CN114793127B - Dual-function radar communication method, device, computer equipment and storage medium - Google Patents

Dual-function radar communication method, device, computer equipment and storage medium Download PDF

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CN114793127B
CN114793127B CN202210419701.3A CN202210419701A CN114793127B CN 114793127 B CN114793127 B CN 114793127B CN 202210419701 A CN202210419701 A CN 202210419701A CN 114793127 B CN114793127 B CN 114793127B
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CN114793127A (en
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塞奥佐罗斯.特斯菲斯
克里斯托斯.齐诺斯
宋子阳
施政
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Jinan University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0456—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting
    • H04B7/046—Selection of precoding matrices or codebooks, e.g. using matrices antenna weighting taking physical layer constraints into account
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0617—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal for beam forming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/06—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station
    • H04B7/0613—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission
    • H04B7/0615—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal
    • H04B7/0619—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the transmitting station using simultaneous transmission of weighted versions of same signal using feedback from receiving side
    • H04B7/0621—Feedback content
    • H04B7/0626—Channel coefficients, e.g. channel state information [CSI]
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00—Reducing energy consumption in communication networks
    • Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks

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Abstract

The invention discloses a difunctional radar communication method, a device, computer equipment and a storage medium, which comprises the following steps: a multi-antenna base station adopts a uniform linear antenna array (ULA) to transmit signals to a plurality of single-antenna users on a downlink, and simultaneously adopts a special ULA to receive radar signals at a receiving end; the base station side collects the statistical knowledge of the channel state information and constructs the problem of minimum transmission total power by meeting the service quality constraint of the communication and radar parts; giving a precoding matrix standard orthogonalization constraint to maximize radar output signal-to-noise ratio to obtain an optimal radar receiving beamforming matrix; giving a receiving beam forming matrix, simplifying a power minimization problem into a semi-definite programming problem by using a rank-one method, and solving an optimal precoding matrix by using an interior point method; the optimal precoding matrix is further modified by power control to meet communication and radar sensing requirements. The communication method effectively reduces the design complexity of the radar communication system and ensures the power consumption requirement.

Description

Dual-function radar communication method, device, computer equipment and storage medium
Technical Field
The present invention relates to the field of wireless communications technologies, and in particular, to a method and apparatus for dual-function radar communication, a computer device, and a storage medium.
Background
Fifth generation (5G) and dual-function radar communication are urgent in demands for low design complexity, low power consumption, high reliability and the like. Fifth generation (5G) and later wireless technologies must meet the exponentially growing demands for high quality wireless communication services that wireless communication systems can benefit from additional spectrum resources to meet. Among the various schemes, the problem of joint communication-radar spectrum sharing has attracted a great deal of attention in recent years.
The goal of the DFRC system is to design an operating system that can jointly handle radar and communication systems. This design can be applied to real-time joint sensing/communication operations through a single hardware setup, which requires less hardware complexity, implementation cost, and communication overhead. The DFRC system is implemented by designing the transmit waveforms such that both radar and communication related performance metrics are optimized by space/time constraints. By adopting the method, the space freedom degree of the DFRC system, namely the multi-transmitting antenna, can be effectively utilized. For such multiple-input multiple-output (MIMO) systems, the transmit waveforms are designed to enable high information transmission rates to the target users and reliable operation of the radar system. The linear precoding matrix is decomposed into two parts, one for communication and one for radar systems. The focus of the current work is also the development of linear precoding solutions in DFRC systems. In the previous work, a linear precoder for DFRC systems was designed in order to optimize the performance of the radar system under the constraint of maintaining a certain predefined quality of service (QoS) for the communication users and the transmission power. On the other hand, such a dual-function radar communication system has two different objectives to be optimized, one for the radar and one for the communication part, typically providing different design options, tailored to a specific scene. For example, an application may require a minimum QoS for target detection performance. Therefore, a design that aims to optimize the performance of the communication section as much as possible is more appropriate under the constraints of the QoS of the radar section described above. In addition, the concept of the internet of things relates to low power consumption systems, such as sensors and the like. In the latter case, it is more interesting to have a DFRC system whose aim is to minimize the total transmit power while maintaining the ideal QoS in the radar and communication parts.
Disclosure of Invention
The invention aims to solve the urgent demands of mission-critical dual-function radar communication in the prior art on low design complexity, low power consumption, high reliability and the like, and provides a dual-function radar communication method, a device, computer equipment and a storage medium. The invention achieves the aims of low power consumption and low design complexity by combining the precoding technology and the beam forming technology. The invention minimizes the total power transmitted by optimally designing the optimal precoding matrix and meeting the quality of service constraints of the communication and radar parts. In consideration of the characteristics of low power consumption, limited computing resources and the like in the dual-function radar communication, the power minimization problem is simplified into a semi-definite programming problem to be solved by utilizing a rank one method. Finally, the optimal precoding matrix is further modified by power control to meet communication and radar sensing requirements.
The first object of the present invention is to provide a dual-function radar communication method, which comprises the following implementation steps:
s1, in a dual-function radar communication system, a multi-antenna base station adopts a uniform linear antenna array on a downlink to send signals to a plurality of single-antenna user terminals, and meanwhile, a receiving end adopts a uniform linear antenna array to receive and transmit radar detection waveforms and detect point targets at the same time, wherein the dual-function radar communication is hereinafter referred to as DFRC, the uniform linear antenna array is hereinafter referred to as ULA, the base station is hereinafter referred to as BS, and the user terminals are hereinafter referred to as UT;
S2, the base station collects the statistical knowledge of the channel state information, and constructs the problem of total transmission power minimization by meeting the service quality constraint of the communication and radar parts, namely
Figure BDA0003607048510000021
s.t.ξ m (W)≥η m ,1≤m≤M,
γ(W,c)≥η,
Where W is a T×M complex linear precoding matrix, c is a linear R×1 receive beamforming vector,
Figure BDA0003607048510000031
and
Figure BDA0003607048510000032
threshold values related to communication and radar quality of service, respectively,/->
Figure BDA0003607048510000033
Representing a positive real number, T representing the number of elements transmitting ULA, R represents the number of elements that receive the ULA, M represents the total number of user terminals, I.I F Representing the Frobenius matrix norm, ζ m (W) represents the received signal-to-interference-and-noise ratio of the mth UT, expressed as +.>
Figure BDA0003607048510000034
Wherein the signal-to-interference-plus-noise ratio is hereinafter referred to as SINR, (-) H Self-co-ordinating representing vectors/matricesYoke matrix, w m And w k Is the m-th column and the k-th column of the matrix W,>
Figure BDA0003607048510000035
and->
Figure BDA0003607048510000036
Respectively represent w m And w k Is a self-conjugate matrix of h m Represents the mth column of matrix H, +.>
Figure BDA0003607048510000037
Represents h m Self-conjugate matrix of>
Figure BDA0003607048510000038
Represents the noise variance of the vector z, z is an Mx1 additive Gaussian white noise vector, and γ (W, c) represents the output SINR of the radar beamforming, expressed as +.>
Figure BDA0003607048510000039
Wherein->
Figure BDA00036070485100000310
And->
Figure BDA00036070485100000311
Representing the complex amplitudes of the target and the kth interferer, c H Is the self-conjugate matrix of vector c, W H Is the self-conjugate matrix of matrix W, +.>
Figure BDA00036070485100000312
Represents the noise variance of the vector u, which represents the circularly symmetric complex Gaussian white noise vector, θ 0 And theta k Representing the angles of the target and the kth interference source in the azimuth, A (theta 0 ) And A (theta) k ) Positive definite matrix representing the azimuth angles of the target and the kth interference source respectively, A H (θ 0 ) And A H (θ k ) Respectively represent A (theta) 0 ) And A (theta) k ) Self-conjugate matrix of>
Figure BDA00036070485100000313
a r (θ) is the R1 vector of propagation delays from the source at angle θ to the radar receiving element, (-) T Representing a transpose of the vector/matrix expressed as
Figure BDA00036070485100000314
Is a t Transpose of (θ), a t (θ) represents a T×1 emission steering vector expressed as
Figure BDA00036070485100000315
S3, giving an optimal value W of the precoding matrix * Optimizing radar receive beamforming matrix c by maximizing radar output SINR * The optimization problem is as follows:
Figure BDA00036070485100000316
s4, the optimal radar beam forming matrix c * Substitution into
Figure BDA0003607048510000041
In (1) rank one method is adopted>
Figure BDA0003607048510000042
The reduction of the power minimization problem to the semi-definite programming SDP problem is as follows
Figure BDA0003607048510000043
Figure BDA0003607048510000044
Figure BDA0003607048510000045
X m ≥0,
