receive one or more input signals and provide a second subset
of output signals. The first subset of output signals are composited with
the second subset of output signals to generate a representation of the
desired information bearing function of time. The compositing includes
mapping of one or more signals or portions of one or more signals to
ranges or domains of functions and their subordinate values according to
a dynamic covariance or crosscorrelation of the functions that
distribute blended controls to an apparatus which generates signals. The
composite statistic of the blended controls is determined by an
information source with source entropy of H(x), the number of the
available degrees of freedom for the apparatus, the efficiency of each
degree of freedom, and the corresponding potential to distribute a
specific signal rate as well as information in each degree of freedom.
The compositing process may include, for example: examining covariance of
statistical parameters of a signal of interest; and crosscorrelations
and/or calculated dependencies.
[0111] Yet another embodiment of the present invention is directed to the
apparatus described above, wherein the first module and the second module
are nonlinear modules. That is, the first and second modules obtain
nonlinear input signals.
[0112] Yet another embodiment of the present invention is directed to the
apparatus described above and also includes a node, operatively coupled
to the second module, adapted to receive the representation of the
desired information bearing function of time and provide a linear
representation of the desired information bearing function of time.
[0113] Yet another embodiment of the present invention is directed to the
apparatus described above, wherein the signal is reconstituted during
compositing of the one or more first subset of input signals, which are
derived from blended controls, and one or more of the second subset of
input signals, which are derived from blended controls. The
reconstitution is a desired information bearing function of time which is
compliant to a quality metric, often a standard, for example.
Another Embodiment: A Method of Rendering Representation of an Information
Bearing Function of Time
[0114] Yet another embodiment of the present invention is directed to a
method for rendering a representation of an information bearing function
of time. The information bearing function of time may be, for example, a
signal, waveform, RF modulated signal, an RF carrier signal, or wave
representation or composite waveforms or electronic representation
thereof.
[0115] The method includes utilizing one or more energy sources. These
energy sources may be, for example, one or more batteries, one or more
power supplies, other power source or sources, or combinations of these
energy sources. The one or more energy sources are partitioned within
selected domains to efficiently generate signals used to form a rendered
information bearing function of time. Domains, for example, include a
range of values or functions of values relevant to mathematical and/or
logical operations or calculations within the FLUTTER.TM. algorithm.
Domains may apply to multiple dimensions and therefore bound
hypergeometric quantities and they may include real and imaginary
numbers or any suitable mathematical and/or logical function. The
signals, which have been generated, are allocated to render the
representation of the information bearing function of time, such that the
allocation associates with the change of an operational state of at least
one or more than one of the energy sources. The allocation may be
coordinated by a blended control or blended controls, such as BLENDED
CONTROL FUNCTION BY PARKERVISION.TM. according to a FLUTTER.TM.
algorithm.
[0116] Yet another embodiment of the present invention is directed to the
rendering method described above and also includes iteratively optimizing
a blending function for the allocation of the input signals. This
optimization includes characterization of the implementing apparatus and
the information bearing function of time that it renders and constructing
a blended control, such as BLENDED CONTROL FUNCTION BY PARKERVISION.TM.
according to a FLUTTER.TM. algorithm.
[0117] Yet another embodiment of the present invention is directed to the
rendering method described above, wherein the information bearing
function of time is a waveform. This waveform is based on a stimulus
function, which may include the stimulus of some or all of the degrees of
freedom, dimensions and domains of the apparatus.
Another Embodiment: Rendering an Information Bearing Function of Time by
Accessing Parameters
[0118] Yet another embodiment of the present invention is directed to a
method for rendering a representation of an information bearing function
of time. The method includes accessing parameters of a plurality of
desired information bearing functions of time, such as signals,
waveforms, RF modulated signals, and RF carrier signals, or wave
representations or composite waveforms. The plurality of desired
information bearing functions of time may be rendered substantially
simultaneously (or concurrently or in parallel). Multiple signals (signal
subsets) associated with each of the plurality of desired information
bearing functions of time are composited. This composition includes, for
example, mapping of one or more signals or portions of one or more
signals to ranges or domains of functions and their subordinate values
according to a dynamic covariance or crosscorrelation of said functions
that distribute blended controls to an apparatus which generates signals.
The composite statistic of the blended controls is determined by an
information source with source entropy of H(x), the number of the
available degrees of freedom for the apparatus, the efficiency of each
degree of freedom, and the corresponding potential to distribute a
specific signal rate as well as information in each degree of freedom. A
representation of each of the plurality of the desired information
bearing functions of time is generated as a part of the compositing step.
This representation may be, for example, a waveform, a signal, an RF
modulated signal or electronic data that may be stored on an electronic
storage medium, computerreadable medium and/or transmitted to a remote
location via a communication medium, such as a network, wireless medium
or wired medium.
Another Embodiment: Accounting for Degrees of Freedom
[0119] Yet another embodiment of the present invention is directed to a
method that includes accounting for a number and/or impact of desired
degrees of freedom in a system and accounting for a number and/or impact
of undesired degrees of freedom in the system. One or more of the desired
degrees of freedom are excited with energetic waveforms and/or signals
and/or other excitation source. A response by one or more of the
undesired degrees of freedom is assessed. This embodiment is used in a
system that has desired degrees of freedom and undesired degrees of
freedom. Energy may be applied to the system to excite one or more of the
desired degrees of freedom. Undesired degrees of freedom will be excited
by the applied energy and a response to the applied energy by the
undesired degrees of freedom can be assessed. Also desired degrees of
freedom may be monitored and assessed for corresponding excitations.
[0120] Yet another embodiment of the present invention is directed to the
method described above and also includes utilizing prior characterization
(prior knowledge) of the apparatus and desired signal, apriori
information, to identify and/or characterize the desired degrees of
freedom. This prior knowledge is previously obtained, or previously
acquired data about the apparatus and desired information bearing
function of time prior to final rendering. The desired information
bearing function of time may be, for example, a signal, waveform, RF
modulated signal, an RF carrier signal, or wave representation or
composite waveforms.
[0121] Yet another embodiment of the present invention is directed to the
method described above and also includes characterizing the desired
degrees of freedom for the system. This includes, for example, degrees of
freedom that are purposefully designed into the system.
[0122] Yet another embodiment of the present invention is directed to the
method described above, wherein the undesired degrees of freedom include
undesirable phenomena scavenging energy. This may include, for example,
rotational, translational vibrational, as well as other forms of energy,
including apparatus modes which generate heat or any undesirable spurious
phenomena. The undesired degrees of freedom include degrees of freedom
that are not purposefully designed into the system.
[0123] Yet another embodiment of the present invention is directed to the
method described above and also includes identifying and/or
characterizing a total number of degrees of freedom.
[0124] Yet another embodiment of the present invention is directed to the
method described above and also includes estimating a probability or
probabilities that one or more of the undesired degrees of freedom will
be in an excited state or an relatively unexcited state as well as the
probability vs. energy distributed in those states. The effect(s) of one
or more of the undesired degrees of freedom are controlled, or moderated,
utilizing the estimated probability or probabilities. The probability or
probabilities is/are estimated based on prior, or apriori, apparatus
characterization and the statistics of the desired information bearing
function of time.
[0125] Yet another embodiment of the present invention is directed to the
method described above and also includes identifying one or more thermal
characteristics to calculate the probability that one or more of the
undesired degrees of freedom will be in an excited or unexcited state as
well as the probability vs. energy level distributed in those states.
Another Embodiment: Multiple Input Multiple Output Systems
[0126] Yet another embodiment of the present invention is directed to a
method that includes processing one or more information source inputs,
H.sub.1(x), H.sub.2(x) . . . H.sub.m(x), where m is any suitable integer
using FLUTTER.TM. and blended control algorithms to produce one or more
information bearing functions of time. Such information bearing functions
of time, known also as output signals are enumerated 1, 2 . . . n where n
is a suitable integer, are rendered from any number m information sources
and FLUTTER.TM. algorithms via blended controls. For example, any number
of m inputs may be mapped to any number of n outputs where m may or may
not equal n. Each of the n output signals or alternatively output
channels may be a result of independent or dependent compositing. That
is, each of the n outputs may share information to any extent required or
desired. This algorithm may be used in applications such as multiple
input multiple output (MIMO) and diversity processing. In addition, n may
be less than m, thus mapping m input information sources to fewer output
signals.
[0127] Accordingly, embodiments of the present invention are desired to
not encompass any previously known product, process of making the
product, or method of using the product such that Applicants reserve the
right and hereby disclose a disclaimer of any previously known product,
process, or method. It is further noted that embodiments of the present
invention do not intend to encompass within the scope of the invention
any product, process, or making of the product or method of using the
product, which does not meet the written description and enablement
requirements of the USPTO (35 U.S.C. .sctn.112, first paragraph) or the
EPO (Article 83 of the EPC), such that Applicants reserve the right and
hereby disclose a disclaimer of any previously described product, process
of making the product, or method of using the product.
[0128] It is noted that in this disclosure and particularly in the claims
and/or paragraphs, terms such as "comprises", "comprised", "comprising"
and the like can have the meaning attributed to it in U.S. Patent law;
e.g., they can mean "includes", "included", "including", and the like;
and that terms such as "consisting essentially of" and "consists
essentially of have the meaning ascribed to them in U.S. Patent law,
e.g., they allow for elements not explicitly recited, but exclude
elements that are found in the prior art or that affect a basic or novel
characteristic of the invention.
[0129] These and other embodiments are disclosed or are obvious from and
encompassed by, the following Detailed Description.
BRIEF DESCRIPTION OF THE DRAWINGS
[0130] The patent or application file contains at least one drawing
executed in color. Copies of this patent or patent application
publication with color drawing(s) will be provided by the Office upon
request and payment of the necessary fees.
[0131] To the accomplishment of the foregoing and related ends, certain
illustrative aspects of the invention are described herein in connection
with the following description and the annexed drawings. These aspects
are indicative, however, of but a few of the various ways in which the
principles of the invention may be employed and embodiments of the
present invention are intended to include such aspects and their
equivalents. Other advantages, embodiments and novel features of the
invention may become apparent from the following description of
embodiments of the present invention when considered in conjunction with
the drawings. The following description, given by way of example, but not
intended to limit the invention solely to the specific embodiments
described, may be understood in conjunction with the accompanying
drawings, in which:
[0132] FIG. 1 shows a block diagram of inter connect and relation between
FLUTTER.TM., blended control and compositing.
[0133] FIG. 2 shows a block diagram of a modulator apparatus with blended
controls.
[0134] FIG. 3 shows a diagram of energy transformation and entropy
processing with blended controls.
[0135] FIG. 4 shows a block diagram that illustrates parsing information
metric H(x).sub..nu.,i .nu.=1, 2, 3 . . . n (where "n" is any suitable
number), i=1, 2, 3 . . . l (where "l" is any suitable number).
[0136] FIG. 5 shows a block diagram illustrating modification of H(x) by a
channel.
[0137] FIG. 6 shows a graphical representation of an approximate Gaussian
Probability Density Function (pdf) with 0.5 mean.
[0138] FIG. 7 shows a graphical representation of an approximate truncated
Gaussian Probability Density Function (pdf).
[0139] FIG. 8 shows a schematic of a summing node with two input signals
and/or waveforms and one output signal.
[0140] FIGS. 9A and 9B show representations of a differential and single
ended Type I series modulator, respectively, that may be used with
embodiments of the present invention.
[0141] FIGS. 10A and 10B show representations of a differential and single
ended Type I shunt modulator, respectively, that may be used with
embodiments of the present invention.
[0142] FIG. 11 shows a graphical representation of an approximately
Gaussian Probability Density Function (pdf) for output voltage at
particular parameters.
[0143] FIG. 12 shows a graphical representation of a Probability Density
Function (pdf) for the instantaneous efficiency of a particular Type I
modulator.
[0144] FIG. 13 illustrates a method, using a block diagram, for generating
an information bearing function of time using blended controls and
compositing.
[0145] FIG. 14 illustrates a method, using a block diagram, of generating
an information bearing function of time using blended controls and
compositing.
[0146] FIG. 15 shows an example of a parallel channel configuration to
reduce Peak Average Power Ratio (PAPR) per branch.
[0147] FIG. 16 shows an example of pseudophase space samples with three
possible energy partitions.
[0148] FIG. 17 shows a graphical representation of an approximate Gaussian
Probability Density Function (pdf) for output voltage at certain
parameters, illustrating an example associated with three energy
partitions.
[0149] FIG. 18 shows a block diagram of a circuit that transitions as a
statistically influenced boundary is traversed.
[0150] FIG. 19 shows a graphical representation of instantaneous waveform
efficiency as a function of energy partition number for a modulator.
[0151] FIG. 20 shows an example of a series Type 11 modulator.
[0152] FIG. 21 shows an example of a shunt Type 11 modulator.
[0153] FIG. 22 illustrates an information and energy partition
organization in terms of topological signal flow.
[0154] FIGS. 23A and 23B show a particular graphical illustration of
differential magnitude and differential phase entropy surfaces,
respectively.
[0155] FIGS. 24A and 24B show a particular graphical illustration of
reduced differential magnitude and differential phase entropy surfaces,
respectively.
[0156] FIG. 25 shows an example of a composite statistic of the
information bearing function of time and statistics of domains of signals
plotted on voltage and probability axes.
[0157] FIG. 26 shows a flowchart for synthesizing FLUTTER.TM. and blended
controls.
[0158] FIG. 27 shows an example of a circuit using FLUTTER.TM. with (i)
fixed power source partitions and .nu. auxiliary degrees of freedom.
[0159] FIG. 28 shows an example of a Thevenized equivalent of FIG. 27.
[0160] FIG. 29 shows an example of a circuit using FLUTTER.TM. with
switching or variable power supplies for one or more of the energy
partitions.
[0161] FIG. 30 shows of a series equivalent of FIG. 29.
[0162] FIG. 31 shows an example of a modulator architecture which may be
used with the FLUTTER.TM. algorithm.
[0163] FIG. 32 shows an example of a modulator architecture which may be
used with the FLUTTER.TM. algorithm.
[0164] FIG. 33 shows an example of some signals associated with
application of blended controls as part of the FLUTTER.TM. algorithm.
[0165] FIG. 34 shows an example of some signals associated with
application of blended controls as part of the FLUTTER.TM. algorithm.
[0166] FIG. 35 shows a cascaded switch structure.
[0167] FIG. 36 shows a parallel switch topology.
[0168] FIG. 37 shows an example of one or more composite information
bearing functions of time, constructed from one or more information
sources, using a FLUTTER.TM. or blended control based architecture.
[0169] FIG. 38 shows an example of two dimensional geometrical structures
for forming differential surfaces.
[0170] FIG. 39 shows an example of thermodynamic efficiency enhancement
performance plot associated with applications of a FLUTTER.TM. algorithm
to a Type 1 modulator.
DETAILED DESCRIPTION
[0171] The embodiments of the invention and the various features and
advantageous details thereof are explained more fully with reference to
the nonlimiting embodiments, aspects and examples that are described
and/or illustrated in the accompanying figures and detailed in the
following description. It should be noted that the features of one
embodiment or aspect may be employed with other embodiments as the
skilled artisan would recognize, even if not explicitly stated herein.
The examples used herein are intended merely to facilitate an
understanding of ways in which the invention may be practiced and to
further enable those of skill in the art to practice the embodiments of
the present invention. Accordingly, the examples and embodiments herein
should not be construed as limiting the scope of the invention, which is
defined solely by the appended claims.
DEFINITIONS
[0172] 1.sup.st Law of Thermodynamics: The first law is often formulated
by stating that the change in the internal energy of a closed system is
equal to the amount of heat supplied to the system, minus the amount of
work done by the system on its surroundings. Other forms of energy
(including electrical) may be substituted for heat energy in an extension
of the first law formulation. The first law of thermodynamics is an
energy conservation law with an implication that energy cannot be created
or destroyed. Energy may be transformed or transported but a numerical
calculation of the sum total of energy inputs to an isolated process or
system will equal the total of the energy stored in the process or system
plus the energy output from the process or system. The law of
conservation of energy states that the total energy of an isolated system
is constant. The first law of thermodynamics is referenced occasionally
as simply the first law.
[0173] 2.sup.nd Law of Thermodynamics: The second law is a basic postulate
defining the concept of thermodynamic entropy, applicable to any system
involving measurable energy transfer (classically heat energy transfer).
In statistical mechanics information entropy is defined from information
theory using Shannon's entropy. In the language of statistical mechanics,
entropy is a measure of the number of alternative microscopic
configurations or states of a system corresponding to a single
macroscopic state of the system. One consequence of the second law is
that practical physical systems may never achieve 100% thermodynamic
efficiency. Also, the entropy of an isolated system will always possess
an ever increasing entropy up to the point equilibrium is achieved. The
second law of thermodynamics is referred to as simply the second law.
[0174] ACPR: Adjacent Channel Power Ratio usually measured in decibels
(dB) as the ratio of an "out of band" power per unit bandwidth to an "in
band" signal power per unit bandwidth. This measurement is usually
accomplished in the frequency domain. Out of band power is typically
unwanted.
[0175] A.C.: An alternating current which corresponds to a change in the
direction of charge transport and/or the electromagnetic fields
associated with moving charge through a circuit. One direction of current
flow is usually labeled as positive and the opposite direction of current
flow is labeled as negative and direction of current flow will change
back and forth between positive and negative over time.
[0176] Access: Obtain examine or retrieve; ability to use; freedom or
ability to obtain or make use of something.
[0177] Account: Record, summarize; keeping a record of; reporting or
describing an existence of.
[0178] A.C. Coupled: A circuit or system/module is A.C. coupled at is
interfaced to another circuit or system/module if D.C. current cannot
pass through the interface but A.C. current or signal or waveform can
pass through the interface.
[0179] A.C.L.R.: Adjacent channel leakage ratio is a measure of how much
signal from a specific channel allocation leaks to an adjacent channel.
In this case channel refers to a band of frequencies. Leakage from one
band or one channel to another band or channel occurs when signals are
processed by nonlinear systems.
[0180] A/D: Analog to digital conversion.
[0181] Adapt: Modify or adjust or reconstruct for utilization.
[0182] Adjust: Alter or change or arrange for a desired result or outcome.
[0183] Algorithm: A set of steps that are followed in some sequence to
solve a mathematical problem or to complete a process or operation such
as (for example) generating signals according to FLUTTER.TM..
[0184] Align: Arrange in a desired formation; adjust a position relative
to another object, article or item, or adjust a quality/characteristic of
objects, articles or items in a relative sense.
[0185] Allocate: Assign, distribute, designate or apportion.
[0186] Amplitude: A scalar value which may vary with time. Amplitude can
be associated as a value of a function according to its argument relative
to the value zero. Amplitude may be used to increase or attenuate the
value of a signal by multiplying a constant by the function. A larger
constant multiplier increases amplitude while a smaller relative constant
decreases amplitude. Amplitude may assume both positive and negative
values.
[0187] Annihilation of Information: Transfer of information entropy into
noninformation bearing degrees of freedom no longer accessible to the
information bearing degrees of freedom of the system and therefore lost
in a practical sense even if an imprint is transferred to the environment
through a corresponding increase in thermodynamic entropy.
[0188] Apparatus: Any system or systematic organization of activities,
algorithms, functions, modules, processes, collectively directed toward a
set of goals and/or requirements: An electronic apparatus consists of
algorithms, software, functions, modules, and circuits in a suitable
combination depending on application which collectively fulfill a
requirement. A set of materials or equipment or modules designed for a
particular use.
[0189] Application Phase Space: Application phase space is a higher level
of abstraction than phase space. Application phase space consists of one
or more of the attributes of phase space organized at a macroscopic level
with modules and functions within the apparatus. Phase space may account
for the state of matter at the microscopic (molecular) level but
application phase space includes consideration of bulk statistics for the
state of matter where the bulks are associated with a module function, or
degree of freedom for the apparatus.
[0190] Approximate: Approximate: almost correct or exact; close in value
or amount but not completely precise; nearly correct or exact.
[0191] apriori: What can be known based on inference from common knowledge
derived through prior experience, observation, characterization and/or
measurement. Formed or conceived beforehand; relating to what can be
known through an understanding of how certain things work rather than by
observation; presupposed by experience. Sometimes separated as a priori.
[0192] Articulating: Manipulation of multiple degrees of freedom utilizing
multiple facilities of an apparatus in a deliberate fashion to accomplish
a function or process.
[0193] Associate: To be in relation to another object or thing; linked
together in some fashion or degree.
[0194] Auto Correlation: Method of comparing a signal with or waveform
itself. For example, TimeAuto Correlation function compares a time
shifted version of a signal or waveform with itself. The comparison is by
means of correlation.
[0195] Auto Covariance: Method of comparing a signal or waveform with
itself once the average value of the signal/or waveform is removed. For
example, a time auto covariance function compares a signal or waveform
with a time shifted version of said signal or waveform.
[0196] Bandwidth: Frequency span over which a substantial portion of a
signal is restricted or distributed according to some desired performance
metric. Often a 3 dB power metric is allocated for the upper and lower
band (span) edge to facilitate the definition. However, sometimes a
differing frequency span vs. power metric, or frequency span vs. phase
metric, or frequency span vs. time metric, is allocated/specified.
Frequency span may also be referred to on occasion as band, or bandwidth
depending on context.
[0197] Baseband: Range of frequencies near to zero Hz. and including zero
Hz.
[0198] Bin: A subset of values or span of values within some range or
domain.
[0199] Bit: Unit of information measure (binary digit) calculated using
numbers with a base 2.
[0200] Blended Controls: A set of dynamic distributed control signals
generated as part of the FLUTTER.TM. algorithm, used to program,
configure, and dynamically manipulate the information encoding and
modulation facilities of a communications apparatus.
[0201] Blended Control Function: Set of dynamic and configurable controls
which are distributed to an apparatus according to an optimization
algorithm which accounts for H(x), the input information entropy, the
waveform standard, significant hardware variables and operational
parameters. Blended control functions are represented by {tilde over
(I)}{H(x).sub..nu.,i} where .nu.+i is the total number of degrees of
freedom for the apparatus which is being controlled. BLENDED CONTROL BY
PARKERVISION.TM. is a registered trademark of ParkerVision, Inc.,
Jacksonville, Fla.
[0202] Branch: A path within a circuit or algorithm or architecture.
[0203] Bus: One or more than one interconnecting structure such as wires
or signal lines which may interface between circuits or modules and
transport digital or analog information or both.
[0204] C: An abbreviation for coulomb, which is a quantity of charge.
[0205] Calculate: Solve; probe the meaning of; to obtain the general idea
about something; to determine by a process. Solve a mathematical problem
or equation.
[0206] Capacity: The maximum possible rate for information transfer
through a communications channel, while maintaining a specified quality
metric. Capacity may also be designated (abbreviated) as C, or C with
possibly a subscript, depending on context. It should not be confused
with Coulomb, a quantity of charge. On occasion capacity is qualified by
some restrictive characteristics of the channel.
[0207] Cascading: Transferring or representing a quantity or multiple
quantities sequentially. Transferring a quantity or multiple quantities
sequentially.
[0208] Cascoding: Using a power source connection configuration to
increase potential energy.
[0209] Causal: A causal system means that a system's output response (as a
function of time) cannot precede its input stimulus.
[0210] CDF or cdf: Cumulative Distribution Function in probability theory
and statistics, the cumulative distribution function (CDF), describes the
probability that a realvalued random variable X with a given probability
distribution will be found at a value less than or equal to x. Cumulative
distribution functions are also used to specify the distribution of
multivariate random variables. A cdf may be obtained through an
integration or accumulation over a relevant pdf domain.
[0211] Characterization: Describing the qualities or attributes of
something. The process of determining the qualities or attributes of an
object, or system.
[0212] Channel Frequency: The center frequency for a channel. The center
frequency for a range or span of frequencies allocated to a channel.
[0213] Charge: Fundamental unit in coulombs associated with an electron or
proton, .about..+.1.602.times.10.sup.19 C., or an integral multiplicity
thereof.
[0214] Code: A combination of symbols which collectively possess an
information entropy.
[0215] Communication: Transfer of information through space and time.
[0216] Communication Channel: Any path possessing a material and/or
spatial quality that facilitates the transport of a signal.
[0217] Communications Sink: Targeted load for a communications signal or
an apparatus that utilizes a communication signal. Load in this
circumstance refers to a termination which consumes the application
signal and dissipates energy.
[0218] Complex Correlation: The variables which are compared are
represented by complex numbers. The resulting metric may have a complex
number result.
[0219] Complex Number: A number which has two components; a real part and
an imaginary part. The imaginary part is usually associated with a
multiplicative symbol i) or j) which has a value {square root over
(1)}. The numbers are used to represent values on two different number
lines and operations or calculations with these numbers require the use
of complex arithmetic. Complex arithmetic and the associated numbers are
used often in the study signals, mathematical spaces, physics and many
branches of science and engineering.
[0220] Complex Signal Envelope: A mathematical description of a signal,
x(t), suitable for RF as well as other applications. The various
quantities and relationships that follow may be derived from one another
using vector analysis and trigonometry as well as complex arithmetic.
x(t)=a(t)e.sup.j(.omega..sup.c.sup.t+.phi.(t))
x(t)=a.sub.l(t)cos(.omega..sub.ct+.phi.(t))a.sub.Q(t)sin(.omega..sub.ct
+.phi.(t))
.omega..sub.c.ident.Carrier Frequency .phi.(t).ident.Phase Information
vs. Time a(t).ident.Amplitude Information vs. Time
a(t)= {square root over (a.sub.I.sup.2(t)+a.sub.Q.sup.2(t))}
.phi. ( t ) = arctan [ a Q ( t ) a I ( t )
] [ sign ] ##EQU00001##
[sign].ident.A function which accounts for the quadrant of S(t) in the
complex signal/waveform plane. Sometimes referred to as complex envelope
or simply envelope.
[0221] Compositing: The mapping of one or more constituent signals or
portions of one or more constituent signals to domains and their
subordinate functions and arguments according to a FLUTTER.TM. algorithm.
Blended controls developed in the FLUTTER.TM. algorithm, regulate the
distribution of information to each constituent signal. The composite
statistic of the blended controls is determined by an information source
with source entropy of H(x), the number of the available degrees of
freedom for the apparatus, the efficiency of each degree of freedom, and
the corresponding potential to distribute a specific signal rate, as well
as information, in each degree of freedom.
[0222] Consideration: Use as a factor in making a determination.
[0223] Constellation: Set of coordinates in some coordinate system with an
associated pattern.
[0224] Constellation Point: A single coordinate from a constellation.
[0225] Constituent Signal: A signal which is part of a parallel processing
path in FLUTTER.TM. and used to form more complex signals through
compositing or other operations.
[0226] Coordinate: A value which qualifies and/or quantifies position
within a mathematical space. Also may possess the meaning, to manage a
process.
[0227] Correlation: The measure by which the similarity of two or more
variables may be compared. A measure of 1 implies they are equivalent and
a measure of 0 implies the variables are completely dissimilar. A measure
of (1) implies the variables are opposite or inverse. Values between
(1) and (+1) other than zero also provide a relative similarity metric.
[0228] Covariance: This is a correlation operation between two different
random variables for which the random variables have their expected
values or average values extracted prior to performing correlation.
[0229] Crete: To make or produce or cause to exist; to being about; to
bring into existence. Synthesize, generate.
[0230] CrossCorrelations: Correlation between two different variables.
[0231] CrossCovariance: Covariance between two different random
variables.
[0232] Current: The flow of charge per unit time through a circuit.
[0233] d2p.TM.: Direct to Power (Direct2Power.TM.) a registered trademark
of ParkerVision Inc., corresponding to a proprietary RF modulator and
transmitter architecture and modulator device.
[0234] D/A: Digital to Analog conversion.
[0235] Data Rates: A rate of information flow per unit time.
[0236] D.C.: Direct Current referring to the average transfer of charge
per unit time in a specific path through a circuit. This is juxtaposed to
an AC current which may alternate directions along the circuit path over
time. Generally a specific direction is assigned as being a positive
direct current and the opposite direction of current flow through the
circuit is negative.
[0237] D.C. Coupled: A circuit or system/module is D.C. coupled at its
interface to another circuit or system/module if D.C. current or a
constant waveform value may pass through the interface.
[0238] DCPS: Digitally Controlled Power or Energy Source
[0239] Decoding: Process of extracting information from an encoded signal.
[0240] Decoding of Time: The time interval to accomplish a portion or all
of decoding.
[0241] Degrees of Freedom: A subset of some space (for instance phase
space) into which energy and/or information can individually or jointly
be imparted and extracted according to qualified rules which may
determine codependences. Such a space may be multidimensional and
sponsor multiple degrees of freedom. A single dimension may also support
multiple degrees of freedom. Degrees of freedom may possess any dependent
relation to one another but are considered to be at least partially
independent if they are partially or completely uncorrelated. Degrees of
freedom also possess a corresponding realization in the information
encoding and modulation functions of a communications apparatus.
