CN115426020B - Low-complexity general sense integrated transmitting precoding optimization method - Google Patents

Low-complexity general sense integrated transmitting precoding optimization method Download PDF

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CN115426020B
CN115426020B CN202211170385.7A CN202211170385A CN115426020B CN 115426020 B CN115426020 B CN 115426020B CN 202211170385 A CN202211170385 A CN 202211170385A CN 115426020 B CN115426020 B CN 115426020B
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radar
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matrix
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CN115426020A (en
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王超
李果
曾心远
张海宾
李赞
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Xidian 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
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/86—Combinations of radar systems with non-radar systems, e.g. sonar, direction finder
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/023—Interference mitigation, e.g. reducing or avoiding non-intentional interference with other HF-transmitters, base station transmitters for mobile communication or other radar systems, e.g. using electro-magnetic interference [EMI] reduction techniques
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03891—Spatial equalizers
    • H04L25/03898—Spatial equalizers codebook-based design
    • H04L25/0391—Spatial equalizers codebook-based design construction details of matrices
    • 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

Abstract

The invention discloses a low-complexity general sense integrated transmitting precoding optimization method, relates to the technical field of wireless communication, and mainly solves the problems that a precoding optimization design problem in an existing dual-function radar communication system is difficult to solve and the computational complexity is high. Aiming at the downlink of a DFRC system, the optimization problem of maximizing the SINR (signal to interference plus noise ratio) of the radar sensing is constructed by considering interference signal influence of the radar sensing, antenna transmitting power constraint and minimum communication SINR constraint of communication users in the downlink, and then the distance optimization algorithm and Lagrangian dual theory are used jointly to convert the original constrained non-convex optimization problem into a series of unconstrained convex optimization problems with closed solutions for iterative solution. The invention not only greatly simplifies the calculation complexity of the design of the DFRC system precoder, but also obtains better dual-function waveform design performance compared with the prior method.

Description

Low-complexity general sense integrated transmitting precoding optimization method
Technical Field
The invention relates to the technical field of wireless communication, in particular to a low-complexity universal induction integrated transmitting precoding optimization method.
Background
As a key technology integrating two Functional modules of sensing and Communication, a Dual-Functional Radar-Communication (DFRC) technology can provide target sensing and Communication services in 5G-Advanced and 6G simultaneously. The DFRC uses a generic precoder to generate a sense-integrated waveform, which is then transmitted and based on the received echo signal to achieve a perceptual service on the unknown target. Optimizing the DFRC precoder requires a balance between communicating and perceiving the metrics corresponding to these two functions, resulting in the DFRC precoder optimization problem being non-convex in most cases.
In document "Joint transmit beamforming for multiuser MIMO communications and MIMO radar," IEEE trans.signal process, "vol.68, pp.3929-3944, jun 2020, a method of constructing a DFRC integrated waveform by using a weighted sum of a radar waveform and a communication signal is proposed, and a precoder based on semi-defined-Relaxation (SDR) algorithm is proposed to jointly design the communication signal and the radar waveform. However, from the communication interference point of view, the radar signal is regarded as an interference signal at the receiving end, and the design method that the communication signal and the radar waveform are separated reduces the communication capability of the system. On the other hand, from the system optimization perspective, SDR-based algorithms require increasing the dimensionality of the optimization variables, which will also greatly increase the computational complexity. In the literature "Generalized transceiver beamforming for DFRC with MIMO radar and MU-MIMO communication," IEEE j.sel.areas Commun, vol.40, no.6, pp.1795-1808, jun 2022, it is proposed to use a Multi-Input Multi-Output (MIMO) radar for Multi-user broadcast communication while targeting the communication signals for radar waveform use and employing a continuous convex approximation (Successive Convex Approximation, SCA) to design a precoder for the sense-of-general integrated signal. However, SCA-based algorithms require a feasible solution to start the iterative algorithm, but a feasible solution to the non-convex optimization problem is also often difficult to obtain.
