Register or Login To Download This Patent As A PDF
United States Patent Application 
20170318474

Kind Code

A1

FARSHCHIAN; Masoud
; et al.

November 2, 2017

METHODS, DEVICES AND SYSTEMS FOR ENABLING SIMULTANEOUS OPERATION OF
DIFFERENT TECHNOLOGY BASED DEVICES OVER A SHARED FREQUENCY SPECTRUM
Abstract
In one example embodiment, a device includes a memory configured to store
computerreadable instructions therein and a processor. The processor is
configured to execute the computerreadable instructions to determine a
first signal of a first technology in presence of interference from at
least a second signal of a second technology, the first signal and the
second signal being overlappingly transmitted, the determined first
signal being used for processing of information associated with the first
signal.
Inventors: 
FARSHCHIAN; Masoud; (BOSTON, MA)
; YASSINIFARD; Rouzbeh; (BOSTON, MA)

Applicant:  Name  City  State  Country  Type  RadComm, Inc.  BOSTON  MA  US 
 
Assignee: 
RadComm, Inc.
BOSTON
MA

Family ID:

1000002739629

Appl. No.:

15/650449

Filed:

July 14, 2017 
Related U.S. Patent Documents
       
 Application Number  Filing Date  Patent Number 

 14804445  Jul 21, 2015  9713012 
 15650449   

Current U.S. Class: 
1/1 
Current CPC Class: 
G01S 7/021 20130101; H04W 84/12 20130101; G01S 7/023 20130101; H04W 16/14 20130101 
International Class: 
H04W 16/14 20090101 H04W016/14; G01S 7/02 20060101 G01S007/02; G01S 7/02 20060101 G01S007/02 
Claims
1. A device comprising: a memory configured to store computerreadable
instructions therein; and a processor configured to execute the
computerreadable instructions to, receive a signal including at least a
first signal operating based on a first technology and a second signal
operating based on a second technology, the second signal having been
transmitted simultaneously with the first signal over the same frequency
and time domains for reception by the device, form a cost function based
on at least the received signal, a parameter associated with the first
signal and a power spectral density of the second signal, determine the
first signal from the signal based on the formed cost function, and
determine the second signal based on the signal and the first signal for
processing of information associated with the second signal.
2. The device of claim 1, wherein the first signal is transmitted by a
first system operating based on the first technology and the second
signal is transmitted by a second system operating based on the second
technology.
3. The device of claim 2, wherein the first signal and the second signal
are transmitted without any coordination between the first system and the
second system.
4. The device of claim 2, wherein the first system is a radar system and
the first technology is a radar technology, the second system is a
wireless communication system and the second technology is a wireless
access technology, the device is a receiver of the wireless
communications system, the first signal is a radar signal transmitted by
a transmitter of the radar system, and the second signal is a signal
transmitted by a transmitter of the wireless communications system.
5. The device of claim 1, wherein the first signal and the second signal
overlap spatially.
6. The device of claim 1, wherein the signal includes the first signal
with additive noise corresponding to at least the second signal, and the
processor is further configured to, minimize the cost function associated
with the received signal, and determine the first signal as possible
values of the first signal that minimize the cost function.
7. The device of claim 1, wherein the first signal is a radar
fasttime/slowtime data matrix.
8. The device of claim 7, wherein the parameter is a rangefrequency
spectrum associated with a transmission of the first signal, and the
processor is configured to form the cost function based on the
rangefrequency spectrum associated with the transmission of the first
signal, a set of Doppler weights, at least one regularization function,
at least one datafidelity term, at least one regularization parameter, a
stepsize parameter and the power spectral density of the second signal.
9. The device of claim 1, wherein the first signal is a radar data
timeseries.
10. The device of claim 9, wherein the parameter is a frequency response
of a filter associated with a transmission of the first signal, and the
processor is configured to form the cost function based on at least the
received signal, the frequency response of the filter associated with the
transmission of the first signal, a regularization parameter, at least
one regularization function, at least one datafidelity term, at least
one regularization parameter a stepsize parameter and the power spectral
density of the second signal.
11. A method comprising: receiving, at a device, a signal including at
least a first signal operating based on a first technology and a second
signal operating based on a second technology, the second signal having
been transmitted simultaneously with the first signal over the same
frequency and time domains for reception by the device; forming, at the
device, a cost function based on at least the received signal, a
parameter associated with the first signal and a power spectral density
of the second signal; determining, at the device, the first signal from
the signal based on the formed cost function; and determining, at the
device, the second signal based on the signal and the first signal for
processing of information associated with the second signal.
12. The method of claim 11, wherein the first signal is transmitted by a
first system operating based on the first technology and the second
signal is transmitted by a second system operating based on the second
technology.
13. The method of claim 12, wherein the first signal and the second
signal are transmitted without any coordination between the first system
and the second system.
14. The method of claim 12, wherein the first system is a radar system
and the first technology is a radar technology, the second system is a
wireless communication system and the second technology is a wireless
access technology, the device is a receiver of the wireless
communications system, the first signal is a radar signal transmitted by
a transmitter of the radar system, and the second signal is a signal
transmitted by a transmitter of the wireless communications system.
15. The method of claim 11, wherein the first signal and the second
signal overlap spatially.
16. The method of claim 11, wherein the signal includes the first signal
with additive noise corresponding to at least the second signal, and the
method further comprises: minimizing the cost function associated with
the received signal, and determining the first signal as possible values
of the first signal that minimize the cost function.
17. The method of claim 11, wherein the first signal is a radar
fasttime/slowtime data matrix.
18. The method of claim 17, wherein the parameter is a rangefrequency
spectrum associated with a transmission of the first signal, and the
forming forms the cost function based on the rangefrequency spectrum
associated with the transmission of the first signal, a set of Doppler
weights, at least one regularization function, at least one datafidelity
term, at least one regularization parameter, a stepsize parameter and
the power spectral density of the second signal.
19. The method of claim 11, wherein the first signal is a radar data
timeseries.
20. The method of claim 19, wherein the parameter is a frequency response
of a filter associated with a transmission of the first signal, and the
forming forms the cost function based on at least the received signal,
the frequency response of the filter associated with the transmission of
the first signal, a regularization parameter, at least one regularization
function, at least one datafidelity term, at least one regularization
parameter a stepsize parameter and the power spectral density of the
second signal.
Description
BACKGROUND
[0001] The radiofrequency (RF) electromagnetic spectrum, extending from
below 1 MHz to above 100 GHz, represents a finite resource that is shared
by variety of devices including devices operating using wireless
communications standards, radar devices, television broadcasts, radio
navigation and other RF devices. The increasing demand by consumers for
higher data rates induces competition among RF devices for accessing the
finite RF spectrum. Accordingly, appropriate federal agencies have
recently recommended that 1000 MHz of federallycontrolled RF spectrum
should be freed or shared with the private industry in order to meet the
ever growing need for wireless communicationsbased services.
[0002] Radars are used for a variety of applications including
airtrafficcontrol, weather forecasting, automotive collision avoidance
systems, ground penetrating radars for finding underground resources,
altimeters for elevation measurements, geophysical monitoring of
resources by synthetic aperture radar (SAR) systems, etc. Studies have
shown that the effect of wireless communications interference on radar
systems may severely inhibit the performance of radar devices/systems.
Therefore, conventionally, when a primary device (e.g., a radar device)
operates in a given spectrum (e.g., frequency band), secondary devices
such as devices communicating using wireless communications technologies,
have not been allowed to operate in the given spectrum.
[0003] Various solutions have been proposed for enabling the use of "white
spectrum" (e.g., RF spectrum used by primary devices) by the secondary
devices. This means allowing secondary wireless devices to operate when
the primary wireless device(s) are not active within a frequency band and
geographical area. One such proposed solution is referred to as Dynamic
Spectrum Access (DSA), with Dynamic Frequency Selection (DFS) being a
particular example of the DSA solution.
[0004] Another proposed solution (not currently implemented or not
implemented for spectrum sharing purposes) might be radar systems such as
passive systems and multipleinput multipleoutput (MIMO) radars to
alleviate the spectrum congestion problem and make more spectrum
available for use by wireless communications systems. However these
systems are much more complex than the existing deployed radar systems.
Furthermore, replacements of existing radar systems may be cost
prohibitive and consequently such proposed systems are not currently
feasible.
[0005] Therefore, more robust methods allowing for simultaneous operation
of wireless communications and radar devices/systems are desirable.
SUMMARY
[0006] Some example embodiments relate to methods, apparatuses and systems
for enabling simultaneous operation of different technology based devices
over a shared spectrum.
[0007] In one example embodiment, a device includes a memory configured to
store computerreadable instructions therein and a processor. The
processor is configured to execute the computerreadable instructions to
determine a first signal of a first technology in presence of
interference from at least a second signal of a second technology, the
first signal and the second signal being overlappingly transmitted, the
determined first signal being used for processing of information
associated with the first signal.
[0008] In yet another example embodiment, the overlapping transmission of
the first signal and the second signal includes transmission of the first
signal and the second signal over a shared spectrum.
[0009] In yet another example embodiment, the overlapping transmission of
the first signal and the second signal includes transmission of the first
signal and the second signal over a shared spectrum.
[0010] In yet another example embodiment, the overlapping transmission of
the first signal and the second signal includes a spatial overlap of the
first signal and the second signal as well as overlaps of the first
signal and the second signal in time and frequency domains.
[0011] In yet another example embodiment, the processor is further
configured to receive a signal, the signal including the first signal
with additive noise corresponding to at least the second signal, and
minimize a cost function associated with the received signal, wherein the
processor is configured to determine the first signal as possible sets of
values of the first signal that minimize the cost function.
[0012] In yet another example embodiment, the processor is further
configured to minimize the cost the function based on an iterative
process.
[0013] In yet another example embodiment, the first signal is a radar
fasttime/slowtime data matrix, and the cost function is formed based on
at least the received signal, a rangefrequency spectrum associated with
a transmission of the first signal, a set of Doppler weights, at least
one regularization function, at least one datafidelity term, at least
one regularization parameter, a stepsize parameter and a power spectral
density of the second signal.
[0014] In yet another example embodiment, the first signal is a radar data
timeseries, and the cost function is formed based on at least the
received signal, a frequency response of a filter associated with a
transmission of the first signal, a regularization parameter, at least
one regularization function, at least one datafidelity term, at least
one regularization parameter, a stepsize parameter and a power spectral
density of the second signal.
[0015] In yet another example embodiment, the device is a receiver of a
radar system, the first signal is a radar signal transmitted by a
transmitter of the radar system, the second signal is a signal