Different mechanisms for encoding information in the apparatus may be
considered as degrees of freedom.
[0242] Delta Function: In mathematics, the Dirac delta function, or
.delta. function, is a generalized function, or distribution, on the real
number line that is zero everywhere except at the specified argument of
the function, with an integral equal to the value one when integrated
over the entire real line. A weighted delta function is a delta function
multiplied by a constant or variable.
[0243] Density of States for Phase Space: Function of a set of relevant
coordinates of some mathematical, geometrical space such as phase space
which may be assigned a unique time and/or probability, and/or
probability density. The probability densities may statistically
characterize meaningful physical quantities that can be further
represented by scalars, vectors and tensors.
[0244] Derived: Originating from a source in a manner which may be
confirmed by measure, analysis, or inference.
[0245] Desired Degree of Freedom: A degree of freedom that is efficiently
encoded with information. These degrees of freedom enhance information
conservation and are energetically conservative to the greatest practical
extent. They are also known as information bearing degrees of freedom.
These degrees of freedom may be deliberately controlled or manipulated to
affect the causal response of a system through, and application of,
algorithm or function such as a blended control function enabled by a
FLUTTER.TM. algorithm.
[0246] Dimension: A metric of a mathematical space. A single space may
have one or more than one dimension. Often, dimensions are orthogonal.
Ordinary space has 3dimensions; length, width and depth. However,
dimensions may include time metrics, code metrics, frequency metrics,
phase metrics, space metrics and abstract metrics as well, in any
suitable quantity or combination.
[0247] Domain: A range of values or functions of values relevant to
mathematical or logical operations or calculations. Domains may encompass
processes associated with one or more degrees of freedom and one or more
dimensions and therefore bound hypergeometric quantities. Domains may
include real and imaginary numbers, and/or any set of logical and
mathematical functions and their arguments.
[0248] Encoding: Process of imprinting information onto a waveform to
create an information bearing function of time.
[0249] Encoding Time: Time interval to accomplish, a portion or all,
encoding.
[0250] Energy: Capacity to accomplish work where work is defined as the
amount of energy required to move an object or associated physical field
(material or virtual) through space and time. Energy may be measured in
units of Joules.
[0251] Energy Function: Any function that may be evaluated over its
arguments to calculate the capacity to accomplish work, based on the
function arguments. For instance, energy may be a function of time,
frequency, phase, samples, etc. When energy is a function of time it may
be referred to as instantaneous power or averaged power depending on the
context and distribution of energy vs. some reference time interval One
may interchange the use of the term power and energy given implied or
explicit knowledge of some reference interval of time over which the
energy is distributed. Energy may be quantified in units of Joules.
[0252] Energy Partition: A function of a distinguishable gradient field,
with the capacity to accomplish work. Partitions may be specified in
terms of functions of energy, functions of power, functions of current,
functions of voltage, or some combination of this list.
[0253] Energy partitions are distinguished by distinct ranges of variables
which define them. For instance, out of i possible energy domains the
k.sup.th energy domain may associate with a specific voltage range or
current range or energy range or momentum range . . . etc.
[0254] Entropy Source or Sources: A device or devices which supplies or
supply energy from one or more access nodes of the source or sources to
one or more apparatuses. One or more energy sources may supply a single
apparatus. One or more energy sources may supply more than one apparatus.
[0255] Entropy: Entropy is an uncertainty metric proportional to the
logarithm of the number of possible states in which a system may be found
according to the probability weight of each state.
[0256] {For example: Information entropy is the uncertainty of an
information source based on all the possible symbols from the source and
their respective probabilities.}
[0257] {For example: Physical entropy is the uncertainty of the states for
a physical system with a number of degrees of freedom. Each degree of
freedom may have some probability of energetic excitation.}
[0258] Equilibrium: Equilibrium is a state for a system in which entropy
is stable, i.e., no longer changing.
[0259] Ergodic: Stochastic processes for which statistics derived from
time samples of process variables correspond to the statistics of
independent ensembles selected from the process. For ergodic ensemble,
the average of a function of the random variables over the ensemble is
equal with probability unity to the average over one or more possible
time translations of a particular member function of the ensemble, except
for a subset of representations of measure zero. Although processes may
not be perfectly ergodic they may be suitably approximated as so under a
variety of practical circumstances.
[0260] Ether. Electromagnetic transmission medium, usually ideal free
space unless otherwise implied. It may be considered as an example of a
physical channel.
[0261] EVM: Error Vector Magnitude applies to a sampled signal that is
described in vector space. The ratio of power in the unwanted variance
(or approximated variance) of the signal at the sample time to the root
mean squared power expected for a proper signal.
[0262] Excite: A stimulated state or evidence of a stimulated state
relative to some norm.
[0263] Feedback: The direction of signal flow from output to input of a
circuit or module or apparatus. Present output values of such
architectures or topologies are returned or "fed back" to portions of the
circuit or module in a manner to influence future outputs using control
loops. Sometimes this may be referred to as closed loop feed forward
(CLFF) to indicate the presence of a control loop in the architecture.
[0264] Feed forward: The direction of signal flow from input to output of
a circuit or module or apparatus. Present output values of such
architectures or topologies are not returned or "fed back" to portions of
the circuit or module in a manner to influence future outputs using
control loops. Sometimes this may be referred to as open loop feed
forward (OLFF) to indicate the absence of a control loop in the
architecture.
[0265] FLUTTER.TM.: Algorithm which manages one or more of the degrees of
freedom of a system to efficiently distribute energy via blended control
functions to functions/modules within a communications apparatus.
FLUTTER.TM. is a registered trademark of ParkerVision, Inc. Jacksonville,
Fla.
[0266] Frequency: (a) Number of regularly occurring particular
distinguishable events per unit time, usually normalized to a per second
basis. Number of cycles or completed alternations per unit time of a wave
or oscillation, also given in Hertz (Hz) or radians per second (in this
case cycles or alternations are considered events). The events may also
be samples per unit time, pulses per unit time, etc. An average rate of
events per unit time.
[0267] (b) In statistics and probability theory the term frequency relates
to how often or how likely the occurrence of an event is relative to some
total number of possible occurrences. The number of occurrences of a
particular value or quality may be counted and compared to some total
number to obtain a frequency.
[0268] Frequency Sean: Range of frequency values. Band of frequency
values. Channel.
[0269] Function of: I{ } or {tilde over (I)}{ } are used to indicate a
"function of" the quantity or expression (also known as argument) in the
bracket { }. The function may be a combination of mathematical and/or
logical operation.
[0270] Harmonic: Possessing a repetitive or rhythmic quality, rhythm or
frequency which may be assigned units of Hertz (Hz) or radians per second
(rad/s) or integral multiples thereof. For instance a signal with a
frequency of f.sub.c possesses a first harmonic of 1f.sub.c Hz, a second
harmonic of 2f.sub.c Hz, a third harmonic of 3f.sub.c Hz, so on and so
forth. The frequency 1f.sub.c Hz or simply f.sub.c Hz is known as the
fundamental frequency.
[0271] HyperGeometric Manifold: Mathematical surface described in a space
with 4 or more dimensions. Each dimension may also consist of complex
quantities.
[0272] Impedance: A measure to the opposition of time varying current flow
in a circuit. The impedance is represented by a complex number with a
real part or component also called resistance and an imaginary part or
component also called a reactance. The unit of measure is ohms.
[0273] Imprint: The process of replicating information, signals, patterns,
or set of objects. A replication of information, signals, patterns, or
set of objects.
[0274] Information: A message (sequence of symbols) contains a quantity of
information determined by the accumulation of the following; the
logarithm of a symbol probability multiplied by the negative of the
symbol probability, for one or more symbols of the message. In this case
symbol refers to some character or representation from a source alphabet
which is individually distinguishable and occurs with some probability in
the context of the message. Information is therefore a measure of
uncertainty in data, a message or the symbols composing the message. The
calculation described above is an information entropy measure. The
greater the entropy the greater the information content. Information can
be assigned the units of bits or nats depending on the base of the
logarithm.
[0275] In addition, for purpose of disclosure information will be
associated with physical systems and processes, as an uncertainty of
events from some known set of possibilities, which can affect the state
of a dynamic system capable of interpreting the events. An event is a
physical action or reaction which is instructed or controlled by the
symbols from a message.
[0276] Information Bearing: Able to support the encoding of information.
For example, information bearing degrees of freedom are degrees of
freedom which may be encoded with information.
[0277] Information Bearing Function: Any set of information samples which
may be indexed.
[0278] Information Bearing Function of Time: Any waveform, that has been
encoded with information and therefore becomes a signal. Related indexed
values may be assigned in terms of some variable encoded with information
vs. time.
[0279] Information Entropy: H(p(x)) is also given the abbreviated notation
H(x) and refers to the entropy of a source alphabet with probability
density p(x), or the uncertainty associated with the occurrence of
symbols (x) from a source alphabet. The metric H(x) may have units of
bits or bits/per second depending on context but is defined by
H = ( x ) i  p ( x i ) log b ( p
( x i ) ) ##EQU00002##
in the case where p(x).sub.i is a discrete random variable. If p(x) is a
continuous random variable then;
H ( x ) =  .intg. p ( x ) log b p ( x )
x m ( x ) ##EQU00003##
[0280] Using mixed probability densities, mixed random variables, both
discrete and continuous entropy functions may apply with a normalized
probability space of measure 1. Whenever b=2 the information is measured
in bits. If b=e then the information is given in nats. H(x) may often be
used to quantity an information source. (On occasion H(x), H.sub.x or its
other representations may be referred to as "information", "information
uncertainty" or "uncertainty". It is understood that a quantity of
information, its entropy or uncertainty is inherent in such a shorthand
reference.
[0281] Information Stream: A sequence of symbols or samples possessing an
information metric. For instance, a code is an example of an information
stream. A message is an example of an information stream.
[0282] Input Sample: An acquired quantity or value of a signal, waveform
or data stream at the input to a function, module, apparatus, or system.
[0283] Instantaneous: Done, occurring, or acting without any perceptible
duration of time; Accomplished without any delay being purposely
introduced; occurring or present at a particular instant.
[0284] Instantaneous Efficiency: This is a time variant efficiency
obtained from the ratio of the instantaneous output power divided by the
instantaneous input power of an apparatus, accounting for statistical
correlations between input and output. The ratio of output to input
powers may be averaged.
[0285] Integrate: This term can mean to perform the mathematical operation
of integration or to put together some number of constituents or parts to
form a whole.
[0286] Interface: A place or area where different objects or modules or
circuits, meet and communicate or interact with each other or values or
attributes or quantities are exchanged.
[0287] Intermodulation Distortion: Distortion arising from nonlinearities
of a system. These distortions may corrupt a particular desired signal as
it is processed through the system.
[0288] Iterative: Involving repetition. Involving repetition while
incrementing values, or changing attributes.
[0289] k.sub.B: (See Boltzmann's Constant)
[0290] Line: A geometrical object which exists in two or more dimensions
of a referenced coordinate system. A line possesses a continuous specific
sequence of coordinates within the reference coordinate system and also
possesses a finite derivative at every coordinate (point) along its
length. A line may be partially described by its arc length and radius of
curvature. The radius of curvature is greater than zero at all points
along its length. A curved line may also be described by the tip of a
position vector which accesses each point along the line for a prescribed
continuous phase function and prescribed continuous magnitude function
describing the vector in a desired coordinate system.
[0291] Line Segment: A portion of a line with a starting coordinate and an
ending coordinate.
[0292] Linear: Pertaining to a quality of a system to convey inputs of a
system to the output of the system. A linear system obeys the principle
of superposition.
[0293] Linear Operation: Any operation of a module system or apparatus
which obeys the principle of superposition.
[0294] LQ: Local Oscillator
[0295] Logic: A particular mode of reasoning viewed as valid or faulty, a
system of rules which are predictable and consistent.
[0296] Logic Function: A circuit, module, system or processor which
applies some rules of logic to produce an output from one or more inputs.
[0297] Macroscopic Degrees of Freedom: The unique portions of application
phase space possessing separable probability densities that may be
manipulated by unique physical controls derivable from the function
{tilde over (I)}{H(x).sub..nu..sub.i} and/or {tilde over
(I)}{H(x).sub..nu.,i} sometimes referred to as blended controls or
blended control signals. This function takes into consideration, or
accounts for, desired degrees of freedom and undesired degrees of freedom
for the system. These degrees of freedom (undesired and desired) can be a
function of system variables and may be characterized by prior knowledge
of the apparatus a priori information.
[0298] Magnitude: A numerical quantitative measurement or value
proportional to the square root of a squared vector amplitude.
[0299] Manifold: A surface in 3 or more dimensions which may be closed.
[0300] Manipulate: To move or control; to process using a processing
device or algorithm:
[0301] Mathematical Description: Set of equations, functions and rules
based on principles of mathematics characterizing the object being
described.
[0302] Message: A sequence of symbols which possess a desired meaning or
quantity and quality of information.
[0303] Metrics: A standard of measurement; a quantitative standard or
representation; a basis for comparing two or more quantities. For
example, a quantity or value may be compared to some reference quantity
or value.
[0304] Microscopic Degrees of Freedom: Microscopic degrees of freedom are
spontaneously excited due to undesirable modes within the degrees of
freedom. These may include, for example, unwanted Joule heating,
microphonics, photon emission, electromagnetic (EM) field emission and a
variety of correlated and uncorrelated signal degradations.
[0305] MIMO: Multiple input multiple output system architecture.
[0306] MISO: Multiple input single output operator.
[0307] Mixture: A combination of two or more elements; a portion formed by
two or more components or constituents in varying proportions. The
mixture may cause the components or constituents to retain their
individual properties or change the individual properties of the
components or constituents.
[0308] Mixed Partition: Partition consisting of scalars, vectors tensors
with real or imaginary number representation in any combination.
[0309] MMSE: Minimum Mean Square Error. Minimizing the quantity
(XX).sup.2 where X is the estimate of X, a random variable. X is usually
an observable from measurement or may be derived from an observable
measurement, or implied by the assumption of one or more statistics.
[0310] Modes: The manner in which energy distributes into degrees of
freedom. For instance, kinetic energy may be found in vibrational,
rotational and translation forms or modes. Within each of these modes may
exist one or more than one degree of freedom. In the case of signals for
example, the mode may be frequency, or phase or amplitude, etc., Within
each of these signal manifestations or modes may exist one or more than
one degree of freedom.
[0311] Modify: To change some or all of the parts of something.
[0312] Modulation: A change in a waveform, encoded according to
information, transforming the waveform to a signal.
[0313] Modulation Architecture: A system topology consisting of modules
and/or functions which enable modulation.
[0314] Modulated Carrier Signal: A sine wave waveform of some physical
quantity (such as current or voltage) with changing phase and/or changing
amplitude and/or changing frequency where the change in phase and
amplitude are in proportion to some information encoded onto the phase
and amplitude. In addition, the frequency may also be encoded with
information and therefore change as a consequence of modulation.
[0315] Module: A processing related entity, either hardware, software, or
a combination of hardware and software, or software in execution. For
example, a module may be, but is not limited to being, a process running
on a processor or microprocessor, an object, an executable, a thread of
execution, a program, and/or a computer. One or more modules may reside
within a process and/or thread of execution and a module may be localized
on one chip or processor and/or distributed between two or more chips or
processors. The term "module" also means software code, machine language
or assembly language, an electronic medium that may store an algorithm or
algorithms or a processing unit that is adapted to execute program code
or other stored instructions. A module may also consist of analog, or
digital and/or software functions in some combination or separately. For
example an operational amplifier may be considered as an analog module.
[0316] Multiplicity: The quality or state of being plural or various.
[0317] Nat: Unit of information measure calculated using numbers with a
natural logarithm base.
[0318] Node: A point of analysis, calculation, measure, reference, input
or output, related to procedure, algorithm, schematic, block diagram or
other hierarchical object. Objects, functions, circuits or modules
attached to a node of a schematic or block diagram access the same signal
and/or function of signal common to that that node.
[0319] Non Central: As pertains to signals or statistical quantities; the
signals or statistical quantities are characterized by nonzero mean
random processes or random variables.
[0320] NonExcited: The antithesis of excited. (see unexcited)
[0321] NonLinear. Not obeying the principle of super position. A system
or function which does not obey the superposition principle.
[0322] NonLinear Operation: Function of an apparatus, module, or system
which does not obey superposition principles for inputs conveyed through
the system to the output.
[0323] Nyquist Rate: A rate which is 2 times the maximum frequency of a
signal to be reproduced by sampling.
[0324] NyquistShannon Criteria: Also called the NyquistShannon sampling
criteria; requires that the sample rate for reconstructing a signal or
acquiring/sampling a signal be at least twice the bandwidth of the signal
(usually associated as an implication of Shannon's work). Under certain
conditions the requirement may become more restrictive in that the
required sample rate may be defined to be twice the frequency of the
greatest frequency of the signal being sampled, acquired or reconstructed
(usually attributed to Nyquist). At baseband, both interpretations apply
equivalently. At pass band it is theoretically conceivable to use the
first interpretation, which affords the lowest sample rate.
[0325] Object: Some thing, function, process, description,
characterization or operation. An object may be abstract or material, of
mathematical nature, an item or a representation depending on the context
of use.
[0326] Obtain: To gain or acquire.
[0327] "on the fly": This term refers to a substantially real time
operation which implements an operation or process with minimal delay
maintaining a continuous time line for the process or operation. The
response to each step of the operation, or procedure organizing the
operation, responds in a manner substantially unperceived by an observer
compared to some acceptable norm.
[0328] Operation: Performance of a practical work or of something
involving the practical application of principles or processes or
procedure; any of various mathematical or logical processes of deriving
one entity from others according to a rule. May be executed by one or
more processors or processing modules or facilities functioning in
concert or independently.
[0329] Operational State: Quantities which define or characterize an
algorithm, module, system or processor a specific instant
[0330] Operatively Coupled: Modules or Processors which depend on their
mutual interactions.
[0331] Optimize: Maximize or Minimize one or more quantities and/or
metrics of features subject to a set of constraints.
[0332] PAPR: Peak to Average Energy Ratio which can be measured in dB if
desired. It may also be considered as a statistic or statistical quantity
for the purpose of this disclosure. It is obtained by dividing the peak
energy for a signal or waveform by its average energy.
[0333] PAPR: Peak to Average Power Ratio which can be measured in dB if
desired. For instance PAPR is the peak to average power of a signal or
waveform determined by dividing the instantaneous peak power excursion
for the signal or waveform by its average power value. It may also be
considered as a statistic or statistical quantity for the purpose of this
disclosure.
[0334] Peak to Average Power Ratio which can be measured in dB if desired.
For instance PAPR.sub.sig is the peak to average power of a signal
determined by dividing the instantaneous peak power excursion for the
signal by its average power value. It may also be considered as a
statistic or statistical quantity for the purpose of this disclosure
[0335] Parallel Paths: A multiplicity of paths or branches possessing the
attribute of a common direction of signal or process flow through a
module, circuit, system or algorithm. In a simple case parallel paths may
possess a comment source terminal or node and a common ending node or
terminus. Each path or branch may implement unique processor or similar
processes.
[0336] Parameter: A value or specification which defines a characteristic
of a system, module, apparatus, process, signal or waveform. Parameters
may change.
[0337] Parsing: The act of dividing, sub dividing, distributing or
partitioning.
[0338] Partial: Less than the whole.
[0339] Partitions: Boundaries within phase space that enclose points,
lines, areas and volumes. They may possess physical or abstract
description, and relate to physical or abstract quantities. Partitions
may overlap one or more other partitions. Partitions may be described
using scalars, vectors, tensors, real or imaginary numbers along with
boundary constraints. Partitioning is the act of creating partitions.
[0340] Pass band: Range of frequencies with a substantially defined range
or channel not possessing DC response or zero Hz frequency content.
[0341] Patches: A geometrical structure used as a building block to
approximate a surface rendering from one or more patches.
[0342] PDF or Probability Distribution: Probability Distribution Function
is a mathematical function relating a value from a probability space to
another space characterized by random variables.
[0343] pdf or Probability Density: Probability Density Function is the
probability that a random variable or joint random variables possess
versus their argument values. The pdf may be normalized so that the
accumulated values of the probability space possesses a measure of the
CDF.
[0344] Phase Space: A conceptual space that may be composed of real
physical dimensions as well as abstract mathematical dimensions, and
described by the language and methods of physics, probability theory and
geometry. In general, the phase space contemplates the state of matter
within the phase space boundary, including the momentum and position for
material of the apparatus.
[0345] Plane: Two dimensional geometrical object which, is defined by two
straight lines.
[0346] Point: One dimensional mathematical or geometrical object, a single
coordinate of a coordinate system.
[0347] Portion: Less than or equal to the whole.
[0348] Possess: To have, or to exhibit the traits of what is possessed.
[0349] Power Differential: Comparison of a power level to a reference
power level by calculating the difference between the two.
[0350] Power Function: Energy function per unit time or the partial
derivative of an energy function with respect to time. If the function is
averaged it is an average power. If the function is not averaged it may
be referred to as an instantaneous power. It has units of energy per unit
time and so each coordinate of a power function has an associated energy
which occurs at an associated time. A power function does not alter or
change the units of its time distributed resource (i.e. energy in
Joules).
[0351] Power Level: A quantity with the metric of Joules per second.
[0352] Power Source or Sources: An energy source or sources which is/are
described by a power function or power functions. It may possess a single
voltage and/or current or multiple voltages and/or currents deliverable
to an apparatus or a load. A power source may also be referred to as
power supply.
[0353] Probability: Frequency of occurrence for some event or events which
may be measured or predicted from some inferred statistic.
[0354] Processing: The execution of a set of operations to implement a
process or procedure.
[0355] Processing Paths: Sequential flow of functions, modules, and
operations in an apparatus, algorithm, or system to implement a process
or procedure.
[0356] Provide: Make available, to prepare.
[0357] PseudoPhase Space: A representation of phase space or application
phase space which utilizes variables common to the definition of the
apparatus such as voltage, current, signal, complex signal, amplitude,
phase, frequency, etc. These variables are used to construct a
mathematical space related to the phase space. That is, there is a known
correspondence in change for the pseudophase space for a change in phase
space and vice versa.
[0358] Q Components: Quadrature phase of a complex signal also called the
complex part of the signal.
[0359] Radial Difference: Difference in length along a straight line
segment or vector which extends along the radial of a spherical or a
cylindrical coordinate system
[0360] Radio Frequency (RF): Typically a rate of oscillation in the range
of about 3 kHz to 300 GHz, which corresponds to the frequency of radio
waves, and the alternating currents (AC), which carry radio signals. RF
usually refers to electrical rather than mechanical oscillations,
although mechanical RF systems do exist.
[0361] Random: Not deterministic or predictable.
[0362] Random Process: An uncountable, infinite, time ordered continuum of
statistically independent random variables. A random process may also be
approximated as a maximally dense time ordered continuum of substantially
statistically independent random variables.
[0363] Random Variable: Variable quantity which is nondeterministic, or
at least partially so, but may be statistically characterized. Random
variables may be real or complex quantities.
[0364] Range: A set of values or coordinates from some mathematical space
specified by a minimum and a maximum for the set
[0365] Rate: Frequency of an event or action.
[0366] Real Component: The real portion/component of a complex number
sometimes associated with the inphase or real portion/component of a
signal, current or voltage. Sometimes associated with the resistance
portion/component of an impedance.
[0367] Related: Pertaining to, associated with.
[0368] Reconstituted: A desired result formed from one or more than one
operation and multiple contributing portions.
[0369] Relaxation Time: A time interval for a process to achieve a
relatively stable state or a relative equilibrium compared to some
reference event or variable state reference process. For instance a mug
of coffee heated in a microwave eventually cools down to assume a
temperature nearly equal to its surroundings. This cooling time is a
relaxation time differentiating the heated state of the coffee and the
relatively cool state of the coffee?
[0370] Rendered: Synthesized, generated or constructed or the result of a
process, procedure, algorithm or function.
[0371] Rendered Signal: A signal which has been generated as an
intermediate result or a final result depending on context. For instance,
a desired final RF modulated output can be referred to as a rendered
signal.
[0372] Rendering Bandwidth: Bandwidth available for generating a signal or
waveform.
[0373] Rendering Parameters: Parameters which enable the rendering process
or procedure.
[0374] Representation: A characterization or description for an object, or
entity. This may be for example, a mathematical characterization,
graphical representation, model, . . . etc.
[0375] Rotational Energy: Kinetic energy associated with circular or
spherical motions.
[0376] Response: Reaction to an action or stimulus.
[0377] Sample: An acquired quantity or value. A generated quantity or
value.
[0378] Sample Functions: Set of functions which consist of arguments to be
measured or analyzed or evaluated. For instance, multiple segments of a
waveform or signal could be acquired or generated ("sampled") and the
average, power, or correlation to some other waveform, estimated from the
sample functions.
[0379] Sample Regions: Distinct spans, areas, or volumes of mathematical
spaces which can contain, represent and accommodate a coordinate system
for locating and quantifying the metrics for samples contained within the
region.
[0380] Scalar Partition: Any partition consisting of scalar values.
[0381] Set: A collection, an aggregate, a class, or a family of any
objects.
[0382] Signal: An example of an information bearing function of time, also
referred to as information bearing energetic function of time and space
that enables communication.
[0383] Signal Constellation: Set or pattern of signal coordinates in the
complex plane with values determined from a.sub.I(t) and a.sub.Q(t) and
plotted graphically with a.sub.I(t) versus a.sub.Q(t) or vice versa. It
may also apply to a set or pattern of coordinates within a phase space.
a.sub.I(t) and a.sub.Q(t) are in phase and quadrature phase signal
amplitudes respectively. a.sub.I(t) and a.sub.Q(t) are functions of time
obtained from the complex envelope representation for a signal.
[0384] Signal Efficiency: Thermodynamic efficiency of a system accounting
only for the desired output average signal power divided by the total
input power to the system on the average.
[0385] Signal Ensemble: Set of signals or set of signal samples or set of
signal sample functions.
[0386] Signal Envelope Magnitude: This quantity is obtained from
(a.sub.I.sup.2+a.sub.Q.sup.2).sup.1/2 where a.sub.I is the in phase
component of a complex signal and a.sub.Q is the quadrature phase
component of a complex signal. a.sub.I and a.sub.Q may be functions of
time.
[0387] Signal of Interest: Desired signal. Signal which is the targeted
result of some operation, function, module or algorithm.
[0388] Signal Phase: The angle of a complex signal or phase portion of
a(t)e.sup.j.omega..sup.c.sup.t+.phi. where .phi. can be obtained from
.phi. = ( sign ) tan  1 a Q a I ##EQU00004##
and the sign function is determined from the signs of a.sub.Q, a.sub.I to
account for the repetition of modulo tan a.sub.Q/a.sub.I.
[0389] a.sub.I(t) and a.sub.Q(t) are in phase and quadrature phase signal
amplitudes respectively. a.sub.I(t) and a.sub.Q(t) are functions of time
obtained from the complex envelope representation for a signal.
[0390] Signal Partition: A signal or signals may be allocated to separate
domains of a FLUTTER.TM. processing algorithm. Within a domain a signal
may possess one or more partitions. The signal partitions are distinct
ranges of amplitude, phase, frequency and/or encoded waveform
information. The signal partitions are distinguishable by some number of
up to and including .nu. degrees of freedom they associate with where
that number is less than or equal to the number of degrees of freedom for
a domain or domains to which a signal partition belongs.
[0391] Sources: Origination of some quantity such as information, power,
energy, voltage or current.
[0392] Space: A region characterized by span or volume which may be
assigned one or more dimensional attributes. Space may be a physical or
mathematical construct or representation. Space possesses a quality of
dimension or dimensions with associated number lines or indexing
strategies suitable for locating objects assigned to the space their
relative positions as well as providing a metric for obtaining
characteristics of the assigned objects. Space may be otherwise defined
by an extent of continuous or discrete coordinates which may be accessed.
Space may be homogeneous or nonhomogeneous. A nonhomogeneous space has
continuous and discrete coordinate regions or properties for calculations
of metrics within the space which change from some domain or region
within the space to another domain or region within the space. A
homogeneous space possesses either a continuum of coordinates or a
discrete set of coordinates and the rules for calculating metrics do not
change as a function of location within the space. Space may possess one
or more than one dimension.
[0393] Spawn: Create, generate, synthesize.
[0394] Spectral Distribution: Statistical characterization of a power
spectral density.
[0395] Spurious Energy: Energy distributed in unwanted degrees of freedom
which may be unstable, unpredictable, etc.