While current traditional methods mainly employ SDR or SCA algorithms to handle such non-convex problems, while such methods can approximate the non-convex problem as a series of convex problems to obtain sub-optimal solutions, the higher computational complexity and the difficulty in obtaining an initial feasible solution search have been the main dilemma to extend such methods to practical applications.
Disclosure of Invention
The invention aims at: a low-complexity DFRC precoder optimization algorithm is provided for performing fast precoder design under the conditions of interference, power limitation and communication performance requirements, and reducing hardware cost and power consumption.
The invention considers the DFRC downlink broadcast link with interference, and establishes the optimization problem of maximizing the radar perceived SINR under the constraint of the lowest communication SINR of a communication user and the antenna transmitting power. And then the original non-convex optimization problem is converted into a series of unconstrained convex optimization problems with closed solutions by using a distance optimization algorithm and Lagrangian dual theory. Finally, a series of convex optimization problems are solved through iteration to obtain an efficient solution of the original non-convex problem, and the DFRC precoding design with low complexity is realized.
The technical scheme adopted by the invention is as follows:
the invention relates to a low-complexity general sense integrated emission precoding optimization method, which comprises the following steps:
step 1, constructing a dual-function radar communication system model, wherein the model comprises the following steps: one is provided with N t Root transmit antenna and N r Dual-function radar communication base station with root receiving antenna, and K single-antenna users U 1 ,U 2 ,...,U K ；
Step 2, selecting a channel model according to the communication system model constructed in the step 1:
selecting Rayleigh channel model to construct channel h between difunctional radar communication base station and kth user k ；
Constructing a radar sensing channel model A (v) with an azimuth angle v by using a line-of-sight propagation model;
modeling an interference signal c by using a complex Gaussian signal irrelevant to a transmitting signal;
step 3, according to the channel model selected in step 2, calculating the SINR value of all users and the SINR value omega (t, W) of radar perception SINR in the dual-function radar communication system model, wherein the SINR value of the kth user is used for the communication SINR value of the kth user
Figure BDA0003860130060000033
Denoted as W is the precoder and t is the receive filter, then the optimal receive filter t for the radar is designed given the precoder W by using the minimum variance with no optimal solution to the distortion response problem * Then bringing the signal into omega expression omega (t, W) to obtain the SINR value of radar perception signal-to-interference-plus-noise ratio (SINR)>
Figure BDA0003860130060000031
Step 4, the optimal receiving filter constructed in the step 3Radar-aware signal-to-interference-plus-noise ratio SINR value under a wave filter
Figure BDA0003860130060000032
The approximation reduction is performed and then the optimization problem P1 of the precoder W is constructed based thereon. Under the conditions of single antenna power constraint C0 and minimum communication signal to interference plus noise ratio SINR constraint C1 of each communication user, the problem maximizes the radar perceived signal to interference plus noise ratio SINR value;
step 5, constructing a feasible optimization problem by carrying out equivalent transformation on the optimization problem P1, namely converting the precoder W into a vector W, and converting the optimization problem P1 of a complex number domain into an equivalent problem P2 of a real number domain;
step 51, introducing additional phase bias to the precoder
Step 52, converting the precoder from matrix form W to vector form W;
step 53, splitting the real part and the imaginary part of the parameter in the problem P1, and converting the real part and the imaginary part into a corresponding real matrix or vector form;
step 54, performing equivalence replacement on complex matrix multiplication by using real matrix multiplication, and converting the objective function of the problem P1 and the constraint term thereof into a real form;
step 55, constructing an optimization problem P2 based on the results of the steps 53 and 54;
step 6, converting the constrained non-convex optimization problem P2 into an unconstrained convex optimization problem P5 with a closed solution;
step 61, merging inequality constraints in P2 into an objective function through a penalty function method, and converting into a problem P3;
step 62, converting the solution problem P3 into an iterative solution problem P4 by using a distance optimization method;
step 63, converting P4 into its Lagrangian dual problem P5 according to the strong dual, and giving its KKT condition;
step 7, obtaining a closed solution of the optimization problem according to the KKT condition of step 63, and further iteratively solving the problem P5 to obtain an optimal precoder W * ；
Step 71, solving the problem using closed-form solution iteration according to the KKT condition of step 63P5, obtaining the precoder optimization result in real number vector form
Figure BDA0003860130060000041
Step 72, real number vector is calculated according to the rules of step 52 and step 53
Figure BDA0003860130060000042
Converting back to the corresponding complex matrix form to obtain the final optimal precoder W * 。
In summary, by adopting the technical scheme, the invention has the beneficial effects that:
1. the invention is a low-complexity communication-sense integrated transmitting precoding optimization method, and the communication signal is completely used as radar sensing waveforms, so that the communication efficiency is higher compared with other radar waveforms independently designed methods.