Wherein X is m Rank 1, tr (·) represents the trace of the matrix,
Figure BDA0003607048510000046
w j is the j-th column of the matrix W, +.>
Figure BDA0003607048510000047
Is w j Self-conjugate matrix of>
Figure BDA0003607048510000048
And is also provided with
Figure BDA0003607048510000049
(c * ) H Is c * Self-conjugate matrix of>
Figure BDA00036070485100000410
And->
Figure BDA00036070485100000411
Represents the target and the kth modified optimal radar beamforming matrix, respectively,/for each radar beam>
Figure BDA00036070485100000412
And->
Figure BDA00036070485100000413
Are respectively->
Figure BDA00036070485100000414
And->
Figure BDA00036070485100000415
Solving the optimization problem by an interior point method, and if the rank one is not satisfied, finding the problem by Gaussian randomization >
Figure BDA00036070485100000416
Is a solution to the approximation of (a),for each precoding vector w m L candidate vectors generated, i.e.>
Figure BDA00036070485100000417
Wherein U is m And->
Figure BDA00036070485100000418
Respectively a matrix consisting of eigenvectors and a diagonal matrix,>
Figure BDA00036070485100000419
representing variance as unit matrix I T Complex gaussian matrix of (a), matrix U m Sum sigma m Calculating and decomposing the optimal matrix from the eigenvalues>
Figure BDA00036070485100000420
I.e. < ->
Figure BDA00036070485100000421
Generating candidate vectors such that
Figure BDA00036070485100000422
Representing a desired operator;
s5, further correcting the optimal precoding matrix through power control to meet communication and radar sensing requirements, and constructing an optimization problem
Figure BDA00036070485100000423
Figure BDA00036070485100000424
Figure BDA00036070485100000425
p m ≥0,
Wherein,,
Figure BDA00036070485100000426
is the square value of the European norm of the precoding matrix,>
Figure BDA00036070485100000427
and->
Figure BDA0003607048510000051
Respectively representing the mth precoding vector parameter corrected by the mth channel matrix and the jth precoding vector parameter corrected by the mth channel matrix,/>
Figure BDA0003607048510000052
And->
Figure BDA0003607048510000053
Respectively w m And w j W is a self-conjugate matrix of m And w j Respectively denoted as mth candidate vector and jth candidate vector, gamma m,m And gamma k,m Representing the output SINR received at the mth UT interfered by the mth interferer and the output SINR received at the mth UT interfered by the kth interferer, respectively,>
Figure BDA0003607048510000054
scaling parameters for the mth and jth precoding vectors, respectively,/for the mth and jth precoding vectors>
Figure BDA0003607048510000055
Representing real numbers, problem->
Figure BDA0003607048510000056
For linear programming with M non-negative variables and M+1 linear inequality constraints, solving the problem by the interior point method +. >
Figure BDA0003607048510000057
Further, two other optimization problems can be constructed by the control variable method in the step S2 as follows: if the robustness of the signal-to-interference-and-noise ratio is set under the constraint of the total transmitting powerAnd (3) calculating, ensuring the service quality of the radar and constructing the optimization problem:
Figure BDA0003607048510000058
wherein P is max Is the maximum transmitting power supported by the DFRC system, and the constant weight is 1/eta m Different service levels between UTs are illustrated;
if the signal-to-interference-and-noise ratio performance of the radar is maximized, the total transmitting power is limited and the communication service quality is guaranteed, and the optimization problem is constructed as follows:
Figure BDA0003607048510000059
further, in the step S3, when the radar receiving beamforming matrix is optimized, in order to obtain the analysis result of the optimal radar receiving beamforming matrix, assume W * (W * ) H ＝I T Further converting the optimization problem into
Figure BDA00036070485100000510
The optimal radar receiving beam forming matrix corresponding to the optimization problem is as follows
Figure BDA00036070485100000511
Wherein the method comprises the steps of
Figure BDA0003607048510000061
Is the principal eigenvector of the matrix.
A second object of the present invention is to provide a dual function radar communication method apparatus including:
the signal receiving and transmitting module is used for introducing a receiving uniform linear antenna array, namely receiving the uniform linear antenna array is called ULA (ultra low power) for short, a base station at a transmitting end in the dual-function radar communication system transmits signals to a plurality of single-antenna users through the ULA, and meanwhile, a receiving end receives radar signals by adopting a special ULA;
A total power minimization construction module for collecting statistical knowledge of channel state information at the base station end, and constructing transmission total power minimization problem by satisfying service quality constraint of communication and radar parts, namely
Figure BDA0003607048510000062
Wherein W is a T×M complex linear precoding matrix and c is a linear Rx1 receive beamforming vector,/I>
Figure BDA0003607048510000063
And->
Figure BDA0003607048510000064
Threshold values related to communication and radar quality of service, respectively,/->
Figure BDA0003607048510000065
Representing a positive real number, T representing the number of elements transmitting ULA, R represents the number of elements that receive the ULA, M represents the total number of user terminals, I.I F Representing the Frobenius matrix norm, ζ m (W) represents the received signal-to-interference-and-noise ratio of the mth UT, expressed as +.>
Figure BDA0003607048510000066
Wherein the signal-to-interference-plus-noise ratio is hereinafter referred to as SINR, (-) H Self-conjugate matrix representing vector/matrix, w m And w k Is the m-th column and the k-th column of the matrix W,>
Figure BDA0003607048510000067
and->
Figure BDA0003607048510000068
Respectively represent w m And w k Is a self-conjugate matrix of h m Represents the mth column of matrix H, +.>
Figure BDA0003607048510000069
Represents h m Self-conjugate matrix of>
Figure BDA00036070485100000610
Represents the noise variance of the vector z, z is an Mx1 additive Gaussian white noise vector, and γ (W, c) represents the output SINR of the radar beamforming, expressed as +.>
Figure BDA00036070485100000611
Wherein->
Figure BDA00036070485100000612
And->
Figure BDA00036070485100000613
Representing the complex amplitudes of the target and the kth interferer, c H Is the self-conjugate matrix of vector c, W H Is the self-conjugate matrix of matrix W, +. >
Figure BDA00036070485100000614
Represents the noise variance of the vector u, which represents the circularly symmetric complex Gaussian white noise vector, θ 0 And theta k Representing the angles of the target and the kth interference source in the azimuth, A (theta 0 ) And A (theta) k ) Positive definite matrix representing the azimuth angles of the target and the kth interference source respectively, A H (θ 0 ) And A H (θ k ) Respectively represent A (theta) 0 ) And A (theta) k ) Self-conjugate matrix of>
Figure BDA0003607048510000071
a r (θ) is the R1 vector of propagation delays from the source at angle θ to the radar receiving element, (-) T Representing a transpose of the vector/matrix expressed as
Figure BDA0003607048510000072
Is a t Transpose of (θ), a t (θ) represents a T×1 emission steering vector expressed as
Figure BDA0003607048510000073
A beam forming module for giving the optimal value W of the precoding matrix * Optimizing radar receive beamforming matrix c by maximizing radar output SINR * The optimization problem is as follows:
Figure BDA0003607048510000074
a pre-coding module for forming the optimal radar beam forming matrix c * Substitution into
Figure BDA0003607048510000075
In (1) rank one method is adopted>
Figure BDA0003607048510000076
The reduction of the power minimization problem to the semi-definite programming SDP problem is as follows
Figure BDA0003607048510000077
Figure BDA0003607048510000078
Figure BDA0003607048510000079
X m ≥0,
Wherein X is m Rank 1, tr (·) represents the trace of the matrix,
Figure BDA00036070485100000710
w j is the j-th column of the matrix W, +.>
Figure BDA00036070485100000711
Is w j Self-conjugate matrix of>
Figure BDA00036070485100000712
And is also provided with
Figure BDA00036070485100000713
(c * ) H Is c * Self-conjugate matrix of>
Figure BDA00036070485100000714
And->
Figure BDA00036070485100000715
Represents the target and the kth modified optimal radar beamforming matrix, respectively,/for each radar beam >
Figure BDA00036070485100000716
And->
Figure BDA00036070485100000717
Are respectively->
Figure BDA00036070485100000718
And->
Figure BDA00036070485100000719
Solving the optimization problem by an interior point method, and if the rank one is not satisfied, finding the problem by Gaussian randomization>
Figure BDA00036070485100000720
For each precoding vector w m L candidate vectors generated, i.e.>
Figure BDA00036070485100000721
Wherein U is m And->
Figure BDA00036070485100000722
Respectively a matrix consisting of eigenvectors and a diagonal matrix,>
Figure BDA0003607048510000081
representing variance as unit matrix I T Complex gaussian matrix of (a), matrix U m Sum sigma m By characteristics ofValue calculation decomposition optimal matrix +.>
Figure BDA0003607048510000082
I.e. < ->
Figure BDA0003607048510000083
Generating candidate vectors such that
Figure BDA0003607048510000084
Representing a desired operator;
the power control module is used for further correcting the optimal precoding matrix through power control to meet communication and radar sensing requirements, and the optimization problem is constructed
Figure BDA0003607048510000085
Figure BDA0003607048510000086
Figure BDA0003607048510000087
p m ≥0,
Wherein,,
Figure BDA0003607048510000088
is the square value of the European norm of the precoding matrix,>
Figure BDA0003607048510000089
and->
Figure BDA00036070485100000810
Respectively representing the mth precoding vector parameter corrected by the mth channel matrix and the jth precoding vector parameter corrected by the mth channel matrix,/>
Figure BDA00036070485100000811
And->
Figure BDA00036070485100000812
Respectively w m And w j W is a self-conjugate matrix of m And w j Respectively denoted as mth candidate vector and jth candidate vector, gamma m,m And gamma k,m Representing the output SINR received at the mth UT interfered by the mth interferer and the output SINR received at the mth UT interfered by the kth interferer, respectively, >
Figure BDA00036070485100000813
Scaling parameters for the mth and jth precoding vectors, respectively,/for the mth and jth precoding vectors>
Figure BDA00036070485100000814
Representing real numbers, problem->
Figure BDA00036070485100000815
For linear programming with M non-negative variables and M+1 linear inequality constraints, solving the problem by the interior point method +.>
Figure BDA00036070485100000816
A third object of the present invention is to provide a computer device including a processor and a memory for storing a program executable by the processor, wherein the processor implements the above-mentioned dual function radar communication method when executing the program stored by the memory.