[0396] Statistic: A measure calculated from sample functions of a random
variable.
[0397] Statistical Dependence: The degree to which the values of random
variables depend on one another or provide information concerning their
respective values.
[0398] Statistical Parameter: Quantity which affects or perhaps biases a
random variable and therefore its statistic.
[0399] Statistical Partition: Any partition with mathematical values or
structures, i.e., scalars, vectors, tensors, etc., characterized
statistically.
[0400] Stimulus: An input for a system or apparatus which elicits a
response by the system or apparatus.
[0401] Storage Module: A module which may store information, data, or
sample values for future use or processing.
[0402] Subset: A portion of a set A portion of a set of objects.
[0403] SubSurfaces: A portion of a larger surface.
[0404] Subsystem: A portion of a system at a lower level of hierarchy
compared to a system.
[0405] Subordinate: A lower ranking of hierarchy or dependent on a higher
priority process, module, function or operation.
[0406] Substantially: An amount or quantity which reflects acceptable
approximation to some limit.
[0407] Suitable: Acceptable, desirable, compliant to some requirement,
specification, or standard.
[0408] Superposition: A principle which may be given a mathematical and
systems formulation. For n given inputs (x.sub.1, x.sub.2, . . . x.sub.n)
to a system the output y of the system may be obtained from either of the
following equations if the principle of superposition holds;
I{x.sub.1+x.sub.2+ . . . x.sub.n}=y or I{x.sub.1}+I{x.sub.2}+ . . .
I(x.sub.n)=y
[0409] That is, the function I{ } may be applied to the sum of one or more
inputs or to each input separately then summed to obtain an equivalent
result in either case. When this condition holds then the operation
described by I{ } for instance a system description or an equation, is
also said to be linear.
[0410] Switch or Switched: A discrete change in a values and/or processing
path, depending on context. A change of functions may also be
accomplished by switching between functions.
[0411] Symbol: A segment of a signal (analog or digital), usually
associated with some minimum integer information assignment in bits, or
nats.
[0412] System Response: A causal reaction of a system to a stimulus.
[0413] Tensor: A mathematical object formed from vectors and arrays of
values. Tensors are geometric objects that describe linear relations
between vectors, scalars, and other tensors. Elementary examples of such
relations include the dot product, the cross product and linear maps.
Vectors and scalars themselves are also tensors. A tensor can be
represented as a multidimensional array of numerical values
[0414] Tensor Partition: Any partitionqualified or characterized by
tensors.
[0415] Thermal Characteristics: The description or manner in which heat
distributes in the various degrees of freedom for an apparatus.
[0416] Thermodynamic Efficiency: Usually represented by the symbol .eta.
or .eta. and may be accounted for by application of the 1.sup.st and
2.sup.nd Laws of Thermodynamics.
.eta. .ident. P out P in ##EQU00005##
where P.sub.out is the power in a proper signal intended for the
communication sink, load or channel. P.sub.in is measured as the power
supplied to the communications apparatus while performing it's function.
Likewise, E.sub.out corresponds to the proper energy out of an apparatus
intended for communication sink, load or channel, while E.sub.in is the
energy supplied to the apparatus.
.eta. .ident. E out E in ##EQU00006##
[0417] Thermodynamic Entropy: A probability measure for the distribution
of energy amongst one or more degrees of freedom for a system. The
greatest entropy for a system occurs at equilibrium by definition. It is
often represented with the symbol S. Equilibrium is determined when
S tot t .fwdarw. 0. ##EQU00007##
".fwdarw." in this case means "tends toward the value of".
[0418] Thermodynamic Entropy Flux: A concept related to the study of
transitory and nonequilibrium thermodynamics. In this theory entropy may
evolve according to probabilities associated with random processes or
deterministic processes based on certain system gradients. After a long
period, usually referred to as the relaxation time, the entropy flux
dissipates and the final system entropy becomes the approximate
equilibrium entropy of classical thermodynamics, or classical statistical
physics.
[0419] Thermodynamics: A physical science that accounts for variables of
state associated with the interaction of energy and matter. It
encompasses a body of knowledge based on 4 fundamental laws that explain
the transformation, distribution and transport of energy in a general
manner.
[0420] Transformation: Changing from one form to another.
[0421] Transition: Changing between states or conditions.
[0422] Translational Energy: Kinetic energy associated with motion along a
path or trajectory.
[0423] Uncertainty: Lack of knowledge or a metric represented by H(x),
also Shannon's uncertainty.
[0424] Undesired Degree of Freedom: A subset of degrees of freedom that
give rise to system inefficiencies such as energy loss or the
nonconservation of energy and/or information loss and nonconservation
of information with respect to a defined system boundary. Loss refers to
energy that is unusable for its original targeted purpose.
[0425] Unexcited State: A state that is not excited compared to some
relative norm defining excited. A state that is unexcited is evidence
that the state is not stimulated. An indication that a physical state is
unexcited is the lack of a quantity of energy in that state compared to
some threshold value.
[0426] Utilize: Make use of.
[0427] Variable: A representation of a quantity that may change.
[0428] Variable Energy Source: An energy source which may change values,
with or without the assist of auxiliary functions, in a discrete or
continuous or hybrid manner.
[0429] Variable Power Supply: A power source which may change values, with
or without the assist of auxiliary functions, in a discrete or continuous
or hybrid manner.
[0430] Variance: In probability theory and statistics, variance measures
how far a set of numbers is spread out. A variance of zero indicates that
one or more of the values are identical. Variance is always nonnegative:
a small variance indicates that the data points tend to be very close to
the mean (expected value) and hence to each other, while a high variance
indicates that the data points are very spread out around the mean and
from each other.
[0431] The variance of a random variable X is its second central moment,
the expected value of the squared deviation from the mean .mu.=E[X]:
Var(X)=E[(X.mu.).sup.2].
[0432] This definition encompasses random variables that are discrete,
continuous, neither, or mixed. The variance can also be thought of as the
covariance of a random variable with itself:
Var(x)=Cov(X,X).
[0433] The variance is also equivalent to the second cumulant of the
probability distribution for X. The variance is typically designated as
Var(X), .sigma..sub.X.sup.2, or simply .sigma..sup.2 (pronounced "sigma
squared"). The expression for the variance can be expanded:
Var ( X ) = E [ ( X  E [ X ] ) 2 ]
= E [ X 2  2 XE [ X ] + ( E [ X ] ) 2
] = E [ X 2 ]  2 E [ X ] E [ X
] + ( E [ X ] ) 2 = E [ X 2 ]  ( E
[ X ] ) 2 ##EQU00008##
[0434] A mnemonic for the above expression is "mean of square minus square
of mean".
[0435] If the random variable X is continuous with probability density
function f(x), then the variance is given by;
Var(X)=.sigma..sup.2=.intg.(x.mu.).sup.2f(x)dx=.intg.x.sup.2f(x)dx.mu.
.sup.2
where .mu. is the expected value,
.mu.=.intg.xf(x)dx
and where the integrals are definite integrals taken for x ranging over
the range of the random variable X.
[0436] Vector Partition: Any partition consisting of or characterized by
vector values.
[0437] Vibrational Energy: Kinetic energy contained in the motions of
matter which rhythmically or randomly vary about some reference origin of
a coordinate system.
[0438] Voltage: Electrical potential difference, electric tension or
electric pressure (measured in units of electric potential: volts, or
joules per coulomb) is the electric potential difference between two
points, or the difference in electric potential energy of a unit charge
transported between two points. Voltage is equal to the work done per
unit charge against a static electric field to move the charge between
two points in space. A voltage may represent either a source of energy
(electromotive force), or lost, used, or stored energy (potential drop).
Usually a voltage is measured with respect to some reference point or
node in a system referred to a system reference voltage or commonly a
ground potential. In many systems a ground potential is zero volts though
this is not necessarily required.
[0439] Voltage Domain: A domain possessing functions of voltage.
[0440] Voltage Domain Differential: Differences between voltages within a
domain.
[0441] Waveform Efficiency: This efficiency is calculated from the average
waveform output power of an apparatus divided by its averaged waveform
input power.
[0442] Work: Energy exchanged between the apparatus and its communications
sink, load, or channel as well as its environment, and between functions
and modules internal to the apparatus. The energy is exchanged by the
motions of charges, molecules, atoms, virtual particles and through
electromagnetic fields as well as gradients of temperature. The units of
work may be Joules. The evidence of work is measured by a change in
energy.
[0443] . . . : A symbol (typically 3 dots or more) used occasionally in
equations, drawings and text to indicate an extension of a list of items,
symbols, functions, objects, values, etc. . . . as required by the
context. For example the notation .nu..sub.1, .nu..sub.2 . . . .nu..sub.n
indicates the variable .nu..sub.1, the variable .nu..sub.2, and all
variables up to and including .nu..sub.n, where n is a suitable integer
appropriate for the context. The sequence of dots may also appear in
other orientations such as vertical column or semicircle configuration.
[0444] .nu.+i: This is the total of the number of desirable degrees of
freedom of a FLUTTER.TM. based system also known as the blended control
Span, composed of some distinct number of degrees of freedom .nu. and
some number of energy partitions i. .nu. and i are suitable integer
values.
[0445] .nu..sub.i: .nu..sub.i is the i.sup.th subset of .nu. degrees of
freedom. Each .nu..sub.1, .nu..sub.2, . . . .nu..sub.i of the set may
represent a unique number and combination of the .nu. distinct degrees of
freedom. The subscript i indicates an association with the i.sup.th
energy partition. .nu..sub.1 is sometimes utilized as a subscript for
FLUTTER.TM. system variables and/or blended control functions
[0446] .nu.,i: This represents a joint set of values which may be assigned
or incremented as required depending on context. The set values .nu., i
are typically utilized as an index for blended control enumeration. For
example {tilde over (I)}{H(x).sub..nu.,i} has the meaning; The
.nu..sup.th, i.sup.th function of system information entropy H(x), or
some subset of these functions. H(x).sub..nu.,i may represent some
portion of the system entropy H(x) depending on the values assumed by
.nu., i.
[0447] x.fwdarw.y: The arrow (.fwdarw.) between two representative symbols
or variables means that the value on the left approaches the value on the
right, for instance, x.fwdarw.y means x becomes a value substantially the
same as y or the variable x is approximately the same as y. In addition,
x and y can be equations or logical relationships.
[0448] {tilde over (I)}{H(x).sub..nu.,i}: This notation is generally
associated with blended controls. It has several related meanings
including;
a) A function of the .nu..sup.th, i.sup.th Information Entropy Function
parsed from H(x). b) A subset of blended controls for which .nu., i may
assume appropriate integer values. c) An expanded set in matrix form
~ H ( x ) 1 , 1 , H ( x ) 1 , 2
H ( x ) 1 , i H ( x ) v , 1 ,
H ( x ) v , 2 H ( x ) v , i ##EQU00009##
[0449] The meaning of {tilde over (I)}{H(x).sub..nu.,i} from the
definitions a), b), c) depends on the context of discussion.
[0450] + or +/: The value or symbol or variable following this .+. may
assume positive or negative values. For instance, +/V.sub.s means that
V.sub.s may be positive or negative.
[0451] .+. or /+: The value or symbol or variable following this .+.
may assume negative or positive values. For instance, /+V.sub.s means
that V.sub.s may be negative or positive.
[0452] .intg..sub.ll.sup.ulf(x)dx: Integration is a mathematical operation
based on the calculus of Newton and Leibnitz which obtains a value for
the area of a curve under the function of variable x, f(x) between the
function limits of ll a lower limit value and ul the upper limit value.
[0453] .SIGMA..sub.nx.sub.n: Summation is a mathematical operation which
sums together all x.sub.n=x.sub.1, x.sub.2, . . . of a set of values over
the index n which may take on integer values.
[0454] : The brackets indicate a time domain average of the quantity
enclosed by the bracket.
[0455] Embodiments of the present invention are directed to modulation
(including RF modulation) as well as information encoding architectures
and include allocating resources of the architecture to optimize various
forms of power efficiency including thermodynamic efficiency while
optimizing the conservation of information transfer through
(FLUTTER.TM.). This architecture can be described as FLUTTER.TM.
(FLUTTER.TM. is a registered trademark of ParkerVision Inc.,
Jacksonville, Fla.) which is a term applied to an algorithm which
controls fluctuation of one or more energy partitions and any number of
signal parameters and/or partitions within a transmitter or modulator
device to render an information bearing function of time in an optimally
efficient manner based on available apparatus resources. For instance, a
variable power supply is an example of an agile energy partition. One
such class of power supplies may be a switching power supply, which
converts variable charge increments per unit time to a specified voltage
by using an impedance and an appropriate filter. Such a supply may also
distribute charge to a load where variable potentials may be generated.
[0456] FLUTTER.TM. is a distributed modulation algorithm that enables the
synthesis of communications signals at specified output powers and
frequencies with optimized efficiency. The input interface can be any
collection of information samples or suitable continuous information
streams. The input information possesses entropy H(x) which may be
measured in bits or bits/second. Both discrete and continuous information
entropy metrics H(x) may be accommodated. The apparatus may encode
information onto the transmitted signal so as to possess multiple degrees
of freedom that are excited by parallel domains of information {tilde
over (I)}{H(x).sub..nu.,i} which are constructed from the source entropy
H(x). .nu. is a number of degrees of freedom usually associated with a
modulator or encoder and i (also degrees of freedom) is a number of
partitions usually associated with one or more power sources for the
modulator or encoder. H(x).sub..nu.,i may also be represented as
H x v , i , H x v i , ##EQU00010##
or H(x).sub..nu..sub.i depending on the context and organization of
distributed blended controls. These shorthand notations are related to
one another through the counting indices of suitable integer values,
.nu., i. The random variable x is an argument from a probability density
function used to characterize the stochastic nature of the samples from
the information process. {tilde over (I)}{H(x).sub..nu.,i} is a function
with input H(x) and multiple outputs generated from the function of
H(x).sub..nu.,i. FIG. 1 illustrates a high level operational flow 100 of
the FLUTTER.TM. algorithm (module) 130 along with the analog and
compositing segment (module) 131 of the transmitter.
[0457] The set {tilde over (I)}{H(x).sub..nu.,i} may partially share
domains which are dependent through statistical correlations determined
from H(x) 101 and the characteristics of the compositing and/or Multiple
Input Single Output (MISO) and/or operator 131 segment (module).
Therefore, the relative prominence or weighting of the {tilde over
(I)}{H(x).sub..nu.,i} blended controls are dynamically variable according
to the FLUTTER.TM. algorithm. The blended controls {tilde over
(I)}{H(x).sub..nu.,i} may be realized as sampled functions and/or
continuous signals generated and distributed by the (VSE) vector
synthesis engine (module) 130. Furthermore, the sampled rate of any
member of the set of blended controls may be less than the minimum
Nyquist sampling rate associated with a final output signal, 120,
providing certain signal processing advantages without sacrificing signal
quality or losing information in the modulation process. The bandwidths
and power spectral densities associated with each of the blended controls
102 may be unique.
[0458] The compositing and/or MISO and/or operator (module) 131
operations integrate and statistically adjust parallel processing paths,
which may be nonlinear. The nonlinearity, when present, extends through
the FLUTTER.TM. algorithm and blended controls, analog compositing and/or
MISO operations. FLUTTER.TM. refers to the statistical parsing of
information to each blended control from the set {tilde over
(I)}{H(x).sub..nu.,i} in a manner which excites the multiple degrees of
freedom in the apparatus to form the final desired signal in the most
efficient manner to conserve power, conserve information and reduce
thermal footprint.
[0459] The nature of the algorithm 100 is feed forward and does not
require feedback. Circuits forming the analog paths are not required to
be linear although the final output 120 represents a desired signal with
minimal ACPR, harmonics, noise and other artifacts usually associated
with nonlinear operations on signals.
[0460] Accordingly, it is an embodiment of the present invention to
utilize one or more novel power source(s), which may be described as a
digitally controlled power source (DCPS), which may be, for example,
unipolar, or bipolar. These novel power source(s) may be described in
terms of a digitally controlled switching power supply that is adjustable
over a range of values from, for example, approximately 0 volts to
V.sub.s volts, or V, to +V, volts, accommodating maximum and minimum
charge transfer at a voltage (for any corresponding load) which may have
a relatively low source impedance Z.sub.s for the frequency range of
interest. Low impedance in this case means, R.sub.s, the real portion of
Z.sub.s, is low compared to the load that is attached to the DCPS. The
lowest possible "real" portion of the source impedance Z.sub.s is usually
desired. The novel power sources, according to one or more embodiments of
the present invention, provides an alternative, providing efficient "on
the fly" signal envelope reconstruction, for RF modulators. As data rates
and peak to average power ratios (PAPR) increase for signaling standards,
the switching power supply becomes more difficult to design if it is used
to track the envelope for a waveform during the modulation process. This
issue is due, in part, to the rate of change of charge transfer allocated
to follow the signal envelope with a specified precision under
significant load. The envelope reconstruction in a modern standards based
application must be nearly exact.
[0461] Switching power supplies generate significant distortion over
portions of the output dynamic range and also sacrifice some efficiency.
Therefore, it is difficult for envelope restoration or envelope tracking
based modulators to effectively reconstruct signal envelopes using
switching supplies over the full dynamic range without utilizing feedback
loops. Embodiments of the present invention are directed to architectures
and algorithms that can be open loop feed forward schemes (OLFF). Thus,
embodiments of the present invention offer a solution to a Legacy
challenge in the DCPS switching art.
[0462] For example, FLUTTER.TM. may be used to facilitate practical DCPS
design, diverting resources to other degrees of freedom to reconstruct
the information bearing function of time, which may be, for example, a
waveform, or signal. Manipulation of the energy partition over a
specified dynamic range in concert with additional modulator degrees of
freedom enhances efficiency and preserves waveform quality. The
techniques described in relation to the DCPS may also be used with other
suitable switching power supply and energy source technologies as well.
FLUTTER.TM. algorithms control the DCPS by assigning optimal transition
states and voltage or current amplitudes at specifically designed
instants of time given a fixed number of power source levels and the
desired signal statistic. Optimization is determined as a maximization of
thermodynamic Efficiency vs. Signal/Waveform quality.
[0463] A modulation device suitable for use with FLUTTER.TM., may be, for
example, an RF power modulation apparatus capable of implementing
standards based communications, yet possessing appropriate degrees of
freedom whenever the tradeoff between information capacity and power
efficiency and signal quality is a driving concern. It is usually
desirable for the modulator to possess more degrees of freedom than
legacy modulator architectures reflecting current state of the art.
[0464] FIG. 2 shows a block diagram 200 that illustrates a modulator, such
as, for example a d2p.TM. apparatus, 214, power source, or energy source
208 and local oscillator 210.
[0465] FIG. 2 illustrates a set of controls 202 referred to herein as a
blended control function, {tilde over (I)}{H(x).sub.1,i, H(x).sub.2,i, .
. . H(x).sub..nu.,i}. {tilde over (I)}{H(x).sub.1,i}, and {tilde over
(I)}{H(x).sub.2,i}, shown as 202(a) and 202(b), respectively, are two of
the set of controls 202 that manipulate degrees of freedom for the energy
and entropy conversion functions 215, power source 208 and local
oscillator (LO) 210, respectively. Degrees of freedom may include, for
example, undesired degrees of freedom and desired degrees of freedom. The
undesired degrees of freedom, scavenge power from the system 200. The
scavenged power is wasted and therefore is not available to support the
intended apparatus function and dissipates as unwanted heat. Undesired
degrees of freedom include degrees of freedom that are not deliberately
designed into the system 200. The desired degrees of freedom are
information bearing and include degrees of freedom that are deliberately
designed as part of the system 200. Typically, the desired degrees of
freedom are excited or stimulated and the response or reaction of the
undesired degrees of freedom is minimized by the FLUTTER.TM. algorithms,
with respect to the degrees of freedom, .nu..sub.(tot):
[0466] .nu..sub.(tot)=total number of degrees of freedom. .nu..sub.(tot)
includes desired degrees of freedom as well as undesired degrees of
freedom. i=subset of desired degrees of freedom and may also be referred
to as a number of energy partitions. Domains are distinguished by, for
example, one or more deliberate groupings from the joint set or subsets
of .nu., i where .nu., i are suitable integers with a span of .nu.+i. The
indices .nu., i enable mathematical accounting associated with operations
and functions of the domains.
[0467] It is an embodiment of the present invention to minimize the
reaction of the undesired degrees of freedom to an excitation or
stimulation of the desired degrees of freedom. The response to the
excitation of the desired degrees of freedom is a known quantity, since
the apparatus, or system is programmed for a desired response based on
inputs. The apparatus or system may be characterized to obtain
parameters, constants and variables associated with the system which
become collectively prior knowledge and from a random processes
perspective apriori information or knowledge. An embodiment of the
present invention, for example the system 200 minimizes the probability
of exciting undesired degrees of freedom by maximizing the information
rate subject to minimized averaged power and constraining quality metric
for the output signal 220 through resource allocation to the desired
degrees of freedom. Embodiments of the present invention also
monitor/analyze the response of the desired degrees of freedom and the
undesired degrees of freedom. The optimization technique allocates
resources to desired degrees of freedom to minimize influence of the
undesired degrees of freedom, given the goals of efficiency and signal
quality.
[0468] The overall purpose for blended controls {tilde over
(I)}{H(x).sub.1,i, H(x).sub.2,i, . . . H(x).sub..nu.,i} 202 is to
manipulate degrees of freedom for the modulator apparatus 214 in such a
manner to maximize .eta. the thermodynamic efficiency of the modulator
apparatus 214 while minimizing unwanted degrees of freedom and
constraining the modulator apparatus 214 according to a function of a
specified information metric H(x), (see FIG. 3 element 309) known as
Shannon's Information Entropy. Minimizing the unwanted, or undesired,
degrees of freedom controls the probability that the undesired degrees of
freedom will be excited when energy is applied to the system, in
accordance with information encoding and modulation.
[0469] Proper thermodynamic efficiency is defined consistent with the
1.sup.st Law of Thermodynamics and given by;
.eta. = P ~ out P i n = E out
E s i n ##EQU00011## [0470] P.sub.out.DELTA. Time
Averaged power of output contained by the signal of interest only, this
excludes noise, ACPR, harmonics, spurious, etc. according to a [0471]
P.sub.in.DELTA. Time Averaged power of input provided by one or more
power sources such as a battery, for example. [0472] E.sub.out.DELTA.
Time Averaged output energy for the signal of interest. [0473]
E.sub.s.sub.in.DELTA. Time Averaged input energy from sources, also
labeled as E.sub.s.
[0474] While FIG. 2 illustrates the LO (local oscillator) 210 and power
source, E.sub.s, 208 separate from the modulator apparatus 214, which may
be, for example, a d2p.TM. modulator apparatus, this is only one
embodiment. Architectures, which include the LO synthesizer 210 and an
agile E.sub.s, 208 as well as partitions that completely exclude their
control are also embodiments of the present invention and may be
considered as part of the algorithm options and technology. Also shown in
FIG. 2 is P.sub.in 212, P.sub.out 216 and output signal 220. Energy and
entropy conversion unit 215 receives input with power P.sub.in 212 from
E.sub.s 208 and input from LO synthesizer 210. The power or energy source
208 may be any A.C. or D.C current or voltage source or combination
thereof. The associated characterization pdf for the source may possess
stochastic and deterministic attributes. The energy and entropy
conversion unit 215 generates output signal 220, according to a portion
of the blended control input 202. Each of the blended controls (202) from
subsets of combinations and permutations of .nu.. i indices, may be
realized by multiple signals per control path. For instance {tilde over
(I)}{H(x).sub.z,i} may be instantiated using multiple signals. The
signals may be digital, analog, serial, parallel or multiplexed with one
or more than one connecting structure such as a wire or bus and a
suitable number of connecting nodes.
[0475] In one embodiment of the present invention, architectures which
contemplate "on the fly" control of the system energy source, E.sub.s,
208 as one of several degrees of freedom are described. Control of
E.sub.s 208 over some portion of the dynamic range of signal envelope
along with any number of other signal parameters, is one embodiment of
FLUTTER.TM..
[0476] FIG. 3 shows an architecture 300 that illustrates an example using
optimization parameters. FIG. 3 shows one example of a model that may be
adapted to multiple applications that are appropriate for analyzing
communication's systems to determine thermodynamic quantities.
[0477] As shown in FIG. 3, energy partitions 324(a) . . . (n) (where "n"
is any suitable number) from the source E.sub.s 308 are weighted and
transformed according to the associated .lamda..sub..nu..sub.i 326(a) . .
. (n) (where "n" is any suitable number) and .gradient. operators to
produce a result, as shown in block 319. In this circumstance the
subscript .nu..sub.i pertains to the i.sup.th subset from .nu. degrees of
freedom. Each .nu..sub.i forms a domain for degrees of freedom associated
with i partitions where .nu., i are suitable integers which may vary.
.nu. may vary for each i. Also sets of degrees of freedom up to and
including .nu. degrees of freedom may associate with each value of i. ""
operators are a class of mathematical and logical operations which
optimize the compositing step in a FLUTTER.TM. algorithm according to a
blended control. The blended controls 330, 332 and 334 are derived from
{tilde over (I)}{H(x).sub..nu.,i} 309. The thermodynamic entropy flux,
S.sub.j, 350 as well as E.sub.e.sub.out 352, gives rise to signals and
signal energy, which are referred to as essential signals and essential
energy. Energy 321, shown as essential energy, as well as unwanted
phenomena 322 such as heat, ACPR, inter modulation distortion (IMD)
Harmonics, quantization noise, thermal noise, radiation, and/or other
waste energy, is also partially stimulated as a function of {tilde over
(I)}{H(x).sub..nu.,i} 309. FIG. 3 does not explicitly illustrate the
specific entropy flow; however, it is implied since the input includes
Shannon's metric for information entropy. Information entropy and apriori
system knowledge is used as a prescription or instruction for developing
blended control which motivate or stimulate or excite the various
physical degrees of freedom within the apparatus, in turn generating a
corresponding causal rise to thermodynamic entropy flux S.sub.j 350 which
is manifest as a perturbation of the variables within the system phase
space. This process is coupled to a modulator apparatus that generates
the output signal constellation 318. FIG. 3 is useful to follow the
optimization theory, and the description below provides expressions for
Energy and Entropy flux. Energy and Entropy flux are functions of time
coordinates in addition to the indices .nu., i. The expanded equations
illustrate the dependency on time with the time sample t.sub.k where k=0,
1, 2, 3 . . . .
E e out ( t k ) = v i [ .lamda. v i
.eta. v i E S v i ] ( t k ) ##EQU00012## E
w out ( t k ) = v i [ .lamda. v i (
.eta. v i  1 ) E S v i ] ( t k )
##EQU00012.2## S J tot ( t k ) = v i [
v , i { E S v i } ] ( t k ) ##EQU00012.3##
[0478] Additional variable definitions generally apply to the model and
will be employed herein.
.eta. ( t k ) = ( E e out E e out + E w out )
( t k ) ##EQU00013## E s i n = E e out + E w
out ##EQU00013.2## [0479] E.sub.s.sub.in a System Input Energy
[0480] E.sub.e.sub.out Effective System Output Energy [0481]
E.sub.w.sub.out Waste System Output Energy [0482] .eta..sub.t.sub.k
Efficiency as a Function of the Time at Sample k
[0483] .nu. pertains to the macroscopic partition of the information
source domains {tilde over (I)}{H.sub..nu..sub.1, H.sub..nu..sub.2, . . .
H.sub..nu..sub.i}. (i) accounts for the macroscopic energy partitions
which are also dependent on H(x) as a function {tilde over
(I)}{H.sub.x.sub..nu.,i} (shown in FIG. 3 as element 309). The assignment
of energy partitions to information domains is flexible and depends on
particular design considerations.
[0484] H(x) or alternatively, H(p(x)) is known as Shannon's information
entropy, uncertainty or measure of information or information metric.
These may be referred to herein by the shorthand notations H(x) and
H.sub.x. Also the information metric may be enumerated according to
H(x).sub..nu.,i or
H x v i ##EQU00014##
or H.sub.x.sub..nu.,i or H.sub..nu..sub.i where .nu. and i are integers
corresponding to degrees of freedom and partitions. Subsets of index
values (.nu., i) can be used to define domains. Each of the i energy
partitions may possess any number of degrees of freedom up to and
including .nu.. Any subset from the .nu. degrees of freedom is
permissible. H(x) is given in the discrete and continuous forms;
[0485] The metric H(x) may have units of bits or bits/per second depending
on context but is defined by
H ( x ) =  l p l ln ( p ( x ) l )
##EQU00015##
in the case where p(x).sub.l is the pdf of a discrete random variable
where the index l accounts for the l.sup.th probability in the pdf.