transmitted by a transmitter of a wireless communications system, the
radar system operates based on the first technology, and the wireless
communications system operates based on the second technology.
[0016] In yet another example embodiment, the first technology is a radar
technology, and the second technology is a wireless communications
standard, the wireless communications standard being at least one of a
wireless local area networking standard and a radio access technology.
[0017] In yet another example embodiment, the radar system is configured
to operate simultaneously with at least one additional radar system, and
the processor is further configured to suppress radar signals of the
least one additional radar system, when the processor determines the
first signal.
[0018] In yet another example embodiment, the processor is further
configured to suppress the radar signals of the least one additional
radar system by adjusting power spectral densities in a cost function on
frequencies on which the radar signals of the least one additional radar
system are transmitted.
[0019] In one example embodiment, a device includes a memory configured to
store computerreadable instructions therein and a processor. The
processor is configured to determine a first signal of a first technology
from a signal received at the device, the signal including at least the
first signal and a second signal of a second technology transmitted for
reception by the device. The processor is further configured to determine
the second signal based on the signal and the first signal, the
determined second signal being used for processing of information
associated with the second signal.
[0020] In yet another example embodiment, the overlapping transmission of
the first signal and the second signal includes transmission of the first
signal and the second signal over a shared spectrum.
[0021] In yet another example embodiment, the overlapping transmission of
the first signal and the second signal includes a spatial overlap of the
first signal and the second signal as well as overlaps of the first
signal and the second signal in time and frequency domains.
[0022] In yet another example embodiment, the processor is further
configured to receive the signal, the signal including the first signal
with additive noise corresponding to at least the second signal, and
minimize a cost function associated with the received signal, wherein the
processor is configured to determine the first signal as possible values
of the first signal that minimize the cost function.
[0023] In yet another example embodiment, the processor is further
configured to minimize the cost function based on an iterative process.
[0024] In yet another example embodiment, the first signal is a radar
fasttime/slowtime data matrix, and the cost function is formed based on
at least the received signal, a rangefrequency spectrum associated with
a transmission of the first signal, a set of Doppler weights, at least
one regularization function, at least one datafidelity term, at least
one regularization parameter, a stepsize parameter and a power spectral
density of the second signal.
[0025] In yet another example embodiment, the first signal is a radar data
timeseries, and the cost function is formed based on at least the
received signal, a frequency response of a filter associated with a
transmission of the first signal, a regularization parameter, at least
one regularization function, at least one datafidelity term, at least
one regularization parameter a stepsize parameter and a power spectral
density of the second signal.
[0026] In yet another example embodiment, the device is a receiver of a
wireless communications system, the first signal is a radar signal
transmitted by a transmitter of a radar system, the second signal is a
signal transmitted by a transmitter of the wireless communications
system, the radar system operates based on the first technology, and the
wireless communications system operates based on the second technology.
[0027] In yet another example embodiment, the first technology is a radar
technology, and the second technology is a wireless communications
standard, the wireless communications standard being at least one of a
wireless local area networking standard and a radio access technology.
[0028] In yet another example embodiment, the processor is further
configured to receive the signal, the signal including the first signal,
the second signal and at least one additional radar signal, determine the
first signal and the at least one additional radar signal, and subtract a
combination of the first signal and the at least one additional radar
signal from the signal to determine the second signal.
[0029] In yet another example embodiment, the wireless communications
system is configured to operate simultaneously with at least one
additional wireless communications system, and the processor is further
configured to suppress wireless communications signals of the least one
additional wireless communications system, when the processor determines
the second signal.
BRIEF DESCRIPTION OF THE DRAWINGS
[0030] Example embodiments will become more fully understood from the
detailed description given herein below and the accompanying drawings,
wherein like elements are represented by like reference numerals, which
are given by way of illustration only and thus are not limiting of the
present disclosure, and wherein:
[0031] FIG. 1 illustrates a setting in which a wireless communications
system and a radar system operate simultaneously, according to an example
embodiment;
[0032] FIG. 2 illustrates a setting in which a wireless communications
system and a moving radar system operate simultaneously, according to an
example embodiment;
[0033] FIG. 3 illustrates a receiver for receiving signals of the first
system shown in FIG. 1, according to an example embodiment;
[0034] FIG. 4 illustrates a receiver for receiving signals of the second
system shown in FIG. 1, according to an example embodiment;
[0035] FIG. 5 is a flowchart describing a method of determining a signal
in presence of interference induced by an overlappingly transmitted
signal of a different technology, according to an example embodiment; and
[0036] FIG. 6 is a flowchart describing a method of determining a signal
in presence of interference induced by an overlappingly transmitted
signal of a different technology, according to an example embodiment.
DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS
[0037] Various embodiments will now be described more fully with reference
to the accompanying drawings. Like elements on the drawings are labeled
by like reference numerals.
[0038] Detailed illustrative embodiments are disclosed herein. However,
specific structural and functional details disclosed herein are merely
representative for purposes of describing example embodiments. This
disclosure may, however, be embodied in many alternate forms and should
not be construed as limited to only the embodiments set forth herein.
[0039] Accordingly, while example embodiments are capable of various
modifications and alternative forms, the embodiments are shown by way of
example in the drawings and will be described herein in detail. It should
be understood, however, that there is no intent to limit example
embodiments to the particular forms disclosed. On the contrary, example
embodiments are to cover all modifications, equivalents, and alternatives
falling within the scope of this disclosure. Like numbers refer to like
elements throughout the description of the figures.
[0040] Although the terms first, second, etc. may be used herein to
describe various elements, these elements should not be limited by these
terms. These terms are only used to distinguish one element from another.
For example, a first element could be termed a second element, and
similarly, a second element could be termed a first element, without
departing from the scope of this disclosure. As used herein, the term
"and/or," includes any and all combinations of one or more of the
associated listed items.
[0041] When an element is referred to as being "connected," or "coupled,"
to another element, it can be directly connected or coupled to the other
element or intervening elements may be present. By contrast, when an
element is referred to as being "directly connected," or "directly
coupled," to another element, there are no intervening elements present.
Other words used to describe the relationship between elements should be
interpreted in a like fashion (e.g., "between," versus "directly
between," "adjacent," versus "directly adjacent," etc.).
[0042] The terminology used herein is for the purpose of describing
particular embodiments only and is not intended to be limiting. As used
herein, the singular forms "a", "an", and "the" are intended to include
the plural forms as well, unless the context clearly indicates otherwise.
It will be further understood that the terms "comprises", "comprising,",
"includes" and/or "including", when used herein, specify the presence of
stated features, steps, operations, elements, and/or components, but do
not preclude the presence or addition of one or more other features,
integers, steps, operations, elements, components, and/or groups thereof.
[0043] It should also be noted that in some alternative implementations,
the functions/acts noted may occur out of the order noted in the figures.
For example, two figures shown in succession may in fact be executed
substantially concurrently or may sometimes be executed in the reverse
order, depending upon the functionality/acts involved.
[0044] Specific details are provided in the following description to
provide a thorough understanding of example embodiments. However, it will
be understood by one of ordinary skill in the art that example
embodiments may be practiced without these specific details. For example,
systems may be shown in block diagrams so as not to obscure the example
embodiments in unnecessary detail. In other instances, wellknown
processes, structures and techniques may be shown without unnecessary
detail in order to avoid obscuring example embodiments.
[0045] In the following description, illustrative embodiments will be
described with reference to acts and symbolic representations of
operations (e.g., in the form of flow charts, flow diagrams, data flow
diagrams, structure diagrams, block diagrams, etc.) that may be
implemented as program modules or functional processes include routines,
programs, objects, components, data structures, etc., that perform
particular tasks or implement particular abstract data types and may be
implemented using existing hardware at existing network elements. Such
existing hardware may include, but is not limited to, one or more of
Central Processing Units (CPUs), Digital Signal Processors (DSPs),
Graphical Processing Units (GPUs), Very Large Scale Integration (VLSI)
circuits, ApplicationSpecificIntegratedCircuits (ASICs), Field
Programmable Gate Arrays (FPGAs), computers or the like.
[0046] Although a flow chart may describe the operations as a sequential
process, many of the operations may be performed in parallel,
concurrently or simultaneously. In addition, the order of the operations
may be rearranged. A process may be terminated when its operations are
completed, but may also have additional steps not included in the figure.
A process may correspond to a method, function, procedure, subroutine,
subprogram, etc. When a process corresponds to a function, its
termination may correspond to a return of the function to the calling
function or the main function.
[0047] As disclosed herein, the term "storage medium" or "computer
readable storage medium" may represent one or more devices for storing
data, including read only memory (ROM), random access memory (RAM),
magnetic RAM, core memory, magnetic disk storage mediums, optical storage
mediums, flash memory devices and/or other tangible machine readable
mediums for storing information. The term "computerreadable medium" may
include, but is not limited to, portable or fixed storage devices,
optical storage devices, and various other mediums capable of storing,
containing or carrying instruction(s) and/or data.
[0048] Furthermore, example embodiments may be implemented by hardware,
software, firmware, middleware, microcode, hardware description
languages, or any combination thereof. When implemented in software,
firmware, middleware, or microcode, the program code or code segments to
perform the necessary tasks may be stored in a machine or computer
readable medium such as a computer readable storage medium. When
implemented in software, a processor or processors will perform the
necessary tasks.
[0049] A code segment may represent a procedure, function, subprogram,
program, routine, subroutine, module, software package, class, or any
combination of instructions, data structures or program statements. A
code segment may be coupled to another code segment or a hardware circuit
by passing and/or receiving information, data, arguments, parameters or
memory content. Information, arguments, parameters, data, etc. may be
passed, forwarded, or transmitted via any suitable means including memory
sharing, message passing, token passing, network transmission, etc.
[0050] Example embodiments described herein enable simultaneous operation
of devices/systems of different technologies over a shared frequency
spectrum while detrimental interference of signals of one of the
different technologies on signals of another one of the different
technologies is minimized.
[0051] Example embodiments described herein provide a signal processing