A fourth object of the present invention is to provide a storage medium storing a program which, when executed by a processor, implements the above-described dual function radar communication method.
Compared with the prior art, the invention has the following advantages and effects:
1. one object of the present invention to design a dual function radar communication system is to minimize the total power of its transmissions under the constraints of the received SINR at the user and the radar output SINR, which is solved for the first time in the present invention.
2. Another object of the present invention to design a dual function radar communication system that optimizes the performance of the communication part by maximizing the minimum received SINR between users constrained by the total transmitted power and radar output SINR. This problem is also solved for the first time in the present invention.
3. The invention simplifies the optimal design of the dual-function radar communication system by utilizing the pre-coding technology and the beam forming technology, effectively reduces the design complexity of the system and ensures the power consumption requirement.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings that are required in the embodiments or the description of the prior art will be briefly described, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to the structures shown in these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of an implementation of the dual function radar based communication method in embodiment 1 of the present invention;
FIG. 2 is a schematic diagram of a system model based on a dual function radar communication method in embodiment 1 of the present invention;
FIG. 3 is a graph of total transmit power minimization versus noise variance for a communication system under different communication and radar QoS constraints in accordance with embodiment 1 of the present invention;
fig. 4 is a block diagram showing the configuration of a dual function radar communication device in embodiment 2 of the present invention;
fig. 5 is a block diagram showing the structure of a computer device in embodiment 3 of the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Example 1:
for the convenience of description of the present embodiment, the following symbols are first defined: bold uppercase and lowercase letters are used to represent matrices and vectors, respectively; i N Representing an n×n identity matrix; 0 N A zero identity matrix representing n×n;
Figure BDA0003607048510000101
and->
Figure BDA0003607048510000102
Domains representing complex, real and positive real numbers, respectively; the |·| represents the modulus of the complex number; />
Figure BDA0003607048510000103
Representing a desired operator; I.I F Representing the Frobenius norm; (. Cndot. H And ( T Representing the self-conjugate matrix and transpose of the vector/matrix, respectively; tr (·) and rank (·) represent the trace and rank, respectively, of the matrix; a is more than or equal to 0 and is expressed as a positive definite matrix A; CN (·, ·) represents a complex circularly symmetric gaussian distribution;
system model and performance index
The present invention contemplates a dual function radar communication system (fig. 1) employing a uniform linear antenna array (ULA) of T elements with a half wavelength element spacing on the transmitter side. The DFRC system is intended to serve M single antenna users in downlink operation, while at the receiving end the DFRC system is also equipped with a dedicated ULA of R elements for receiving radar signals, following a radar system model with collocated transmit and receive antenna arrays.
For simplicity, by deleting the time index, the signal received at the communication user of a single time slot is given by: y= HWs +z (1)
Wherein the method comprises the steps of
Figure BDA0003607048510000104
Is a vector whose entry y m Is the signal received at the mth user, W is the T×M complex lineThe linear precoding matrix is updated based on the channel coherence time, s is a complex M x 1 vector, its entry s m Is the symbol sent to the mth user, drawn by a known constellation, T represents the number of elements of the transmitted ULA, R represents the number of elements of the received ULA, M represents the total number of user terminals,/user terminals>
Figure BDA0003607048510000105
Is a matrix of frequency flat fading channels between DFRC system and users, z is an Additive White Gaussian Noise (AWGN) complex vector variable of mx 1, corrupting the corresponding transmission,/- >
Figure BDA0003607048510000106
Representing the noise variance of z.
From the perspective of the communication system, the performance index available to design the system is the received signal to interference and noise ratio (SINR) for each user, given by:
Figure BDA0003607048510000107
wherein ( H Self-conjugate matrix representing vector/matrix, w m And w k Is the m-th and k-th columns of the matrix W,
Figure BDA0003607048510000111
and
Figure BDA0003607048510000112
respectively represent w m And w k Is a self-conjugate matrix of h m Represents the mth column of matrix H, +.>
Figure BDA0003607048510000113
Represents h m And in the self-conjugate matrix of
Figure BDA0003607048510000114
And->
Figure BDA0003607048510000115
The expression in (2) is deduced in the case of (2), whereins H And z H Representing the self-conjugate matrix of s and z, respectively, I M And 0 (0) M Representing an M x M identity matrix and an M x M zero identity matrix. Because the received SINR of each user is related to its achievable rate, r m ＝log 2 (1+ξ m (W)) (3)
The DFRC system transmits a tx 1 signal at each slot, which is constructed by linear precoding of the desired symbol, and transmits the signal to the user, i.e., W s . For simplicity, the time index is deleted again. For this transmitted signal, the signal seen at the position of angle θ is given by,
a t (θ)W s (4) Wherein a is t And (θ) represents a tx 1 transmit steering vector. Here, it is assumed that ULA with half wavelength element pitch is used. Thus, the emission steering vector is given by,
Figure BDA0003607048510000116
assuming that the target is at an angle theta 0 . In addition, there are K signal-dependent interferers located at angle θ k ≠θ 0 K=1, …, K. The baseband signal vector of the radar receiving array during the symbol time is given by,
Figure BDA0003607048510000117
wherein ( T Representing the transpose of the vector/matrix, alpha 0 And alpha k The complex amplitudes of the target and kth interferer respectively,
Figure BDA0003607048510000118
u is the mean value of the circularly symmetric complex Gaussian white noise vector is zero and the covariance matrix is equal to
Figure BDA0003607048510000119
Is the noise variance of u, θ 0 And theta k Representing the direction in which the target and the kth source of interference are located, respectivelyAngle (S)>
Figure BDA00036070485100001110
Is a t Self-conjugate matrix of (θ), +.>
Figure BDA00036070485100001111
Is a r (θ), a r (θ) is an r×1 vector of propagation delays from a source located at an angle θ to a radar receiving element. Also, under the assumption of ULA with half-wavelength spacing between adjacent elements, i.e
Figure BDA00036070485100001112
By defining A (θ) of the angle θ as
Figure BDA0003607048510000121
The writing of (6) is as follows
Figure BDA0003607048510000122
Wherein A (θ) 0 ) And A (theta) k ) Representing the positive definite matrix of the azimuth angles of the target and the kth interference source respectively.
From the perspective of radar systems, one common approach to designing radar waveforms is based on output signal-to-noise metrics. The detection probability is typically a monotonically increasing function of the output SINR assuming that a linear rx 1 receive beamforming vector c is applied across the radar receiving array to maximize the output signal-to-noise ratio. The output signal after the beamforming vector is applied is,
Figure BDA0003607048510000123
Wherein c H Is the self-conjugate matrix of vector c, beta k Is after correctionFor this signal model, the output SINR can be expressed as the complex amplitude of the kth interferer
Figure BDA0003607048510000124
Wherein the method comprises the steps of
Figure BDA0003607048510000125
And->
Figure BDA0003607048510000126
Representing the complex amplitudes of the target and the kth source, W H Is a self-conjugate matrix of matrix W, A H (θ 0 ) And A H (θ k ) Respectively represent A (theta) 0 ) And A (theta) k ) Is self-conjugate matrix of (1), assuming->
Figure BDA0003607048510000127
And is also provided with
Figure BDA0003607048510000128
Represents I M Representing an m×m identity matrix; 0 R Representing the zero identity matrix of R x R.
(II) description of problem
The present invention proposes three different and novel approaches that look at DFRC systems from three different angles, resulting in three different problem expressions: 1) a total transmission power constrained by communication and radar QoS, 2) a minimum received SINR at users constrained by radar QoS and total transmission power, and 3) a maximum radar received SINR constrained by communication QoS and total transmission power. The core idea behind the following approach is to focus on optimizing one part/metric of the DFRC system at a time while meeting the minimum QoS requirements of the other part/metric to produce an easy-to-process formula.
Furthermore, the derivation of the precoding matrix and beamforming matrix requires knowledge of the channel matrix H and radar parameters θ k And
Figure BDA0003607048510000131
for k=0, 1, …, K. The estimation methods employed by the independent communication and radar systems may also be employed by the DFRC system. That is, the channel matrix may be estimated by a training-based scheme. The radar parameters may be estimated by using an environmental dynamics database, following a cognitive radar paradigm.