[0486] If p(x) is a continuous random variable then;
H ( x ) =  .intg.  .infin. + .infin. p ( x )
ln p ( x ) m ( x ) x ##EQU00016##
[0487] With mixed probability densities, composed of mixed random
variables, both discrete and continuous entropy functions may apply with
a normalized probability space of measure 1. Whenever the logarithm b=2,
the information is measured in bits. If b the base=e, then the
information is given in nats.
[0488] p(x) is the probability density functions (pdf) of symbols emitted
from the information source.
[0489] m(x) normalizes Shannon's continuous entropy formulation to avoid
conditions of negative entropy.
[0490] The functions of interest are obtained from;
[0491] The physical restrictions imposed by the apparatus and its
environment. [0492] a) Mapping of H(x) to the available degrees of
freedom of the apparatus subject to the optimization considerations;
[0492] max{.eta.}
min{H(x)H(y)}
max{S.sub.J.sub.es.sub.J.sub.w} [0493] h(x).DELTA. information
entropy of the source [0494] H(y).DELTA. Information Entropy referenced
to the Modulated Signal [0495] S.sub.J.sub.e.DELTA. Effective
Thermodynamic Entropy Flux [0496] S.sub.J.sub.w.DELTA. Waste
Thermodynamic Entropy Flux
[0497] The total thermodynamic entropy flux of the system is given by;
S.sub.J.sub.tot=S.sub.J.sub.e+S.sub.J.sub.w
S.sub.J.sub.e.varies.{tilde over (I)}{H(x)}t.sub.k
[0498] The flux S.sub.J.sub.e is part of the total entropy flux
S.sub.J.sub.tot and not in full relaxation with the environment in a
thermal sense until some period after entropy production ceases. In cases
of full relaxation and long observation time constants, t.sub.eq, the
following entropy relationship applies in a specified irreversible
direction, consistent with the 2.sup.nd Law of Thermodynamics.
{tilde over (I)}{H(x)}.fwdarw.S.sub.e+S.sub.w:t.sub.eq.fwdarw..infin.
S.sub.e+S.sub.w.ltoreq.S.sub.tot
[0499] The arrow .fwdarw. can be interpreted as "tends toward".
[0500] A message duration in time is given by .tau.. Thus, the total
decoding time, which is the time interval to extract information from an
encoded signal, is greater than or equal to message length, which can
become arbitrarily large depending on the required channel capacity. In
this specific case, channel refers to the modulator apparatus and
portions of surrounding support circuitry. When the observation time
exceeds the decoding time by a very significant amount in the prior
equation, the implication is that the communication has reached a
quasistatic state and information transfer is terminated during the
remainder of t.sub.0.tau., where t.sub.0 is the total observation time.
[0501] The entropies S.sub.e and S.sub.w are equilibrium entropies since
they approach a maximum, and
S tot t > 0. ##EQU00017##
The implication is that consumption of H(x) through signal generation and
transport increases environmental entropy, which can be measured for
finite messages if the system is closed. In a perfect system
S.sub.w.fwdarw.0 and there would be no heat generated by the apparatus.
The only heat would appear due to S.sub.e in the test load (communication
sink), via the test channel, once the system reaches equilibrium.
[0502] This acknowledges that S.sub.J.sub.e, the essential entropy flux,
does ultimately dissipate whenever the communication process is
suspended, and that energetic modes associated with transporting H(x)
eventually degrade to a maximum entropy state, thus preserving the
2.sup.nd Law of Thermodynamics.
[0503] In this treatment, spontaneous reconstitution of the information
associated with H(x) from S.sub.tot cannot be obtained even if
fluctuations in the thermalized environmental entropy occur, after full
dissipation of information. Information is annihilated or channel
capacity diminished as S.sub.J.sub.w (waste thermodynamic entropy flux)
increases and S.sub.i (essential thermodynamic entropy flux) decreases.
In this case, reference is made to the term "annihilation" as transfer of
information entropy into non information bearing degrees of freedom that
are no longer accessible to the information bearing degrees of freedom of
the system and therefore "lost" in a practical sense even if an imprint
is transferred to the environment through a corresponding increase in
thermodynamic entropy. Also, the term channel may be any medium used to
transport some portion of information entropy H(x) even if the channel
(medium) is bound to some portion of an apparatus. Noise processes and
thermal conduction arising from energy dissipation are contemplated along
with causal perturbations determined by the apparatus response to a
function of H(x) (shown in FIG. 3 as element 309). Hence, both driving
forces and spontaneous actions coexist.
[0504] Typically, practical applications demand some consideration of open
systems, which can complicate the definitions for waste and effective
entropies. In order to explain embodiments of the present invention,
waste entropy may be defined as the logarithm of the number of
significant accessible states associated with the portions of the phase
space containing undesirable degrees of freedom and their cascaded
energetic modes for the apparatus, multiplied by Boltznmann's constant
for consistency with general thermodynamic treatments. The application
density of states within the phase space consists of functions of
particle and charge motion, dq/dt, their electromagnetic fields, as well
as undesired molecular thermal agitation, translation, rotation, and/or
vibration (molecular kinetic energy), and other kinetic anomalies which
may be described as undesired degrees of freedom.
[0505] Likewise, the effective entropy is derived from the number of
accessible states attributed to the portion of phase space encompassing
the desirable energetic modes encompassing or enabling desired degrees of
freedom. These definitions capture the spirit of a statistical mechanics
description without demanding conditions of thermal equilibrium. However,
it should also be noted that both forms of entropy (waste and effective)
may assume intermediate flux expressions, which ultimately will seek a
maximum entropy state when fully absorbed by the environment. This
dissipation is eventually realized as heat, or other waste energy.
Nonetheless, system thermal relaxation times may be significant when
compared to intermediate modes of entropic transfer. This fact promotes
efficient transport of energy within the multiple degrees of freedom for
the apparatus to physically encode information in a form compliant for
consumption by an information sink once the component entropies are
reintegrated, or composited.
[0506] This reintegration or compositing enables functions of the
information domains (subsets of H(x).sub..nu.,i) to be used with
appropriate statistical weight, substantially simultaneously (or
concurrently or in parallel) to render a representation of an information
bearing function of time, such as a signal, waveform, electronic
representation of an information bearing function of time or a facsimile
of an information bearing function of time. Statistical parsing
associated with a compositing procedure may also occur sequentially
according to a FLUTTER.TM. algorithm. This compositing may form the
representation of the information bearing function of time and/or
reconstruct an information bearing function of time and/or render the
information bearing function of time, or a facsimile thereof.
[0507] Compositing involves combining, mixing and/or
unifying/integrating/reintegrating, a collection of signals, into an
information bearing function of time.
[0508] Another embodiment of the present invention is directed to a method
for assigning {tilde over (I)}{H(x).sub..nu.,i} (generally shown in FIG.
3 as element 309) the weighting of .lamda..sub..nu..sub.1,
.lamda..sub..nu..sub.2, . . . .lamda..sub..nu..sub.i, (generally 326) the
partitions of E.sub.s, (308) (generally 324) and the optimization process
in a modulation system that utilizes FLUTTER.TM.. This approach maximizes
efficiency, minimizes waste entropy production and conserves information
transfer. Embodiments of the present invention contemplate exploiting an
advantageous hardware architecture given practical technology
restrictions, while applying the optimization criteria of the FLUTTER.TM.
algorithm.
[0509] The description herein uses {.nu., I} subscripts to account for
.nu. distinct degrees of freedom and i energy partitions. The i energy
partitions also represent particular degrees of freedom. Macroscopic
degrees of freedom may be defined as the unique portions of application
phase space whose separable probability densities may be manipulated by
unique physical controls derivable from the function or set of functions
{tilde over (I)}{H(x).sub..nu.,i}. This function takes into
consideration, or is influenced by, desired degrees of freedom and
undesired degrees of freedom for the system. These degrees of freedom
(undesired and desired) can be a function of system variables, such as
temperature, and may be characterized by prior knowledge of the
apparatus/system. The two indices .nu., i may include any number of
operations, manipulations or processes that can be described
mathematically or with logic or both mathematically and with logic. Thus,
an overall density of states for the application phase space is dependent
on applicable subsets of .nu., i probability distributions. These domain
distributions will have varying degrees of statistical codependence.
[0510] As described herein, it is possible to use a less rigorous
definition between the available physical controls and the distributions
of the resources they affect to expedite a particular example. Typically,
at a fundamental level, the degree of freedom will possess two
attributes: 1) be associated with some portion of the density of states
within the phase space; which in turn relate to physical encoding
mechanisms/facility of the apparatus and 2) permit articulation of
energetic functions which are encoded with information, distributed
according to {tilde over (I)}{H(x).sub..nu.,i}, where {tilde over
(I)}{H(x).sub..nu.,i} controls the encoding mechanism/facilities of the
apparatus.
[0511] These two attributes possess correspondence to the random variables
describing quantities within the phase space. Thus, these attributes may
be considered when the term "degrees of freedom" is used herein.
[0512] FIG. 4 shows an alternate block diagram 400 illustrating the
parsing of H(x) through a control {tilde over (I)}{H(x).sub..nu.,i} 402.
FIG. 4 is a particular example of a portion of the embodiment of FIG. 3
and shows some examples of additional electronic functions.
[0513] FIG. 4 shows that the energy source E.sub.s 408 is manipulated by
some function of a subset {tilde over (I)}{H(x).sub..nu.,i} of 402(a),
derived from the information metric H(x). In addition {tilde over
(I)}{H(x).sub..nu.,i} 402 is related to the control of magnitude and
phase functions of the carrier wave, where such carrier wave of radian
frequency .omega..sub.c is obtained from one or more local oscillators (a
single local oscillator (LO) 410 is shown). It is also an embodiment of
the present invention that there may be any suitable number of local
oscillators 410. The embodiments contemplated herein may utilize multiple
LOs, such that the number of LOs is based on design considerations.
.omega..sub.c may be greater than or equal to zero radians per second.
[0514] Additionally, there may be a plurality of carrier waves.
[0515] H(x) 402 is translated to the load encoded in the form of a signal
while minimizing distortions at specified power and maximum efficiency
through a large dynamic range for a number of operational variables.
Potential energy from E.sub.s 408 is converted to a desired form, via the
transimpedance of the multiple input single output module (MISO) 466, as
shown by transimpedance node 462, and transferred directly from the
power source 408 to the output load R.sub.L 464 through energy storage
elements 467 and complex impedance Z.sub.m 469, in charge increments,
dq/dr. The algorithm for distribution of {tilde over
(I)}{H(x).sub..nu.,i} (402) is open loop, yet based on prior knowledge
concerning the physical principles and characterized parameters of the
apparatus 400.
[0516] The multiple input single output operator module MISO 466 is
implemented by hardware and algorithms, which in aggregate may be
associated with the operators .lamda..sub..nu..sub.i, .gradient.,
referenced in FIG. 3. Degrees of freedom implemented via MISO module 466
are assigned in a manner that permits separate and joint manipulation of
composite and other subordinate phase spaces.
[0517] The energy flow path 465 through energy storage element 467, which
may be, for example, an inductive element and energy flow path 468
through element 469, which is shown as an impedance element, are also
shown. The energy paths 465 and 468 are used to illustrate that the
energy is displaced from one point in time and space to a second point in
time and space. The energy storage element and related circuits use space
and time as required to transport charge. Alternately the energy storage
element may be any combination of reactive elements, for instance
capacitors and inductors as well as transmission lines, or resonators
arranged in any suitable circuit topology. The power or energy source 408
may be any A.C., D.C. current or voltage source or combination thereof.
The associated characterizing pdf for the source may possess Stochastic
and deterministic quantities.
[0518] Each of the blended controls 402 from subsets of combinations and
permutations of .nu., i indicies may be accomplished by distribution of
multiple signals per control path. For instance path 402(a) may be
digital, analog, serial, parallel or multiplexed with one or more than
one connecting structure such as a wire or bus and suitable number of
connecting nodes.
[0519] The use of phase space herein is expanded from that of Statistical
Mechanics. The phase space, as described herein, accommodates the
consideration of both apparatus macroscopic and microscopic degrees of
freedom. The expanded definition recognizes joint evolution of these
domains over variable relaxation times. This definition is consistent
with maximal entropy nonequilibrium statistical characterizations as
well as nonequilibrium thermodynamics.
[0520] Traditionally, heat energy is the motivator for classical
thermodynamics. In addition, multiple forms of energy can coexist.
Notably, dynamic charge and its electromagnetic field and thermal
agitation play roles in electronics though heat is usually not desired
for most modern forms of communication and therefore is generally
regarded as the degradation of energy to a form possessing maximum
entropy. The majority of (1.eta.)E.sub.s may consist of Joule heat,
though not exclusively. Intermediate energetic expressions such as noise,
harmonics, intermodulation distortion, unwanted oscillations, crosstalk,
interference, rotational, vibrational, translational and spurious
waveforms, represent examples of scavenging phenomena, which decrease
.eta. at the point of delivery. Of course, these other forms eventually
also degrade to the most primitive form, heat, after causing errors such
as distortions and defects in signals.
[0521] According to embodiments of the present invention, practical
scenarios will possess a relatively few degrees of freedom (compared to
.nu..sub.tot) within the portion of the device that articulates charge
transfer. This is due to considerations for signal management complexity
and the associated 2.sup.nd Law of Thermodynamics consequences. Though
large quantities of charge can be transported with some undesired
variation, there is typically a dominant bulk statistic on a
sampletosample basis. Sample in this circumstance may include the
numerical quantization of signals. This quantization is typically subject
to the NyquistShannon sampling criteria and sampling theorems. Relevant
units are in terms of charge per unit information per sample per unit
time. The charge transport may be interpreted in terms of currents,
energies, as well as magnitude and phase functions of currents in the
case of complex signal spaces. Charge transport may also be given in
terms of voltage functions given knowledge of system impedances.
[0522] According to an embodiment of the present invention, as described
herein, an apparatus phase space contemplates one or more degrees of
freedom, which may include macroscopic and microscopic degrees of
freedom. Furthermore, the phase space will typically possess transitory
properties. Both circumstances can include a nonhomogeneous phase space.
Statistical properties of constituent phase space domains can be
exploited in concert with the diversity of phenomena relaxation time
constants to decouple otherwise intractable dependencies. Semiconductors,
conductors, inductors, and capacitors transport charge, and energy
characterized by microscopic and/or macroscopic statistics. However,
these infra structures are also composed of matter that is subject to
thermal agitation at the microscopic level. When describing efficiency
and information transport, to be complete, both regimes should be
addressed, explicitly or implicitly. These extended concepts of
application phase space may be referred to herein as simply "phase
space".
[0523] FIG. 5 show a circuit representation treated as a channel 500. This
circuit representation 500 includes a signal source 570 which possesses a
describing a pdf p(x) possessing information entropy H.sub.x The variable
x is mapped into voltage V.sub.src 572. The signal source 570 has a
source impedance with real part R.sub.s 571. The signal V.sub.src 572
traverses a channel 573. The output of the channel 573 is a load voltage
V.sub.L. 574. The information entropy associated with the load voltage is
H.sub.y 575 and the signal V.sub.L. 574 is dissipated by the real part of
a load impedance R.sub.L 564. Collectively 500 can conceptually represent
some portion of an apparatus of system which transports or processes a
signal, at a high level of abstraction. The input signal voltage
V.sub.src 572 may be different than V.sub.L 574 the output signal voltage
because the channel 573 may modify the input V.sub.src 572 by some
nonlinear distortion and/or addition of noise interference. Likewise, the
original mapping of information and its associate entropy H.sub.x (see
570) can be modified by the channel with the loss of information. In this
representation 500 the channel and its distortions represents apparatus
imperfections which may be included in the definition of or description
of phase space or application phase space or pseudophase. The
probability densities (pdf's) used to describe charge, voltage,
information and related functions of those quantities also may be
distorted by the channel 573.
[0524] The pdf (probability density function) describes the distribution
of a parameter, or quantity, such as voltage or charge of functions
thereof, which may be utilized. This is useful since such parameters can
be related to properties of the phase space. Also, their distributions
play a significant role in allocating {tilde over (I)}{H(x).sub..nu.,i}.
V(dq) represents energy where dq plays the extensive role. V can be a
complex quantity and therefore provides a minimum of two degrees of
freedom in signal space or pseudophase space. The pseudophase space may
be, for example, an abstract representation or approximation of a portion
of phase space or application phase space. Distortions that impact the
phase space and pseudophase space may sometimes be corrected, or
avoided, by exploiting additional degrees of freedom. Distortions affect
the manner in which information is mapped into voltage and current within
the apparatus. Undesirable mappings can annihilate information and
decrease efficiency. By parsing H(x) 570 into multiple constituents
H(x).sub..nu.,i and mapping functions of the constituents along certain
trajectories of phase space or pseudophase space a composite output
derived from said trajectories may conserve information and maximize
efficiency. As discussed in the Background section, this is fundamentally
different than predistortion technology, which counters the nonlinearity
with an inverse transfer characteristic, which modifies the phase or
pseudophase space in a certain way without consideration of the most
efficient phase space or pseudophase space trajectories for transitions
between system states. Hereafter, it is understood that the term phase
space may be used to encompass the meanings of pseudophase space or
application phase space depending on context.
[0525] It is useful to consider some rudimentary aspects of relevant pdfs
for subsequent reference (probability density functions). Consider the
simple onedimensional case of a pdf (probability density function) for
V.sub.src to be approximately Gaussian as illustrated in FIG. 6.
[0526] Specifically, FIG. 6 shows a graphical representation 600 of an
approximate Gaussian PDF with 0.5 mean. As shown in FIG. 6, V.sub.src is
plotted on the Xaxis (horizontal) 672 and the probability for a specific
value of V.sub.src, p(V.sub.src), is plotted on the Yaxis (vertical)
676. Curve or plot 677 implies a linear channel.
[0527] Another embodiment of the present invention is that, for example,
suppose an asymmetric nonlinear function is applied to a channel with a
Gaussian signal which limits values of V.sub.src above V.sub..epsilon..
The Gaussian signal may have the pdf for V.sub.src depicted in FIG. 6
applied to the channel nonlinearity of FIG. 5.
[0528] A pdf (probability density function) is shown in FIG. 7. FIG. 7
shows a graphical representation 700, which shows V.sub.src is plotted on
the Xaxis (horizontal) 772 and p(V.sub.src) is plotted on the YAxis
(vertical) 776. Curve or plot 777 is shown. At point 0.6, as shown by 773
a vertical delta function, the curve 777 is truncated.
[0529] V.sub.src which has a new maximum at the value V.sub..epsilon.=0.6
773 is the new signal derived from V.sub.src after clipping (application
of nonlinearity of FIG. 5). The asymmetry of p(V.sub.src) and the
inclusion of an appended delta function accountfor the displaced
probability mass of the original p(V.sub.src). With the appended delta
function, the total probability measure is,
.intg..sub..infin..sup..infin.p(V.sub.src)dV.sub.src=1
[0530] As shown in FIG. 7, the uncertainty for the signal has been removed
for V.sub.src>V.sub..epsilon.. Likewise, the uncertainty metric H(y)
is also affected because the correspondence between the mapping of H(x)
and its component density function p(V.sub.src) plotted on Yaxes has
been significantly altered. Using Shannon's notation the capacity will
also be modified.
H(x)+H.sub.x(y)=H(y)+H.sub.y(x)
H(x)H.sub.y(x)=H(y)H.sub.x(y)
RH(x)H.sub.y(x)
max{R}.DELTA.C [0531] H(x): Uncertainty metric or information entropy
of the source in bits (or bits/sec). [0532] H.sub.x(y): Uncertainty of
the channel output given precise knowledge of the channel input. [0533]
H(y): Uncertainty metric for the channel output in bits (bits/s). [0534]
H.sub.y(x): Uncertainty of the input given knowledge of the output
observable (this quantity is also called equivocation). [0535] R: Rate of
the signal moving through the channel in bits/sec. [0536] C: Capacity
given H(x), H(y), H.sub.y(x), H.sub.x(y)
[0537] Examination of p(V.sub.src) indicates that V.sub.src is ambiguous
once V.sub..epsilon. is exceeded on the input to the channel where
V.sub..epsilon. is the voltage at which V.sub.src clips. That is,
H.sub.y(x) is increased for this case. Hence
H.sub.y.fwdarw.V.sub.src(x)>H.sub.y.fwdarw.V.sub.src(x)
Therefore;
max{H(x)H.sub.y.fwdarw.V.sub.src(x)}>max{H(x)H.sub.y.fwdarw.V.sub.s
rc(x)}
C.sub.V.sub.src>C.sub.{tilde over (V)}.sub.src
[0538] This proof is consistent with Shannon's theorems. The proof
supports the information loss proposition. It is ascertained that for
certain value ranges of V.sub..epsilon. that the link can be broken
(through information loss) beyond an acceptable limit. A quality metric
for assessing the degradation is given by;
C V _ STC C V STC = 1  C deg ##EQU00018##
where C.sub.deg represents the percentage channel capacity degradation.
C.sub.deg may be a useful metric for assessing the information impact of
algorithm nonlinearities.
[0539] Manipulation of the pdf (probability density function) conserves
charge and associated fields related to the physical processes but the
uncertainty of the charge functional may be reduced and therefore
Shannon's information uncertainty metric may be reduced, resulting in
information loss. Under certain conditions, partial information can be
preserved and operation of the apparatus efficiency significantly
enhanced. This consequence will be addressed in greater detail herein.
[0540] There is a onetoone correspondence between the information
entropy H(x) emitted from the source per unit time and the values of the
signal V.sub.src. The uncertainty of the source is given by;
H ( x V STC ) =  .intg. p ( x V STC ) log
p ( x V STC ) m ( x V STC ) ( x V STC )
##EQU00019##
[0541] In this case
p ( x V STC ) = 1 2 .pi. P  ( x V
STC 2 2 P ) ##EQU00020##
and
m ( x x V STC ) ##EQU00021##
is a suitable normalization function for Shannon's differential entropy.
where P is the average power of V.sub.src, proportional to the second
moment of the signal of interest through efficiency. That is,
P.about..uparw.V.sub.src.sup.2.about..eta.{tilde over (V)}.sub.src.sup.2
where V.sub.src.sup.2 is the normalized power delivered to the apparatus.
[0542] Whenever the conditional uncertainties H.sub.y(x)=H.sub.x(y)=0 then
information is conveyed and R is maximized, H(x)=H(y).
[0543] There is a correspondence between H(x) and the values of V.sub.src,
and dynamic charges due to currents resulting from V.sub.src and
associated circuit impedances, through the association of symbols from an
alphabet with voltages as a function of time, V.sub.src(t). The
quantities of interest in phase space have an association with the
degrees of freedom available through probability densities of
V.sub.src(t), (P.sub..nu..sub.src) a density of states for the physical
system is also implicit in the representation of uncertainty indicated by
H(x)
.varies.  .intg.  .infin. .infin. p v ST C ln [
p v ST C ] v STC . ##EQU00022##
[0544] The physical degrees of freedom associated with S.sub.J.sub.e and
S.sub.J.sub.w are dynamic quantities, defined by the disciplines of
irreversible nonequilibrium based thermodynamics or extended
irreversible thermodynamics, using the concept of entropy flux whenever
the system is not in equilibrium. These flux variables are causally
related to functions of H(x), H.sub.x(y), H(y), H.sub.y(x).
[0545] Expressions of physical entropies in flux may be recognized as more
familiar concepts such as uncertainty in changes of phase and magnitudes
of signals along with their corresponding time dependent fluctuating
crosscorrelation functions. This includes the related signals of
interest as well as spurious waveforms, harmonics, amplitude and phase
noise, and intermodulation distortions. Heat may be measured separately,
though in some cases the list above demonstrates some thermal
dependencies. The correspondence of these quantities and the functional
descriptions that link them to various physical and information forms of
entropy is an embodiment of the present invention, which is an
advancement in the art. Likewise, the association of information useful
in communications application with the time dependent configuration of
matter and energy at fundamental scales is also an embodiment of the
present invention and is also an advancement in the state of the art.
[0546] RF modulation is the process of imparting information from the
information source possessing H(x) to the complex envelope of the RF
carrier. In other words, the uncertainty metric quantified by H(x)
possesses a physical counterpart mimicking the component symbol
probabilities in units of charge transfer per unit time. The resulting
signal takes the form
x(t)=a.sub.I(t)cos(.omega..sub.ct)+a.sub.Q(t)sin(.omega..sub.ct)
a.sub.I(t).DELTA. Time variant In Phase component of the Carrier Envelope
also called the inphase amplitude (component) or real amplitude
(component). [0547] a.sub.Q(t).DELTA. Time variant Quadrature Phase
component of the Carrier Envelope also called the quadrature amplitude
(component) or imaginary amplitude(component). [0548]
.omega..sub.c.DELTA. Carrier Frequency.gtoreq.0 radians/second
[0549] Any point in the complex signaling plane can be traversed by using
the appropriate mapping of a.sub.I(t) and a.sub.Q(t). Alternatively, it
is possible to use a description based on the magnitude and phase of the
complex carrier envelope. Battery operated mobile communications
platforms typically possess unipolar energy sources. In such cases, the
random variables defining a.sub.I(t) and a.sub.Q(t) are characterized by
noncentral statistical parameters. A case of interest arises whenever
a.sub.I(t) and a.sub.Q(t) are nonzero mean quasiGaussian. It is
possible to refer to this case as a complex nonzero mean Gaussian pdf or
Gaussian with 2 macroscopic statistical degrees of freedom, not to be
confused with the .nu. of the apparatus. Analysis of the RF modulator and
unipolar amplifier ought to consider the offset because of the associated
energy impacts. This can adversely affect the efficiency of a
transmitter. A subsequent analysis provides a general treatment for an
apparatus that transfers power to a load given a unipolar energy source
and a signal that is approximately Gaussian. The signal plus offset may
be DC coupled or AC coupled to a load. In general, AC coupled
circumstances are more efficient. The analysis can be extended to the
complex Gaussian case by deploying an apparatus for an in phase signal
and one for a quadrature phase signal. The signal modulations defining
a.sub.I(t) and a.sub.Q(t) thus correspond to a 2dimensional signaling
space that can approach Shannon's capacity limit. This represents a
classical case suitable for bounding performance of efficiency for
signals that possess large PAPRs.
[0550] Circuits designed as embodiments of the present invention to
accomplish these modulations can fit many topologies and architectures.
However, for linear modulations with unipolar offset, they reduce to two
general classes for the amplitude envelope modulator, namely; series and
shunt impedance control. The following discussion progresses around these
models in terms of efficiency performance for series and shunt
configurations as examples suitable for advancing concepts. The treatment
for efficiency enhancement illustrated for the following simple models
also enjoys common principles which apply to other classes of more
advanced modulators. FIGS. 13 and 14 represent higher level architectures
which absorb modulator functions such as the ones to be subsequently
discussed.
[0551] FIG. 8 shows a schematic 800 of a summing node with two input
signals and/or waveforms 878, 879 and one output signal 881. This summing
node 880 is a linear processing operator enabling the superposition of
its inputs. For example x(t) 878 may be a complex signal of interest and
n(t) 879 may be a complex noise or interference process.
[0552] FIGS. 9A, 9B and 10A, 10B show examples of differential and single
ended versions of the series modulator and shunt modulator topology,
respectively. Two of these models may be used to create a complex signal.
These models represent examples for implementing some portion of the
degrees of freedom for an apparatus which may be associated with
modulation derived from FLUTTER.TM. algorithm, for instance portions of
FIGS. 13 and 14. Examination of these models provide insight into the
nature of efficiency enhancement.
[0553] In FIGS. 9A, and 9B, the impedance Z.sub..DELTA. is variable from
(0+0.sup.j).OMEGA. to (.infin.+.infin.).OMEGA.. In these extreme states
of the models, the power transfer is a maximum only when the series
impedance is zero or when the shunt impedance is infinite. Although these
models may represent general classes of linear devices, depending on the
selection of the complex impedances, the models may be nonlinear as well.
It is helpful to focus on those devices first that possess at least some
nonzero real components for Z.sub.s Z.sub.L, and Z.sub..DELTA.. These
models are hereafter referred to as Type I models. They are useful for
reference analysis and do not represent specific implementation. For
example, FIG. 9A shows a differential Type I series modulator 900. This
modulator 900 includes V.sub.s 982, Z.sub.s/2 983, 986, Z.DELTA./2 984,
987 blended control function {tilde over (I)}{H(x).sub..nu.,i} 985,
Z.sub.L 988, and V.sub.L 974 blended control function {tilde over
(I)}{H(x).sub..nu.,i} 985. FIG. 9B shows a single ended Type I series
modulator 910 embodiment that includes V.sub.s 982, Z.sub.s 989
Z.sub..DELTA. 990, V.sub.L 974 and Z.sub.L 988. Blended control function
{tilde over (I)}{H(x).sub..nu.,i} 985 provides input to Z.sub..DELTA.