approach, in which a first device of a first technology
determines/estimates a signal transmitted according to the first
technology and destined for the first device, from a mixed signal
received at the first device. The mixed signal includes, among various
types of interference signals, a signal simultaneously transmitted
according to a second technology over the same frequency spectrum (the
first and second signals overlap in time and frequency domains). The
first device may then utilize the determined/estimated first signal for
further processing of information associated with the first signal.
[0052] Example embodiments may be utilized in conjunction with various
known or to be developed Wireless Local Area Network Technologies
(WLANs). Furthermore, example embodiments may also be utilized in
conjunction with Radio Access Networks (RANs) such as: Universal Mobile
Telecommunications System (UMTS); Global System for Mobile communications
(GSM); Advance Mobile Phone Service (AMPS) system; the Narrowband AMPS
system (NAMPS); the Total Access Communications System (TACS); the
Personal Digital Cellular (PDC) system; the United States Digital
Cellular (USDC) system; the code division multiple access (CDMA) system
described in EIA/TIA IS95; a High Rate Packet Data (HRPD) system,
Worldwide Interoperability for Microwave Access (WiMAX); 4G Long Term
Evolution (LTE); WiFi; Ultra Mobile Broadband (UMB); and 3.sup.rd
Generation Partnership Project LTE (3GPP LTE).
[0053] FIG. 1 illustrates a setting in which a wireless communications
system and a radar system operate simultaneously, according to an example
embodiment. As shown in FIG. 1, in a setting 100 two different systems
coexist. The first system is the system 120 and the second system is the
system 130. The systems 120 and 130 may operate based on different
technologies. In the example embodiment shown in FIG. 1, the system 120
may be a radar system and the system 130 may be a wireless communications
system. However, example embodiments are not limited to wireless
communications and radar systems but may encompass any two systems
operating according to different technologies. For purposes of describing
example embodiments, the first system 120 and the second system 130 are
considered to exist in vicinity of one another or having spatially
overlapping signals (i.e., the first system 120 and the second system 130
overlap spatially such that when the first system 120 and the second 130
transmit signals on the same or overlapping frequencies and same or
overlapping time, the signals of each induce interference on the signals
of the other of the two systems (each of the first system 120 and the
second system 130 experience degradation in their performance due to the
spatial overlap of the signals (e.g. in the radiated electromagnetic
waves form) of the other of the two systems.)
[0054] The first system 120 may be a system that operates based on a
different technology than the technology based on which the second system
130 operates. For example and as shown in FIG. 1, the first system 120
may be a radar system. The radar system 120 may include a radar receiver
122, a radar 124, and a radar object of detection 126. The radar receiver
122 may control the operation of the radar 124, as will be described
below. The radar 124 may transmit a signal 128 to the radar object of
detection 126. The echo/reflection of the signal 128 may be the signal
129 received back/detected by the radar 124 and processed by the radar
receiver 122. The radar object of detection may be any type of
object/information to be detected, imaged, tracked, processed, and/or
monitored by the radar 124.
[0055] The radar system 120 may be any coherent based radar system such as
a weather radar system, surveillance radar system, airport traffic radar
system, ground penetrating radar system, search and rescue radar system,
car radar system including those with multiple array elements and
multiple antennas (MIMO). The radar may be in a staring mode, scanning
mode, circling mode, stripmap mode, etc. The radar may also be in any one
of an imaging, tracking, detection or other modes.
[0056] The second system 130 may include components necessary for enabling
communication according to the corresponding technology. For example, in
FIG. 1 and assuming that the second system 130 operates according to a
wireless communications technology (e.g., GSM based wireless
communications system, CDMA based communications system, etc.), the
second system 130 may include a wireless access point 132 communicating
with communication client devices 134 (which may be hereinafter referred
to as user equipment (UE)) via exchange of signals 136. The Wireless
access point 132 may differ from one wireless communications technology
to another but regardless of the underlying technology, enables the UEs
134 to establish voice/data communication with other devices and/or
network components.
[0057] In one example embodiment and as shown in FIG. 1, the wireless
access point 132 may be a base station (e.g., macro cell base station,
small cell base station, femto cell base station, etc.). However, the
example embodiments are not limited thereto but may encompass any other
type of access point through which the UEs 134 may establish voice/data
communications with other UEs (in the same network or different networks)
or other network components. For example, the wireless access point 132
may be a router, when the wireless communications system 130 is a
wireless local area network (WLAN) operating according to known WLAN
standards such as IEEE 802 standards. Furthermore, while some components
of the second system 130 are illustrated in FIG. 1, any other component
necessary for enabling wireless communication within the second system
130 is implicitly included (e.g., network access points, core network
elements, etc.).
[0058] More generally, the first system 120 and the second system 130 may
be systems of sensors and/or system of communication devices using the
same spectrum resources where the waveforms may be electromagnetic,
acoustic or otherwise. The wireless communications and radar platforms
may be stationary or moving on the ground, in the air/space or at the
sea.
[0059] The radar system 120 may operate in one or more frequency bands
(e.g., 5 GHz band).
[0060] In one example embodiment, the signals 136 of the wireless
communications system 130 and the signals 128/129 of the radar system 120
may be transmitted simultaneously over the same (or overlapping)
frequency band/spectrum such that the signals 136 and 128/129 overlap in
time and/or frequency domains (i.e., the signals 136 and 128/129 may be
said to share a spectrum, with the shared spectrum being associated with
one or more specific frequencies such as 2 GHz, 5 GHz, etc.). For
example, signals 136 and 128/129 may be transmitted over the entire
and/or overlapping portions of the 5 GHz frequency band. Accordingly, the
signals of each of the systems 120 and 130 (e.g., signals 136, 128 and
129) may induce interference on signals of the other one of the systems
120 and 130. The interference caused by each of the signals 136 and
128/129 on the other one of the signals 136 and 128/129 is illustrated as
interference signals 140 in FIG. 1.
[0061] For example, the signals 136 of the system 130 may interfere with
the transmitted and received signals 128/129 of the system 120.
Accordingly, the signal 129, as received at the radar receiver 122 may
include both the intended signal 129 as well as the interference
induced/caused by the signal 136 of the system 130, in the form of signal
140. Similarly, the signals 128/129 of the system 120 may interfere with
the signals 136 of the system 130. Accordingly, the signal 136, as
received at a receiver of any one or more of the components in the system
130 (e.g., a receiver of any one of the UEs 134 and/or the wireless
access point 132) may include the signal 136 as well as the interference
induced/caused by the signals 128/129 of the system 120, in the form of
signal 140. Accordingly, and as will be described in greater detail
below, example embodiments enable a receiver in each of the systems 120
and 130 to determine/estimate the corresponding one of the signals 136 or
129 from the mixture of the corresponding one of the signals 136 or 129
and the interference induced at least in part by the interference signals
140 of the other one of the systems 120 and 130.
[0062] While FIG. 1 illustrates a setting in which only two systems
(system 120 and system 130) operating according to different technologies
are deployed, example embodiments are not limited thereto. For example,
there may be a more than two systems deployed in the setting 100 each of
which operates based on a different technology and/or any pair of two or
more of the deployed systems may operate based on the same technology
while at least one of the deployed system operates based on a different
technology. Regardless of the number of systems in the setting 100, each
system's transmitted signals may induce interference such as interference
signal 140 on the other systems in the setting 100.
[0063] FIG. 2 illustrates a setting in which a wireless communications
system and a moving system operate simultaneously, according to an
example embodiment. As shown in FIG. 2, in a setting 200 two different
systems coexist (i.e., physically coexist meaning that the two systems
(and/or alternatively the signals transmitted by the two systems) are in
the geographical vicinity of one another). The first system is a radar
system formed by the radar 201 and the radar objects of interest 203,
similar to the system 120 shown in FIG. 1, except that in FIG. 2, the
radar 201 moves (electronically, mechanically, manually, etc.) along the
direction 207. The moving radar system may be shipborn, airborne,
satellite or moving on land. The movement of the radar 201 is shown by
three different radar 201s each illustrating a different position of the
radar 201 at a different location along the line/axis 207. In one example
embodiment, the radar 201 may be positioned on a movable platform
enabling the radar 201 to be moved to different locations. The systems
shown in FIG. 2 may operate based on different technologies including
wireless communications and radar systems, as also described above with
reference to FIG. 1. However, example embodiments are not limited to
wireless communications and radar systems but may encompass any two
systems operating according to different technologies.
[0064] The second system in FIG. 2 is the system comprising the wireless
access point 205 and the communication client device 206 (which may also
be referred to as the user equipment (UE) 206), similar to the system 130
shown in FIG. 1. While not shown and as also described above, the second
system in FIG. 2 may include any other number of system components in
accordance with the technology based on which the second system operates.
[0065] In FIG. 2, at the different locations, the radar 201 may observe a
radar scene 204 for detecting (and/or imaging, tracking, monitoring,
etc., depending on the functionality of the radar system) one or more of
the radar objects 203. The radar objects 203 may be located in the
vicinity of the second system of which the wireless access point 205 and
the UE 206 are part of. Accordingly, the signals of the two systems,
which are transmitted overlappingly over a shared frequency
spectrum/bandwidth (the shared spectrum associated with one or more
particular frequencies), may interfere with one another when a radar
footprint 204 formed by the main beam (or sidelobe or backlobe) 202 of
the radar 201 overlaps the radiated energy from the wireless
communications system formed by the wireless access point 205 and the UE
206. In one example embodiment, the signals of the two systems may
interfere in time and frequency domains either completely or partially.
[0066] FIG. 3 illustrates a receiver for receiving signals of the first
system shown in FIG. 1, according to an example embodiment. In the
example embodiment described above with reference to FIG. 1, the first
system 120 is described as a radar system. However, as mentioned, the
first system 120 is not limited to a radar system.
[0067] The receiver of FIG. 3 may be the radar receiver 122 of the first
system 120 of FIG. 1 that is to receive an echo from the radar signal
transmitted by the radar 124 to the radar object of detection 126 and
reflected back to the radar 124 from the radar object of detection 126.
[0068] As shown in FIG. 3, the radar receiver 122 may include a storage
medium device 345 and a processor 350. While FIG. 3 illustrates the radar
receiver 122 as including two components, example embodiments are not
limited thereto and the radar receiver 122 may include any number of
additional components necessary for performing various functions within
the radar system 120.
[0069] The storage medium device 345 may store, among other information, a
set of computerreadable instructions and parameters for determining a
signal of the first system 120 transmitted to the radar receiver 122 in
presence of interference induced by the signal 140 described above with
reference to FIG. 1, as will be described below.
[0070] The processor 350 may execute the set of computerreadable
instructions for performing the functions necessary to determine a signal
of the first system 120 transmitted to the radar receiver 122, as will be
described below. Accordingly, the execution of the computerreadable
instructions by the processor 350 may transform the processor 350 into a
special purpose processor for performing the underlying functions. In