In this approach, the goal is to minimize the total power transmitted by the system while maintaining the minimum QoS for the communication and radar parts. This is achieved by keeping the received SINR and radar output SINR of the user above a predefined threshold associated with the target QoS. Thus, the optimization problem of deriving optimal W and c is defined as
Figure BDA0003607048510000132
Wherein->
Figure BDA0003607048510000133
And->
Figure BDA0003607048510000134
Threshold values related to communication and radar QoS, respectively,/-for>
Figure BDA0003607048510000135
Represents a positive real number and, I.I F Representing the Frobenius matrix norm. Problem->
Figure BDA00036070485100001310
Is a quadratic programming with non-convex constraint (qqp) problem.
In this approach, the goal is to optimize the performance of the communication part by following the max-min SINR approach, while maintaining the minimum QoS of the radar part and meeting the constraints on the total power transmitted. Thus, the optimal W and c can be deduced as solutions
Figure BDA0003607048510000136
Wherein P is max Is the maximum transmit power supported by the DFRC system and is constant weighted 1/η m Different service levels between users are illustrated. Due to the non-convexity sum of the cost functionsNon-convex constraint of radar part QoS, +.>
Figure BDA0003607048510000137
The problem is non-convex.
In a third approach, the DFRC system designs the W and c variables to optimize the performance of the radar section by maximizing its output SINR while maintaining minimum QoS for the serving user and meeting the constraints on the total power transmitted. In this case, the optimization problem to be solved is defined as
Figure BDA0003607048510000138
s.t.ξ m (W)≥η m
Figure BDA0003607048510000139
Since the objective function and the constraint on the SINR of the user are non-convex, the
Figure BDA0003607048510000141
And is also a non-convex optimization problem.
(III) solution
In this section, derive
Figure BDA0003607048510000142
Is a solution to (a). In general, joint optimization of the precoding matrix W and the radar receive beamforming matrix c is a very difficult task, as these two variables are coupled by the radar output SINR expression. Therefore, to simplify the problem->
Figure BDA0003607048510000143
Consider a method of decoupling this transmit-receive design problem.
From the slave
Figure BDA0003607048510000144
Can be defined directly byIt is seen that the beamforming matrix c only appears in the radar output SINR expression. Thus, its optimization will only involve this performance index. Assume the optimal value W of the precoding matrix * Are known. Method for deriving optimal radar reception beamforming matrix by maximizing radar output SINR, i.e
Figure BDA0003607048510000145
Such a selection corresponds to
Figure BDA0003607048510000146
I.e. to maximize the radar system received SINR. Furthermore, it may only increase +.>
Figure BDA0003607048510000147
And->
Figure BDA0003607048510000148
Due to the performance of the radar part of (c) * ,W * )≥γ(c,W * ) And c * Is taken as->
Figure BDA0003607048510000149
Is used for solving the derived optimal radar receiving beamforming matrix.
Even if calculate c * As just discussed, by solving for
Figure BDA00036070485100001410
Is an optimization question of all examined->
Figure BDA00036070485100001411
This is not a simple task. This is so because of +.>
Figure BDA00036070485100001412
The solution of (a) requires knowledge of the optimal precoding matrix W * . Generally, due to the radar transmission and reception in questionThe coupling between the problems, the latter cannot be deduced under the assumption of an unknown radar beamforming matrix. To circumvent this, observe that in case the optimal precoding matrix is an orthogonal matrix, i.e. W * (W * ) H ＝I T The optimal receive beamforming matrix c may be obtained by first deriving it * To decouple radar transmission and reception problems.
As a simplified version
Figure BDA00036070485100001413
Solution of (2)
Figure BDA00036070485100001414
Then, by replacing c with c * At the position of
Figure BDA00036070485100001415
W * Can be derived by solving the decoupling problem, defined in broad terms as: />
Figure BDA0003607048510000151
Wherein f (W) represents based on
Figure BDA0003607048510000152
Cost function with minimized or maximized considered problem, +.>
Figure BDA0003607048510000153
Is a related set of constraints. Now, since the orthogonal constraint is a very strict and non-convex constraint, this will further plague the problem of being already very difficult +. >
Figure BDA0003607048510000154
And therefore discarded in the subsequent derivation. Relaxation problem with->
Figure BDA0003607048510000155
And (3) representing.In the question->
Figure BDA0003607048510000156
In (a) a feasible solution must exist in the set +.>
Figure BDA0003607048510000157
And an intersection of complex T x M matrices with orthonormal properties. This set is denoted as
Figure BDA0003607048510000158
Furthermore, when the orthogonality constraint is discarded, one possible solution has to be in the set +.>
Figure BDA0003607048510000159
Is a kind of medium. Can be easily seen
Figure BDA00036070485100001510
The former in fact means if the question +.>
Figure BDA00036070485100001511
There is an optimal solution to the precoding matrix W with orthogonal properties, which also exists in the feasible solution set +.>
Figure BDA00036070485100001512
In, therefore, it is also +.>
Figure BDA00036070485100001513
Is a solution to the optimization of (3). Otherwise, if->
Figure BDA00036070485100001514
Does not have orthogonal properties, it generally corresponds to a solution of +.>
Figure BDA00036070485100001515
The optimal target value is better than the solution forced orthogonal structure. In other words, by giving up the orthogonal constraint, there is no negative impact on performance, since +.>
Figure BDA00036070485100001516
Is +.>
Figure BDA00036070485100001517
Lower limit of (2).
Before continuing to derive the solution for each of the three inspection cases, it is still necessary to derive
Figure BDA00036070485100001518
Is a solution to (a). By examining this unconstrained optimization problem, it can be seen that it can be converted into a generalized eigenvalue problem that accepts a closed form solution given by
Figure BDA00036070485100001519
Wherein the method comprises the steps of
Figure BDA00036070485100001520
Is the principal eigenvector of the matrix.
C after changing the optimal radar beam forming matrix * The optimal precoding matrix W can be derived by solving the result problem and is defined as
Figure BDA00036070485100001521
Wherein->
Figure BDA0003607048510000161
(c * ) H Is c * Self-conjugate matrix of>
Figure BDA0003607048510000162
And->
Figure BDA0003607048510000163
Represents the target and the kth modified optimal radar beamforming matrix, respectively,/for each radar beam>
Figure BDA0003607048510000164
And->
Figure BDA0003607048510000165
Are respectively->
Figure BDA0003607048510000166
And->
Figure BDA0003607048510000167
Is a self-conjugate matrix of (a). The resulting equivalent optimization problem is given by
Figure BDA0003607048510000168
Figure BDA0003607048510000169
Figure BDA00036070485100001610
X m ≥0,rank(X m )＝1,1≤m≤M.
Wherein the method comprises the steps of
Figure BDA00036070485100001611
Is the j-th column of the matrix W, +.>
Figure BDA00036070485100001612
Is w j Self-conjugate matrix of>
Figure BDA00036070485100001613
tr (·) and rank (·) represent the trace and rank, respectively, of the matrix. Removing M non-convex rank constraint to obtain ∈K>
Figure BDA00036070485100001614
The following loose version of (c):
Figure BDA00036070485100001615
Figure BDA00036070485100001616
Figure BDA00036070485100001617
X m ≥0,1≤m≤M.
problem(s)
Figure BDA00036070485100001618
Is composed of a linear objective function, M+1 linear inequality constraints and M positive semi-definite constraints. Thus, this is a semi-definite programming (SDP) problem that can be effectively solved by the interior point method. In the question->
Figure BDA00036070485100001619
In case of acceptable solution +.>
Figure BDA00036070485100001620
And also acceptable for solution. However, since it is a loose version, it does not necessarily acknowledge the first-level solution. For this purpose, the problem can be found by means of the Gaussian randomization technique>
Figure BDA00036070485100001621
Is a solution to the approximation of (a). For each precoding vector w, according to the following method m L candidate vectors generated, i.e.>
Figure BDA00036070485100001622
Wherein U is m And->
Figure BDA00036070485100001623
Respectively a matrix consisting of eigenvectors and a diagonal matrix, >
Figure BDA00036070485100001624
Representative ofVariance is unit matrix I T Complex gaussian matrix of (a), matrix U m Sum sigma m Calculating and decomposing the optimal matrix from the eigenvalues>
Figure BDA00036070485100001625
I.e. < ->
Figure BDA00036070485100001626
Generating candidate vectors such that->
Figure BDA00036070485100001627
Representing the desired operator.