990, changing its impedance in some proportion to a desired modulation
amplitude with an appropriate statistic.
[0554] FIGS. 10A, 10B show a differential and single ended Type I shunt
modulator, respectively. The differential Type I shunt modulator 1000 of
FIG. 10A includes V.sub.s 1082, Z.sub.s/2 1083, Z.sub..DELTA. 1090,
Z.sub.L 1088, V.sub.L 1074, Z.sub.s/2 1086. Blended control function
{tilde over (I)}{H(x).sub..nu.,i} 1085 provides input to Z.sub..DELTA.
1090.
[0555] The single ended Type I shunt modulator 1010 of FIG. 10B includes
V.sub.s 1082, Z.sub.s 1089, V.sub.s 1090, V.sub.L 1074, Z.sub.L1088,
blended control function {H(x).sub..nu.,i} 1085. This shunt modulator
includes a differential voltage source, V.sub.s 1082, differential source
impedances Z.sub.s 1089, differential shunt impedance Z.sub..DELTA. 1090,
and load impedance Z.sub.L 1088. Blended control 1085 in both 1000 and
1010 (configurations 1000,1010) provide a signal to Z.sub..DELTA. 1090 in
both configurations, changing its impedance in some proportion to a
desired modulation amplitude, with an appropriate statistic for output
voltages.
[0556] As shown in FIGS. 9B and 10B, V, (982, 1082, respectively) provides
a voltage source. The control statistic for {tilde over
(I)}{H(x).sub..nu.,i} (985, 1085, respectively) can be fairly intricate
depending on the impedances Z.sub.s, Z.sub..DELTA. and Z.sub.L (i.e.,
989, 1089, 990, 1090 and 988, 1088, respectively). Z.sub..DELTA.+Z.sub.s
must not equal zero in this (shunt) topology for practical application.
The dynamics of {tilde over (I)}{H(x).sub..nu.,i} (shown in FIGS. 9B and
10B as elements 985, 1085, respectively) are governed by a desired
complex signal and the suitable transforms (linear or nonlinear) to
create the necessary statistic in V.sub.L (shown in FIGS. 9B and 10B as
element 974 and 1074, respectively). The voltage V.sub.L 974, 1074, which
changes as a function of Z.sub..DELTA. 990, 1090, controlled by {tilde
over (I)}{H(x).sub..nu.,i} 985, 1085 may therefore be represented by the
function of a complex phasor, where the subscripts I, Q refer to inphase
and quadrature phase components of the signal, respectively.
V .DELTA. = { a ( t )  .omega. t +
.theta. ( t ) } ##EQU00023## a ( t ) = a I
( t ) 2 + a Q ( t ) 2 ##EQU00023.2## .theta. ( t )
= ( arctan [ a Q ( t ) a I ( t ) ] ) (
sign ) ##EQU00023.3##
a(t).ident.Complex Waveform Amplitude
[0557] The sign operator keeps track of the complex signal quadrant and
further defines .theta.(t), which represents the phase angle. The phase
angle describes the angle of a vector representation of a complex signal.
[0558] FIGS. 13 and 14 illustrate two architectural methods of
implementing modulators based on FLUTTER.TM. and blended controlcentric
algorithms which can be used to render information bearing functions of
time. These architectural methods can apply to the ongoing discussions
concerning efficiency optimization. That is, the Type I modulator
structures as well as virtually any suitable modulator or encoding method
may be absorbed by FIGS. 13 and 14 for baseband or RF application.
Architectural figures, such as, FIGS. 1, 2, 3, 4, 9A, 9B, 10A, 10B, 15,
18, 20, 21, 22, 27, 28, 29, 30, 31, and 32 are relevant instantiations
related to aspects of discussions for FIGS. 13 and 14. Hence, the various
functions, structures and modules illustrated in these, FIGS. 1, 2, 3,
9A, 9B, 10A, 10B, 15, 18, 20, 21, 22, 27, 28, 29, 30, 31, and 32 as well
as their respective descriptions, are considered as possible structures
and/or algorithms or modules which may be distributed as some subset of
the FIGS. 13 and 14 architectures and modules.
[0559] FIG. 13 illustrates an example of a general architecture 1300
suitable for implementing the portion of the FLUTTER.TM. algorithm which
encodes or modulates information onto a waveform. The FLUTTER.TM.
encoding or modulation segment 1300 is capable of producing baseband
signals as well as RF signals at the output (1370). Load 1380 may be
driven by output 1370. A baseband signal may be produced by suitable
choice of .omega..sub.c and .phi. in function/module 1341.
Function/module 1341 can also become a local oscillator (LO) by suitable
selection of .omega..sub.c the carrier frequency and .phi. the phase of
the carrier frequency. In the baseband mode we and .phi. are selected
along with amplitude (A) to render 1340 as a suitable constant. When the
output signal 1370 is a carrier then .omega..sub.c selects the
operational frequency and .phi. sets the operational phase of 1340 the LO
waveform. Blended controls 1301 manipulate multiple degrees of freedom by
adjusting the power source 1320 with output signals 1321 and MISO and/or
compositing function 1360. The blended controls are functions of system
input entropy H(x), represented by {tilde over (I)}{H(x)}.sub..nu.,i
where .nu., i are indices suitable for managing the controls. The blended
controls are generated in a vector synthesis engine (VSE) according to
the FLUTTER.TM. algorithm. k.sub.A bits from the blended control are
allocated 1302 to control the variable or switched energy or power source
1320, to a desired resolution, maximizing efficiency for a minimum number
k.sub.A. k.sub.B bits of control 1303 from the blended control 1301 are
allocated as additional degrees of freedom to generate an information
bearing function of time via a MISO and/or compositing function 1360.
k.sub..phi. bits of the control 1304 from the blended control 1301 are
allocated to select .omega..sub.c and/or .phi. to a desired value and
resolution. In addition, both .omega..sub.c and/or .phi. may be functions
of time. k.sub.A, k.sub.B, k.sub..phi. are allocated based on the number
of available degrees of freedom for the apparatus, 1300, the efficiency
for each degree of freedom, and the corresponding potential to distribute
a specific signal rate in each degree of freedom.
[0560] FIG. 14 illustrates an example of a general architecture 1400
suitable for implementing a portion of the FLUTTER.TM. algorithm which
encodes or modulates complex information onto a waveform. The FLUTTER.TM.
based modulator segment 1400 produces RF signals with corresponding
output 1470 that can accomplish universal modulation of a carrier. A
local oscillator 1441 can be selected or adjusted for a carrier
frequency, .omega..sub.c, and phase .phi., where one or both may be
functions of time and an input information source. The local oscillator
(LO) waveform 1440 is distributed in quadrature at a relative phase of
0.degree. 1451 and 90.degree. 1452 with respect to waveform 1440 using a
quadrature generating function 1450. The MISO and/or compositing function
module 1460 utilizes inputs 1451 and 1452 as quadrature carrier inputs
which may be frequency and phase agile functions of time (They may be
modulated, and encoded with information). The output of module 1460 is an
RF modulated signal 1470. The blended control 1401 are functions of
system input information entropy and generated by a vector synthesis
engine (VSE). Controls 1402 and 1404 select or adjust the variable or
switched energy or power sources, 1420 and 1430 respectively, for
inphase and quadrature branches of the MISO and/or compositing function
1460. The resolutions, in bits, for selecting power in these branches are
k.sub.Q.sub.A and k.sub.I.sub.A, associated with waveforms 1421 and 1431.
k.sub.Q.sub.B and k.sub.I.sub.B, are the number of bits from the blended
controls 1403 and 1405 respectively, providing additional degrees of
freedom for the compositing function 1460. k.sub..phi. is the number of
bits of resolution allocated for signal or waveform 1406 which selects or
determines .omega..sub.c and .phi. in the LO function 1441 associated
with signals or waveform 1440. k.sub.Q.sub.A, k.sub.Q.sub.B,
k.sub.I.sub.A, k.sub.I.sub.B, and k.sub..phi. are allocated based on the
number of degrees of freedom for the apparatus 1400 the efficiency for
each degree of freedom, and corresponding, potential to distribute a
specific signal rate as well as information in each degree of freedom.
The output signal 1470 can be provided to load 1480.
[0561] As efficiency increases, PAPR for the output signal typically
decreases. It can be shown from fundamental principles that a lossless
Type I modulator possesses a thermodynamic efficiency of
.eta. .apprxeq. 1 2 PAPR ##EQU00024##
(i.e. when Z.sub.s=0). A maximum efficiency results when the output
signal PAPR=1 but this s not consistent with amplitude modulation, of
.alpha..sub.I and a.sub.Q. Thus to encode amplitude information PAPR>1
for the modulator. However, it is possible to increase the total
effective bandwidth as one possible option for expansion of phase space
to maintain capacity while reducing PAPR, or provide multiple parallel
channel branches for transport of information. This can be represented
topologically as shown in FIG. 15, which shows a parallel channel
configuration to reduce PAPR per branch.
[0562] FIG. 15 shows a representation 1500 of a parallel "branched"
channel configuration to reduce PAPR per branch according to an
embodiment of the present invention. As shown in FIG. 15, H(X.sub.1,
X.sub.2 . . . X.sub..nu.) 1502 is split, or fractured or distributed into
component elements {tilde over (I)}{H.sub.1} 1504(a), {tilde over
(I)}{H.sub.2}, 1504(b) and {tilde over (I)}{H.sub..nu.} 1504(n) (where
"n" is any suitable number). These component elements (generally 1504)
have an associated metrics represented as
C 1 W 1 1505 ( a ) C v W v 1505 (
n ) ##EQU00025##
where "n" is any suitable number). The branches of 15 are joined, or
merged, or composited to obtain H(y.sub.1, y.sub.2 . . . y.sub..nu.)
1575. This composite entropy function 1575, is associated with a
rendering, or representation of a desired information bearing function of
time. It may be an information bearing function of time, waveform,
signal, RF modulated carrier signal, or electronic data that can be
converted, downloaded or reproduced as a rendered information bearing
function of time. It may also be some intermediate signal to be further
processed.
[0563] A .nu. branch channel may replace a single branch channel where
each branch possesses a lower PAPR. This is achieved by controlling the
normalized channel capacity C.sub..nu./W.sub..nu. (generally 1505) per
branch such that;
C=C.sub.1+C.sub.2 . . . C.sub..nu.
[0564] Each ratio C.sub..nu./W.sub..nu. (generally 1505) may be set as
desired. The derivations have assumed certain aspects of the waveform
statistic in the given bounds. Each separate branch of the composited
channel can possess a smaller PAPR and therefore a correspondingly
greater .eta.. However, the topological information flow indicated in
FIG. 15, which illustrates a distribution, or dispersal, of information
in the form {tilde over (I)}{H.sub.1}, {tilde over (I)}{H.sub.2}, . . .
{tilde over (I)}(H.sub..nu.), (generally 1504) does not specify how the
information is parsed to each path 1504(a) . . . (n) (where "n" is any
suitable number) nor reassimilated at an output node of composite
entropy function 1575, from a physical model perspective. In general this
can be accomplished by weighting the use of each path to maximize
efficiency whilst preserving C to the greates practical extent.
[0565] Whenever the output node of composite entropy function 1575 of the
conceptual topology is constrained by a continuous time linear electronic
circuit model, it may be verified that summation of linear signals in a
physical sense also may use a .nu.way power combiner that redistributes
the energy of each separate branch 1504 whenever the .nu. signals are
statistically independent.
[0566] FLUTTER.TM. permits the trade between efficiency and capacity by
manipulating smaller portions of phase space volume 1504(a) . . . (n)
that collectively reconstitute 1575 statistically while regulating domain
interactions. This can be a timevariant nonlinear operation. The time
variant nonlinear operations may be distributed to each branch 1504,
absorbed by the operator or some combination thereof. The domain
interactions may be managed in a way that moderates the effects of
multibranch loading phenomena described above through the proper design
of .
[0567] Consider the following volume of phase space which in general could
be hypergeometric but is represented in FIG. 16 with a 3dimensional
geometry. FIG. 16 illustrates an example 1600 of a conceptual phase space
or pseudophase space, which has been arranged in three tiers
corresponding to regions of differing energy levels, or energy
partitions. Coordinates within the phase space are randomly highlighted
to illustrate the arbitrary samples within partition ranges. The max
radii of the concentric scatter volumes roughly mark the energy
boundaries. Each unique point in the space represents a member from a
signal ensemble. FIG. 16 shows phase space 1600 with three axes. Xaxis
1602, Yaxis 1604 and Zaxis 1606.
[0568] It is not necessary to maintain symmetry of the volume and it may
assume many shapes depending on the corresponding apparatus constraints.
However, it is instructive to maintain the total volume substantially
constant for purposes of this disclosure, though the shape could morph.
By doing so, it is useful to conserve the total uncertainty for
accessibility to each coordinate within the space and therefore the
information capacity of the space.
[0569] Let p({tilde over (.eta.)}) be the probability density for the
instantaneous waveform efficiency associated with FIG. 9B. p({tilde over
(.eta.)}) can be used for both the series and the shunt cases and will be
obtained to facilitate an example.
[0570] Let p(V.sub.L) be given approximately by;
p ( V L ) = 1 2 .pi. .sigma. V L 
( V L  V L ) 2 2 .sigma. V L 2
##EQU00026##
[0571] The quantity (V.sub.LV.sub.L) is also equal to V.sub.L, the AC
signal. FIG. 11 depicts this pdf (probability density function), which is
a quasiGaussian pdf (probability density function) for Output Voltage,
V.sub.L, with V.sub.s=2, V.sub.L=V.sub.s/4(0.5V), and
.sigma..sub.V.sub.L=0.15. FIG. 11 shows graph 1100 that has Xaxis
(horizontal) 1102 showing V.sub.L and Yaxis (vertical), 1104 showing
p(V.sub.L). Curve 1106 is a plot of the Gaussian pdf (probability density
function).
[0572] The average of the instantaneous efficiency, {hacek over (.eta.)},
is obtained from;
.eta. = Re { V L 2 ( V L V S )  Z r (
V L 2 ) } = P out P in ##EQU00027##
[0573] Also note the supplemental relationships;
Z L = Z s * Z r = Z s Z L V L max =
V s 2 V L = V s 4 V L = .eta.
V s ( 1 + .eta. ) ##EQU00028##
[0574] The transformation,
p .eta. = p ( V L ) ( V L ) ( .eta. i )
, ##EQU00029##
enables the result;
p ( .eta. ) = V s ( 1 + .eta. ) 2 1 2
.pi..sigma. V L 2  ( .eta. V s V s
( 1 + .eta. ) 4 ) 2 2 .sigma. V L 2
##EQU00030##
[0575] {hacek over (.eta.)} is an instantaneous waveform efficiency. It is
not the proper thermodynamic efficiency. However, optimization of {hacek
over (.eta.)} can be shown to optimize proper thermodynamic efficiency
under certain conditions contemplated by the FLUTTER.TM. algorithm.
Sometimes this alternate efficiency metric ({hacek over (.eta.)}) is a
desirable object of optimization.
[0576] A plot of this pdf (probability density function) is shown in FIG.
12 as graph 1200. Xaxis (horizontal) 1202 and Yaxis (vertical) 1204 are
used to plot a pdf (probability density function) 1206 for {hacek over
(.eta.)} given Gaussian pdf for Output Voltage, V.sub.L, with V.sub.s=2,
V.sub.L=4 (0.5V), and .sigma..sub.V.sub.L=0.15, {hacek over
(.eta.)}.apprxeq.0.34.
[0577] The efficiency associated with FIG. 12 possesses an {hacek over
(.eta.)} of approximately 0.34. FIGS. 11 and 12 represent a starting
reference point for enhanced efficiency example, given the assumption of
the simplified amplitude/envelope modulator models. The signal PAPR for
this example is approximately 11.11.
[0578] One explanative example describes a method for using a portion of a
FLUTTER.TM. algorithm to select energy partitions of the variable
V.sub.L. The phase space from FIG. 16 corresponds to the partitions for
the random variable V.sub.L, as shown in FIG. 17, which shows an example
plot 1700. The Xaxis 1702 shows V.sub.L and the Yaxis shows p(V.sub.L)
1704. Curve 1706 is shown as having three distinct portions. Portion 1716
shows E.sub.1, portion 1718 shows E.sub.2 and portion 1720 shows E.sub.3.
An area under curve 1706 is shown as 1714. Specifically, the plot 1700 of
FIG. 17 shows an approximate Gaussian pdf (probability density function)
for Output Voltage, V.sub.L, with V.sub.s=2, V.sub.L=V.sub.s/4(0.5V), and
.sigma..sub.V.sub.L=0.15 three Separate Energy Partitions, E.sub.1,
E.sub.2, E.sub.3. Note, the energies are actually the squared values for
V.sub.L over the indicated ranges.
[0579] In this example, the apparatus, as described herein, can be
considered as possessing three separate energy sources that are
multiplexed at the interface between the potential boundaries,
V.sub.1,V.sub.2, (shown as elements 1712 and 1713, respectively) as the
amplitude statistic dictates. Voltages V.sub.1(1712) and V.sub.2 (1713)
may assume values from 0 to 1 volt as required for an application
associated with the statistic of FIG. 17. It is possible to define the
domain association rule as; [0580] E.sub.1 if; V.sub.L<V.sub.1
[0581] E.sub.2 if; V.sub.1.ltoreq.V.sub.L.ltoreq.V.sub.2 [0582] E.sub.3
if; V.sub.L<V.sub.2
[0583] Notice the distinction between the partitioned pdf (probability
density function) of FIG. 17 and the pdf (probability density function)
of FIG. 7. In FIG. 17 information is preserved across the energy domain
boundaries while in FIG. 7 information is lost, or annihilated and
environmental entropy is correspondingly increased. The situation of FIG.
7 has been avoided for this example.
[0584] In the following discussion n can be a thermodynamic efficiency or
an instantaneous waveform efficiency depending on the suitable choice of
the definition for (.eta.) or pdf ({hacek over (.eta.)}), a derived
quantity based on the signal statistic and circuit parameters and
topology. In the case of a thermodynamic efficiency, the kernels of the
integrals are constant functions which are calculated from the ratios of
pre averaged quantities, .sigma..sub.L.sup.2.sub.i/P.sub.in.sub.i.
.sigma..sub.L.sup.2.sub.i is the output signal variance (output signal
power) of the i.sup.th partition. (P.sub.in).sub.i is the input power for
the circuit in the L.sup.th partition.
[0585] The calculations of .eta..sub.1,2,3. may also be obtained from
(where .zeta. is associated with a threshold index);
.eta..sub.i=k.sub.i.sub._.sub.norm.intg..sub.{tilde over
(.eta.)}.sub..zeta.1.sup.{tilde over
(.eta.)}.sup..zeta..eta.p(n)d(n);i=1,2,3
[0586] provides the domain (in this case the domain corresponds to
partition) increment control for the calculations and
k.sub.i.sub._.sub.norm provides a normalization of each domain such that
each separate domain possesses a cdf (cumulative distribution function)
equal to a maximum measure of 1 at the upper boundary. In some of the
subsequent treatments k.sub.i.sub._.sub.norm, or suitable equivalents,
will be included in the factors .lamda..sub.i also known as weighting
factors. In some discussions these factors shall remain separate.
[0587] The following equations for averaged instantaneous efficiency and
thermodynamic efficiency (respectively) apply to a Type I series
dissipative modulator with a power source resistance equal to the load
resistance.
.eta. .DELTA. _ V L 2 V L V s  V L 2
##EQU00031## .eta. .DELTA. _ V _ L 2 V L V
s  V L 2 = .sigma. 2 P in ##EQU00031.2##
[0588] Suppose we recursively apply this efficiency calculation to
separate partitions with the first boundary @ V.sub.1=0.25 volts and the
second boundary @ V.sub.2=0.75 volts. These thresholds correspond to a 2
bit resolution over a 1 volt dynamic range. In this circumstance the
averaged normalized efficiencies for the 3 regions are associated with a
probability weighting for each region;
TABLEUS00001
Instantaneous Efficiency Weighting Factor
{hacek over (.eta.)}.sub.1 .674 .lamda..sub.1 .035
{hacek over (.eta.)}.sub.2 .5174 .lamda..sub.2 .928
{hacek over (.eta.)}.sub.3 .672 .lamda..sub.3 .035
[0589] The final weighted average is;
{hacek over (.eta.)}.sub.tot=.eta..sub.sx(.lamda..sub.1{hacek over
(.eta.)}.sub.1+.lamda..sub.2{hacek over
(.eta.)}.sub.2+.lamda..sub.3{hacek over (.eta.)}.sub.3).apprxeq.0.517
[0590] The final weighted average is:
{hacek over (.eta.)}.sub.tot=.eta..sub.sx(.lamda..sub.1{hacek over
(.eta.)}.sub.1+.lamda..sub.2{hacek over
(.eta.)}.sub.2+.lamda..sub.3{hacek over (.eta.)}.sub.3).apprxeq.0.517
[0591] In this case, the switch efficiency .eta..sub.sx is set to the
value of 1.
[0592] The corresponding block diagram for an architecture associated with
this calculation is shown as FIG. 18.
[0593] FIG. 18 shows a power switching module and series type 1 modulator
1800. This switching module and series modulator 1800 includes
I{H(x).sub..nu..sub.1, H(x).sub..nu..sub.2, . . . H(x).sub.V.sub.i}
1802,(a) . . . (n) (blended controls where "n" is any suitable number).
V.sub.s.sub.1 1812, V.sub.s.sub.2 1813 and V.sub.s.sub.3 1814. Blocks
1888, 1889 and 1890, which are impedances associated with a shunt
modulator, are also shown. V.sub.L 1874 is developed by an output current
flowing through Z.sub.L1888. As shown in FIG. 18, the apparatus 1800
transitions as each statistical boundary is traversed, selecting a new
energy partition according to {tilde over (I)}{H(x).sub..nu..sub.1,
H(x).sub..nu..sub.2, . . . H(x).sub..nu..sub.i}(generally 1802).
[0594] The final weighted average of this solution for this particular
FLUTTER.TM. example has not yet been optimized. As will be discussed
herein, a FLUTTER.TM. energy partitioning optimization algorithm can
improve on the results of this example.
[0595] From the prior example, it is possible to obtain an optimization of
the form
max{{hacek over (.eta.)}.sub.tot}=max{.lamda..sub.1{hacek over
(.eta.)}.sub.1+.lamda..sub.2{hacek over
(.eta.)}.sub.2+.lamda..sub.3{hacek over (.eta.)}.sub.3}
.lamda. i = 1 min { H ( x )  H ( y ) }
##EQU00032##
[0596] It is also noted that [0597] {hacek over (.eta.)}.sub.1={tilde
over (I)}{V.sub.s.sub.1}, {hacek over (.eta.)}.sub.2={tilde over
(I)}{V.sub.s.sub.3, V.sub.s.sub.2}, {hacek over (.eta.)}.sub.3={tilde
over (I)}{V.sub.s.sub.2, V.sub.s.sub.3}
[0598] The overall goal is to solve for the optimum energy partitions
E.sub.1, E.sub.2, E.sub.3 (see FIG. 17, elements 1716, 1718 and 1720,
respectively) by selecting the most efficient voltages
V.sub.s.sub.1=2V.sub.1, V.sub.s.sub.2=2V.sub.2, V.sub.s.sub.3=2V.
V.sub.s.sub.3 is selected as the maximum available supply by definition
and was set to 2V for the prior example. The minimum available voltage is
set to V.sub.s.sub.0=0. Therefore only V.sub.s.sub.1 and V.sub.s.sub.2
are calculated for the optimization that simultaneously (or concurrently
or in parallel) determines .lamda..sub.1, .lamda..sub.2 and .lamda..sub.3
for this particular scenario.
[0599] For the present, assume that H(x)H(y) can be minimized so that the
desired signal is faithfully composited. This is accomplished by
manipulating i degrees of freedom as well as other degrees of freedom in
the modulator, for example the .nu..sub.i degrees of freedom associated
with Z.sub..DELTA. 1890, of FIG. 18. Then application of the maximization
algorithm max{{hacek over (.eta.)}.sub.tot} may be solved using the
calculus of variations to obtain solution for V.sub.s.sub.1 and
V.sub.s.sub.2.
[0600] The improved solution for this 3 partition example becomes
V.sub.s1=2V.sub.1.apprxeq.0.97, V.sub.s2=2V.sub.2.apprxeq.1.3V. The
comparative domain efficiencies and weightings are given by;
TABLEUS00002
Instantaneous Efficiency Weighting Factor
{hacek over (.eta.)}.sub.1 .667 .lamda..sub.1 .466
{hacek over (.eta.)}.sub.2 .396 .lamda..sub.2 .399
{hacek over (.eta.)}.sub.3 .566 .lamda..sub.3 .141
and the final total average is {hacek over (.eta.)}.sub.tot 0.692.
[0601] Thus, the FLUTTER.TM. energy partition optimization solution
provides a noticeable improvement over an arbitrary 2 bit assignment for
thresholds. Moreover, the improvement over a single power source
partition is approximately a factor of 2 or 100% improvement of the
instantaneous waveform efficiency metric.
[0602] The FLUTTER.TM. algorithm demonstrates that application of optimal
thresholds is not ad hoc or arbitrary. For instance, ad hoc binary
weighting was illustrated to be inferior to a FLUTTER.TM. optimization.
Standard Legacy envelope tracking schemes which have been digitized do
not optimize according to a FLUTTER.TM. algorithm and therefore are
different as well as inferior. A significant benefit of FLUTTER.TM. is
evident in the relatively reduced number of partitions required to
provide relative efficiency enhancement. In addition, the partition
selection rate may be reduced when additional information entropy is
distributed in alternate degrees of freedom. Furthermore, the other
degrees of freedom .nu. restore information in the signal envelope not
accommodated by the sparse number of partitions. These .nu. degrees of
freedom also smooth and/or interpolate the envelope to a desired
standard. Legacy approaches and technologies do not restore an envelope
using a small number of quantization levels for power supply envelope
restoration or envelope following.
[0603] When it is desired to ascertain an optimal theoretical solution for
both number of energy partitions and their potentials for the case where
amplitude is exclusively considered as a function of any statistical
distribution p(V.sub.L) (shown in FIG. 11 as Yaxis 1104, FIG. 13 as
Yaxis 1304 and FIG. 17, Yaxis 1704 as an example). It is reasonable to
begin by using PAPR and .eta. definitions.
PAPR .DELTA. _ P out_peak P out ##EQU00033##
.eta. .DELTA. _ P out P in .thrfore.
.eta. = P out_peak ( PAPR ) P in
##EQU00033.2##
[0604] This defines .eta. for a single energy partition. The following
expression may be used for i energy partitions;
.eta. = i .eta. i .lamda. i = i P
out i .lamda. i ( PAPR ) i P in i = i
.lamda. i P out i P in i ##EQU00034##
[0605] From the 1.sup.st and 2.sup.nd Laws of Thermodynamics, it can be
determined that
P out i P in i .ltoreq. 1 ##EQU00035##
.eta. i .ltoreq. 1 ##EQU00035.2##
[0606] .lamda..sub.i is the statistical weighting for .eta..sub.i over the
i.sup.th partition so that
i .lamda. i = 1 ##EQU00036##
[0607] Given these conditions, it is possible to write the following
optimization
.eta. .DELTA. _ max { i .eta. i .lamda. i
} = max { i .lamda. i P out i P in i
} ##EQU00037##
[0608] Thus, each and every in .eta..sub.i.fwdarw.1 for .eta. to become
one. That is, it is impossible to achieve an overall efficiency of
.eta..fwdarw.1 unless each and every partition is also 100% efficient.
Hence,
max .eta. = i .lamda. i = 1 ##EQU00038##
[0609] It has already been shown that the .lamda..sub.i are calculated as
the weights for each i.sup.th partition such that;
.lamda. i = .intg. V L ( .zeta.  1 ) V L .zeta.
p ( V L ) V L ##EQU00039##
[0610] It follows for the continuous analytical density function
p(V.sub.L) that
.lamda. tot = .intg. 0 V L max p ( V L )
V L = 1 ##EQU00040##
[0611] Analogously,
i .lamda. i = .intg. 0 V L max p ( V L )
V L = 1 ##EQU00041##
[0612] As stated herein, it is possible to generalize the prior
optimization procedure to emphasize the calculation of sufficient
partitions which can approach an acceptable tradeoff efficiency, .eta.,
yet minimizes the number of energy partitions according to practical
resource constraints.