addition to determining the signal of the first system 120, the processor
350 may further execute additional computerreadable instructions for
processing information associated with the received signal, as will be
further described below.
[0071] FIG. 4 illustrates a receiver for receiving signals of the second
system shown in FIG. 1, according to an example embodiment. In the
example embodiment described above with reference to FIG. 1, the second
system 130 is described as a wireless communications system. However, as
mentioned, the second system 130 is not limited to a wireless
communications system.
[0072] The receiver 450 shown in FIG. 4 may be a receiver at any one of
the components in the second system 130 of FIG. 1 that is to receive a
signal transmitted according to the technology based on which the second
system 130 operates. For example, the receiver 450 shown in FIG. 3 may be
a receiver at the UE 134, a receiver at the wireless access node 132 or a
receiver at any other network component within the second system 130.
[0073] As shown in FIG. 4, the receiver 450 may include a storage medium
device 455, a processor 460 and an antenna 465. While FIG. 4 illustrates
the receiver 450 as including three components, example embodiments are
not limited thereto and the receiver 450 may include any number of
additional components necessary for performing various functions within
the second system 130.
[0074] The storage medium device 455 may store, among other information, a
set of computerreadable instructions and parameters for determining a
signal of the second system 130 transmitted to the receiver 450, as will
be described below.
[0075] The processor 460 may execute the set of computerreadable
instructions for performing the functions necessary to determine a signal
of the second system 130 transmitted to the receiver 450, as will be
described below. Accordingly, the execution of the computerreadable
instructions by the processor 460 may transform the processor 460 into a
special purpose processor for performing the underlying functions. In
addition to determining the signal of the second system 130 in presence
of interference signal 140 described above with reference to FIG. 1, the
processor 450 may further execute additional computerreadable
instructions for processing information associated with the received
signal, as will be further described below.
[0076] The antenna 465 may be any known or to be developed antenna
installed/incorporated into the receiver 450 (which may vary depending on
the component of the second system 130 in which the receiver 450 is
embedded). The antenna 465 may be used to receive signals (which may be a
mixture of the signal of the second system 130 as well as interference
induced by an overlappingly transmitted signal of the first system 120
(in the form of interference signal 140 discussed above with reference to
FIG. 1, as well as additional noise interference)). The antenna 465 may
additionally be used to transmit data/information/signals to other
components of the second system 130 (e.g., the antenna 465 may be a
transceiver antenna).
[0077] Prior to describing example embodiments directed to
determining/estimating a particular signal from mixed signal received at
a receiver (the mixed signal including an overlappingly transmitted
signal of a different technology), several definitions and conditions for
doing so are defined first.
[0078] As mentioned above, example embodiments provide spectrum sharing
algorithms between systems operating based on different technologies
(e.g., wireless communications and radar technologies). For example, the
spectrum sharing algorithms enable determining a corresponding signal by
one of the different systems in presence of interference from
overlappingly transmitted signals of other systems, as Fast Transforms
(such as Fast Fourier Transform (FFT)based, Discrete Cosine Transform
(DCT)based, Waveletbased) iterative solutions to an optimization cost
function. Example embodiments of spectrum sharing methods described
herein may be applied by each of the different systems (i.e., may be
implemented at a receiver in each of the different systems) without any
prior communications between the different systems. However, in some
example embodiment, minimal amount of priori information may also be
shared among components of the different systems.
[0079] Hereinafter, example embodiments will be described with respect to
radar and wireless communications systems as specific examples of the
different technologybased systems (e.g., systems 120 and 130 of FIG. 1,
described above) that may coexist and overlap in spectrum for
transmission of signals. However as indicated, the first and second
systems 120 and 130 may be any two systems operating based on different
technologies.
[0080] In example embodiments described hereinafter, a radar system (i.e.,
the first system 120 described above with reference to FIG. 1) is assumed
to transmit a periodic series of pulses where the interval between each
successive pulse is denoted as T. Furthermore, a pulse repetition
interval (PRI) is defined as the interval between each successive pulse
with the inverse thereof being denoted as the pulse repetition frequency
(PRF). The PRF may be given by f.sub.r=1/T. In such pulse radar system, a
modulated pulsed waveform p(t) with a bandwidth B.sub.p may be
transmitted every T seconds. In particular, p(t) may be a frequency,
phase or amplitude modulated waveform or a combination thereof. For
example, in many currently deployed radar systems, p(t) is a linear
frequency modulated chirp signal. However, example embodiments described
herein are applicable to other types of sampled transmittable waveforms.
Furthermore, the example embodiments are not limited to periodically
pulsed radars and may encompass nonperiodically pulsed radars as well as
continuous wave radars.
[0081] In order to propagate in the RF environment, p(t) may be
upconverted to an appropriate carrier frequency before transmission
thereof by a radar (e.g., the radar 124 shown in FIG. 1). Furthermore,
the radar 124 may transmit a total of M (with M being a positive integer)
pulses in a coherent pulse interval (CPI). The radar 124 may receive
echoes from the M pulses, which may then be downconverted and sampled at
a rate B.sub.h and stored in a data matrix y(m,l) by the radar receiver
122, where m denotes the m.sup.th pulse in a CPI and l indexes the
rangecell return data. In one example embodiment, the data matrix y(m,l)
may denote both the pulse/range matrix obtained prior to pulse
compression or after pulse compression. Furthermore, the data matrix may
be taken as a digital dataset after sampling of the returns of each PRI.
Such data matrix, as is known in the art, may also be referred to as a
slowtime/fasttime data matrix. Accordingly, the index l may denote the
rangesamples or fasttime data with the awareness that l is index for
the scattered return of each PRI, and the index m may denote the
pulsesamples or slowtime data.
[0082] In one example embodiment, B.sub.h, which is the sampling rate used
to obtain the fasttime data, is greater than the Nyquist bandwidth of
p(t) for some signal processing tasks such as filtering. Furthermore, the
received signal in the range dimension may be modeled as a linear
convolution of the range reflectivity function and the modulated radar
transmit pulse p(t). After demodulation of the echoes received from
target objects (e.g., radar object of detection 126) and sampling, each
row of the data matrix y(m,l) may represent a linear convolution of a
waveform filter with the radar reflectivity of the scene. The term
"scene" may refer to the radar object of detection 126, as shown in FIG.
1 and/or an area that is an antenna footprint such as the area 204 in
FIG. 2.
[0083] In one example embodiment, the linear convolution represented by
each row of the data matrix y(m,l) may be transformed into a circular
convolution by appropriate zeropadding of a waveform filter and a
complex baseband reflectivity. The waveform filter may be the transmit
filter which generates the transmit pulse. Alternatively, the waveform
filter may be the transmit filter convolved with the receiver transfer
function response. The complex baseband reflectivity represents the
reflectivity of the scene.
[0084] In addition to the scattered return PRI, the data matrix y(m,l) may
also include additive system noise, where an overlappingly transmitted
signal of another coexisting system (e.g., the wireless communications
system) is part of the additive noise. Accordingly, the data matrix y(m,
l) may also be referred to as the noisy data matrix y(m, l). The noisy
data matrix y(m, l) may be written as:
y=h*.sub.rx+w (1)
x,y,w .epsilon..sup.N.sup.d.sup..times.N.sup.r,h.epsilon..sup.N.sup.r
(2)
where the operation *.sub.r is the circular convolution operation
performed on each row of the data matrix y(m, l), as shown in Equation
(3) below.
y=h*.sub.rxy(m,l)=.SIGMA..sub.kh(k)x(m,lk.sub.N.sub.r) (3)
[0085] In Equation (1) above, w is composed of two components w.sub.n and
w.sub.i. The component w.sub.n denotes an additive system noise term
which may be considered as white noise. The component w.sub.i represents
interference induced by other devices (e.g., due to the interference
signal 140 shown in FIG. 1). In general, w may be a colored noise
process. Furthermore, in Equation (1) x is the complex baseband
reflectivity of the radar scene with row dimension size of M, which is,
as described above, the number of slowtime pulses. Moreover, in Equation
(1) h, which is the waveform filter, is the sampled discrete signal
obtained from sampling transmit pulse p(t) that has been through the
receiver at the rate of B.sub.h. One objective of example embodiments
described herein, is to determine/estimate x from the received
signal/data matrix y.
[0086] In one example embodiment and based on Equation (1), the sampled
discrete signal h and each row of complex baseband reflectivity x are
zeropadded to a length N.sub.r, so that the linear convolution between
the discrete signal h and any row of the complex reflectivity may be
expressed as a circular convolution operation *.sub.r defined above in
Equation (3). Similarly, each column in the datamatrix is zeropadded
appropriately to a size N.sub.d (In one example embodiment, N.sub.d is
greater than the number of pulses in a CPI) so that Doppler MTI filtering
may be performed in the frequency domain without any wraparound effects.
[0087] In example embodiment, the Fourier transform for Doppler and range,
which is implemented as the FFT solution to an optimization problem, is
used. The Fourier transform for Doppler is denoted as F.sub.D and the
Fourier transform for range is denoted as F.sub.R. The range Fourier
transform F.sub.R is set to be a unitary transform, i.e., such that
F.sub.R.sup.HF.sub.R=I,F.sub.RF.sub.R.sup.H=I (4a)
where F.sup.H denotes the complex conjugate transpose of F and I is the
identity matrix with diagonal elements being equal to 1 and the remaining
element being equal to zero.
[0088] The Doppler Fourier transform F.sub.D may be set to be an
overcomplete Parseval transform, i.e., such that
F.sub.D.sup.HF.sub.D=I,F.sub.DF.sub.D.sup.H.noteq.I (4b)
Where the operator F.sub.D is `tall` and F.sub.D.sup.H is `wide`, as is
known in the art. F.sup.H and I are as described above with reference to
Equations (4a). While F.sub.D has been described as an overcomplete
transform in one example embodiment, example embodiments are not limited
thereto. In example embodiments F.sub.D, may be an undercomplete
transform or a complete transform.
[0089] In one example embodiment, the range Fourier transform is applied
along the rows of the data matrix y while the Doppler Fourier transform
is applied on each individual column of the data matrix y. Because the
range and Doppler Fourier transforms are applied along separate
dimensions of a data matrix y, the range and Doppler Fourier transforms
are said to commute. Accordingly, the range Fourier transform of the
convolution of the sampled discrete signal h and the baseband
reflectivity x is given by:
F.sub.R(h*.sub.rx)= {square root over (N.sub.r)}(H.circlew/dot..sub.RX)
(5)
Where .circlew/dot..sub.R is a pointwise multiplication and H and X are
defined as the range Fourier transform of h and x. Furthermore, h and H
are one dimensional vectors while x and X are two dimensional vectors
(i.e., a matrix). In order for pointwise multiplication to be defined
between H and X, the one dimensional vector H must be expanded to a two
dimensional vector. Therefore, the operator .circlew/dot..sub.R is
defined to expand H so as to have an equal number of rows as X, i.e.,
Y=H.circlew/dot..sub.RXY(m,k)=H(k)X(m,k) (6)
where m is as defined above and k is an index in the rangefrequency
domain (which corresponds to the radiofrequency domain).
[0090] In operator notation, .circlew/dot..sub.R may be defined as:
H.circlew/dot..sub.RX=rpm(H)X (7)
where rpm(H) is defined as `range pointwise multiplication` and denotes
the diagonal operator defined by (7), i.e.:
[rpm(H)X].sub.m,k=H(k)X(m,k) (8)
[0091] By applying Equation (7) to Equation (5), the following identity is
obtained:
F.sub.R(h*.sub.r,x)= {square root over (N.sub.r)} rpm(H)X (9)
[0092] Given the commuting property of the Doppler Fourier transform and
range Fourier transform, as described above, the following identities may
be established:
rpm(H)F.sub.D=F.sub.Drpm(H) (10)
rpm(H)F.sub.D.sup.H=F.sub.D.sup.H rpm(H) (11)
[0093] The energy metric, and the l.sub.2 and l.sub.1 norms of x may be
written respectively as:
x 2 2 = m k x ( m , k ) 2 , x
2 = m k x ( m , k ) , x 1 =