2. The invention is a low-complexity general sense integrated transmitting precoding optimization method, and considers the influence of interference signals in radar echo, so that the method has higher robustness.
3. The invention relates to a low-complexity general sense integrated emission precoding optimization method, which has lower computational complexity compared with the traditional method and is beneficial to improving the real-time performance of precoding design.
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For a clearer description of the technical solutions of the embodiments of the present invention, the drawings that are needed in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention, and should not be considered as limiting the scope, for those skilled in the art, without performing creative efforts, other related drawings may be obtained according to the drawings, where the proportional relationships of the components in the drawings in the present specification do not represent the proportional relationships in actual material selection design, and are merely schematic diagrams of structures or positions, where:
FIG. 1 is a flow chart of an implementation of the present invention;
FIG. 2 is a block diagram of a DFRC system constructed in the present invention;
FIG. 3 is a graph comparing waveforms obtained by the present invention and the prior SDR algorithm under a single target condition;
FIG. 4 is a graph comparing waveforms obtained by the present invention and the prior SDR based algorithm in a multi-objective situation;
fig. 5 is a graph comparing perceived signal-to-interference-plus-noise ratio SINR with maximum transmit power for the present invention and for the prior SDR-based approach.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the particular embodiments described herein are illustrative only and are not intended to limit the invention, i.e., the embodiments described are merely some, but not all, of the embodiments of the invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
It should be noted that the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus.
Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by a person skilled in the art without making any inventive effort, are intended to be within the scope of the present invention.
All of the features disclosed in this specification, or all of the steps in a method or process disclosed, may be combined in any combination, except for mutually exclusive features and/or steps.
The present invention will be described in detail with reference to the accompanying drawings.
The specific embodiments are implemented as follows:
the invention relates to a low-complexity general sense integrated emission precoding optimization method, which comprises the following steps:
step 1: construction of a model of a bifunctional radar communication system
Referring to fig. 2: the dual-function radar communication system model constructed in the step comprises the following steps: one is provided with N t Root transmit antenna and N r Dual-function radar communication base station with root receiving antenna, and K single-antenna legal users U 1 ,U 2 ,...,U K Wherein the transmitting and receiving antennas of the radar communication base station employ the same set of Uniform Linear Arrays (ULA).
Step 11, constructing a communication model, and the kth user U k Received signal
Figure BDA0003860130060000061
Expressed as:
Figure BDA0003860130060000062
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003860130060000063
is the downlink rayleigh fading channel for the kth user. />
Figure BDA0003860130060000064
Representing a precoding matrix, wherein ∈>
Figure BDA0003860130060000065
Representing the precoding vector of the kth user in the precoding matrix.
Figure BDA0003860130060000066
An information matrix representing all K users, L representing the information length, wherein +>
Figure BDA0003860130060000067
Representing transmissions to kth user U k And the different user information is not related, satisfying +.>
Figure BDA0003860130060000068
Figure BDA0003860130060000069
Representing the received noise subject to complex Gaussian distribution +.>
Figure BDA00038601300600000610
Step 12, constructing a radar sensing channel model based on the communication signals in step 11, wherein the signals received by the DFRC base station radar are as follows:
x 0 ＝t H y 0 ＝t H a(v)Ws+t H c+t H z 0
in the method, in the process of the invention,
Figure BDA00038601300600000611
linear receive filter representing DFRC base station, < >>
Figure BDA00038601300600000612
Representing the received signal echo. />
Figure BDA00038601300600000613
Represents the channel corresponding to the radar signal, wherein v=
[v 1 ,…, k ,…, M ]A set of spatial departure angles representing all perceived objects, wherein the kth element v k Representing the departure angle from the base station to the kth perception target, M is the perception target number,
Figure BDA0003860130060000071
representing the interference signal received by the radar,
Figure BDA0003860130060000072
representing the received noise of a DFRC base station, each element obeying a complex Gaussian distribution +.>
Figure BDA0003860130060000073
Step 2: and (3) establishing a corresponding channel model according to the system model constructed in the step (1).