[0613] Turning now to a discussion of the efficiency gains vs. the number
(i) when (i) is finite: Efficiency gain, vs. complexity, technology
restrictions and perhaps cost would set an upper lower bound on (i).
[0614] The generalized q optimization procedure (Type I modulator) may be
prescribed for setting partition threshold .alpha..sub..zeta.. .zeta.
will be used an index associated with threshold number at the boundary of
the partition. The number of thresholds is one less than the number of
partitions. The differences between adjacent threshold are considered as
differential quantities in this example.
max { .eta. tot } = max { i .lamda. i k i norm
.intg. .alpha. { .zeta.  1. .zeta. } .alpha. .zeta.
.alpha. ~ .zeta. p ( .alpha. ~ .zeta. )
.alpha. ~ .zeta. } ##EQU00042## .alpha. .zeta. .DELTA.
_ V L .zeta. 2 V L .zeta. V S .zeta.  Z r V
L .zeta. 2 , .alpha. [ .zeta.  1. .zeta. ] .DELTA. _
V L .zeta.  1 2 V L .zeta.  1 V S .zeta.  Z
r V L .zeta.  1 2 ##EQU00042.2## .alpha. ~ .zeta.
.DELTA. _ V L 2 V L V S .zeta.  Z r V L 2
##EQU00042.3## .alpha. ~ .zeta. = ( V s ( V s  Z
r V L ) 2 ) V L , .zeta. = 1 , 2 , 3
.lamda. i = .intg. V L .zeta.  1 V L .zeta.
p ( V L ) V L i .lamda. i
.DELTA. _ 1 V L .zeta. .DELTA. _ V S .zeta. 2
Z r .DELTA. _ Z S Z L ##EQU00042.4##
Z.sub.s.ident.Modulator Energy Source Impedance
Z.sub.L.ident.Modulator Load Impedance
[0615] FIG. 19 shows a graph 1900 that illustrates the trend of plotted on
Yaxis (vertical) 1904 as a function of the number of partitions, plotted
on Xaxis (horizontal) 1902, as curve 1906. Specifically, FIG. 19 shows
instantaneous waveform efficiency (plotted as curve 1906) as a function
of energy partition number for an example of a Type I modulator model
processing signal amplitudes characterized by non central Gaussian
statistics, for a particular Z.sub.r. Notice how the {hacek over (.eta.)}
(instantaneous efficiency) is greatly enhanced for the allocation of only
several partitions.
[0616] It can be shown that the thermodynamic efficiency .eta. and the
instantaneous efficiency {hacek over (.eta.)}, for this modulator, are
related by (for a single energy partition);
.eta. .apprxeq. 1 V s V L PAPR sig + ( 1 .eta.
 V s V L ) ( PAPR sig ) ##EQU00043##
[0617] PAPR.sub.sig is the peak to average power ratio for the signal
portion of the waveform.
[0618] Thus, increasing {hacek over (.eta.)} also increases .eta. where
0.ltoreq.{hacek over (.eta.)}.ltoreq.1/2 for a Type I modulator.
[0619] Although the particular optimization is in terms of {hacek over
(.eta.)} suitable efficiency choices such as .eta.={tilde over
(I)}{{hacek over (.eta.)}} may also be directly optimized. In particular,
the thermodynamic efficiency
.eta. = P out P in ##EQU00044##
may also be directly optimized. An additional example will illustrate the
results of optimizing thermodynamic efficiency using a direct approach.
[0620] Suppose that the prior example is modified so that a nearly
Gaussian signal of .about.11.1 PAPR is produced at the output load of a
type 1 modulator. Furthermore, suppose that the source resistance is
negligible and may be approximated as zero. Now the signal of interest at
the output can vary between zero volts and V.sub.s=2V. We may apply the
same procedures as before to obtain results for the proper thermodynamic
efficiency. Furthermore, we calculate the efficiency improvement obtained
for the partitioning algorithm compared to a modulator with a single
power source. The result is indicated in a graphic plot 3901 in FIG. 39
thermodynamic efficiency improvement .eta..sub.l/.eta..sub.1 vs.
partition number. Notice that the percentage improvement is 40% for 2
partitions, 54% for 3 partitions and 73.5% for 8 partitions. The ratio is
the efficiency for the modulator using i partitions divided by the
efficiency for a single power source based modulator. Thus, when
Flutter.TM. is applied and optimal thresholds for partitions employed,
only a few power source partitions are required for significant
thermodynamic efficiency improvement.
[0621] This optimization procedure is in general applicable for all forms
of p(V.sub.L) (and therefore different modulator types) even those with
discrete Random Variables (RVs), provided care is exercised in defining
the partition boundaries and domains for the RV. In this manner very
complex Probability Distribution Functions (PDFs) with pdf (probability
density functions) subspaces may be processed, though calculation of
solutions can prove challenging.
[0622] Nevertheless, there are several solution techniques that yield
favorable results. Locations of the potentials V.sub.L.sub..zeta. are not
uniformly spaced along the V.sub.L axis. Likewise, .lamda..sub.i are not
equally weighted in general. However, as .zeta. or consequently i becomes
quite large the partitions obtain greater parity. It is an embodiment of
the present invention that moderate to low values for .zeta. or i, demand
optimized partition differentials with threshold boundaries that are not
necessarily coincident with quantization differentials or sample
thresholds used in envelope restoration or envelope tracking
reconstructions. In addition to the prior comments, it should be noted
that a change in source impedance of power sources may change efficiency
and the threshold optimization of partitions.
[0623] In terms of the information quality that has been introduced;
min{H(x)H(y)}
[0624] This calculation may also be approximated by a more tangible
associated metric that is particularly convenient for lab application as
most modern signal analyzers may be equipped with crosscorrelation or
other relevant error metric measurement capabilities. The minimization is
often accomplished by one of several means; [0625] Calculation of Error
Vector Magnitude (EVM) [0626] Calculation of Minimum Mean Square Error
(MMSE) [0627] Calculation of CrossCorrelation and/or Covariance
[0628] Crosscorrelation is addressed since it maintains continuity of the
present themes. It is possible to define the crosscorrelation between
input and output as (x.fwdarw.input variable, y.fwdarw.output variable)
R.sub.xy=.intg..sub..infin..sup..infin..intg..sub..infin..sup..infin.x
yp(y,x)dxdy
[0629] This form is a statistical crosscorrelation. The crosscovariance
which may be used in certain circumstances is the same operation after
extracting the mean values of x, y. It is noted that they variable is
often normalized or scaled to compensate for test system scaling.
[0630] Now the example as presented would appear perfectly linear in
concept since V.sub.L 1874 should be a faithful reproduction of {tilde
over (I)}{H(x).sub..nu.,i} 1802 by definition. However, in a practical
system with a more complicated modulation requirement, Z.sub..DELTA.
1890, may be distributed with many controls. Voltages 1812, 1813, 1814,
may be nonlinear and each may be determined by multiple controls. In such
cases, imprecision, quantization noise and a host of other variables may
potentially compromise the desired crosscorrelations thereby increasing
S.sub.J.sub.w. Hence, the crosscorrelation or crosscovariance or
covariance metric or a reasonable similar metric may be employed to
assess the particular synthesized architecture. Statistical calculations
for the crosscorrelation may be used whenever p(x,y) can be obtained or
suitably approximated. In cases where this is not convenient, the time
crosscorrelation may be employed for a conditionallystationary random
process. This form of crosscorrelation is given by;
R xy ( .tau. ) = lim T o cc .fwdarw. .infin. .intg.
 T o cc T o cc x ( t ) y ( t + .tau. )
t ##EQU00045## [0631] T.sub.O.sub.cc.DELTA.Observation Time
Interval for CrossCorrelation
[0632] The input and output spectral masks are compared from;
.intg..sub..infin..sup..infin.R.sub.x(.tau.)e.sup.j.omega..tau.d.tau.
.intg..sub..infin..sup..infin.R.sub.y(.tau.)e.sup.j.omega..tau.=S.sub.c(
.omega.)
where R.sub.x(.tau.) and R.sub.y(.tau.) are suitable auto correlations.
[0633] In this manner compliance can also be assessed in the frequency
domain. Other comparison metrics are useful as well, such as covariance,
MMSE, phase error versus frequency, phase error versus time, and
variations thereof.
[0634] E. T. Whittaker published a paper in 1915 concerning the
interpolation of functions. Shannon borrowed this theory and that of
Nyquist to obtain the cardinal series for sampling, given by
X ( t ) = 1 .pi. n =  .infin. .infin. X ( n
2 W ) sin [ .pi. ( 2 Wt  n ) ] 2 Wt  n
##EQU00046## [0635] W.ident.Bandwidth [0636] .eta..ident.Sample
Number [0637] t.ident.Time
[0638] A finite information bearing function of time may be reproduced by
suitable application of the Cardinal series. Shannon went on to show that
the number of samples sufficient for reconstruction of any waveform of
finite duration .tau. using the Cardinal series is given by Shannon's
number N.sub.s.
N.sub.s=2W.tau.
[0639] In the most general case for n.fwdarw.large and samples obtained
from X(t), which may be composed of an arbitrary sum of Gaussian random
variables, there exists a hyperspace containing the hyper sphere with
volume given by;
V n = .pi. n / 2 .GAMMA. ( n 2 + 1 ) ( 2 .tau.
W ( P + N ) ) n ##EQU00047## [0640]
P.ident.Average Signal Power [0641] N.ident.Average Gaussian Noise Power
[0642] This hyper sphere possesses an analog in statistical mechanics
related to the states of particles in phase space, where the coordinates
in classical phase space are defined by momentum p and position q,
respectively. The probability densities for the degrees of freedom and
their energy distributions, as well as corresponding information
distributions, have been absorbed into the construct of application phase
space at a higher level of abstraction for the purpose of this
disclosure. This higher level of abstraction may also be referred to as a
pseudophase space.
[0643] As noted, i.fwdarw..infin. whenever the pdf (probability density
function) is parsed in infinitesimal differential increments. In
practice, modern day communications systems often quantize the variable
(V.sub.L) associated with an output voltage across a load impedance. Even
though it may be continuous or discrete at the source, it is often
quantized at the apparatus interface. N.sub.s=2W.tau. is a prescription
for the number of samples over the dimensionality of signal space to
reconstruct the message without losing information. The Nyquist sample
rate then is given by;
R N = N s .tau. = 2 W ##EQU00048##
[0644] N.sub.s samples amongst the i partitions will distribute according
to the probability density p(V.sub.L) and the ancillary rules that assign
the respective domains. These samples are only partially utilized by the
energy partitioning facilities of the apparatus. Additional samples may
be required to support .nu. degrees of freedom. In general, it is
possible to assign i.ltoreq.2.sup.k partitions to enable an efficient
system. The average frequency of samples within each bin (a bin may be
thought of as a subset of values or span of values within some range or
domain) can be calculated from;
.DELTA. V L .DELTA. _ V L max 2 k ##EQU00049##
p .DELTA. V L i .DELTA. _ ( .intg. V L i 
1 V L i p ( V L ) V L ) = .lamda. l
##EQU00049.2##
.DELTA.V.sub.L.ident.Average Voltage Increment per Sample
[0645] The number of samples per bin is thus
N S p .DELTA. V L i . ##EQU00050##
Additionally, 2.sup.k sets the sampling resolution for the system.
[0646] The potential between fixed and/or sampled energy partitions can be
greater than or equal to V.sub.L.sub.max/2.sup.k specifically set by the
FLUTTER.TM. algorithm to realize an optimized efficiency gain. The rules
for assigning the number and frequency of the samples N.sub.s to each of
the i bins may be directly attributed to the mapping of H(x) symbol
emission to V.sub.L and (V.sub.L), via {tilde over (I)}{H(x).sub..nu.,i}.
[0647] Note that optimal assignment of partition boundaries is very
specific (according to FLUTTER.TM.) and will not in general correspond to
binary sampling thresholds determined solely from interpolation theory or
envelope tracking/restoration theories.
[0648] (i) energy partitions with properly assigned sample clusters,
n.sub.i, preserve the sampling space and therefore the information space.
The sample clusters fall within the boundaries of the i.sup.th energy
partition and are further processed by other degrees of freedom to
enhance efficiency and quality metrics of the signal. These additional
distinct degrees of freedom have also been enumerated by an index .nu..
The .nu. degrees of freedom within the modulation method described herein
can span a portion of, a single, or all i partitions.
[0649] The number of partition transitions per unit time per degree of
freedom fluctuate in each path of a FLUTTER.TM. algorithm according to
signal statistics and therefore these partition sampling events may be
slower than the final composited signal envelope Nyquist sampling rate or
bandwidth. The additional (nonenergy partition selection) required
signal reconstruction sample clusters are distributed to other degrees of
freedom and composited through other blended control paths, thus
preserving the requirements of the sampling theorem. This is a preferred
approach given the minimum fixed number of energy partitions to
practically achieve a specified efficiency.
[0650] Reconstruction of a sampled signal envelope by linear interpolation
and/or filtering such as the type used in Legacy envelope tracking and
envelope restoration techniques, does not constitute an efficiency
optimization algorithm. An efficient algorithm should also accommodate
simultaneous or joint (or concurrent or parallel) optimization
max{.eta.}, min{H.sub.xH.sub.y}. If joint dependency of efficiency and
quality are not explicitly contemplated then the algorithm is `ad hoc`.
[0651] As described above, it is useful to substantiate that the variable
for amplitude of a signal may be quantized and that the energy partitions
be less than or equal to the number of quantization levels. This is a
flexible, or loose, upper bound. The idea of quantization is justified
since the continuous random variable V.sub.L can be exactly reproduced
according to the sampling theorem and could correspond to an efficiency
optimization without requiring an infinite number of differentially
spaced partition potentials.
[0652] FIGS. 20 and 21 show examples of a Type II modulator model for
series and shunt realization, respectively. Equivalent differential
topologies are possible and may be assumed in the treatment just as
single ended and differential topologies were included for Type I models,
as described herein.
[0653] FIG. 20 shows an example of a series Type II modulator 2000. This
modulator 2000 includes a phase/frequency control input 2092, time
variant source voltage V.sub.s 2082, source impedance Z 2089. Also shown
is variable branch impedance Z.sub..DELTA. 2090, which receives control
input from amplitude control 2091 and signal input from source V.sub.s
2082. The output from Z.sub..DELTA. 2090 is provided to Z.sub.L 2088 and
V.sub.L 2074. V.sub.s 2082, may for example be an agile RF carrier with
phase modulation from control 2092. The amplitude of V.sub.L 2074 may be
changed by changing Z.sub..DELTA. 2090 via control 2091. Therefore,
output V.sub.L may be phase modulated and amplitude modulated through
changes imparted by controls 2092 and 2091.
[0654] FIG. 21 shows an example of a shunt Type II modulator 2100. This
modulator 2100 includes a phase/frequency control input 2192, time
variant source voltage V.sub.s 2182, Z.sub.s 2189. Also shown is a
variable impedance Z.sub..DELTA. 2190, which receives control input from
amplitude control 2191. The impedance from Z.sub..DELTA. 2190 is in
parallel with Z.sub.L 2188 and affects the amplitude of V.sub.L 2174. The
output voltage amplitude of V.sub.L 2174 and phase of V.sub.L 2174 may be
changed by varying controls 2191 and 2192.
[0655] The series modulator instantaneous waveform efficiency can be
derived similar to the methods developed for analyzing the Type 1
modulators. The partially reduced result is;
.eta. = P out WF P in = Re V L 2 V S V
L  V L 2 ( Z S / Z L ) ##EQU00051##
[0656] It is noted that the efficiency {hacek over (.eta.)} reduces to
that of the Type I model when the overhead for creating a sine wave from
a fixed potential is minimal. However, if D.C. blocking is used, for
example a capacitor or high pass filter in series with the load output of
Z.sub.s 2089, efficiency may be increased.
[0657] In addition it is verified that Type II shunt model yields
approximately the following provided the condition of a short circuit is
avoided.
.eta. = P out WF P in = Re { V L 2
V S V L  V L 2 ( Z S / Z L ) }
##EQU00052##
[0658] The proper thermodynamic efficiency
P.sub.out.sub.sig/P.sub.in=.eta. also increases as {hacek over (.eta.)}
increases for these Type II modulator examples. Again, the use of a D.C.
blocking circuit such as capacitor or other filter, as part of Z.sub.s
2189 may improve efficiency in this case.
[0659] Hence, the Type II modulator models follow the Type I model
performance closely over significant dynamic range of the relevant
signals. One possible difference is the explicit inclusion of an
oscillator source with phase/frequency control as a unique control. A
plurality of Type I models can also create complex passband signals. Also
Z.sub..DELTA. 2090, 2190, may be in general a complex function and its
control may likewise be considered as a complex number, thus suitable for
complex envelope generation. However, a Type II model is convenient for
complex signal generation since the controls may be independently
manipulated by scalar functions if desired. However, reserving the
ability to drive Z.sub..DELTA. 2090, 2190 by a signal consisting of
complex numbers can offer some desirable degrees of freedom. The complex
numbers may control the real and imaginary portions of the complex
impedance Z.sub..DELTA. 2090, 2190. Many useful complex signaling scheme
can be realized with this model by applying the circuit architectures of
FIGS. 20 and 21 to inphase and quadraturephase modulation schemes.
[0660] As described herein, the focus has been on discussions of
optimization of thermodynamic efficiency, .eta., with respect to
application variable energy partitions applied to modulation techniques,
such as those techniques using any modulator technology, or such as
d2p.TM. technology. It is useful to develop the similar efficiency themes
but relate the discussion to the encoding of the information metric H(x)
into phase, since this is a significant macroscopic degree of freedom for
signals and such agility is helpful for modern signaling standards.
[0661] There is a common assumption in the communications industry that
constant envelope signals given by;
a(t)= {square root over (a.sub.I(t).sup.2+a.sub.Q(t).sup.2)}=constant
possess maximum efficiency performance. This rule of thumb is
approximately true under restricted circumstances but becomes challenged
as capacity increases for at least two reasons. The application phase
space is smaller dimensionally whenever amplitude modulation is denied
and therefore capacity decreases for specified link performance. This
usually demands greater transmitter power and bandwidth to offset
capacity losses. In fact, regulatory and standards body restrictions
render some phase modulation waveforms as obsolete or of narrow
application, so as to have limited use.
[0662] In addition, the phase modulation, when required to support greater
information rates, begins to impact the efficiency of practical
infrastructure electronics. This is especially true for significant
transmitter power requirements. Changing phase of a carrier at
increasingly greater rates corresponds to accelerating and decelerating
electrons, which have mass and are also associated with the corresponding
electromagnetic fields of radiation possessing momentum. The greater the
increase or decrease (+/) accelerations of the electrons and the
uncertainty of their changes, the greater the impact on the efficiency of
practical phase modulation schemes. The changing inertia associated with
accelerating and decelerating electrons and their fields requires more
energy than the case where currents are relatively constant.
[0663] Nevertheless, it is also true in practice that phase modulation can
be a powerful technique to conserve energy if the phase changes are
properly controlled and of moderate rates. The most beneficial solutions
address both amplitude and phase, which is assumed in the subsequent
portions of this disclosure.
[0664] Embodiments of the present invention are also directed to criteria
for obtaining energy partitions, which can enhance efficiency for RF
modulation processes which includes amplitude and phase modulated
signals. The signal envelope magnitude often drives these criteria and
the greater the uncertainty metric H(x) the greater the uncertainty for
the signal envelope. Rapid and uncertain carrier phase fluctuations, can
also impact efficiency. Unipolar signals can be defined as being positive
so that 0.ltoreq.a(t).ltoreq.V.sub.L.sub.max. This range is parsed into
(i) domains consistent with the FLUTTER.TM. algorithm to improve
efficiency. .nu. degrees of freedom may also be independently deployed to
control signaling degrees of freedom within the modulation, such as
d2p.TM. modulation, so that signals may be reconstructed, or rendered,
accurately while optimizing efficiency. .nu. degrees of freedom may also
control magnitude and phase of the complex signal given the constraints
imposed within the i.sup.th energy partition. The indices, .nu.,i thus
point to portions of information space {tilde over (I)}{H(x).sub..nu.,i})
which are accessed to generate the physical expression of the .nu.
domains. A final output is obtained as a function of blended controls
according to
a(t)e.sup.j.omega..sup.c.sup.t+.theta.(t)=I{H(x).sub..nu.,i}
[0665] E.sub.e.sub.out the effective energy in the output signal and the
waste energy E.sub.w.sub.out, are given by;
E e out = v i .lamda. v i ( .eta. v i )
E s v i ##EQU00053## E w out = v i
.lamda. v i ( 1  .eta. v i ) E s v i
##EQU00053.2## E s v i = E e out + E w out
##EQU00053.3##
[0666] E.sub.e is maximized and E.sub.w is minimized. In order to
accomplish this optimization, the effective entropy flux
S J e i , ##EQU00054##
is generated so that waste entropy flux
S J w i ##EQU00055##
is minimized. The term "effective entropy flux" and "waste entropy flux"
as applied here refers to perturbations of phase space that impart
information through physical means. Such fluctuations possess relatively
short time constraints on the order of a symbol duration compared to
thermal equilibrium, which can take many symbols to stabilize. Hence, the
fluctuations they may be analyzed using methods of extended
nonequilibrium thermodynamics.
[0667] E.sub.e is the effective output signal energy. One quality of the
E.sub.e metric is given by;
.eta. = E e E e + E w ##EQU00056##
[0668] The other quality metric can be related to the difference in
uncertainties H(x) and H(y) for the input and output of the modulation
process respectively;
min{H.sub.xH.sub.y}.ltoreq..epsilon.
[0669] .epsilon. can be an arbitrarily small number which may be estimated
using error vector magnitudes and minimum mean square error techniques
which calculate energy differences between the input variable x and
output variable y. As a consequence, the additional metric
max { S J e i  S J w i } ##EQU00057##
becomes important because the entropy flux captures the system state
uncertainty in a context which ties the emission of symbols from H.sub.x
to phase space perturbations expressed by
S J e i . ##EQU00058##
Each symbol emitted from the information source is distributed into
multiple FLUTTER.TM. algorithm branches, which may be in general
nonlinear. Therefore, as previously described, the nonlinear tradeoff for
efficiency should be balanced with the concern for information loss. This
tradeoff is managed by the FLUTTER.TM. algorithm and BLENDED CONTROL
FUNCTION BY PARKERVISION.TM..
[0670] FIG. 22 is another illustration of a blended control function
distribution architecture which processes vectors of FLUTTER.TM.
algorithm values per each sample or state. These parallel vector states
enable .nu. degrees of freedom and i partitions to synthesize portions of
subordinate signals with statistical codependencies. A vector synthesis
engine (VSE) module 2203 calculates the blended control function and
renders the parallel control vector per sample of the information bearing
function of time. In this example architecture each of the .nu..sub.1
processing branches possesses its distinct set of degrees of freedom and
i.sup.th energy partition. The degrees of freedom and partitions may
overlap domains between the branches. The prominence of each branch or
the weighting of each branch is a random variable .lamda..sub.1 (part of
2211a) through .lamda..sub.i (part of 2211n) (effective weighting
factors) and each branch will possess a corresponding variable efficiency
through {tilde over (.eta.)}.sub.i. The variable efficiency {tilde over
(.eta.)}.sub.i may also be expressed in terms of {tilde over (.eta.)}
and/or .eta. the instantaneous and thermodynamic efficiencies
respectively.
[0671] The subordinate signals are in general complex quantities, which
are functions of the final desired output amplitude a.sub.n and phase
.THETA..sub.n at n.sup.th the sample. Each branch may possess a nonlinear
characteristic and a final signal synthesis is composited through the
action of the output operator .gradient. 2217 and distributed blended
controls that optimally integrates each statistically weighted nonlinear
branch.
[0672] FIG. 22 is a diagram that illustrates one embodiment 2200 and how
information and energy partitions may be organized in terms of
topological signal flow. This representation 2200 shows assignment of
information resources to each branch with consideration of nonlinearity.
As shown in FIG. 22, flow diagram 2200 includes portions of VSE (Vector
Synthesis Engine) 2203. The VSE module 2203 generates I{H.sub..nu.,i}
2205(a) . . . (n) (where "n" is any suitable number). These functions
(generally 2205) .nu..sub.1 . . . .nu..sub.i and produce an associated
energy, E.sub.s.sub.1 2207(a), E.sub.s.sub.2 2207(b) and E.sub.s.sub.i
2207(n) (where "n" is any suitable number) and a derived function 2209(a)
. . . (n) (where "n" is any suitable number). The output of function
2209(a) . . . (n) (generally 2209) is shown as 2211(a) . . . (n),
respectively (generally 2211). The signals 2211(a) . . . (n) are provided
to and associated with NL.sub.1 2215(a), NL.sub.22215 (b) . . . NL.sub.i
2215 (n) (where "n" is any suitable number). The outputs from 2215(a) . .
. (n) are composited by operation module ".gradient." 2217 and operations
of each algorithm branch and render output 2219. The operator .gradient.
module 2217 leverages the FLUTTER.TM. algorithm using apriori knowledge
of the apparatus and a desired signal as well relationships derived from
the following variables, functions and parameters: [0673] .nu..sub.i,l: A
set of degrees of freedom ranging from 1 to .mu.. That is, [0674] Here
the l.sup.th instantiation of the .nu. indices may assume any combination
from the set 1.ltoreq..mu.. i, is a partition number and l may contain
any grouping of partitions. .gradient. may operate on these sets and
groupings internally. [0675] i: i.sup.th energy partition increment,
which can be associated with a subset of up to .nu. system degrees of
freedom. [0676] {tilde over (.eta.)}.sub.i: .eta. or suitable function of
.eta. in i.sup.th path considering one or more inefficiencies of that
path, including the interacting (compositing) of the .nu..sub.i subsets
of degrees of freedom. [0677] H(x): Information source (or other suitable
representation) input whose pdf (probability density function) is p(x)
(or other suitable representation). [0678] H(y): Information output (or
other suitable representation) whose pdf (probability density function)
is p(y) (or other suitable representation). [0679] X.sub.n(t): n.sup.th
signal sample for ideal reference. [0680] Y.sub.n(t): n.sup.th signal
sample for system output.
[0681] The vector synthesis engine (VSE) module 2203 calculates the per
sample, functions for the .nu..sub.i, domains supporting functions 2207,
2209, 2211, and 2215. The calculations include apriori knowledge of the
apparatus configuration and technology characterization. Models consider
efficiency and signal space geometries for one or more system states
.gamma. which contemplate, signal type, signal rate, temperature, dynamic
range, power supply variation, etc.
[0682] FIG. 22 is an operational mixture of functions that illustrate the
joint processing of signal energy and the associated information metrics
encoded into y.sub.n(t) 2219 mapping, or blending, or compositing, at the
output.
[0683] Functions/modules 2209 (a . . . n), 2211 (a . . . n), 2215 (a . . .
n), 2217, 2205 (a . . . n), and 2203, may be implemented by a suitable
blend of hardware and software using microprocessor and/other appropriate
configurable and/or programmable technologies. Also analog technology may
be used to implement these functions with suitable A/D and D/A interfaces
where applicable to transition between analog and digital processing
functions/modules.
[0684] As previously indicated R.sub.xy or corresponding covariance is a
useful metric for indirectly assessing S.sub.J.sub.e, S.sub.J.sub.w.
1R.sub.xy.parallel..varies.kS.sub.J.sub.w
[0685] If this quantity is zero then S.sub.J.sub.e is maximized and
S.sub.J.sub.w is minimized, as a necessary but not sufficient condition.
[0686] Since x and y are complex signals the crosscorrelation may also be
a complex number. R.sub.xy may therefore also be used to obtain errors
for signal magnitudes and phase. This is necessary and sufficient.
[0687] An apparatus that includes multiple technologies operated in
nonlinear regions is difficult to model. The complex impulse response
consists of a series of Volterra kernels. FIG. 22 illustrates the Vector
Synthesis Engine (VSE) 2203, which generates the intermediate blended
controls 2211 based on knowledge of the apparatus partitions, desired
output signal 2219, targeted efficiency vs. signal quality metric, and
modeled or characterized nonlinearities, NL.sub.1, NL.sub.2, . . .
NL.sub.i 2215 (a), 2215(b) . . . 2215(n) (where "n" is any suitable
number). Models based on Volterra functional series are usually complex
and, therefore, typically difficult to analyze and compensate in hardware
for real time application. Rather, embodiments of the present invention
are directed to creating an image that provides what may be described as
an "entropy flux surface", or herein after, simply "differential
surface". The surfaces (entropy flux surfaces) are extracted as sets of
3dimensional cross sections of higher order complex hypergeometric
manifolds. Each set of surfaces corresponds to a particular state of one
or more modulators plus supporting functions, or collectively the
apparatus and each state is characterized by at least 2 differential
surfaces that may be obtained from a crosscorrelation function, or a
corresponding covariance.