m k x ( m , k ) ( 12 ) ##EQU00001##
where the twonorm applied elementwise on the elements of a matrix x may
also be referred to as the Frobenius norm.
[0094] Using the Parseval's property known in the art, the l.sub.2 norm of
x may be written as:
.parallel.x.parallel..sub.2=.parallel.F.sub.Dx.parallel..sub.2=.parallel
.F.sub.Rx.parallel..sub.2 (13)
[0095] In example embodiments described herein, x may also be considered
the inverse Fourier transform of the rangeDoppler profile of the input
scene (e.g., the first signal to be determined/estimated from the
received signal y), denoted by s:
x=F.sub.D.sup.HS (14)
where each row of s represents one Doppler Frequency and each column of s
represents one range cell.
[0096] Accordingly, one objective of example embodiments described herein
is to determine/estimate s when there is simultaneous transmission of
signals by systems operating based on different technologies (e.g.,
signals transmitted by a wireless communications system and a radar
system, described above with reference to FIG. 1).
[0097] Example embodiments for determining/estimating s include minimizing
an inverse problem (e.g. minimize a cost function) with an appropriate
data fidelity term, regularization term and an estimated noise statistics
(the noise including the corresponding system noise w.sub.n as well as
noise w.sub.i induced by an interfering and overlappingly transmitted
signal of another system operating based on a different technology, as
described above) such as the power spectral density of the noise.
Accordingly, in order to determine/estimate s, a proper cost function may
be formulated. The cost function may include, among other terms, a data
fidelity term, a regularization term and an estimation of the noise
statistics. Therefore, prior to describing example embodiments for
determining/estimating s, a general discussion will be provided with
respect to formulation of the cost function. Thereafter, the example
processes of determining/estimating s will be described with reference to
FIGS. 5 and 6.
[0098] First, a formulation of a cost function (which may also be referred
to as an optimization cost function) is described. Optimization cost
functions may be formulated in terms of analysis or synthesis
regularization terms or a mixture thereof. Example embodiments herein are
only meant to describe some specific cases of the formulation of such
optimization cost functions and therefore, the choice of analysis or
synthesis terms or a combination thereof presented herein, are
demonstrative and not meant to be limiting. Alternatively, an
optimization cost function may be formulated from a Bayesian estimation
theory perspective and estimate the desired signal (e.g. through the
maximum a posteriori (MAP) estimate). Such alternative formulations of
the cost function and the corresponding solutions may be derived by those
skilled in the art and example embodiments of the optimization cost
function formulation presented herein, are meant to be demonstrative only
and thus are not meant to be limiting.
[0099] In example embodiments, a cost function may be defined as J(s)
shown in Equation (15) below, the solution to which provides an
estimation of s denoted by s given y.
s ^ = argmin s { J ( s ) = 1 2 y  F D H
( h * r s ) 2 2 + .PHI. ( .lamda. .circlew/dot. s
) } ( 15 ) ##EQU00002##
where 1/2.parallel.yF.sub.D.sup.H(h*.sub.rs).parallel..sub.2.sup.2 is
the data fidelity term using the energy metric, .phi.(z) is the
regularization function (the determination of which will be described
below), .lamda. is the regularization parameter, and the remaining
notations used in Equation (15) are as defined above. Furthermore, s in
Equation (15) may be considered to be one of possible sets of values that
minimize the cost function given by Equation (15).
[0100] Using Parseval's theorem, the convolution theorem, the commutative
property of the range and Doppler Fourier transforms and Equations
(10)(14), the cost function J(s) of Equation (15) may be rewritten as
below:
J ( s ) = 1 2 F R ( y  F D H ( h
* r s ) ) 2 2 + .PHI. ( .lamda. .circlew/dot. s )
= 1 2 F R y  F R F D H ( h * r
s ) 2 2 + .PHI. ( .lamda. .circlew/dot. s ) =
1 2 F R y  F D H F R ( h * r s )
2 2 + .PHI. ( .lamda. .circlew/dot. s ) = 1 2
F R y  N r F D H ( F R h * r F R
S ) 2 2 + .PHI. ( .lamda. .circlew/dot. s ) =
1 2 Y  N r F D H ( H .circlew/dot. R S )
2 2 + .PHI. ( .lamda. .circlew/dot. s ) = 1
2 Y  N r F D H rpm ( H ) S 2 2 + .PHI.
( .lamda. .circlew/dot. s ) 1 2 Y  N r
rpm ( H ) F D H S 2 2 + .PHI. ( .lamda.
.circlew/dot. s ) ( 16 ) ( 17 )
( 18 ) ( 19 ) ( 20 ) ( 21 )
( 22 ) ##EQU00003##
where Y, H, and S are defined as the range Fourier transforms of y, h and
s, as shown in Equation (23).
Y=F.sub.Ry,H=F.sub.Rh,S=F.sub.Rs, (23)
[0101] Hence, Equation (15) may be rewritten as:
s ^ = argmin s { J ( s ) = 1 2 Y  N r
rpm ( H ) F D H S 2 2 + .PHI. ( .lamda.
.circlew/dot. s ) } , where S = F R s
( 24 ) ##EQU00004##
[0102] The solution to Equation (24) may be obtained by using the
Alternating Direction Method of Multipliers (ADMM). However, example
embodiments are not limited to using ADMM and other methods may be used
instead, including but not limited to, dual decomposition method, the
method of multipliers, DouglasRachford splitting, Spingarn's method of
partial inverses, Dykstra's alternating projections, Bregman iterative
algorithms for l.sub.1 problems, proximal methods, etc. Furthermore,
other numerical and sparsity optimization methods in solving Equation
(24) may be used.
[0103] Example advantages of ADMM include fast convergence, the use of
fast transforms such as the FFT, and potentially avoiding the need for
performing any matrix inversions or multiplications. In addition to the
basic ADMM algorithm, example embodiments may apply variations of the
ADMM, as is known in the art.
[0104] Using variable splitting, Equation (24) may be expressed as:
s ^ = argmin s { J ( s ) = 1 2 Y  N r
rpm ( H ) F D H S 2 2 + .PHI. ( .lamda.
.circlew/dot. z ) } such that s = z
where S = F R s ( 25 ) ##EQU00005##
[0105] Using ADMM, the solution of Equation (25) may be obtained via a
general algorithm given by:
z ( j ) = argmin z { .PHI. ( .lamda.
.circlew/dot. z ) + .mu. 2 s ( j  1 )  z  d ( j
 2 ) 2 2 } ( 26 ) S ( j ) = argmin s 1
2 Y  N r rpm ( H ) F D H S 2 2 + .mu.
2 F R H S  z ( j )  d ( j  1 ) 2 2 (
27 ) s ( j ) = F R H S ( j ) ( 28 )
d ( j ) = d ( j  1 )  ( s ( j )  z ( j ) )
( 29 ) ##EQU00006##
[0106] where .mu. and .lamda. are the stepsize (also called multipliers)
and regularization parameters, respectively. The regularization parameter
may be a scalar or a higher dimensional vector and .mu. may be adaptable
in each iteration. The variable d is an auxiliary ADMM variable used in
the ADMM algorithm, as is known in the art.
[0107] In Equation (26), optimization is performed over the variable z
while the values of s and d are updated in each iteration of the
iterative algorithm. Similarly, in Equation (27), the optimization is
performed over the variable S while using the new value obtained for z in
Equation (26) and the value of d from the previous iteration. However in
Equation (29), the update of the variable d is based on the new values
obtained for s and z using d from the previous iteration.
[0108] In one example embodiment and in order to solve Equation (27),
Equation (27) may be transformed into the Frequency domain using Equation
(13). Accordingly, Equation (27) may be represented in the frequency
domain as:
S = argmin s 1 2 Y  N r rpm ( H ) F D
H S 2 2 + .mu. 2 S  Z  D 2 2 ( 30 )
##EQU00007##
[0109] where S, D, and Z are defined as the range Fourier transforms of s,
z and d, respectively, as shown below.
S=F.sub.Rs,Z=F.sub.Rz,D=F.sub.Rd, (31)
[0110] Equation (30) may be expressed as:
S = argmin s 1 2 Y  AS 2 2 + .mu. 2 S 
B 2 2 ( 32 ) ##EQU00008##
where
A= {square root over (N.sub.r)} rpm(H)F.sub.D.sup.H,B=Z+D (33)
[0111] The solution of Equation (32) (i.e., the radar signal to be
determined/estimated from the received signal y) is given by:
S=(A.sup.HA+.mu.I).sup.1(A.sup.HY+.mu.B) (34)
[0112] However, the operator A.sup.HA is not diagonal because of Equation
(4b), so determination of the inverse of (A.sup.HA+.mu.I).sup.1 is
computationally complex. Accordingly, the matrix inverse lemma may be
used to simplify the expression in Equation (34). The symbol ".l" is used
to denote elementwise division and the symbol ". " is used to denote
element wise multiplication. Therefore, the inverse of
(A.sup.HA+.mu.I).sup.1 in Equation (34) may be written as:
( A H A + .mu. I )  1 = 1 .mu. I
 N r .mu. F D rpm ( H * ) ( .mu.
I + N r rpm ( H ) F D H F D rpm ( H * )
)  1 rpm ( H ) F D H = 1 .mu. I  N
r .mu. F D rpm ( H * ) ( .mu. I +
N r rpm ( H ) rpm ( H * ) )  1 rpm ( H
) F D H = 1 .mu. I  N r .mu. F D rpm
( H * ) ( .mu. I + N r rpm ( H
. 2 ) )  1 rpm ( H ) F D H = 1
.mu. I  N r .mu. F D rpm ( H * ) ( rpm (
N r H . 2 + .mu. ) )  1 rpm ( H
) F D H = 1 .mu. I  N r .mu. F D rpm
( H * ) rpm ( 1. / ( N r H . 2 +
.mu. ) ) rpm ( H ) F D H = 1 .mu. I 
N r .mu. F D rpm ( ( N r H . 2 . / ( N
r H . 2 + .mu. ) ) F D H
( 35 ) ( 36 )
( 37 ) ) ( 38 )
( 39 ) ( 40 ) ##EQU00009##
[0113] A variable P may be defined as:
P = 1. / ( 1 + ( .mu. N r ) . / .mu. N r . 2
) ( 41 ) ##EQU00010##
Accordingly, the solution of Equation (34) may be given by:
S = ( A H A + .mu. I )  1 ( A H
Y + .mu. B ) = ( 1 .mu. I  1 .mu.
F D rpm ( P ) F D H ) ( N r F D rpm (
H * ) Y + .mu. ( Z + D ) ) = ( I  F D
rpm ( P ) F D H ) ( N r .mu. F D rpm (
H * ) Y + Z + D ) ( 42 )
( 43 ) ##EQU00011##
[0114] In simplifying Equation (43), a new variable R may be defined as:
R = N r .mu. F D rpm ( H * ) Y + Z + D
( 44 ) ##EQU00012##
[0115] Then, Equation (43) may be rewritten as:
S=RF.sub.D rpm(P)F.sub.D.sup.HR (45)
[0116] In one example embodiment, the variable R may also be rewritten as
given below in Equation (46), which in turn may be used to rewrite
Equation (45) as shown below in Equation (47).
R = N r .mu. F D ( H * .circlew/dot. R Y )
+ Z + D ( 46 ) S = R  F D ( P .circlew/dot. R
( F D H R ) ) ( 47 ) ##EQU00013##
[0117] Next the determination of an appropriate regularization term is
described. The regularization function .phi.(z) in equation (26) may be a
reconfigurable function determined based on empirical studies or
mathematical models. In one example embodiment, .phi.(z) is chosen to be
a function that allows for simultaneous operation of radar and wireless
communications systems. For example, the regularization function may be a
combination of regularization functions with different regularization
parameter weights. Furthermore, the regularization function .phi.(z) may
be a sparsity promoting function such as the l.sub.1 norm, the nuclear
norm, group sparse functions, nonconvex penalties, total variation (in
range, Doppler, PRI, CPI or scan, etc.), sparsity in a transform domain
such as wavelets and Fourier domains, sparsity using prior knowledge such
as clutter maps, mixed norms, the Huber function, nonpure sparse
functions, compound functions, sparsity in timefrequency transforms such
as the shorttime Fourier domain, etc., depending on the radar signal
being transmitted and the radar scene to be reconstructed. Accordingly,
particular choice(s) for the regularization function used in the present
disclosure for the radar scenario in consideration, may easily be
modified/replaced by other regularization functions that are known or are
to be developed for achieving simultaneous transmission of radar and
wireless communications systems based signals. Therefore, example
embodiments are not limited to the specific choice(s) of the
regularization function described herein.
[0118] Furthermore, while for purposes of describing example embodiments,
an assumption is made that the data being regularized is in the
Dopplerrange domain, it is also possible to have the regularization
function promote sparsity, groupsparsity, nuclear norm, total variation
etc. on other domains such as the rangepulse domain. For example, by
setting F.sub.D.sup.H=F.sub.D=I.sub.D, where I.sub.D operates on each
column of the data matrix by returning the same column, the terms
F.sub.D.sup.H, F.sub.D will no longer be included in Equations (15), (16)
and the solutions given in Equations (46) and (47). Accordingly, x will
be the same as s (i.e., x=s and therefore X=S) and Equation (27) is
similarly solved in the rangepulse domain. Therefore, the algorithmic
framework provided in example embodiments described herein is equally
applicable to a penalty function set on multiple pulses in other domains
such as the rangepulse domain and range only domain. An example
embodiment, in which the algorithm is applied without using Doppler
information in the range only domain, will be described later below.
[0119] Using the concept of proximity operator, Equation (26) may be
rewritten as:
prox .PHI. , .lamda. , .mu. ( b ) = argmin z {
.PHI. ( .lamda. .circlew/dot. z ) + .mu. 2 b  z 2 2
} ( 48 ) ##EQU00014##
[0120] While closedform expressions of the proximity operators of various
functions exist in order to obtain a solution of Equation (48), if
closedform expressions are not derivable, example embodiments may apply
other known or to be developed numerical optimization methods to obtain
an estimate of the proximity operator in Equation (48).
[0121] As described above, example embodiments may utilize groupsparsity
as the regularization function .phi.(z) in Equation (48) (Equation (49)).
The pulserange or Dopplerrange data may have group sparsity. For
example, an extended target may possess group range sparsity and a
nonconstant radar cross section (RCS) target may possess group Doppler
sparsity. Example embodiments may use groupsparsity in Dopplerrange