One problem with candidate vectors is that, in general, they do not meet communication and radar constraints. Therefore, they should be scaled up to be in the feasible solution set. This can be done by solving the defined power control problem
Figure BDA0003607048510000171
Figure BDA0003607048510000172
Figure BDA0003607048510000173
p m ≥0,1≤m≤M,
Wherein,,
Figure BDA0003607048510000174
is the square value of the European norm of the precoding matrix,>
Figure BDA0003607048510000175
and
Figure BDA0003607048510000176
respectively represent the sum of the mth precoding vector parameters corrected by the mth channel matrixThe j-th precoding vector parameter corrected by the m-th channel matrix,/th precoding vector parameter corrected by the m-th channel matrix>
Figure BDA0003607048510000177
And->
Figure BDA0003607048510000178
Respectively w m And w j W is a self-conjugate matrix of m And w j Respectively denoted as mth candidate vector and jth candidate vector,/>
Figure BDA0003607048510000179
Scaling parameters for the mth and jth precoding vectors, respectively,/for the mth and jth precoding vectors>
Figure BDA00036070485100001710
Representing real number,/->
Figure BDA00036070485100001711
For the mth precoding vector parameter corrected by the kth positive definite matrix,
Figure BDA00036070485100001712
is A (theta) k ) Is a positive matrix of candidates. Utilization problem->
Figure BDA00036070485100001713
The fact that the denominator in the constraint expression is positive can be converted into an equivalent form given by the following formula
Figure BDA00036070485100001714
Figure BDA00036070485100001715
Figure BDA00036070485100001716
p m ≥0,1≤m≤M.
Wherein gamma is m,m And gamma k,m Respectively representing the output SINR received at the mth UT interfered by the mth interference source and the output SINR received at the mth UT interfered by the kth interference source, a problem
Figure BDA00036070485100001717
Is a linear program with M non-negative variables and m+1 linear inequality constraints. This problem can be effectively solved by the interior point method. Suppose a feasible solution is found for the first candidate vector>
Figure BDA0003607048510000181
1.ltoreq.m.ltoreq.m, then for all 1.ltoreq.m.ltoreq.m, the latter is scaled to +.>
Figure BDA0003607048510000182
And selecting the precoding vector with the smallest total power from the L candidate vectors as a column of a precoding matrix w. The overall computational complexity is determined by the SDP problem>
Figure BDA0003607048510000183
And L linear programming. The former needs +.>
Figure BDA0003607048510000184
And the latter->
Figure BDA0003607048510000185
And (5) arithmetic operation.
The precoding matrix w may then be derived by solving the modification problem given by the following equation,
Figure BDA0003607048510000186
Figure BDA0003607048510000187
Figure BDA0003607048510000188
inequality constraints will be satisfied under the optimal equation. If this is not the case and the power budget is left, the remaining power can be evenly distributed among the users, i.e. the precoding vector is scaled by a constant strictly greater than one. This will also increase all SINR for all users and radar systems. The latter contradicts optimality assumptions. By using auxiliary positive variables
Figure BDA0003607048510000189
Can be converted into equivalent form
Figure BDA00036070485100001810
Figure BDA00036070485100001811
Figure BDA00036070485100001812
/>
Figure BDA00036070485100001813
Wherein,,
Figure BDA00036070485100001814
and->
Figure BDA00036070485100001815
Optimum values of parameter correlations of (a). In a similar manner let
Figure BDA00036070485100001816
Use->
Figure BDA00036070485100001817
Is indicative of the associated minimum power. By following a procedure similar to the above, the problem +. >
Figure BDA00036070485100001818
And->
Figure BDA00036070485100001819
The correlation of (2) is as follows:
Figure BDA0003607048510000191
Figure BDA0003607048510000192
can be deduced
Figure BDA0003607048510000193
P max Can solve by iteration +.>
Figure BDA0003607048510000194
For different t values. Furthermore, the question can be proven->
Figure BDA0003607048510000195
And->
Figure BDA0003607048510000196
Is monotonically non-increasing for a given weight eta M M is more than or equal to 1 and less than or equal to M, t and P max Is reduced. Thus, the optimal t value can be found by one-dimensional bisection.
By using transformations
Figure BDA0003607048510000197
Wherein X is m ≥0,rank(X m ) =1 and 1.ltoreq.m.ltoreq.M is +.>
Figure BDA0003607048510000198
And by deleting rank-1 constraints, as if it were about the problem->
Figure BDA0003607048510000199
As in the case of (2), the following problem of scaling results is obtained
Figure BDA00036070485100001910
Figure BDA00036070485100001911
Figure BDA00036070485100001912
Figure BDA00036070485100001913
X m ≥0,t≥0,1≤m≤M,
It can prove that the problem
Figure BDA00036070485100001914
To be similar to the question->
Figure BDA00036070485100001915
Is related by the way of (i.e.)
Figure BDA00036070485100001916
Figure BDA00036070485100001917
In addition, it is also possible to deduce
Figure BDA00036070485100001918
And->
Figure BDA00036070485100001919
Is monotonic for a given weight eta m M is more than or equal to 1 and less than or equal to M, t and P max Neither is reduced.
Figure BDA00036070485100001920
Can be solved by one-dimensional bisection on t such that +.>
Figure BDA00036070485100001921
The dichotomy requires a closed interval t l ,t u ]Wherein the best t is located therein. The lower observation limit may be set to t l =0, because t.gtoreq.0 and the upper limit is set to +.>
Figure BDA00036070485100001922
And assuming that all available power is allocated to a single user.
Due to solving of
Figure BDA00036070485100001923
A relaxed version of (a) and thus the matrix X obtained * m May be higher than 1. Therefore, the application here also has to be adapted to +.>
Figure BDA00036070485100001924
Is a gaussian randomization technique of (c). I.e. generating L candidate vectors- >
Figure BDA00036070485100001925
L is more than or equal to 1 and less than or equal to L is selected from->
Figure BDA0003607048510000201
Is a solution to the approximation of (a).
There remains a need to define and solve the power control problem by which candidate vectors are scaled to lie in a set of viable solutions. The definition of the above-mentioned problem is given by the following formula,
Figure BDA0003607048510000202
Figure BDA0003607048510000203
Figure BDA0003607048510000204
Figure BDA0003607048510000205
p m ≥0,1≤m≤M,t≥0,
wherein alpha is m 、β m,j Sum mu k,m Is defined as
Figure BDA0003607048510000206
And->
Figure BDA0003607048510000207
Again representing the scaling parameters of the mth precoding vector. Can prove that
Figure BDA0003607048510000208
Figure BDA0003607048510000209
In addition, in the case of the optical fiber,
Figure BDA00036070485100002010
and->
Figure BDA00036070485100002011
Is t and P max Are monotonically non-decreasing for a given weight eta m ，1≤m≤M。
In other words, and for
Figure BDA00036070485100002012
Similar bisection methods as described in the solution of (a) can also be used for +.>
Figure BDA00036070485100002013
Is a solution to (a). That is, the bisection method is applied at t such that +.>
Figure BDA00036070485100002014
For dichotomy, t l Again set to zero, t u Set to->
Figure BDA00036070485100002015
Is the optimum value of (3). If a feasible solution of the first candidate vector is found +.>
Figure BDA00036070485100002016
M is equal to or less than 1 and M is equal to or less than 1, and the M is scaled to be +.>
Figure BDA00036070485100002017
A scaled set of precoding vectors among the L candidates that achieve the maximum-minimum communication SINR is selected as a column of the precoding matrix W. Representing that the predefined tolerance dichotomy is running. The overall computational complexity is again determined by the SDP problem
Figure BDA00036070485100002018
And the computational complexity of the L-linear program dominates, for the question +.>
Figure BDA00036070485100002019
The number of solutions of the SDP problem and the L linear programs is as large as the number of iterations of the dichotomy employed. In practice, this is not a big problem, as the aforementioned dichotomies typically require a rather small number of iterations to converge.