[0688] FIGS. 23A and 23B are graphics that illustrate an example of the
differential surfaces for a particular state. Specifically, FIG. 23A
shows a graphical illustration 2300 of a differential magnitude entropy
surface 2307 and FIG. 23B shows a graphical illustration 2301 of a phase
entropy surface 2317.
[0689] As shown in FIG. 23A, the differential magnitude entropy surface
2307 is plotted on Xaxis 2302, Yaxis 2304 and Zaxis 2306. As shown in
FIG. 23A, the differential magnitude entropy surface 2307 has a
substantially flat portion 2308 and a substantially conical portion 2310.
The substantially conical portion 2310 of the phase entropy surface 2307
is illustrated as being "positive" which is merely a convention choice.
The differential surface 2307 could also be represented as "negative".
Also, the designation of the X, Y and Z axes is a convention choice. Any
suitable coordinate system may be used to plot the differential magnitude
entropy surface. Although surface portion 2310 appears conical for this
example, it may assume other forms.
[0690] FIG. 23B shows a graphical illustration 2301 of a differential
phase entropy surface 2317. This differential phase entropy surface 2317
is plotted on a coordinate space, shown as Xaxis 2312, Yaxis 2314 and
Zaxis 2316. Differential phase entropy surface 2317 has a substantially
flat portion 2318 and a substantially conical portion 2320. The
substantially conical portion 2320 of the differential phase entropy
surface 2317 is illustrated as being "negative" which is merely a
convention choice. The surface 2317 could also be represented as
"positive". Also, the designation of the X, Y and Z axes is a convention
choice. Any suitable coordinate system may be used to plot the
differential phase entropy surface. Although surface portion 2320 appears
conical for this example if may assume other forms.
[0691] Sets of such surfaces 2307, 2317 characterize an operational domain
of .gamma. states. Surface data are transformed to function coefficients,
which may be further interpolated and extrapolated over the entire set of
.gamma. states. This interpolated data feeds the FLUTTER.TM. algorithm to
enable the creation of Blended Control.TM. (also known as BLENDED CONTROL
BY PARKERVISION.TM.) {tilde over (I)}{H.sub..nu.,i} in concert with the
other parameters previously listed. The process renders new functions
that possess properties that minimize S.sub.J.sub.w production, the
result of which is illustrated in FIGS. 24A and 24B.
[0692] FIG. 24A shows a graphical illustration 2400 of a reduced
differential magnitude entropy surface 2408. This reduced differential
magnitude entropy surface 2408 is plotted on Xaxis 2402, Yaxis 2404 and
Zaxis 2406. As shown in FIG. 24A, the reduced differential magnitude
entropy surface 2408 has a substantially flat portion. ("Substantially"
is used as a relative term with respect to a quality metric that is a
system design parameter.) The designation of the X, Y and Z axes is a
convention choice. Any suitable coordinate system may be used to plot the
differential magnitude entropy surface.
[0693] FIG. 24B shows a graphical illustration 2401 of a reduced
differential phase entropy surface 2418. This reduced differential phase
entropy surface 2418 is plotted Xaxis 2412, Yaxis 2414 and Zaxis 2416.
The reduced differential phase entropy surface 2418 has a substantially
flat portion 2420 and a substantially conical portion 2419. The
substantially conical portion 2419 of the reduced differential phase
entropy surface 2418 is substantially more narrow (less surface area)
than the phase entropy error conical portion of FIG. 23B. The designation
of the X, Y and Z axes is a convention choice. Any suitable coordinate
system may be used to plot the differential phase entropy surface.
[0694] As shown in FIGS. 24A and 24B, the error metric S.sub.J.sub.w is
reduced to the lowest acceptable, or lowest compliant, value through
{tilde over (I)}{H.sub..nu.,i} while articulating the most efficient
resources available within the apparatus to produce S.sub.J.sub.e. Since
nonlinearities in one branch, as shown in FIG. 22, 2205, may reduce the
capacity of that branch while enhancing efficiency, another branch makes
up the difference in information capacity. The relative partial
information capacities and efficiencies of algorithm branches may
fluctuate dynamically during compositing. Branch domains may overlap
through the sets of {tilde over (I)}{H.sub..nu.,i} even if energy domains
(i) may or may not overlap. Whenever overlap of .nu..sub.1, .nu..sub.2,
.nu..sub.3 control domains overlap, the statistics of the significant
pdfs (probability density functions) p.sub..nu..sub.1, p.sub..nu..sub.2 .
. . will possess crosscorrelation properties. This permits each energy
partition (i) to excite .nu..sub..mu. controls in parallel with the
proper statistical weighting, thus blending, or compositing, information
from {tilde over (I)}{H.sub..nu.,i} domains.
[0695] FIG. 25 shows an example of a joint probability space diagram 2500.
As shown in FIG. 25 an output amplitude domain waveform pdf (probability
density function) p(V.sub.L) 2506 is generated from {tilde over
(I)}{H(p.sub.1, p.sub.2, . . . p.sub..nu.)}, .nu. which is composite, or
blended control, PDFs (probability distribution function). Each member of
this composited set is a pdf (probability density function) of a
nonstationary random variable, which may be continuous, discrete or both
(illustrated as continuous for example).
[0696] As seen in FIG. 25, the solid line 2506 illustrates the composited
pdf (probability density function) p.sub..nu.(V.sub.L) can be considered
as a joint distribution that is dependent on several subordinate pdfs
joint (probability density functions) or joint subdistributions {tilde
over (I)}{p(V.sub.1V.sub.2, V.sub.3 . . . V.sub..nu.)} 2521, {tilde over
(I)}{p(V.sub.2V.sub.1, V.sub.3 . . . V.sub..nu.)} 2522, {tilde over
(I)}{p(V.sub.3V.sub.1, V.sub.2, V.sub.4 . . . V.sub..nu.)} 2523,
{p(V.sub.4V.sub.1, V.sub.2, V.sub.3 . . . V.sub..nu.)}) 2525, and {tilde
over (I)}{p(V.sub..nu.V.sub.1, V.sub.2, . . . V.sub..nu.1)} 2526 in
this example. The graph 2500 is plotted with respect to Xaxis 2502 vs.
Yaxis 2504. Several degrees of freedom (.nu.) were used to form the
example statistic shown in FIG. 25. Specifically, 3 energy partitions
E.sub.1, E.sub.2, E.sub.3(i=3, .zeta.=2) are illustrated (2516, 2518 and
2520) (without any consideration for optimization). Notice that the
subordinate p.sub..nu. functions 2521, 2522, 2523, 2525 and 2526 interact
statistically to form a composite representation, shown as line 2506.
FIG. 25 provides a statistical description of a representation of an
information bearing function of time. Components of phase, amplitude and
frequency are contemplated as extensions of the composited statistic.
Hence, the variables possess some correlation for the region of overlap.
This correlation is a variable which is a function of the set of voltages
or signals V.sub.L, {tilde over (I)}{(V.sub.1, V.sub.2, . . .
V.sub..nu.)}. Also each energy partition 2516, 2518 and 2520 may span a
subset of the blend from the available p.sub..nu..sub..mu.. In addition,
a suitable blend of subordinate joint pdfs is possible which possess
tailored cross covariance.
[0697] FIG. 25 shows a 2dimensional RV; however, the RV is in general
applicable to any suitable number of complex dimensions. FIG. 25
illustrates how an output V.sub.L may be a composited result of several
constituents (V.sub.1, V.sub.2, V.sub.3 . . . V.sub..nu.).
[0698] FIG. 26 shows a flow chart 2600 that illustrates a FLUTTER.TM.
algorithm development approach that considers up to .nu. plus i
additional macroscopic degrees of freedom for the apparatus. As shown in
FIG. 26, the flow chart 2600 begins with start step 2602 having a
particular set of FLUTTER.TM. operational parameters and apriori
knowledge of the apparatus characteristics. Energy partitions (i) are
chosen, as shown in step 2604 according to input 2602. This selection of
a number of energy partitions to partition one or more energy sources
depends on a desired resolution to render a signal or a waveform that can
be encoded with information (generally referred to herein as an
information bearing function of time). The (i) partitions may be fixed
domain (as shown in step 2606) or fixed plus switch PS domain (as shown
in step 2608).
[0699] .nu. degrees of freedom are allocated, as shown in step 2610. The
allocation of step 2610 is used for compositing, as well as
p.sub..nu.(V.sub.L) distributions.
[0700] Joint optimization of .eta., H.sub.xH.sub.y is performed, as shown
in step 2614. This joint optimization of step 2614 also is a function of
.DELTA.S 2612. The result of the joint optimization is analyzed as shown
in step 2616. This analysis includes checking {tilde over
(I)}{.eta..sub.tot} and {tilde over (I)}{R.sub.xy}. The result of this
analysis of step 2616 is either acceptable, as shown by reaching step
2630 or rejected, as shown by line 2618, which shows that the optimized
blending function is iterated, as shown in step 2620. This optimization
may be accomplished by some combination of characterization, measurement
and calculation which can be iterative or solved through the calculus of
variations. The result of the possibly iterative optimization process
(2620) is used in step 2610, as shown by line 2615. The result from the
iterative optimization process (2620) may also be used in the
partitioning step 2604, as shown by line 2622. Once this optimization is
complete, the resulting optimization parameters may be applied in a feed
forward application of FLUTTER.TM.. FIG. 26 illustrates a general method
for obtaining a statistical characterization of an apparatus supporting
the FLUTTER.TM. algorithm which utilizes the characterization as prior
system knowledge and apriori knowledge
[0701] For many applications it is advantageous to reduce individual
FLUTTER.TM. domain sample rates and dynamic ranges, particularly if a
switched or switching power supply is utilized in one or more than one of
the energy partitions.
[0702] The number of signal samples per energy partition can be
approximately obtained from;
n i = .lamda. i 2 W .tau. ##EQU00059## n i max
= .lamda. i max 2 W .tau. ##EQU00059.2## n i min
= .lamda. i min 2 W .tau. ##EQU00059.3## n i min
2 .tau. .lamda. i min .ltoreq. W i .ltoreq. n i max
2 .tau. .lamda. i max ##EQU00059.4##
[0703] The sampling rate for the i.sup.th can then be given by 2W.sub.i,
where W.sub.i is the required bandwidth of joint FLUTTER.TM. processes in
i.sup.th partition, although there is a finite probability of switching
between any of the domains from sample to sample, the averaged switch
frequency on a per domain basis is given by;
R.sub.i=.lamda..sub.iR.sub.sx.ltoreq.2W.sub.i
where R.sub.sx is the maximum switch rate, and .lamda..sub.i is a
suitable rate multiplier.
[0704] This rate can be further reduced by redistribution of, or suitable
distribution of; the frequency components of the FLUTTER.TM. blended
controls. Additional amplitude and phase information not accommodated by
switching power supply or switched power supply control is allocated to
the .nu. remaining degrees of freedom. These parallel paths permit the
full dynamic range and resolution of the signal to be reconstructed "on
the fly", sample by sample, using the VSE (Vector Synthesis Engine)
module to optimize .eta. and R.sub.xy.
[0705] The amplitude modulations are partially instantiated by the energy
domain control at each V.sub.S.sub.i boundary. Additional amplitude
control is facilitated in the .nu. remaining degrees of freedom (as shown
by step 2610) for the modulator device.
[0706] ) It is helpful to describe embodiments of the present invention
using a variety of general topologies, which incorporate FLUTTER.TM. for
a modulator. FIG. 27 shows an example of FLUTTER.TM. with (i) partitions
and .nu. auxiliary degrees of freedom. Indeed, FIG. 27 shows one topology
2700 related to d2p.TM. application with Type I modulation properties.
[0707] The embodiment shown in FIG. 27 shows an example of one embodiment
2700 of the present invention. FIG. 27 shows energy sources
V.sub.S.sub.1, V.sub.S.sub.2 . . . V.sub.S.sub.i 2708(a), 2708(b) and
2708(n), respectively) where "n" is any suitable number. It is an
embodiment of the present invention that any suitable number of energy
sources may be used. Although illustrated as DC batteries for this
example, it is understood that the energy sources may possess any
statistic of voltage or current and may also be encoded with information.
Blended controls, {tilde over (I)}{H(x).sub..nu.,i} 2702 are generated
from a VSE (Vector Synthesis Engine), as described herein. A portion
2702(a) of the control function 2702 is provided to a switching control
to selectively access one of the energy sources (generally 2708)
connection as shown by 2711, 2709 and 2713. The switch contact, 2709 and
connection nodes 2713 (a . . . n) are activated based on the control
signals of 2702(a) and switch control 2711. The selected energy source of
the plurality of sources (generally 2708) provides energy, in any
suitable form, which may include voltage, current, excitation or other
stimulus to impedance module Z.sub.S 2789.
[0708] A second portion of blended control, 2702 is 2702(b), which is
provided to LO (local oscillator) 2710, which then provides input to
modulator module 2766. The modulator module 2766 may be, for example a
MISO (multiple input single output module). The matching impedance 2769
receives the interaction of Z.sub.s 2789modulator module 2766, and the
sources 2708(a) . . . (n). V.sub.L.DELTA.y(t) 2774 is rendered at load
2764. In this example, the energy sources 2708 (generally) are
partitioned according to control signals 2702(a), which partition the
energy samples into a number of partitions, which can be enumerated as
i.ltoreq.2.sup.k where k is the resolution used for reconstructing the
signal amplitude and/or phase typically i<<k for fixed partitions.
Indeed, it is contemplated that i may be a suitable integer of fixed
partitions to obtain a desirable efficiency. For example i could be an
integer such as 2 and offer performance advantage (compared to legacy
technologies) in the rendered output signal V.sub.L 2774 at load R.sub.L
2764. In this example, none of the partitions require switching power
supplies. Switching power supplies may also be used. The additional .nu.
dimensions provide for complex signal reconstruction, or rendering, of
both desired magnitude and phase at the output 2774 given the constraint
of the i.sup.th energy partition. FIG. 28 shows the Thevenized equivalent
of FIG. 27.
[0709] In FIG. 28, the embodiment shown as 2800 shows that the several
voltages of FIG. 27 are replaced by the parallel combination of I.sub.i
and Z.sub.i. These combinations of I.sub.i and Z.sub.i are shown as pairs
2818, 2819; 2820, 2821; and 2822, 2823. Current is provided to Z.sub.s
2889 as a function of control signals, such as FLUTTER.TM. blended
control signals, 2802, which includes 2802(a) and 2802(b). A portion
(2802(a)) of the control function 2802 is provided to a switching control
to selectively access one of the pairs (2818, 2819; 2820, 2821; 2822,
2823) as shown by 2813 and 2811. This selective access is shown as
element 2807. The connections 2815, 2813 and 2811 are activated based on
the control signals of 2802(a). The selected energy source of the
plurality of sources provides energy, in any suitable form, which may
include voltage, current, power or any other excitation force to
impedance module Z.sub.s 2889. Although illustrated as a generic current
sources for this example, it is understood that the energy sources may
possess any statistic of current and may also be encoded with information
(portion of H(x)).
[0710] A second portion of control, or FLUTTER.TM. blended control
function 2802 is 2802(b), which is provided to LO (local oscillator)
2810, which then provides input to a modulator module which may be for
example a MISO 2866.
[0711] Also, a portion of the control signals from 2802 may also be
provided to a modulator module which may be for example a MISO 2866.
[0712] The modulator module 2866 may be, for example a MISO (multiple
input single output module). The matching impedance 2869 receives the
output from Z.sub.s 2889 and the interaction of modulator module 2866
renders V.sub.L 2874 at load 2864.
[0713] Similar to the embodiment described in relation to FIG. 27, the
energy sources of FIG. 28 are partitioned according to control signals
2802(a), which partition the energy sample into a number of partitions,
which can be explained as i.ltoreq.2.sup.k where k is the resolution used
for reconstructing the signal amplitude and/or phase. Typically
i<<k for fixed partitions. Indeed, it is contemplated that i may be
a suitable integer based on the available resources desired efficiency
and signal quality as well cost of implementation, to obtain a desirable
efficiency. For example i may be an integer such as 2 and offer
performance advantage.
[0714] FIG. 29 shows an embodiment 2900 of the present invention. FIG. 29
accommodates variable switching power supplies for one or more of the
partitions. As shown in FIG. 29, power supplies 2908(a) . . . (n) (where
"n" is any suitable number) receive a first portion of control signals
2902(a). For example, the power supplies (generally 2908) receive control
signals 2902(a). Switching of switch 2909, is controlled by switch
control 2911 via some portion of the signals 2902(a). Once selected a
power source 2908 (a) . . . (n) provides energy to Z.sub.s 2989 as well
as other portions of 2900.
[0715] A second portion of the control function signals 2902(b) is
provided to modulator module, which may be, for example a MISO (multiple
input single output module) 2966 and LO (local oscillator) 2910. The
modulator module 2966 power source interacts with circuit impedances
Z.sub.s 2989, Z.sub.m 2969, R.sub.s 2964, LO 2910, switch 2909, power
sources 2908 (a . . . n) and controls 2902 to generate an output V.sub.L
2974.
[0716] The architecture shown in FIG. 29 represents nesting of partitions
within partitions. Each of the (1) partitions 2902 may be separately
subdivided into partitions that can be implemented by a variable, or
switching, power supply. Controls 2902 (c . . . n) provide a means of
adjusting energy source voltages 2908 (a . . . n) within a selected
partition. One or more of the (i) partitions can be realized in this
manner. Depending on the specific partitions, .eta. may be increased
while providing finer control of amplitude reconstruction over some
portion of the envelope dynamic range. Any domain not controlled by a
switching power supply may be supplied by a fixed source (source with a
significantly constant describing pdf for voltage or current). A
Thevenized architecture may replace the variable, or selectable, voltage
sources.
[0717] Alternative strategies may be presumed for power supply
partitioning. This consideration may be applied to any architecture
employing FLUTTER.TM..
[0718] FIG. 30 shows an alternate embodiment 3000 of the present
invention. As shown in FIG. 30, the embodiment 3000 presents the power
source cascading, alternative. Portions of the control function signals
3002 (3002(a) and 3002 (b)) are provided to energy sources 3008 (a) . . .
(n) (where "n" is any suitable number) and to modulator module 3066 as
well as LO 3010. The energy sources (generally 3008) may provide voltage,
current, power, or any other suitable excitation waveform or energy of
any suitable statistic to Z.sub.s module 3089 via controlled switching
mechanisms 3011 and 3009. Node 3062 is also shown. Node 3062 is a node
which possesses a composite signal statistic.
[0719] A signal generated at node 3062 from the interaction of 3066, and
3089, 3009, as well as 3008 is also provided to Z.sub.m 3069, which is
then provided to the load 3064, to render V.sub.L 3074.
[0720] The structure may also be Thevenized. In addition, both series and
parallel power sources can be utilized in place of the fixed series power
source bank. Also, as an alternative embodiment, none of the power
supplies may be variable or any subset may be variable. Variable supplies
are typically switching power supplies, or other equivalently efficient
technology.
[0721] FIG. 31 illustrates another embodiment 3100 of the invention. 3100
is a modulation architecture which supports the FLUTTER.TM. algorithm.
This structure 3100 may also be referred to as a Type 3 modulator. 3100
may be instantiated one or more times to support complex baseband or pass
band modulations.
[0722] 3101 is any suitable energy source consisting of up to 2(i+1)
distinct sources and associated branches which may possess currents which
have D.C., A.C. characteristics or both. The voltages +/V.sub.s.sub.1
3102, +/V.sub.s.sub.2 3103 up to +/V.sub.i+1 3104 where i+1 is some
suitable integer supporting up to i partitions, along with the voltages
/+{circumflex over (V)}.sub.s.sub.1 3105, /+{circumflex over
(V)}.sub.s.sub.2 3106 up to /+{circumflex over (V)}.sub.i+1 3107 are
supplied by module 3101.
[0723] Impedance Z.sub.1, 3108, is allocated to the circuit branch
associated with +/V.sub.s.sub.1 3102. Impedance Z.sub.2, 3109 is
allocated to the circuit branch associated with +/V.sub.s.sub.2 3103.
Impedance Z.sub.i+1 3110 is allocated for the circuit branch associated
with the voltage +/V.sub.s.sub.i+1 3104 in the (i+1).sup.th power supply
branch. Impedance {circumflex over (Z)}.sub.1 3111, is allocated to the
circuit branch associated with /+{circumflex over (V)}.sub.s.sub.i 3105.
Impedance {circumflex over (Z)}.sub.2 3112 is allocated to the circuit
branch associated with /+{circumflex over (V)}.sub.s.sub.2 3106.
Impedance {circumflex over (Z)}.sub.i+1 3113 is allocated to the circuit
branch associated with /+V.sub.s.sub.i+1 3107.
[0724] Switch or Commutator 3114 accesses voltages +/V.sub.s.sub.1 3102,
+/V.sub.s.sub.2 3103 . . . +/V.sub.s.sub.i+1 3104 after interaction
with impedances Z.sub.1, 3108, Z.sub.2, 3109, up to and including
Z.sub.i+1 3110.
[0725] Switch or Commutator 3115 accesses voltages /+{circumflex over
(V)}.sub.s.sub.1 3105, /+{circumflex over (V)}.sub.s.sub.2 3106 . . .
/+{circumflex over (V)}.sub.s.sub.i+1 3107 after interaction with
impedances {circumflex over (Z)}.sub.1 3111, {circumflex over (Z)}.sub.2
3112, up to and including {circumflex over (Z)}.sub.i+1 3113.
[0726] Switches or commutators 3114, 3115 are controlled via function 3119
which is a subset of blended controls {tilde over (I)}{H(x).sub..nu.,i}
distributed from a VSE 3121.
[0727] Z.sub.L 3118 Load Impedance develops a differential output voltage
V.sub.L 3122 according to currents flowing in the circuit determined by
selected power sources, voltages +/V.sub.s.sub.1 3101, +/V.sub.s.sub.2
3103 . . . 30 /V.sub.s.sub.i+1 3104, voltages /+{circumflex over
(V)}.sub.s.sub.1 3105, /+{circumflex over (V)}.sub.s.sub.2 3106 . . .
/+{circumflex over (V)}.sub.s.sub.i+1 3107 as well as impedances
Z.sub.13108, Z.sub.23109, . . . Z.sub.i+1 3110, impedances {circumflex
over (Z)}.sub.1 3111, {circumflex over (Z)}.sub.2 3112 . . . Z.sub.i+1
3113, impedance Z.sub..DELTA./2 3116, impedance {circumflex over
(Z)}.sub..DELTA./2 3117, and Z.sub.L 3118.
[0728] This modulator topology can deliver unipolar, bipolar, balanced or
unbalanced signals, V.sub.L 3122 across the load Z.sub.L 3118 depending
on the choice of supply voltages and their relative average values with
respect to some system reference potential. A fully differential and
balanced output with an average of zero volts at V.sub.L 3122 improves
efficiency.
[0729] The impedances Z.sub..DELTA./2 3116 and {circumflex over
(Z)}.sub..DELTA./2 3117 can be implemented with transistors or other
suitable structure including MISO functions conveying transimpedances
which may be modeled as Z.sub..DELTA./2 3116 and {circumflex over
(Z)}.sub..DELTA./2 3117.
[0730] A Type 4 modulator may be implemented by adding Z.sub..DELTA..sub.s
3125 a shunt impedance used across the Z.sub.L 3118 load impedance
terminals and controlled by a subset of blended control 3119.
[0731] Impedances Z.sub.1 3108, Z.sub.2 3109, up to and including
Z.sub.i+1 3110 as well as {circumflex over (Z)}.sub.1 3111, {circumflex
over (Z)}.sub.2 3112 up to and including {circumflex over (Z)}.sub.i+1
3113 are partially reflective of source power supply parasitic
impedances. However, these impedances may be augmented with reactive
components to assist in the reconstruction of analytic signal envelopes
from circuit currents and voltages.
[0732] The modulator structure 3100 of FIG. 31 may be embedded in FIG. 14
to implement complex modulation schemes. The variable or switched energy
or power source module 3123 may be deployed in part or whole to modules
1420 and 1430 of FIG. 14. Also, module 3124, the variable impedance
module, may be deployed in part or whole to module 1460 of FIG. 14 as
part of the .gradient. operator. It should also be noted that controls
3119 correspond to some subset of the controls 1401 of FIG. 14.
[0733] While a Type 3 modulator requires variable impedances
Z.sub..DELTA./2 3116, {circumflex over (Z)}.sub..DELTA..sub.s/2 3117 is
considered optional. A Type 4 modulator utilizes the shunt impedance
Z.sub..DELTA..sub.s/2 3125.
[0734] The switching and/or switched power supply sources may consist of
up to 2(i+1) discrete fixed/constant power sources or up to 2(i+1)
variable power sources, or a mix of constant and variable types. The
power sources may be current sources or voltage sources. The
characteristics and values associated with each power source giving rise
to voltages +/V.sub.s.sub.1 3102, +/V.sub.s.sub.2 3103 . . .
+/V.sub.s.sub.i+1 3104, /+{circumflex over (V)}.sub.s.sub.1 3105,
/+{circumflex over (V)}.sub.s.sub.2 3106 . . . /+{circumflex over
(V)}.sub.s.sub.i+1 3107, are selected and controlled via a subset of
blended controls 3119 distributed from a VSE 3121 by suitable analog or
digital means.
[0735] The power spectral density (psd) of each blended control may be
unique. The psd of each blended control may be dynamic and a function of
time or state of 3100.
[0736] The rates and/or bandwidths of each blended control may be tailored
to select or adjust each switch, function, or impedance to reconstruct a
desired signal V.sub.L 3122 according to some desired metric. The rates
and/or control bandwidths are distributed to maximize apparatus
efficiency while conserving H(x) some desired information entropy
conveyed through the system to produce V.sub.L 3122.
[0737] In general, each function block of 3100 may possess unique
reference voltages which are distributed to internal circuit nodes of the
indicated or associated impedances or functions. The reference voltage,
V.sub.ref.sub._.sub.sys 3140, is associated with 3101, switching and/or
switched power supply sources. Reference voltage V.sub.ref.sub.1 3130 is
associated with Z.sub.1 3108. Reference voltage V.sub.ref.sub.z 3131 is
associated with Z.sub.2 3109. Reference voltage V.sub.ref.sub.i+1 3132 is
associated with Z.sub.i+1 3110. Reference voltage {circumflex over
(V)}.sub.ref.sub.1 3133 is associated with {circumflex over (Z)}.sub.1
3111. Reference voltage {circumflex over (Z)}.sub.ref.sub.2 3134 is
associated with {circumflex over (Z)}.sub.2 3112. Reference voltage
{circumflex over (V)}.sub.ref.sub.i+1 3135 is associated with {circumflex
over (Z)}.sub.i+1 3113. Reference voltage V.sub.ref.sub..DELTA. 3136 is
associated with Z.sub..DELTA./2 3116.
[0738] Voltage Reference {circumflex over (V)}.sub.ref.sub..DELTA. 3137 is
associated with {circumflex over (Z)}.sub..DELTA./2 3117.
[0739] Voltage Reference
V ref .DELTA. S ##EQU00060##
3138 is associated with Z.sub..DELTA..sub.s 3125.
[0740] Voltage Reference V.sub.ref.sub.out 3139 is associated with Z.sub.L
3118.
[0741] In general the reference voltages for the impedances and functions
of circuit 3100 may possess differing values. The reference voltages may
possess the same values. The reference voltages may be zero or any other
suitable value. The choice of reference voltages will depend on the bias
requirements for each circuit impedance or function, the interface
requirements for connected circuits or functions and the requirement to
implement waveform or signal offsets within 3100.
[0742] Blended control Distribution 3121 provides blended controls {tilde
over (I)}{H(x).sub..nu.,i} 3119 to various functions and impedances
within 3100. The controls 3119 may be digital, analog or a mix of both.
Each control path is labeled with a dimension indicating the number of
unique control signals allocated to the indicated path. k.sub.ps 3150 is
a number of controls less than or equal to 2(.nu.+i) and associated with
the switching and/or switched power supply sources 3101. k.sub.sx 3152 is
a number of controls less than or equal to .nu.+i, and associated with
switch 3114.
3151 is a number of controls less than or equal to .nu.+i, and associated
with switch 3115. k.sub.Z.sub..DELTA. is a number of controls less than
or equal to .nu.+i, and associated with variable impedance
Z.sub..DELTA./2 3116. k.sub.{circumflex over (Z)}.sub..DELTA. is a number
of controls less than or equal to .nu.+i, and associated with variable
impedance {circumflex over (Z)}.sub..DELTA./2 3117. k.sub.Z.sub..DELTA.s
is a number of controls less than or equal to .nu.+i, and associated with
variable impedance Z.sub..DELTA..sub.s 3125. The number of control
signals may or may not correspond exactly to the number of physical
connections in each control path at each function interface. Controls may
be distributed serially or otherwise distributed or multiplexed on a
common connection, wire, or path.