although the same may be used in other domains such as pulserange
domain. Accordingly, it is appropriate to define .phi.(z) so to reflect
the domain part.
[0122] In doing so, example embodiments utilize K.sub.D and K.sub.R to
denote the number of Doppler bins and number of range bins respectively,
to promote Dopplerrange group sparsity. The groupsparsity technique is
meant as an exemplary model of a groupsparse regularization function. To
promote Dopplerrange group sparsity, we define:
.PHI. ( z ) = i n .psi. ( z ( i + (
0 : K D  1 ) , n + ( 0 : K D  1 ) ) 2
) ( 49 ) ##EQU00015##
[0123] The two dimensional array z(i+(0: K.sub.D1),n+(0:K.sub.R1)) is a
subarray of z of size K.sub.D.times.K.sub.R. The first element of the
subarray is z(i, n). The penalty function .psi. may be a convex or
nonconvex sparsitypromoting function, which may depend on one or more
parameters as shown below in Equations (50)(52).
.psi. ( t ) = t ( 50 ) .psi. ( t ; a ) =
1 a log ( 1 + a t ) s . t . a > 0
( 51 ) .psi. ( t ; a ) = 2 a 3 ( tan 
1 ( 1 + 2 a t 3 )  .pi. 6 ) s . t .
a > 0 ( 52 ) ##EQU00016##
where Equations (51) and (52) are equal to Equation (50) (the L1 norm)
when a=0. Equations (51)(52) are examples of different penalty functions
that may be used. However, example embodiments are not limited thereto
and other known or to be developed sparsity promoting penalty functions
may be utilized instead. In one example embodiment, a penalty function
may be defined as a combination of penalty functions or a separate
penalty function for each of the Doppler and range groups may be defined,
with each overlapping or nonoverlapping Doppler and range groups having
different sizes.
[0124] Furthermore, for a>0, the sparsity promoting penalty functions
defined by Equations (51) and (52) may promote a stronger sparsity than
the sparsity promoting penalty function defined by Equation (50).
Furthermore, the sparsity promoting penalty functions (51) and (52) may
be nonconvex.
[0125] Both Equations (15) and (25) contain a convex data fidelity term.
If a nonconvex regularization function for solving Equations (15) and
Equation (25) is used, it is still possible to make the total cost
function as convex by choosing a appropriately in Equations (51) and
(52). For example, a may be selected such that the positive second
derivative in the datafidelity term balances against the negative second
derivative in the nonconvex regularizer function.
[0126] In yet another example embodiment, choosing K.sub.R=1 and
K.sub.D=1, and using Equation (50), the l.sub.1 norm may be obtained,
which is applied on each element of the matrix z as defined above, given
by Equation (53) below.
.PHI. ( z ) = i n z ( i , n )
( 53 ) ##EQU00017##
[0127] Using this regularization function, the proximity operator given in
Equation (48) is the soft threshold function on each element of z.
[0128] The regularization parameter .lamda. in Equation (15) may be a
scalar or a higher dimensional vector. For higher dimensional vectors,
the regularization parameter may be applied elementwise for some
regularization functions such as the l.sub.1 norm and may be cast in a
vector or matrix form. For example, the regularization parameter may be a
matrix .lamda. for the l.sub.1 norm and may be written as:
.PHI. ( .lamda. .circlew/dot. z ) = i
n .lamda. ( i , n ) z ( i , n )
( 54 ) ##EQU00018##
where the proximity operator for such a case is softthreshold applied
elementwise with the threshold parameter being .lamda.(i, n).
Consequently, such extension of the regularization parameter is obvious
to those skilled in the arts and the proximity operator defined in
Equation (48) is meant to also cover cases when the regularization
parameter may be a nonscalar parameter such as vector or matrix.
[0129] As discussed above, it may be possible that Equation (48) does not
have a closed form solution for some regularization functions such as
regularization functions given in Equations (49) and (5052) when the
Dopplerrange group sizes are more than 1 element. In such case and in
order to obtain a solution to Equation (48) for the regularization
function of Equation (49), a pulse filtering convolution operator *.sub.d
is defined. The operator *.sub.d has analogous properties to *.sub.r but
is applied on the pulse dimension (i.e., on each column of the data
matrix y). The pulse filtering convolution function may be given by:
g * D x k g ( k ) x ( m  k
N d , l ) ( 55 ) ##EQU00019##
where x is in the rangepulse domain.
[0130] Appropriate zeropadding may be used in the pulse domain in a
similar manner as described above with respect to the range domain in
order to convert a linear convolution into a circular convolution.
Consequently, the pulse filtering convolution may be implemented in
Doppler Frequency domain by pointwise multiplication, as shown below in
equation (56):
F.sub.D(g*.sub.Dx)= {square root over
(N.sub.D)}(F.sub.Dg.circlew/dot..sub.DF.sub.Dx)= {square root over
(N.sub.D)}G.circlew/dot..sub.Ds (56)
where G is the Doppler Fourier transform of the vector g, and s is the
Doppler Fourier transform of x. In Equation (56) g and G are
onedimensional vectors while x and s are twodimensional vectors. Hence,
for pointwise multiplication to be defined, the one dimensional vector
is expanded to a two dimensional vector. Therefore, an operator
.circlew/dot..sub.D to expand the G vector so as to have equal number of
columns as s, is provided by Equation (57) below.
G.circlew/dot..sub.DsG(i)s(i,k) (57)
[0131] A MajorizationMinimization (MM) algorithm may be used to solve
Equation (48) for the regularization function given by Equation (49). The
MajorizationMinimization (MM) algorithm may allow for the elements of
the group in Equation (49) to be weighted differently. In doing so,
Doppler and Range kernals may be defined as:
p.sub.D=[p.sub.D(1), . . . ,p.sub.D(K.sub.D)] with a length of K.sub.D
(58)
p.sub.R=[p.sub.R(1), . . . ,p.sub.R(K.sub.R)] with a length of K.sub.R
(59)
where p.sub.D and p.sub.R may be conventional symmetric digital signal
processing (DSP) windows such as the triangular or Hamming window.
However, those skilled in the art appreciate that different weighting
functions may be used for p.sub.D and p.sub.R instead of the conventional
DSP windows.
[0132] An iterative algorithm to solve Equation (48) for the
regularization function given by Equation (49) may be given by:
q=(p.sub.D*.sub.Dp.sub.R*.sub.R(z.).sup.. 2).sup.. 1/2 (60)
v=1+.lamda.((p.sub.D*.sub.Dp.sub.R*.sub.R1./.theta.(q)) (61)
z=b./v (62)
where z is initialized to be equal to b and Equations (60)(62) are
repeated until a convergence condition/criteria (which may be determined
based on empirical studies) is satisfied. Furthermore, the operator z.
on a vector or matrix is defined as taking the absolute value of each
element z. In Equations (60)(62), the operation designated by dot (.)
denotes elementwise operation. Furthermore, the function .theta. is
defined as:
.theta. ( t ) = t .psi. ' ( t ) ( 63 )
##EQU00020##
where .psi.'(t) is derivative (whenever it is defined) of the penalty
function .psi.(t) of the group of coefficients in the rangeDoppler
domain. In the example embodiment of the iterative algorithm described
above, .theta.(q) is applied elementwise to each element of the array q.
While the iterative algorithm of Equations (60)(62) has not been solved
in the frequency domain, due to the expectation that the group sizes and
the kernel weights have relatively small lengths, for large group sizes,
Equation (61) and (62) may be solved in the rangefrequency and
Dopplerfrequency domains.
[0133] Satisfying the convergence criteria may be detected by different
methods. For example, satisfying the convergence criteria may be achieved
by monitoring the change in z using an appropriate norm (for example the
Frobenius norm). Alternatively, a fixed number of iterations may be used
as the convergence criteria. However, the convergence criteria is not
limited to the examples provided above and may include any other
convergence criteria.
[0134] As another example of a regularization function, a Doppler filter
within the regularization function may be considered. The Doppler filter
may be used to remove ground clutter for the purpose of moving target
indication (MTI) or conversely enhance near zeroDoppler targets by
removing fast moving targets. Accordingly, Equation (25) may be rewritten
as:
s ^ = argmin s { J ( s ) = 1 2 Y  N r
rpm ( H ) F D H S 2 2 + .PHI. ( .lamda.
.circlew/dot. G .circlew/dot. D s ) } ( 64 )
##EQU00021##
[0135] The effect of the regularization function
.phi.(G.circlew/dot..sub.D s) given in Equation (64) is that it enhances
target detection if the targets are expected to be outside of a
particular Doppler band. For example, in one embodiment G may be zero (0)
for some Doppler frequencies and one (1) for other Doppler frequencies.
Such regularization functions may be appropriate when the groundclutter
of the scene is not sparse but the objective of the radar is to detect a
sparse number of targets whose Doppler frequency partially overlaps or
does not overlap the ground clutter Doppler spectrum.
[0136] In one example embodiment, if the regularization function .phi. is
considered the l.sub.1 norm, the proximal operator in Equation (48) for
.phi.(G.circlew/dot..sub.D s) is given by:
z ( i , k ) = soft ( b ( i , k ) , G (
i ) .lamda. .mu. ) for all i , k (
65 ) ##EQU00022##
where the softthresholding is applied elementwise.
[0137] Next, a modeling of the noise and interference is described. As
described above, the noise/interference may be considered to include both
the corresponding system noise (e.g., the corresponding wireless
communications system noise or the radar system noise) as well as the
interference signal 140, described above with reference to FIG. 1 and in
Equation (1).
[0138] The noise of the radar system 120 at the receiver frontend may be
modelled as a white Gaussian noise. However, after receiver filtering, up
sampling and other RF and signal processing processes, the noise may not
have a flatspectrum. Furthermore, for simultaneous operation of radar
and wireless communications systems, the signal associated with the
wireless communications systems as seen by the radar system may be
modelled as colored noise/interference. Accordingly, the noise w consists
of the total noise process from both the radar receiver chain w.sub.n
(i.e., system noise) and the wireless interference w.sub.i (i.e.,
interference induced by the wireless communications system on radar
signals of the radar system) up to where the optimization algorithm is
performed. The power spectral density (PSD) of w may be denoted by
P.sub.w. Since w depends on the RF frequency, the power spectral density
of the total noise process varies across the rangefrequency. In one
example embodiment, the length of P.sub.w equals N.sub.r, which is the
length of the rangeFourier transform F.sub.R (The rangeFourier
transform is equivalent to the baseband frequencies of the signal for
each pulse). To account for this colored noise, the baseband frequencies
of the data fidelity may be weighted as a function of P.sub.w. In one
example embodiment, the square root of the reciprocal of P.sub.w may be
used as the weight factor while use of other methods of weighting the
frequencies of the data fidelity term based on the power spectral density
of the total noise (consisting of system noise and overlappingly
transmitted signals associated with a coexisting wireless communications
system), is apparent to those having ordinary skill in the art. In one
example embodiment, frequencies that do not correspond to a stationary
process may be notched out by setting values of P.sub.w to infinity
(e.g., in practice to a very large value). Using, the reciprocal of
P.sub.w, Equation (25) may be modified as follows:
s ^ = argmin s { J ( s ) = 1 2 ( 1. /
P w ) .circlew/dot. R ( Y  N r rpm ( H )
F D H S 2 2 + .PHI. ( .lamda. .circlew/dot. s ) }
where S = F R s ( 66 ) ##EQU00023##
[0139] Equation (66) may be further simplified using Equations (7) and
(8), as shown below:
s ^ = argmin s { J = 1 2 rpm ( 1. / P w
) ( Y  N r rpm ( H ) F D H S ) 2 2 +
.PHI. ( .lamda. .circlew/dot. s ) } ( 67 ) =
argmin s 1 2 rpm ( 1. / P w ) Y  N r
rpm ( 1. / P w ) rpm ( H ) F D H S 2 2 +
.PHI. ( .lamda. .circlew/dot. s ) ( 68 ) = argmin s
1 2 ( 1. / P w ) .circlew/dot. R Y  N r
rpm ( H . / P w ) F D H S 2 2 + .PHI. (
.lamda. .circlew/dot. s ) ( 69 ) = argmin s 1
2 ( Y ~  N r rpm ( H ~ ) F D H S 2 2
+ .PHI. ( .lamda. .circlew/dot. s ) ( 70 )
##EQU00024##
where
{tilde over (Y)}=(1./ {square root over
(P.sub.w)}).circlew/dot..sub.RY,{tilde over (H)}=H./ {square root over
(P.sub.w)} (71)
[0140] Since the cost function of Equation (70) has the same form as the
cost function of Equation (25), the same optimization algorithm for the
whitenoise case may be used in the colored noise/interference case with
the change of variables indicated in Equation (71) for the colored
noise/interference case.
[0141] The interference coming from the wireless communications system
into the radar band and seen by the radar receiver 122 maybe generally
modelled as a colored stationary stochastic process (white noise being a
special case of a colored stationary stochastic process). In one example
embodiment, having a model of such interference from wireless
communications systems stored at the radar receiver 122, enables the
radar receiver 122 to use the stored model to estimate the radar signal
from the mixed interfered radar plus wireless communication signals.
However, the model for the interference may not be available.
Accordingly, the radar receiver 122 may overestimate the power of the