Figure BDA0003607048510000211
Deriving a precoding matrix W by solving the resulting problem given by
Figure BDA0003607048510000212
Figure BDA0003607048510000213
/>
Figure BDA0003607048510000214
Wherein the vector is
Figure BDA0003607048510000215
And->
Figure BDA0003607048510000216
K is more than or equal to K and is defined as +.>
Figure BDA0003607048510000217
Below. Application transform->
Figure BDA0003607048510000218
Wherein X is m ≥0，rank(X m ) =1 and 1.ltoreq.m.ltoreq.M is +.>
Figure BDA0003607048510000219
In the present description, the expression is given below
Figure BDA00036070485100002110
Figure BDA00036070485100002111
Figure BDA00036070485100002112
X m ≥0,rank(X m )＝1,1≤m≤M,
Wherein matrix R 0 And R is k K is more than or equal to 1 and less than or equal to K
Figure BDA00036070485100002113
The following definitions. By eliminating the rank-1 constraint and due to the positive nature of the numerator and denominator in the SINR expression and objective function, the relaxation problem is a continuous concave/convex fractional programming problem. Thus, the Dinkelbach method can be used to transform it into a series of sub-problems and guarantee convergence to the global optimum of the original problem. By using
Figure BDA00036070485100002114
Representing the optimal solution of the nth sub-problem, i.e
Figure BDA00036070485100002115
Figure BDA00036070485100002116
Figure BDA00036070485100002117
Figure BDA00036070485100002118
Wherein the method comprises the steps of
Figure BDA00036070485100002119
Is an auxiliary variable. For a fixed zeta n Value, optimal matrix->
Figure BDA00036070485100002120
SDP question obtained by solving by interior point methodThe problem is obtained. Similarly, given an optimal matrix +.>
Figure BDA0003607048510000221
Is known, the auxiliary variable ζ n Can be directly determined by
Figure BDA0003607048510000222
That is, the just described alternating minimization procedure can be applied to solve
Figure BDA0003607048510000223
Since rank-1 is restricted to the sub-problem->
Figure BDA0003607048510000224
Is deleted, the optimal solution may relate to the matrix +.>
Figure BDA0003607048510000225
Its rank is higher than 1, such as +.>
Figure BDA0003607048510000226
Figure BDA0003607048510000227
Is the case in (a). Thus, resorting again to Gaussian randomization techniques to generate L candidate vectors +. >
Figure BDA0003607048510000228
1.ltoreq.l.ltoreq.L is selected from>
Figure BDA0003607048510000229
Is a solution to the approximation of (a). />
Figure BDA00036070485100002210
Figure BDA00036070485100002211
Figure BDA00036070485100002212
p m ≥0,1≤m≤M,t≥0
Wherein alpha is m 、β m,j Sum mu k,m Is defined as
Figure BDA00036070485100002213
And->
Figure BDA00036070485100002214
A scaling parameter representing the mth precoding vector. At->
Figure BDA00036070485100002215
In the definition of +.>
Figure BDA00036070485100002216
And->
Figure BDA00036070485100002217
Is to be added to the fact that (1) is a new product. Thus, the Dinkelbach method can be used again for switching +.>
Figure BDA00036070485100002218
The fractional part of (1) is defined as in the following series of sub-problems
Figure BDA00036070485100002219
Figure BDA00036070485100002220
Figure BDA00036070485100002221
Figure BDA00036070485100002222
Wherein the method comprises the steps of
Figure BDA00036070485100002223
Is the solution of the nth sub-problem, +.>
Figure BDA00036070485100002224
Is an auxiliary variable. />
Figure BDA00036070485100002225
An alternate minimization process may be applied to the solution of (a). Zeta was observed for fixation n The value, the problem that arises is a constraint with M non-negative variables and m+1 linear inequalities. Thus, it can be solved by the interior point method. Then, give +.>
Figure BDA0003607048510000231
Optimum value of variable, auxiliary variable
Figure BDA0003607048510000232
The update is directly carried out as that,
Figure BDA0003607048510000233
given solution
Figure BDA0003607048510000234
The first candidate vector is then scaled to +.>
Figure BDA0003607048510000235
For all 1.ltoreq.m.ltoreq.M. The scaled set of precoding vectors that achieve the maximum radar output selects the L candidate SINRs as columns of the precoding matrix W.
E represents a predefined tolerance for dinkelbach-based method operation. The overall computational complexity is mainly due to the SDP problem
Figure BDA0003607048510000236
The calculation complexity of (a) is determined by (a) and (b) each iteration is respectively>
Figure BDA0003607048510000237
And->
Figure BDA0003607048510000238
Example 2:
as shown in the figure, the present embodiment provides a dual-function radar communication method apparatus, which includes a signal transceiver module 401, a total power minimization construction module 402, a beam forming module 403, a pre-coding module 404, and a power control module 405, wherein:
A signal transceiver module 401, configured to introduce a receiving uniform linear antenna array, hereinafter referred to as ULA, and in the dual-function radar communication system, a base station at a transmitting end sends signals to a plurality of single-antenna users through ULA, and at the same time, a receiving end receives radar signals by using a special ULA;
a total power minimization construction module 402, configured to collect statistical knowledge of channel state information at the base station end, and construct a transmission total power minimization problem by satisfying service quality constraints of communication and radar parts, i.e.
Figure BDA0003607048510000239
s.t.ξ m (W)≥η m ,1≤m≤M,
γ(W,c)≥η,
Where W is a T×M complex linear precoding matrix, c is a linear R×1 receive beamforming vector,
Figure BDA0003607048510000241
and
Figure BDA0003607048510000242
are respectively connected withThreshold value related to signal and radar quality of service, +.>
Figure BDA0003607048510000243
Representing a positive real number, T representing the number of elements transmitting ULA, R represents the number of elements that receive the ULA, M represents the total number of user terminals, I.I F Representing the Frobenius matrix norm, ζ m (W) represents the received signal-to-interference-and-noise ratio of the mth UT, expressed as +.>
Figure BDA0003607048510000244
Wherein the signal-to-interference-plus-noise ratio is hereinafter referred to as SINR, (-) H Self-conjugate matrix representing vector/matrix, w m And w k Is the m-th column and the k-th column of the matrix W,>
Figure BDA0003607048510000245
and->
Figure BDA0003607048510000246
Respectively represent w m And w k Is a self-conjugate matrix of h m Represents the mth column of matrix H, +. >
Figure BDA0003607048510000247
Represents h m Self-conjugate matrix of>
Figure BDA0003607048510000248
Represents the noise variance of the vector z, z is an Mx1 additive Gaussian white noise vector, and γ (W, c) represents the output SINR of the radar beamforming, expressed as +.>
Figure BDA0003607048510000249
Wherein->
Figure BDA00036070485100002410
And->
Figure BDA00036070485100002411
Representing the complex amplitudes of the target and the kth interferer, c H Is the self-conjugate matrix of vector c, W H Is the self-conjugate matrix of matrix W, +.>
Figure BDA00036070485100002412
Represents the noise variance of the vector u, which represents the circularly symmetric complex Gaussian white noise vector, θ 0 And theta k Representing the angles of the target and the kth interference source in the azimuth, A (theta 0 ) And A (theta) k ) Positive definite matrix representing the azimuth angles of the target and the kth interference source respectively, A H (θ 0 ) And A H (θ k ) Respectively represent A (theta) 0 ) And A (theta) k ) Self-conjugate matrix of>
Figure BDA00036070485100002413
a r (θ) is the R1 vector of propagation delays from the source at angle θ to the radar receiving element, (-) T Representing a transpose of the vector/matrix expressed as
Figure BDA00036070485100002414
Is a t (θ), a t (θ) represents a T×1 emission steering vector expressed as +.>
Figure BDA00036070485100002415
Beamforming module 403 for giving an optimal value W of the precoding matrix * Optimizing radar receive beamforming matrix c by maximizing radar output SINR * The optimization problem is as follows:
Figure BDA00036070485100002416
a pre-coding module 404, configured to form an optimal radar beamforming matrix c * Substitution into
Figure BDA0003607048510000251
In (1) rank one method is adopted>
Figure BDA0003607048510000252
The reduction of the power minimization problem to the semi-definite programming SDP problem is as follows
Figure BDA0003607048510000253
Figure BDA0003607048510000254
Figure BDA0003607048510000255
X m ≥0,
Wherein X is m Rank 1, tr (·) represents the trace of the matrix,
Figure BDA0003607048510000256
w j is the j-th column of the matrix W, +.>
Figure BDA0003607048510000257
Is w j Self-conjugate matrix of>
Figure BDA0003607048510000258
And is also provided with
Figure BDA0003607048510000259
(c * ) H Is c * Self-conjugate matrix of>
Figure BDA00036070485100002510
And->
Figure BDA00036070485100002511
Represents the target and the kth modified optimal radar beamforming matrix, respectively,/for each radar beam>
Figure BDA00036070485100002512
And->
Figure BDA00036070485100002513
Are respectively->
Figure BDA00036070485100002514
And->
Figure BDA00036070485100002515
Solving the optimization problem by an interior point method, and if the rank one is not satisfied, finding the problem by Gaussian randomization>
Figure BDA00036070485100002516
For each precoding vector w m L candidate vectors generated, i.e.>
Figure BDA00036070485100002517
Wherein U is m And->
Figure BDA00036070485100002518
Respectively a matrix consisting of eigenvectors and a diagonal matrix,>
Figure BDA00036070485100002519
representing variance as unit matrix I T Complex gaussian matrix of (a), matrix U m Sum sigma m Calculating and decomposing the optimal matrix from the eigenvalues>
Figure BDA00036070485100002520
I.e. < ->
Figure BDA00036070485100002521
Generating candidate vectors such that
Figure BDA00036070485100002522
Representing a desired operator;
a power control module 405 for further modifying the optimal precoding matrix to meet the communication and radar sensing requirements by power control, the optimization problem being constructed as
Figure BDA00036070485100002523
Figure BDA00036070485100002524
Figure BDA00036070485100002525
p m ≥0,
Wherein,,
Figure BDA00036070485100002526
is the square value of the European norm of the precoding matrix,>
Figure BDA00036070485100002527
and->
Figure BDA0003607048510000261
Respectively representing the mth precoding vector parameter corrected by the mth channel matrix and the jth precoding vector parameter corrected by the mth channel matrix,/ >
Figure BDA0003607048510000262
And->
Figure BDA0003607048510000263
Respectively w m And w j W is a self-conjugate matrix of m And w j Respectively denoted as mth candidate vector and jth candidate vector, gamma m,m And gamma k,m Representing the output SINR received at the mth UT interfered by the mth interferer and the output SINR received at the mth UT interfered by the kth interferer, respectively,>
Figure BDA0003607048510000264
scaling parameters for the mth and jth precoding vectors, respectively,/for the mth and jth precoding vectors>
Figure BDA0003607048510000265
Representing real numbers, problem->
Figure BDA0003607048510000266
For linear programming with M non-negative variables and M+1 linear inequality constraints, solving the problem by the interior point method +.>
Figure BDA0003607048510000267
Specific implementation of each module in this embodiment may be referred to embodiment 1 above, and will not be described in detail herein; it should be noted that, the apparatus provided in this embodiment is only exemplified by the division of the above functional modules, and in practical application, the above functional allocation may be performed by different functional modules according to needs, that is, the internal structure is divided into different functional modules, so as to perform all or part of the functions described above.