[0743] Another embodiment 3200 of the invention is illustrated in FIG. 32.
3200 is a general modulation architecture capable of supporting
FLUTTER.TM. algorithms. 3200 can create virtually any signal in an
efficient manner when operated in conjunction with the FLUTTER.TM.
algorithm.
V S U 1 ##EQU00061##
3201,
V S U 2 ##EQU00062##
3202, up to and including
V S U i ##EQU00063##
3203, are variable voltage or current sources associated with upper
branch modulator 3227.
V S L 1 ##EQU00064##
3204,
V S L 2 ##EQU00065##
3205, up to and including
V S L i ##EQU00066##
3206 are variable voltage or current sources associated with the lower
branch modulator 3228. Collectively these sources are controlled via
blended controls distributed through digital and/or analog methods from a
VSE 3219. Collectively the voltage and/or current sources
V S U 1 ##EQU00067##
3201,
V S U 2 ##EQU00068##
3202, up to and including
V S U i ##EQU00069##
3203 are referred to as upper branch sources. Collectively, the voltage
and/or current sources
V S L 1 ##EQU00070##
3204,
V S L 2 ##EQU00071##
3205 up to and including
V S L i ##EQU00072##
3206 are referred to as lower branch sources. The upper branch sources
and lower branch sources may be composed of any combination of current
and voltage sources. The upper branch sources and lower branch sources
may be D.C., A.C., or mixed and possess any suitable statistic of
voltages or currents. The upper branch sources and lower branch sources
may be harmonic functions or modulated harmonic functions. The upper
branch sources and lower branch sources may be random. The upper branch
sources and lower branch sources may possess both harmonic and random
waveform metrics as may be required. The fundamental frequency of each of
the upper branch sources and each of the lower branch sources may be
independently varied from 0 Hz (D.C. case) to any suitable upper
frequency limit. The phase of each of the upper branch sources and each
of the lower branch sources may be independently varied from 0.degree.
degrees to modulo 360.degree. degrees as required. The amplitudes for
each of the upper branch sources and each of the lower branch sources may
be independently controlled as required.
[0744] Z.sub.U.sub.1 3207 is a variable impedance associated with voltage
or current source
V S U 1 ##EQU00073##
3201. Z.sub.U.sub.2 3208 is a variable impedance associated with voltage
or current source
V S U 2 ##EQU00074##
3202 up to and including Z.sub.U.sub.i 3209 variable impedances are
associated with up to and including
V S U i ##EQU00075##
3203 voltage or current sources.
[0745] Z.sub.L.sub.1 3210 is a variable impedance associated with voltage
or current source
V S L 1 ##EQU00076##
3204. Z.sub.L.sub.2 3205 is a variable impedance associated with voltage
or current source
V S L 2 ##EQU00077##
3211 up to and including Z.sub.L.sub.i 3212 variable impedances are
associated with up to and including
V S L i ##EQU00078##
3206 voltage or current sources.
[0746] Collectively Z.sub.U.sub.1 3207, Z.sub.U.sub.23208 up to and
including Z.sub.U.sub.i 3209 variable impedances are referred to as upper
branch source impedances. Collectively Z.sub.L.sub.1 3210, Z.sub.L.sub.2
3211, up to and including Z.sub.L.sub.i 3212 variable impedances are
referred to as lower branch source impedances.
[0747] A variable portion of each upper branch impedance and each lower
branch impedance are controlled via a subset of blended controls 3220
distributed by digital and/or analog means from a VSE 3219.
[0748] The index value i enumerating the upper branch sources, upper
branch source impedances, lower branch sources, and lower branch source
impedances, may assume any suitable integer value.
[0749] An upper branch commutator or switch 3213 selects an upper branch
source via an associated upper branch source impedance based on a subset
of blended controls 3220. A lower branch commutator or switch 3214
selects a lower branch source via an associated lower branch source
impedance based on a subset of blended controls 3220.
[0750] The selected upper branch commutator or switch 3213 output 3222 is
routed to variable upper branch impedance Z.sub..DELTA..sub.U 3215. The
selected lower branch commutator or switch 3214 output 3225 is routed to
variable lower branch impedance Z.sub..DELTA..sub.L 3216.
Z.sub..DELTA..sub.U 3215 and Z.sub..DELTA..sub.L 3216 variable upper
branch and lower branch impedances respectively are controlled by a
subset of blended controls 3220 distributed by digital and/or analog
means from a VSE 3219.
[0751] An output 3222 from variable upper branch impedance
Z.sub..DELTA..sub.U 3215 is routed to output compositing Function 3217
also labeled as .gradient.. An output 3223 from variable lower branch
impedance Z.sub..DELTA..sub.L 3216 is routed to output compositing
Function 3217 also labeled as .gradient..
[0752] Output Compositing Function 3217 operates on inputs 3222 and 3223
to create output composited signal V.sub.L 3226 at load impedance Z.sub.L
3218. Control/s 3221 varies of the output Compositing Function 3217
according to a subset of blended controls 3221.
[0753] The upper branch modulator 3227 and lower branch modulator 3228
along with blended controls 3220 and 3221 distribution of suitable
prepared controls from the VSE 3219 and Compositing Function 3217,
include a universal modulator generating virtually any modulated
waveform/signal at V.sub.L 3226, over frequency spans from baseband to
any suitable carrier frequency. Furthermore, blended controls 3220, 3221,
may be at suitable rates to support desired signal data rates and
bandwidths, any signal path as well as at the output V.sub.L 3226.
[0754] Each upper branch source, each lower branch source, each upper
branch source impedance, each lower branch source impedance, variable
upper branch impedance, variable lower branch impedance as well as
compositing function may possess independent controls with independently
variable information control rates and/or bandwidths.
[0755] A certain portion of information entropy H(x) distributed as a
function of apparatus degrees of freedom and partitions. {tilde over
(I)}(H(x).sub..nu.,i) is distributed via blended controls 3220, 3221, to
each variable functions and modules comprising 3200.
[0756] As a consequence, a differing portion of information entropy H(x)
is supported or conveyed by each variable function or module of 3200 such
that an output compositing function 3217 conserves input information
entropy H(x) at the output V.sub.L 3226 albeit in a signaling format of
choice which may be for example a modulated RF carrier signal. Each
variable function or module of 3200 is assigned some portion of the input
entropy H(x) based on the portion of the originating information
describing probability density function p(x) which exploits the most
efficient modes of the apparatus. That is, an original density function
p(x) with associated information entropy H(x) may be parsed to a set of
joint probability densities p(x).sub..nu.,i each with associated
entropies H(x).sub..nu.,i which may be independent or partially
correlated. The manner in which the set p(x).sub..nu.,i is defined is
based on a maximization of distributed apparatus efficiency (and hence
total efficiency) and the requirement to conserve H(x) in the modulation
process.
[0757] For example, for a particular application of 3200 it may be
efficient to restrict the rate at which the upper branch sources and
lower branch sources may be varied. Amplitudes may be fixed or slowly
varied at one sample rate of bandwidth. Phases may be varied at differing
rates which are more rapidly varying than amplitudes of the sources. The
upper branch source impedances and lower branch source impedances may
vary at unique rates. The commutator or switch 3218, 3214 selection rates
may be unique. The variable upper branch impedance 3215 and the variable
lower branch impedance 3216 may vary at unique rates. Operations within
the output compositing function 3217 may vary at unique rates. Each
blended control may possess an associated unique power spectral density
(psd). Each blended control may possess a power spectral density that
varies. In this manner the output modulation of signal V.sub.L 3226 is a
composited blend of functions within the apparatus which are optimized
according to control rate vs. efficiency and dynamic range vs. efficiency
per function or module. The total efficiency is the average efficiency
for all functions or modules of 3200 operating in concert.
[0758] In general, each unique desired output signal statistic may utilize
new rates for all functions and modules and redefine the set
p(x).sub..nu.,i which in turn modifies the weighting of the blended
controls {tilde over (I)}{H(x).sub..nu.,i}.
[0759] All degrees of freedom illustrated in FIG. 32 may not be required
for every application. For instance, some applications may not require
upper branch source impedances which vary and lower branch source
impedances which vary. In some circumstances upper branch source
frequency and lower branch source frequency may be fixed. Logical
redaction is apparent to those skilled in the art.
[0760] It is also apparent that either the upper branch modulator 3227 or
lower branch modulator 3228 may function as modulators separate from one
another provided they benefit from suitable blended controls 3220, 3219
and output compositing function 3217.
[0761] The output compositing Function 3217 is a specific portion of a
distributed compositing function. Most generally, compositing is a
distributed function embedded in the blended control attributes, in the
form of rates relative sample weighting and nonlinear mappings. However,
the operator .gradient. possesses a prominent position in the modulator
signal processing flow and final entropy reconstruction and thus is also
referred to as an output compositing function in this topology. More
specifically, it is a final mapping in the compositing process which
constructs the desired output signal whilst conserving H(x).
[0762] There are the following reference voltages which may be associated
with internal circuit nodes for the associated impedances and functions
which are subordinate to 3200.
[0763] Reference Voltage ref_u.sub.1 3230 is associated with Z.sub.U.sub.1
3207.
[0764] Reference Voltage ref_u.sub.2 3231 is associated with Z.sub.U.sub.2
3208.
[0765] Reference Voltage ref_u.sub.i 3232 is associated with Z.sub.U.sub.i
3209.
[0766] Reference Voltage ref_L.sub.1 3233 is associated with Z.sub.L.sub.1
3210.
[0767] Reference Voltage ref_L.sub.2 3234 is associated with Z.sub.L.sub.2
3211.
[0768] Reference Voltage ref_L.sub.i 3235 is associated with Z.sub.L.sub.i
3212.
[0769] Reference Voltage ref_.DELTA..sub.U 3236 is associated with
Z.sub..DELTA.U 3215.
[0770] Reference Voltage ref A.sub.L 3237 is associated with Z.sub..DELTA.
3216.
[0771] Reference Voltage ref_.gradient. (3238) is associated with output
Compositing Function (3217).
[0772] Reference Voltage ref out 3239 is associated with output load
Z.sub.L 3218.
[0773] The above listed reference voltages may assume any suitable value
for distribution to circuit nodes internal to the associated impedances
or functions. The reference voltages may or may not be equal. The
reference voltages may or may not be zero. The choice of reference
voltage for each function or impedance depends on whether the functions
impedances require some particular operational bias voltage to implement
a respective function, facilitate interface to connected impedances or
functions, or to implement waveform or signal offset values.
[0774] In general each circuit internal to the impedances Z.sub.U.sub.1
3207, Z.sub.U.sub.2 3208, up to and including Z.sub.U.sub.i 3209,
Z.sub.L.sub.13210, Z.sub.L.sub.2 3211 up to and including Z.sub.L.sub.i
3212, Z.sub..DELTA..sub.U 3215, Z.sub..DELTA..sub.L 3216 and Z.sub.L 3218
may possess series and shunt circuit elements with respect to input,
output, and reference voltage terminals as well as any defined system
ground potential. Likewise, output compositing function .gradient. may
consist of series and shunt circuit elements with respect to input,
output, blended control and reference voltage ref_.gradient. 3238 voltage
terminals as well as any defined system ground potential.
[0775] Blended controls 3220 and 3221 distributed from VSE 3219 consist of
the illustrated control paths from 3219 to each respective applicable
function within 3200. Each illustrated control path is assigned a
dimension labeled k.sub.1 3240, k.sub.2 3241, k.sub.3 3242, k.sub.4 3243,
k.sub.s 3244, k.sub.5 3245, k.sub.7 3246, k.sub.8 3247, k.sub.9 3248.
Each dimension can assume a number less than or equal to the number
.nu.+i the total number of control degrees of freedom. Each of the
dimensions k.sub.1, k.sub.2 k.sub.3, k.sub.4, k.sub.5, k.sub.6 k.sub.7,
k.sub.8 k.sub.9. may be unique. The dimension values indicate the number
of control signals assigned to each control path. Each control path is
some subset of the blended controls 3220, 3221. The number of control
signals per path may or may not correspond to the number of physical
connections between the distribution interface of the VSE 3219 and the
respectively connected function within 3200. Each control path may
support a number of signals different than the number of physical path
connections through techniques of serial control, parallel control, as
well as multiplexing or a mixture of these techniques.
[0776] Control path dimension k.sub.1 3240 is associated with
Z.sub..DELTA..sub.U 3215.
[0777] Control path dimension k.sub.2 3241 is associated with Switch
(3213).
[0778] Control path dimension k.sub.3 3242 is associated with Impedances
Z.sub.U.sub.1 3207, Z.sub.U.sub.23208 . . . Z.sub.U.sub.i 3209.
[0779] Control path dimension k.sub.43243 is associated with Power Sources
V S U 1 ##EQU00079##
3201,
V S U 2 ##EQU00080##
3202 . . . .
V S U i ##EQU00081##
3203.
[0780] Control path dimension k.sub.5 3244 is associated with Power
Sources
V S L 1 ##EQU00082##
3204,
V S L 2 ##EQU00083##
3205 . . . .
V S L i ##EQU00084##
3206.
[0781] Control path dimension k.sub.6 3245 is associated with Impedances
Z.sub.L.sub.1 3210, Z.sub.L.sub.2 3211 . . . Z.sub.L.sub.i 3212.
[0782] Control path dimension k.sub.7 3246 is associated with Switch 3214.
[0783] Control path dimension k.sub.8 3247 is associated with
Z.sub..DELTA..sub.L 3216.
[0784] Control path dimension k.sub.9 3248 is associated with output
composite Function 3217 also on occasion referred to as operator .
[0785] FIG. 33 illustrates a graphic (3300) depicting an example
composited signal 3301 along with 2 constituent signals, constituent
signal (a) 3302 and constituent signal (b) 3303. Each of the illustrated
constituents, 3302 and 3303, may also be a composite of other
constituents, not illustrated.
[0786] The constituent signals (a and b) 3302 and 3303 are used as a part
of a streamlined example to illustrate several aspects of FLUTTER.TM. as
pertains to the use of blended controls which manipulate architectures
such as the kind illustrated in FIGS. 1, 2, 3, 4, 13, 14, 18, 22, 26, 27,
28, 29, 30, 31 and 32.
[0787] Constituent signals (a) 3302 and (b) 3303 are obtained from subsets
of blended controls {tilde over (I)}{H(x).sub..nu.,i} which shall be
labeled {tilde over (I)}{H(x).sub..nu.,i}.sub.a for subset (a)
corresponding to constituent signal (a) 3302 and {tilde over
(I)}{H(x).sub..nu.,i}.sub.b subset (b) corresponding to constituent
signal (b) 3303. {tilde over (I)}{H(x).sub..nu.,i}.sub.a, {tilde over
(I)}{H(x).sub..nu.,i}.sub.b may also be referred to as domains of blended
controls or simply as Domains depending on context.
[0788] Graphic 3301, example output composite, is a desired output signal.
It may also represent an amplitude envelope for the amplitude modulated
portion of an RF carrier modulated signal, where the carrier wave has
been omitted for convenience of illustration. Signal 3301 therefore
possesses the associated desired information entropy H(x). Signal 3302
possesses some information entropy H.sub.a(x) which is less than H(x).
Signal 3303 likewise possesses some information entropy H.sub.b(x) which
is less than H(x). The output composite of constituent signal (a) (3302)
and constituent signal (b) (3303) is obtained through an operator, say
for example operator , which reconstitutes H(x)={tilde over
(I)}{H.sub.a(x),H.sub.b(x)} subject to some time domain signal
requirement, in this case the illustrated signal 3301.
[0789] Close examination of constituent signal (a) 3302 reveals an
apparent bandwidth different than the final composite 3301. This signal
3302 possesses less than half the bandwidth of signal 3301 for purposes
of illustration, and this specific example.
[0790] Examination of constituent signal (b) 3303 reveals an apparent
bandwidth on the order of the output signal 3301.
[0791] Thus, the effective bandwidth and/or sample rate for {tilde over
(I)}{H(x).sub..nu.,i}.sub.a may be different than {tilde over
(I)}{H(x).sub..nu.,i}.sub.b. This can represent an advantage for cases
involving apparatus hardware functions which possess varying degrees of
performance limitations as a function of sample rate and/or bandwidth.
Both efficiency and information entropy conservation may be tailored as
sample rate requirements and bandwidth requirements increase, or
decrease. By distributing the information H(x) into entropies H.sub.a(x)
and H.sub.b(x) the constituent probability densities
{p.sub.a(x)}.sub..nu.,i and {p.sub.b(x)}.sub..nu.,i may be tailored to
match the degrees of freedom available in the apparatus, allocating
information amongst these degrees of freedom to optimize efficiency, and
permit conservation of H(x) in the output signal complex envelope.
[0792] In this simple example the composite output signal 3301 is a simple
sum of constituent (a) 3302 and constituent (b) 3303 to facilitate
disclosure. That is, the output operator is linear in this simplified
example. In general this may not be the case and example may be a more
intricate nonlinear function of its input constituents. Moreover, the
output operator may possess more than two input constituents. The
constituent signals associated with {tilde over
(I)}{H(x).sub..nu.,i}.sub.a and {tilde over (I)}{H(x).sub..nu.,i}.sub.b
may be optional inputs to the output compositing procedure on occasion
referred to as . In general {tilde over (I)}{H(x).sub..nu.,i}.sub.a and
{tilde over (I)}{H(x).sub..nu.,i}.sub.b may be regarded as nonlinear
functions.
[0793] It should be noted that if composite output signal 3301 represents
an output envelope or a signal derived from a complex envelope, that the
constituent signals (a) 3302 and (b) 3303 do not follow the envelope of
3301. This is in contrast to envelope following and envelope restoration
technologies which strive to follow the envelope as accurately as
possible. FLUTTER.TM. relaxes the requirement for signal processing
functions such as switching power supplies, for example, to possess
extreme instantaneous dynamic range in concert with bandwidth. As an
example consider that some portion of {tilde over
(I)}{H(x).sub..nu.,i}.sub.a is allocated to a variable power source. Then
to some extent constituent signal (a) 3302 may be formed from the
variation of such a variable power source. Such a power source may vary
without explicitly tracking the output signal envelope while enhancing
efficiency. In contrast 3303 may possess a single power supply partition
to facilitate {tilde over (I)}{H(x).sub..nu.,i}.sub.b processing for this
example. The allocation of i energy partitions to certain processing
domains depends on the efficiency of functions available to those domains
vs. the linearity requirements (capacity to conserve information)
associated with those processing functions. Therefore, in this simplified
example it is plausible to allocate i=1 or some other relatively low
index for the number of energy partitions to process constituent signal
(b) 3303 as compared to the number of energy partitions allocated to
process constituent signal (a) 3302.
[0794] Constituent signal (a) 3302 and constituent signal (b) 3303 are
characterized by random variables with probability density functions.
These constituents are subordinate to the composite output signal 3301.
The three signals possess differing power spectral densities. In
addition, constituent signals subordinate to constituent (a) 3302 and
constituent signals subordinate to constituent signal (b) 3303 may
possess differing power spectral densities. FLUTTER.TM. trades efficiency
vs. processing bandwidth and spectral characteristics according to the
sustainable efficiency vs. information throughput for each function of
the apparatus.
[0795] Linearity is not required for each function nor is it necessarily
preferred. Rather efficiency is preferred, metering, subordinate signals
approximately through nonlinearities such that the compositing process
reconstitutes a desired signal without waste or distortion. Undesirable
qualities of nonlinear processing are effectively suppressed at the
composited output signal 3301 exploiting algorithm symmetries, nonlinear
discrimination techniques as well as filtering. Thus, the FLUTTER.TM.
technology and philosophy significantly contrast with predistortion
technologies which strive to correct all system nonlinearities.
FLUTTER.TM. accentuates the prominence and role of certain classes of
nonlinearities rather than eliminating them.
[0796] FIG. 34 illustrates an example composite output signal 3401 which
is the same as for the example of FIG. 33. Graphic 3402 illustrates a
waveform corresponding to switched voltages of a variable or switched
power source. For example this graphic could be associated with one or
more outputs of function/module 3101 in FIG. 31. In general it may apply
to any power source for FIGS. 1, 2, 3, 4, 14, 18, 22, 26, 27, 28, 29, 30,
31 and 32.
[0797] Notice the discrete voltage levels depicted in 3402. These levels
may correspond to i energy partitions which are selected by commentator
or switch functions similar to 3116 and 3117 of FIG. 31 for example. It
is apparent after reviewing 3401 and 3402 that the switched voltage power
sources 3402 do not track the example composite output signal 3401. Yet,
the switched power sources 3402 signal/waveform are used to reconstruct
3401. Indeed a portion of the composite output signal 3401 information
entropy is captured in the describing pdf for 3402. It is also apparent
that the average sample rate for 3402 is noticeably less than the
required Nyquist sample rate for a reconstruction of signal 3401. The
number of partition thresholds associated with i partitions of the
waveform 3402 and the threshold levels between partitions are functions
of the required efficiency, limitations of the switched power source
circuitry and the pdf associated with the information entropy allocated
to the switched power source function. Nonlinearities of the waveform
3402 are effectively suppressed by other discriminating techniques of the
FLUTTER.TM. algorithm, as well as filters.
[0798] Since switching efficiency .eta..sub.sx can become a design
consideration, architectures should take advantage of switch topologies
that minimize cascading. Therefore, an example of hierarchical cascading,
which is convenient for binary distributions, is shown in FIG. 35.
[0799] For n such cascades the switch efficiency progresses
.varies..eta..sub.sx.sup.n. This quickly siphons energy at the point of
delivery and increases waste entropy S.sub.w.
[0800] As shown in FIG. 35, embodiment 3500 shows three stages 3501, 3503
and 3505, defined by boundaries 3507 and 3509. 3511, 3520, 3522, 3524,
3526, 3528, and 3530 represent signal paths accessing switching stages
3501, 3503, and 3505 respectively. The switching stages are composed of
one or more switching elements 3515, 3516, 3517 and 3518. Although three
stages are illustrated the architecture may continue, accommodating a
sequence of more stages. Furthermore, one stage may suffice for some
applications. Such switching architectures may also be deployed in
parallel or series.
[0801] Alternatively, parallel switch architectures may be utilized. This
topology is illustrated as shown in FIG. 36 as embodiment 3600. Source
3602 supplies energy or signal or waveform to nodes 3604(a) . . . (n)
where "n" is any suitable number, via the switch selection process. An
"on" switch 3606(a) . . . (n) can connect nodes 3604(a) . . . (n) to
nodes 3608(a) . . . (n). As shown in FIG. 36, each switch possesses a "no
connect" (NC) option 3610(a) . . . (n) respectively. In this embodiment,
only one switch may access a power partition or a signal or a waveform
3602 at any given instant and transfer 3602 to 3606(a) . . . (n). The
efficiency, of this switch topology is on the order of .eta..sub.sx. The
load impedances attached to this switch at nodes 3608(a) . . . (n)
(outputs), as well as "soft" shut down, and "soft" start must be
specifically tailored for the source at 3602 to avoid deleterious
contentions and poorly behaved initial conditions when switching between
outputs. In some cases the equivalent of a time variable transition
conductance may be employed within the switching circuits in conjunction
with adjustment of the source at 3602 and the loads connected to the
switch to eliminate transition discontinuities in charge transfer through
various circuit nodes of 3600. Although loads are not illustrated it is
understood that suitable impedances may be connected to nodes 3608(a) . .
. (n).
[0802] The FLUTTER.TM. algorithms and its related energy partitioning
schemes may be adapted to traditional RF modulators and transmitters to
enhance efficiency. FLUTTER.TM. does not require exclusive
implementation. FLUTTER.TM. processing algorithms may enhance the
efficiency for; [0803] Polar Architectures [0804] Kahn's Technique
[0805] Envelope Restoration [0806] Envelope Tracking [0807] LINC [0808]
Chireix Outphasing [0809] Doherty [0810] Complex Modulators followed by
Amplifier Chains
[0811] Indeed, embodiments of the present invention also apply to
architectures that connect and control with fields and not conductors or
switches. For example apparatus which use electromagnetic coupling,
optical coupling, pressure coupling and combinations thereof.
[0812] There are several aspects of FLUTTER.TM. and the disclosed
architectures that enable standards based communications applications as
well as emerging standards. This includes the support of CDMA, WCDMA,
LTE, OFDM based, GSM, as well as ultra wide band waveforms amongst
others. In addition, spread spectrum as well as frequency hopped
signaling schemes are contemplated in terms of benefits offered by
FLUTTER.TM.. In general, an information bearing function of time (signal)
may be continuous in nature, discrete or a combination. Such signals may
be multiplexed to include time division multiplexed TDM, frequency
division multiplexed (FDM), code division multiple access (CDMA), and
hybrid schemes. The signals may be pulse modulated as well as pulse width
modulated at regular or random intervals of time. The pulses may be of a
variety of shapes such as rectangular, Gaussian, sinelike, etc.,
symmetric or asymmetric in time. Waveforms which may be modulated to
produce these signals may be baseband in nature or based on the
modulation of local oscillators or other harmonic functions produced
through modulation of complex impedances to produce pass band signals as
well.
[0813] Although much of the discussion includes optimization for
information and energy partitions, it should be apparent to those skilled
in the art that a variety of practical tradeoffs in cost, hardware
availability, etc., may on occasion dictate sub optimal partitions which
perhaps perform at some lower efficiency. This disclosure has enabled
such tradeoffs, providing the necessary guidance for design compromises
using the FLUTTER.TM. algorithm.
[0814] FIG. 37 illustrates that FLUTTER.TM. algorithms may be distributed
in nature. Embodiment 3700 includes is a set of information inputs 3710
with uncertainty {H.sub.1(x), H.sub.2(x) . . . H.sub.m(x)}. 3715 is a
FLUTTER.TM. and blended control processor with distributed inputoutput
capability. 3725 is a bank of analog compositing functions. 3300
represents a multiplicity of information bearing functions of time, also
referred to as output signal 1 through "n" where "n" is any suitable
integer.
[0815] Multichannel FLUTTER.TM. algorithms operate on a set (3710) of
information inputs to render information bearing functions of time or
output signals using any number of inputs 3710 up to "m" to render any
number of outputs 3730 up to "n". There are no restrictions on "n" or "m"
other than they be integers greater than or equal to one. Furthermore,
the content of the up to "n" output channels may have some portion of
information in part or in whole, in common between each output. Also,
each output may be completely unique and independent of the other. The
compositing process may be any analog or digital processor and utilize
software and/or microprocessors.
[0816] In another embodiment, blended controls used to access functions
and domains which form statistical composites may access general classes
of mathematical, logical and geometrical functions in any combination
which represent sampled data. The representations may be interpolated,
extrapolated, and approximated in any combination from data sets using
structures such as points, lines, line segments, splines, surface
elements including manifolds, patches, facets and volume elements of any
suitable character. The representations may be in part or in whole
derived from a priori data and/or real time information sources, H(x).
These structures may be employed homogeneously or in any combination to
generate differential entropy surfaces, differential entropy volumes or
suitable transformations thereof. An differential entropy surface is a 2
dimensional representation. A differential entropy volume is a D
dimensional representation where D is an integer greater than or equal to
3. Upon suitable transformation, the resulting composite representations
shall be used to render an information bearing function of time.
[0817] FIG. 38 illustrates three examples of some structures which may be
used to form entropy surfaces. These structures are fit to the surface in
a variety of polygonal shapes, sizes and dimensions to permit efficient
computational representation of the surface. Similar structures may be
conceived in higher dimension geometries but are difficult to represent
graphically.
[0818] It should be understood by those skilled in the art that various
modifications, combinations, subcombinations and alterations may occur
depending on design requirements and other factors insofar as they are
within the scope of the appended claims or the equivalents thereof.
[0819] The foregoing description of embodiments has been presented for
purposes of illustration and description. The foregoing description is
not intended to be exhaustive or to limit embodiments of the present
invention to the precise form disclosed, and modifications and variations
are possible in light of the above teachings or may be acquired from
practice of various embodiments.
[0820] The embodiments discussed herein were chosen and described in order
to explain the principles and the nature of various embodiments and its
practical application to enable one skilled in the art to utilize the
present invention in various embodiments and with various modifications
as are suited to the particular use contemplated. The features of the
embodiments described herein may be combined in all possible combinations
of methods, apparatus, modules, systems and computer program products.
[0821] Having thus described in detail preferred embodiments of the
present invention, it is to be understood that the invention defined by
the above paragraphs is not to be limited to particular details set forth
in the above description as many apparent variations thereof are possible
without departing from the spirit or scope of the present invention.
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