PSD, but may still allow for the recovery of the radar signal.
[0142] The PSD of the colored noise process from the wireless
communications coming into the radar system may be obtained in several
ways. For example, the radar receiver 122 may capture the second order
statistics of the wireless communications system, which includes the PSD.
Standard techniques to estimate the autocorrelation function from the
timeseries samples of the wireless communications data may also be used
to obtain the PSD.
[0143] One example embodiment of obtaining the statistics of the
interference induced on the radar signals by the overlappingly
transmitted signals of the wireless communications system is for the
radar to extend the PRI interval slightly and only use the fasttime
samples obtained at the end of each return from a PRI when the scattering
power from objects (e.g., radar object of detection 126 shown in FIG. 1)
have decreased sufficiently (e.g., a margin below system operating noise
level). Yet, another example embodiment of obtaining the interference
statistics induced on the radar signals by the overlappingly transmitted
signals of the wireless communications system is to estimate the inband
wireless communications signals via measurements of transmitfree or
"listenonly" samples that represent stationary inband interference
during a transmitfree operation at specific intervals. However, if the
interference statistics varies per each azimuth interval of a scan, a
whole scan dedicated to a listening mode may be used to obtain the
autocorrelation function for each azimuth sector of the radar 124.
[0144] In yet another example embodiment, the radar receiver 122 may
obtain the statistics of the interference induced on the radar signals by
the overlappingly transmitted signals of the wireless communications
system, by knowing the location and distance of each wireless
communications device (e.g., the UE 134 and/or the wireless access node
132 in FIG. 1) and using an absolute sum of the transmit power density
formula for each device with a priori knowledge of the frequencies used
for transmission by the wireless communication devices. This may
correspond to an upper bound on the power spectral density. Other methods
to set an upper bound on the maximum power assumed in each frequency that
is used for spectrum sharing are known to those skilled in the art and
are within the scope of the present application.
[0145] In yet another example embodiment, the radar receiver 122 may
obtain the statistics of the interference induced on the radar signals by
the overlappingly transmitted signals of the wireless communications
system, by obtaining a priori knowledge of the frequencies used by
wireless communications devices in a certain geographic location and
setting the upperbound for the power spectral density associated with
such frequencies. Also further coordination between wireless
communications system and the radar system may be performed to obtain the
power spectral density of the wireless communications interference.
[0146] While example embodiments have been described in which the colored
noise PSD is used as a weight factor in the datafidelity term in order
to obtain the best estimate of the rangeDoppler matrix s, the PSD weight
factor may be adapted on a sample by sample basis, pulse by pulse basis
or multiple CPI basis rather than a single CPI. If the colored noise is
stationary in a period less than a single PRI period, the maximum value
of each frequency from a set of powerspectral densities obtained through
an adaptive window may be selected as an upperbound for the whole set of
PSD functions. Alternatively, an average powerspectral density over a
set of PSDs may be determined. Accordingly, the adaptation period for the
colored noise/interference may be designed into the optimization
algorithm as a matrix weight factor for the datafidelity term, as
appreciated by those having ordinary skill in the art.
[0147] Having described the formulation of the cost function, the data
fidelity term, the regularization term and the system noise, hereinafter
example embodiments for determining/estimating s will be provided.
[0148] FIG. 5 is a flowchart describing a method of determining a signal
in presence of interference induced by an overlappingly transmitted
signal of a different technology, according to an example embodiment. For
purposes of describing example embodiments, FIG. 5 will be described in
conjunction with the radar receiver 122 of the first system 120 shown in
FIG. 1. Furthermore, the functionalities of the radar receiver 122
described with reference to FIG. 5, will be implemented by the processor
350 of the radar receiver 122, when the processor 350 executes the
computerreadable instructions stored on the storage medium 345 of the
radar receiver 122.
[0149] At S500, the radar receiver 122 receives a signal y, as defined in
Equation (1) above. The signal y may be a series of pulse/range samples
with additive colored noise interference, which may also be referred to
as slowtime/fasttime data matrix. Given that the signal y includes the
underlying radar signal as well as the system noise and noise induced by
the interference signal 140 described above with reference to FIG. 1,
signal y may be referred to as a mixed signal. Furthermore, the radar
receiver 122 may retrieve a plurality of system parameters from a memory
of the radar receiver 122 (e.g., from the storage medium device 345
described above with reference to FIG. 3). The plurality of system
parameters may be programmed and stored in the storage medium device 345.
The plurality of system parameters may include the rangefrequency
spectrum (H) of a transmission pulse by the radar 124, a set of
nonnegative Doppler weights (G) as described above, and the PSD P.sub.w
that includes the interference and the system noise, as described above.
[0150] At S505, the radar receiver 122 determines a regularization
function .phi.(s), as described above.
[0151] At S510, the radar receiver 122 formulates a cost function
described above with reference to Equation (25), with Y and H of Equation
(25) being replaced with {tilde over (Y)} and {tilde over (H)},
respectively, as shown in Equation (72) below. The radar receiver 122
formulates the cost function based on the signal y, the regularization
function .phi.(s), determined at S505, as well as a regularization
parameter and a stepsize parameter.
[0152] More specifically, the formulated cost function may be represented
by Equation (72) shown below.
s ^ = argmin s { J ( s ) = 1 2 Y ~  N
r rpm ( H ~ ) F D H S 2 2 + .PHI. ( .lamda.
.circlew/dot. s ) } where S = F R s
( 72 ) ##EQU00025##
[0153] The setting of the regularization parameter .lamda. may depend on
system parameters such as the noise variance of the system, the waveform
filters used and the autocorrelation function of the colored noise. The
value of the regularization parameter .lamda. may also be different for
different regularization functions. One method of setting the
regularization parameter .lamda. is through empirical studies that may be
used for different scenarios of spectrum overlap, relative power of the
nonoverlapping spectrum portions, the waveform filter, etc.
[0154] Another method of setting the regularization parameter .lamda. is a
formula based on system parameters. Another method of setting the
regularization parameter .lamda. is to test several different values of
the regularization parameter .lamda. and ascertain the optimal value of
the regularization parameter .lamda., from among the test values of the
regularization parameter .lamda., and the solutions of the costs function
by means of statistical tests. For example, in wireless communications,
the statistical test may be the cyclic redundancy check (CRC) and
soft/hard error correction code metrics. In radar, the statistical test
may be a function of the correlation between the transmit waveform and
the estimated radar scene. Other statistical tests (e.g. generalized
cross validation, the discrepancy principle, the Lcurve criterion,
normalized cumulative periodogram), which are known to those skilled in
the art, may also be used. Henceforth, the choice of the regularization
parameter .lamda. does not change the form of the optimization function
and those skilled in the art may use such methods to set the
regularization parameter .lamda. for different radar and wireless
spectrum sharing scenarios.
[0155] The ADMM algorithm, which may be used in solving the cost functions
formed at S510, will converge for any stepsize parameter .mu.. However
the convergence rate may differ for different values of the stepsize
.mu.. The stepsize parameter .mu. may be chosen based on empirical
studies or as a function of systems parameters (e.g. noise variance).
Alternatively, the stepsize parameter .mu. may be chosen adaptively in
each iteration of the ADMM algorithm based on functions of the difference
between variables in different iterations of the ADMM loop.
[0156] At S515, the radar receiver 122 determines/estimates a radar signal
(first signal), represented by s, as described above. In one example
embodiment, the radar receiver 122 may determine/estimate s by applying
an iterative process to find a solution to cost function represented by
Equation (72) and hence determine/estimate s. In one example embodiment,
the radar receiver 122 applies the iterative process as described below.
[0157] The radar receiver 122 initializes a plurality of variables, one or
more of which may be auxiliary variables defined for purposes of
implementing the iterative process. For example, the radar receiver 122
sets the positive stepsize parameter .mu. determined as described above.
Similarly, the radar receiver 122 may set the regularization parameter
.lamda. to the value of the regularization parameter .lamda. determined
as described above. Furthermore, the radar receiver 122 may initialize
variables s.sup.0 and d.sup.0 to zero.
[0158] Based on the initialized values, the radar receiver 122 may
determine variables {tilde over (Y)}, {tilde over (H)}, P and R.sub.0, as
shown below:
Y ~ = ( 1. / P w ) .circlew/dot. R ( F R y )
( 73 ) H ~ = H . / P w ( 74 ) P = 1. /
( 1 + ( .mu. N r ) / H ~ 2 ) ( 75 )
R 0 = N r .mu. F D ( H ~ * .circlew/dot. R
Y ~ ) ( 76 ) ##EQU00026##
[0159] Furthermore, the radar receiver may define an auxiliary variable
"j" and initialize j to 0. The variable j may indicate the number of
iterations of the iterative process. Furthermore, the radar receiver may
determine a regularization function, which may be the l.sub.1 norm.
[0160] Thereafter, for j varying between 0 up to a number of iterations
where a convergence criterion has been satisfied, the radar receiver 122,
may repeat Equations (77)(81). The convergence criteria may be as
described above.
j = j + 1 ( 77 ) z ( j ) ( i , k ) = soft
( s ( j  1 ) ( i , k )  d ( j  1 ) ( i ,
k ) , G ( i ) .lamda. .mu. ) .Ainverted.
i , k ( 78 ) R ( j ) = R 0 + F R ( z ( j )
+ d ( j  1 ) ) ( 79 ) s ( j ) = F R H (
R ( j )  F D ( P .circlew/dot. R ( F D H R ( j
) ) ) ) ( 80 ) d ( j ) = d ( j  1 )  (
s ( j )  z ( j ) ) ( 81 ) ##EQU00027##
[0161] Upon the convergence criteria being met, the resulting s.sup.(j) at
Equation (80) is the determined/estimated s. The determined/estimated s
may have two properties when the l.sub.1 norm regularization function is
used. First, a majority of the values of s are negligible in amplitude.
Second, a minority of the values s are relatively larger in amplitude,
thus indicating the determined/estimated radar pulses (first signal).
[0162] In another example embodiment, the radar receiver 122 may recover
the radar pulses without using the Doppler frequency. For example, the
phase of the oscillator of wireless communications devices may not be
synchronized with that of the radar 124, or for some radar operations,
even if the Doppler shifts are known, estimating the return for each PRI
independent of other PRIs in the presence of wireless communications may
not be possible. Accordingly, it is possible to recover multiple pulse
returns or portion of a pulse return that is contaminated without using
Doppler frequency information.
[0163] Upon determining/estimating the radar signal at S515, then at S520,
the radar receiver 122 may process information associated with the
determined radar signal. For example, the radar receiver 122 may analyze
the determined radar signal to detect objects corresponding to the
underlying purpose of the radar system, track/monitor variables/objects
of interest (e.g., speed of cars, airplanes, ships, etc.). However, the
processing of the radar signal is not limited to the examples described
above but may encompass any appropriate type of analysis of the
determined/estimated radar signal in order to extract/study/monitor
information included in or associated with the determined/estimated radar
signal.
[0164] Furthermore, while FIG. 5 has been described from the perspective
of the radar system and the radar receiver thereof, FIG. 5 may be easily
modified to be implemented at a receiver of another coexisting system
(e.g., the wireless communications system 130 of FIG. 1). Accordingly, in
such instance, the receiver at a given component of the wireless
communications system 130 may determine/estimate the radar signal as
described above at S515 and then subtract the determined radar signal
from the received signal in order to determine underlying wireless
communications signal.
[0165] Furthermore, when the process of FIG. 5 is applied at a receiver of
a wireless communications system, the processing of information at S520
corresponds to processing of information associated with the determined