Example 3:
the present embodiment provides a computer device, which may be a computer, as shown in fig. 5, and is connected through a system bus 501, where the processor is configured to provide computing and control capabilities, the memory includes a nonvolatile storage medium 506 and an internal memory 507, where the nonvolatile storage medium 506 stores an operating system, a computer program, and a database, and the internal memory 507 provides an environment for the operating system and the computer program in the nonvolatile storage medium, and when the processor 502 executes the computer program stored in the memory, the processor 502 implements a dual-function radar communication method provided in the foregoing embodiment 1, where the implementation steps of the dual-function radar communication method are as follows:
A multi-antenna base station adopts a uniform linear antenna array (ULA) to transmit signals to a plurality of single-antenna users on a downlink, and simultaneously adopts a special ULA to receive radar signals at a receiving end; the base station side collects the statistical knowledge of the channel state information and constructs the problem of minimum transmission total power by meeting the service quality constraint of the communication and radar parts; giving a precoding matrix standard orthogonalization constraint to maximize radar output signal-to-noise ratio to obtain an optimal radar receiving beamforming matrix; giving a receiving beam forming matrix, simplifying a power minimization problem into a semi-definite programming problem by using a rank-one method, and solving an optimal precoding matrix by using an interior point method; and finally, further correcting the optimal precoding matrix through power control to meet the communication and radar sensing requirements.
Example 4:
the present embodiment provides a storage medium, which is a computer readable storage medium storing a computer program, where the computer program is executed by a processor to implement a dual-function radar communication method according to the foregoing embodiment 1, and the implementation steps of the dual-function radar communication method are as follows: a multi-antenna base station adopts a uniform linear antenna array (ULA) to transmit signals to a plurality of single-antenna users on a downlink, and simultaneously adopts a special ULA to receive radar signals at a receiving end; the base station side collects the statistical knowledge of the channel state information and constructs the problem of minimum transmission total power by meeting the service quality constraint of the communication and radar parts; giving a precoding matrix standard orthogonalization constraint to maximize radar output signal-to-noise ratio to obtain an optimal radar receiving beamforming matrix; giving a receiving beam forming matrix, simplifying a power minimization problem into a semi-definite programming problem by using a rank-one method, and solving an optimal precoding matrix by using an interior point method; the optimal precoding matrix is further modified by power control to meet communication and radar sensing requirements.
The storage medium described in the present embodiment may be a magnetic disk, an optical disk, a computer memory, a random access memory (RAM, random Access Memory), a U-disk, a removable hard disk, or the like.
The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present invention should be made in the equivalent manner, and the embodiments are included in the protection scope of the present invention.

Claims (6)

1. The method for the communication of the double-function radar is characterized by comprising the following implementation steps:
s1, in a dual-function radar communication system, a multi-antenna base station adopts a uniform linear antenna array on a downlink to send signals to a plurality of single-antenna user terminals, and meanwhile, a receiving end adopts a uniform linear antenna array to receive and transmit radar detection waveforms and detect point targets at the same time, wherein the dual-function radar communication is hereinafter referred to as DFRC, the uniform linear antenna array is hereinafter referred to as ULA, the base station is hereinafter referred to as BS, and the user terminals are hereinafter referred to as UT;
s2, the base station collects the statistical knowledge of the channel state information, and constructs the problem of total transmission power minimization by meeting the service quality constraint of the communication and radar parts, namely
Figure FDA0003607048500000011
s.t.ξ m (W)≥η m ,1≤m≤M,
γ(W,c)≥η,
Where W is a T×M complex linear precoding matrix, c is a linear R×1 receive beamforming vector,
Figure FDA0003607048500000012
and
Figure FDA0003607048500000013
threshold values related to communication and radar quality of service, respectively,/->
Figure FDA0003607048500000014
Representing a positive real number, T representing the number of elements transmitting ULA, R represents the number of elements that receive the ULA, M represents the total number of user terminals, I.I F Representing the Frobenius matrix norm, ζ m (W) represents the received signal-to-interference-and-noise ratio of the mth UT, expressed as
Figure FDA0003607048500000015
Wherein the signal-to-interference-plus-noise ratio is hereinafter referred to as SINR, (-) H Self-conjugate matrix representing vector/matrix, w m And w k Is the m-th and k-th columns of the matrix W,
Figure FDA0003607048500000016
and->
Figure FDA0003607048500000017
Respectively represent w m And w k Is a self-conjugate matrix of h m Represents the mth column of matrix H, +.>
Figure FDA0003607048500000018
Represents h m Self-conjugate matrix of>
Figure FDA0003607048500000019
Represents the noise variance of the vector z, z is an Mx1 additive Gaussian white noise vector, and γ (W, c) represents the output SINR of the radar beamforming, expressed as
Figure FDA0003607048500000021
Wherein the method comprises the steps of
Figure FDA0003607048500000022
And->
Figure FDA0003607048500000023
Representing the complex amplitudes of the target and the kth interferer, c H Is the self-conjugate matrix of vector c, W H Is the self-conjugate matrix of matrix W, +.>
Figure FDA0003607048500000024
Representing the noise variance of the vector u, u representingCircularly symmetric complex Gaussian white noise vector, θ 0 And theta k Representing the angles of the target and the kth interference source in the azimuth, A (theta 0 ) And A (theta) k ) Positive definite matrix representing the azimuth angles of the target and the kth interference source respectively, A H (θ 0 ) And A H (θ k ) Respectively represent A (theta) 0 ) And A (theta) k ) And (2) self-conjugate matrix of
Figure FDA0003607048500000025
a r (θ) is the R1 vector of propagation delays from the source at angle θ to the radar receiving element, (-) T Representing the transpose of the vector/matrix with the expression +.>
Figure FDA0003607048500000026
Figure FDA0003607048500000027
Is a t Transpose of (θ), a t (θ) represents a T×1 emission steering vector expressed as +.>
Figure FDA0003607048500000028
S3, giving an optimal value W of the precoding matrix * Optimizing radar receive beamforming matrix c by maximizing radar output SINR * The optimization problem is as follows:
Figure FDA0003607048500000029
s4, the optimal radar beam forming matrix c * Substitution into
Figure FDA00036070485000000210
In (1) rank one method is adopted>
Figure FDA00036070485000000211
Minimizing power problemsThe SDP problem reduced to semi-definite programming is as follows
Figure FDA0003607048500000031
Figure FDA0003607048500000032
Figure FDA0003607048500000033
X m ≥0,
Wherein X is m Rank 1, tr (·) represents the trace of the matrix,
Figure FDA0003607048500000034
w j is the j-th column of the matrix W,
Figure FDA0003607048500000035
is w j Self-conjugate matrix of>
Figure FDA0003607048500000036
And is also provided with
Figure FDA0003607048500000037
(c * ) H Is c * Self-conjugate matrix of>
Figure FDA0003607048500000038
And->
Figure FDA0003607048500000039
Represents the target and the kth modified optimal radar beamforming matrix, respectively,/for each radar beam>
Figure FDA00036070485000000310
And->
Figure FDA00036070485000000311
Are respectively->
Figure FDA00036070485000000312
And->
Figure FDA00036070485000000313
Solving the optimization problem by an interior point method, and if the rank one is not satisfied, finding the problem by Gaussian randomization>
Figure FDA00036070485000000314
For each precoding vector w m L candidate vectors generated, i.e.>
Figure FDA00036070485000000315
Wherein U is m And->
Figure FDA00036070485000000316
Respectively a matrix consisting of eigenvectors and a diagonal matrix, >
Figure FDA00036070485000000317
Representing variance as unit matrix I T Complex gaussian matrix of (a), matrix U m Sum sigma m Calculating and decomposing the optimal matrix from the eigenvalues>
Figure FDA00036070485000000318
I.e. < ->
Figure FDA00036070485000000319
Generating candidate vectors such that->
Figure FDA00036070485000000320
Figure FDA00036070485000000321
Representing a desired operator;
s5, further correcting the optimal precoding matrix through power control to meet communication and radar sensing requirements, and constructing an optimization problem
Figure FDA00036070485000000322
Figure FDA00036070485000000323
Figure FDA00036070485000000324
p m ≥0,
Wherein,,
Figure FDA00036070485000000325
is the square value of the European norm of the precoding matrix,>
Figure FDA00036070485000000326
and->
Figure FDA00036070485000000327
Respectively representing the mth precoding vector parameter corrected by the mth channel matrix and the jth precoding vector parameter corrected by the mth channel matrix,/>
Figure FDA00036070485000000328
And->
Figure FDA00036070485000000329
Respectively w m And w j W is a self-conjugate matrix of m And w j Respectively denoted as mth candidate vector and jth candidate vectorAmount of gamma m,m And gamma k,m Representing the output SINR received at the mth UT interfered by the mth interferer and the output SINR received at the mth UT interfered by the kth interferer, respectively,>
Figure FDA0003607048500000041
scaling parameters for the mth and jth precoding vectors, respectively,/for the mth and jth precoding vectors>
Figure FDA0003607048500000042
Representing real numbers, problem->
Figure FDA0003607048500000043
For linear programming with M non-negative variables and M+1 linear inequality constraints, solving the problem by the interior point method +.>
Figure FDA0003607048500000044
2. The method according to claim 1, wherein the construction of two other optimization problems by the control variable method in the step S2 is as follows:
If the signal-to-interference-and-noise ratio is designed in a robust way under the constraint of the total transmitting power, the service quality of the radar is ensured, and the optimization problem is constructed as follows:
Figure FDA0003607048500000045
s.t.γ(W,c)≥η,
Figure FDA0003607048500000046
wherein P is max Is the maximum transmitting power supported by the DFRC system, and the constant weight is 1/eta m Illustrating different service levels between UTs;
if the signal-to-interference-and-noise ratio performance of the radar is maximized, the total transmitting power is limited and the communication service quality is guaranteed, and the optimization problem is constructed as follows:
Figure FDA0003607048500000047
3. the method according to claim 1, wherein in the step S3, when the radar receiving beamforming matrix is optimized, in order to obtain the analysis result of the optimal radar receiving beamforming matrix, assume W * (W * ) H ＝I T Further converting the optimization problem into
Figure FDA0003607048500000051
The optimal radar receiving beam forming matrix corresponding to the optimization problem is as follows
Figure FDA0003607048500000052
Wherein the method comprises the steps of
Figure FDA0003607048500000053
Is the principal eigenvector of the matrix.