wireless communications signal and not the determined/estimated radar
signal.
[0166] FIG. 6 is a flowchart describing a method of determining a signal
in presence of interference induced by an overlappingly transmitted
signal of a different technology, according to an example embodiment. For
purposes of describing example embodiments, FIG. 6 will be described in
conjunction with the radar receiver 122 of the first system 120 shown in
FIG. 1. Furthermore, the functionalities of the radar receiver 122
described with reference to FIG. 6, will be implemented by the processor
350 of the radar receiver 122, when the processor 350 executes the
computerreadable instructions stored on the storage medium 345 of the
radar receiver 122.
[0167] At S600, the radar receiver 122 receives a signal y, as defined in
Equation (1) above. In contrast to S500 of FIG. 5, at S600, the signal y
may be a sampled time series. Given that the signal y includes the
underlying radar signal as well as the system noise and noise induced by
the interference signal 140 described above with reference to FIG. 1,
signal y may be referred to as a mixed signal.
[0168] Furthermore, the radar receiver 122 may retrieve a plurality of
system parameters from a memory of the radar receiver 122 (e.g., from the
storage medium device 345 described above with reference to FIG. 3). The
plurality of system parameters may be programmed and stored in the
storage medium device 345. The plurality of system parameters may include
the rangefrequency spectrum (H) of a transmission pulse by the radar
124, a set of nonnegative Doppler weights (G) as described above, and
the PSD P.sub.w that includes the interference and the system noise, as
described above.
[0169] At S605, the radar receiver 122 determines a regularization
function .phi.(x), as described above.
[0170] At S610, the radar receiver 122 formulates a cost function as shown
below with reference to Equation (83). The radar receiver 122 formulates
the cost function based on the signal y, the regularization function
.phi.(s), determined at S605, as well as a regularization parameter and a
stepsize parameter.
x ^ = argmin x { 1 2 Y ~  N r ( H ~
.circlew/dot. X ) 2 2 + .PHI. ( .lamda. .circlew/dot. X )
} ( 82 ) ##EQU00028##
where {tilde over (Y)} is the frequency transform of timeseries of
samples y, zeropadded appropriately to N.sub.r in order to have the
linear convolution as a circular convolution.
[0171] The setting of the regularization parameter .lamda. may depend on
system parameters such as the noise variance of the system, the waveform
filters used and the autocorrelation function of the colored noise. The
value of the regularization parameter .lamda. may also be different for
different regularization functions. One method of setting the
regularization parameter .lamda. is through empirical studies that may be
used for different scenarios of spectrum overlap, relative power of the
nonoverlapping spectrum portions, the waveform filter, etc.
[0172] Another method of setting the regularization parameter .lamda. is a
formula based on system parameters. Another method of setting the
regularization parameter .lamda. is to test several different values of
the regularization parameter .lamda. and ascertain the optimal value of
the regularization parameter .lamda., from among the test values of the
regularization parameter .lamda., and the solutions of the costs function
by means of statistical tests. For example, in wireless communications,
the statistical test may be the cyclic redundancy check (CRC) and
soft/hard error correction code metrics. In radar, the statistical test
may be a function of the correlation between the transmit waveform and
the estimated radar scene. Other statistical tests (e.g. generalized
cross validation, the discrepancy principle, the Lcurve criterion,
normalized cumulative periodogram), which are known to those skilled in
the art, may also be used. Henceforth, the choice of the regularization
parameter .lamda. does not change the form of the optimization function
and those skilled in the art may use such methods to set the
regularization parameter .lamda. for different radar and wireless
bandwidth sharing scenarios.
[0173] The ADMM algorithm, which will be used in solving the cost function
formed at S610, will converge for any stepsize parameter .mu.. However
the convergence rate may differ for different values of the stepsize
.mu.. The stepsize parameter .mu. may be chosen based on empirical
studies or as a function of systems parameters (e.g. noise variance).
Alternatively, the stepsize parameter .mu. may be chosen adaptively in
each iteration of the ADMM algorithm based on functions of the difference
between variables in different iterations of the ADMM loop.
[0174] At S615, the radar receiver 122 determines/estimates a radar signal
(first signal). In one example embodiment, the radar receiver 122 may
apply an iterative process in order to determine/estimate {circumflex
over (x)}. In one example embodiment, the radar receiver 122 applies the
iterative process as described below.
[0175] The radar receiver 122 may determine variables {tilde over (Y)},
{tilde over (H)}, P and R, as shown below:
Y ~ = ( 1. / P w ) .circlew/dot. ( Fy ) ( 83 )
H ~ = H . / P w ( 84 ) P = 1. / ( 1 + ( .mu.
N r ) / H ~ 2 ) ( 85 ) R = N r
.mu. ( H ~ * .circlew/dot. Y ~ ) ( 86 )
##EQU00029##
[0176] Furthermore, the radar receiver 122 may define an auxiliary
variable "j" and initialize j to 0. The variable j may indicate the
number of iterations of the iterative process. Furthermore, the radar
receiver may determine a regularization function, which may be the
l.sub.1 norm.
[0177] Thereafter, for j varying between 0 up to a number of iterations
where a convergence criterion has been satisfied, the radar receiver 122
may repeat Equations (87)(91). The convergence criteria may be as
described above.
j = j + 1 ( 87 ) v ( j ) = soft ( x ( j  1
)  d ( j  1 ) , .lamda. .mu. ) + d ( j  1 )
( 88 ) X ( j ) = ( Fv ( j ) + R ) .circlew/dot. P
( 89 ) x ( j ) = F H X ( j ) ( 90 ) d (
j ) = v ( j )  x ( j ) ( 91 ) ##EQU00030##
[0178] Upon the convergence criteria being met, the resulting x.sup.(j) at
Equation (91) is the determined/estimated {circumflex over (x)}. The
determined/estimated {circumflex over (x)} may have two properties when
the l.sub.1 norm regularization function is used. First, a majority of
the values of {circumflex over (x)} are negligible in amplitude. Second,
a minority of the values {circumflex over (x)} are relatively larger in
amplitude, thus indicating the determined/estimated returned radar
pulses.
[0179] Upon determining/estimating the radar signal at S615, then at S620,
the radar receiver 122 may process information associated with the
determined radar signal. For example, the radar receiver 122 may analyze
the determined radar signal to detect objects corresponding to the
underlying purpose of the radar system, track/monitor variables/objects
of interest (e.g., speed of cars, airplanes, ships, etc.). However, the
processing of the radar signal is not limited to the examples described
above but may encompass any appropriate type of analysis of the
determined/estimated radar signal in order to extract/study/monitor
information included in or associated with the determined/estimated radar
signal.
[0180] Furthermore, while FIG. 6 has been described from the perspective
of the radar system and the radar receiver thereof, FIG. 6 may be easily
modified to be implemented at a receiver of another coexisting system
(e.g., the wireless communications system 130 of FIG. 1). Accordingly, in
such instance, the receiver at a given component of the wireless
communications system 130 may determine/estimate the radar signal as
described above at S615 and then subtract the determined radar signal
from the received signal in order to determine underlying wireless
communications signal.
[0181] Furthermore, when the process of FIG. 6 is applied at a receiver of
a wireless communications system, the processing of information at S620
will correspond to processing of information associated with the
determined wireless communications signal and not the
determined/estimated radar signal.
[0182] The processing of information associated with the determined signal
at S520 and S620 depends on the underlying system at which the processes
described in FIG. 5 and/or FIG. 6 are implemented.
[0183] While FIGS. 5 and 6 are described above with reference to the radar
receiver 122, example embodiments are not limited thereto. For example
the methods described above with reference to FIGS. 5 and 6, may be
implemented at a receiver in any one of the system components of a
wireless communications system such as the second system 130 shown in
FIG. 1 (e.g., a receiver of any one of the UEs 134, the receiver of the
wireless access node 132, etc.). Accordingly and as described above, such
receiver at a component of the second system 130 may determine
interfering signal(s) (e.g., the interfering radar signal) in a similar
manner as described in example embodiments above and thereafter subtract
the determine signal(s) (combination of the determined radar signals in
case of having more than one interfering radar signal) from the received
signal, in order to determine the wireless communications signal (e.g.,
signal 136 as described above with reference to FIG. 1, and process
information associated with the determined wireless communications
signal.
[0184] In some example embodiments, there may be more than one system of a
particular technology. For example, in the setting shown in FIG. 1, there
may be more than one radar system such as the system 120. In other words,
there may be two radar systems 120 and the wireless communications system
130 whose signals may be simultaneously and overlappingly transmitted.
Accordingly, a radar receiver 122 of any of the radar systems 120 may
suppress the radar signals of the other one of the radar systems 120
(i.e., undesired radar signal) when implementing example embodiments for
determining/estimating the corresponding radar signal (i.e., the desired
radar signal). In this context, suppressing of a radar signal may be
understood to include eliminating the influence of the undesired radar
signal sufficiently so that the undesired radar signal induces minimal
detrimental effect on determining/estimating the desired radar signal.
[0185] In one example embodiment, any of the radar systems 120 may
suppress the undesired radar signals of the other radar system(s) 120 by
adjusting power spectral densities in the cost function on frequencies on
which the undesired radar signals of the other radar system(s) 120 are
transmitted.
[0186] In one example embodiment, there may be more than one wireless
communications system and a radar system. Accordingly, a receiver at a
component of any of the wireless communications systems may suppress the
signals associated with the other wireless communications system(s)
(i.e., the undesired wireless communications signals), when determining
the radar signal and subsequently the intended wireless communications
signal.
[0187] In one example embodiment, the receiver at a component of any of
the wireless communications systems may suppress the undesired wireless
communications signals in a similar manner as described above with
reference to the radar systems (e.g., adjusting power spectral densities
in the cost function on frequencies on which the undesired wireless
communications signals are transmitted).
[0188] In another example embodiment and when the undesired wireless
communications signals are sparse, the receiver at a component of any of
the wireless communications systems may suppress the undesired wireless
communications signals by subtracting the sparse undesired wireless
communications signals from the intended (desired wireless
communications) signal.
[0189] Example embodiments described above provide numerous advantages
over existing methods in the art, as described in the Background Section.
Some of the example advantages are described below. The example
advantages are described with respect to one or more of example
embodiments described herein. However, example advantages are not meant
to limit all example embodiments described herein. One or more example
embodiments may provide advantages other than the example advantages
described below.
[0190] One example advantage over the DSA and DFS technology, described in
the Background Section, is that example embodiments allow for both types
of systems to operate simultaneously, that is, the signals of the two
different systems (e.g., wireless communications and radar systems)
overlap in the time domain while overlapping partially or fully in
frequency domain.
[0191] Another example advantage is that example embodiments allow for the
radar and wireless communications systems to be minimally coordinated.
The only coordination may be related to the radar transmission waveform
in a setting of a simultaneous operation of the two systems. The radar
transmission waveform may also be measured in both the radar and wireless
communications system without coordination. While exchange of more
information between the radar and wireless communications systems may
improve performance of both systems in a simultaneous operation, doing so
according to example embodiments, is not necessary.
[0192] Variations of the example embodiments are not to be regarded as a
departure from the spirit and scope of the example embodiments, and all
such variations as would be apparent to one skilled in the art are
intended to be included within the scope of this disclosure.
* * * * *