4. A dual function radar communication device according to the dual function radar communication method of any one of claims 1 to 3, characterized in that the dual function radar communication device comprises:
the signal receiving and transmitting module is used for introducing a receiving uniform linear antenna array, namely receiving the uniform linear antenna array is called ULA (ultra low power) for short, a base station at a transmitting end in the dual-function radar communication system transmits signals to a plurality of single-antenna users through the ULA, and meanwhile, a receiving end receives radar signals by adopting a special ULA;
A total power minimization construction module, which is used for the base station to collect the statistical knowledge of the channel state information, and constructs the problem of total power minimization of transmission by meeting the service quality constraint of the communication and radar part,
Figure FDA0003607048500000054
i.e. s.t. ζ m (W)≥η m ,1≤m≤M,
γ(W,c)≥η,
Where W is a T×M complex linear precoding matrix, c is a linear R×1 receive beamforming vector,
Figure FDA0003607048500000055
and
Figure FDA0003607048500000056
threshold values related to communication and radar quality of service, respectively,/->
Figure FDA0003607048500000057
Representing a positive real number, T representing the number of elements transmitting ULA, R represents the number of elements that receive the ULA, M represents the total number of user terminals, I.I F Representing the Frobenius matrix norm, ζ m (W) represents the received signal-to-interference-and-noise ratio of the mth UT, expressed as
Figure FDA0003607048500000058
Wherein the signal-to-interference-plus-noise ratio is hereinafter referred to as SINR, (-) H Self-conjugate matrix representing vector/matrix, w m And w k Is the m-th and k-th columns of the matrix W,
Figure FDA0003607048500000061
and->
Figure FDA0003607048500000062
Respectively are provided withRepresents w m And w k Is a self-conjugate matrix of h m Represents the mth column of matrix H, +.>
Figure FDA0003607048500000063
Represents h m Self-conjugate matrix of>
Figure FDA0003607048500000064
Represents the noise variance of the vector z, z is an Mx1 additive Gaussian white noise vector, and γ (W, c) represents the output SINR of the radar beamforming, expressed as
Figure FDA0003607048500000065
Wherein the method comprises the steps of
Figure FDA0003607048500000066
And->
Figure FDA0003607048500000067
Representing the complex amplitudes of the target and the kth interferer, c H Is the self-conjugate matrix of vector c, W H Is the self-conjugate matrix of matrix W, +.>
Figure FDA0003607048500000068
Represents the noise variance of the vector u, which represents the circularly symmetric complex Gaussian white noise vector, θ 0 And theta k Representing the angles of the target and the kth interference source in the azimuth, A (theta 0 ) And A (theta) k ) Positive definite matrix representing the azimuth angles of the target and the kth interference source respectively, A H (θ 0 ) And A H (θ k ) Respectively represent A (theta) 0 ) And A (theta) k ) And (2) self-conjugate matrix of
Figure FDA0003607048500000069
a r (θ) is the Rx1 vector of propagation delay from the source at angle θ to the radar receiving elementAmount (·) T Representing the transpose of the vector/matrix with the expression +.>
Figure FDA00036070485000000610
Figure FDA00036070485000000611
Is a t Transpose of (θ), a t (θ) represents a T×1 emission steering vector expressed as +.>
Figure FDA00036070485000000612
A beam forming module for giving the optimal value W of the precoding matrix * Optimizing radar receive beamforming matrix c by maximizing radar output SINR * The optimization problem is as follows:
Figure FDA00036070485000000613
a pre-coding module for forming the optimal radar beam forming matrix c * Substitution into
Figure FDA00036070485000000614
In (1) rank one method is adopted>
Figure FDA00036070485000000615
The reduction of the power minimization problem to the semi-definite programming SDP problem is as follows
Figure FDA0003607048500000071
Figure FDA0003607048500000072
Figure FDA0003607048500000073
X m ≥0,
Wherein X is m Rank 1, tr (·) represents the trace of the matrix,
Figure FDA0003607048500000074
w j is the j-th column of the matrix W,
Figure FDA0003607048500000075
is w j Self-conjugate matrix of>
Figure FDA0003607048500000076
And is also provided with
Figure FDA0003607048500000077
(c * ) H Is c * Self-conjugate matrix of>
Figure FDA0003607048500000078
And->
Figure FDA0003607048500000079
Represents the target and the kth modified optimal radar beamforming matrix, respectively,/for each radar beam >
Figure FDA00036070485000000710
And->
Figure FDA00036070485000000711
Are respectively->
Figure FDA00036070485000000712
And->
Figure FDA00036070485000000713
Solving the optimization problem by an interior point method, and if the rank one is not trueFind problem by gaussian randomization +.>
Figure FDA00036070485000000714
For each precoding vector w m L candidate vectors generated, i.e.>
Figure FDA00036070485000000715
Wherein U is m And->
Figure FDA00036070485000000716
Respectively a matrix consisting of eigenvectors and a diagonal matrix,>
Figure FDA00036070485000000717
representing variance as unit matrix I T Complex gaussian matrix of (a), matrix U m Sum sigma m Calculating and decomposing the optimal matrix from the eigenvalues>
Figure FDA00036070485000000718
I.e. < ->
Figure FDA00036070485000000719
Generating candidate vectors such that
Figure FDA00036070485000000720
Figure FDA00036070485000000721
Representing a desired operator;
the power control module is used for further correcting the optimal precoding matrix through power control to meet communication and radar sensing requirements, and the optimization problem is constructed
Figure FDA00036070485000000722
Figure FDA00036070485000000723
Figure FDA00036070485000000724
p m ≥0,
Wherein,,
Figure FDA00036070485000000725
is the square value of the European norm of the precoding matrix,>
Figure FDA00036070485000000726
and->
Figure FDA00036070485000000727
Respectively representing the mth precoding vector parameter corrected by the mth channel matrix and the jth precoding vector parameter corrected by the mth channel matrix,/>
Figure FDA00036070485000000728
And->
Figure FDA00036070485000000729
Respectively w m And w j W is a self-conjugate matrix of m And w j Respectively denoted as mth candidate vector and jth candidate vector, gamma m,m And gamma k,m Representing the output SINR received at the mth UT interfered by the mth interferer and the output SINR received at the mth UT interfered by the kth interferer, respectively, >
Figure FDA0003607048500000081
Scaling parameters for the mth and jth precoding vectors, respectively,/for the mth and jth precoding vectors>
Figure FDA0003607048500000082
Representation ofReal number, problem->
Figure FDA0003607048500000083
For linear programming with M non-negative variables and M+1 linear inequality constraints, solving the problem by the interior point method +.>
Figure FDA0003607048500000084
5. A computer device comprising a processor and a memory for storing a program executable by the processor, wherein the processor, when executing the program stored in the memory, implements the method of bi-functional radar communication of any of claims 1-3.
6. A storage medium storing a program, wherein the program, when executed by a processor, implements the method of dual function radar communication of any one of claims 1-3.
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