Step 21, modeling the antenna array response:
a r and a t ULA array steering vectors representing base station receive and transmit antennas, respectively, are expressed as:
Figure BDA0003860130060000074
Figure BDA0003860130060000075
where v denotes the incidence and emergence angles of the signal at the DFRC base station, N r And N t Indicating the number of receiving antennas and transmitting antennas, respectively, delta t And delta r Respectively representing the distance between a transmitting antenna and a receiving antenna after wavelength normalization;
step 22, constructing the channel between the DFRC base station and the kth user in step 11 by utilizing the Rayleigh channel model
Figure BDA0003860130060000076
Obeying complex Gaussian distribution->
Figure BDA0003860130060000077
Step 23, modeling the radar channel in step 12 by using the line-of-sight propagation model, where the radar sensing channel model a (v) may be expressed as:
Figure BDA0003860130060000078
wherein v= [ v ] 1 ,…,v k ,…,v M ]，a k Representing perceived objectsReflected signal amplitude, v k Representing the departure angle from the base station to the kth perception target, wherein M is the perception target number;
step 23, modeling the interference signal c by using the complex Gaussian distribution signal, wherein the covariance matrix R of the interference signal c in step 11 c Is constant:
Figure BDA0003860130060000081
wherein beta is i Sum phi i The amplitude of the ith interference signal and the angle of incidence I of the interference source to the base station, respectively, are the total number of interference sources.
Step 3: calculating the SINR value of the kth user in the DFRC system model
Figure BDA0003860130060000082
And a radar perceived signal to interference plus noise ratio SINR value ω (t, W).
Step 31, calculating the SINR value of the kth user in the DFRC system
Figure BDA0003860130060000083
Figure BDA0003860130060000084
Step 32, calculating the SINR (signal to interference plus noise ratio) value (t, W):
Figure BDA0003860130060000085
step 33, calculating the optimal solution t of the radar receiving filter under the minimum variance distortion-free response according to the radar perceived SINR value omega (t, W) in step 32 * ：
Figure BDA0003860130060000086
Step 34 t of the radar receiving filter in step 33 * The expression of the SINR (t, W) with step 32 is carried out to calculate the SINR value of the radar perception when the optimal radar receiving filter is calculated
Figure BDA0003860130060000087
Figure BDA0003860130060000091
Step 4: the precoder optimization problem P1 is constructed based on statistical channel state information, taking into account the power limit of each antenna and the communication signal-to-interference-and-noise ratio value SINR lower bound of each user.
Step 41, progressively increasing with the information length L, and
Figure BDA0003860130060000092
step 34>
Figure BDA0003860130060000093
The progressive result can be expressed as +.>
Figure BDA0003860130060000094
Namely:
Figure BDA0003860130060000095
step 42, constructing a precoder optimization problem P1 based on step 41:
P1:max W Tr(ΘWW H )
s.t.C0:
Figure BDA0003860130060000096
C1:
Figure BDA0003860130060000097
in the method, in the process of the invention,
Figure BDA0003860130060000098
P tot represents maximum transmit power, R k Representing the lowest communication signal-to-interference-and-noise ratio SINR of the kth user, diag (·) represents taking the dominant diagonal matrix. "s.t." represents that the optimization problem is constrained, and "C0" and "C1" represent two constraint conditions to be satisfied, where constraint C0 is a transmit power limit of a single antenna, ensuring that each antenna adopts a maximum transmit power, and constraint C1 is a communication signal-to-interference-and-noise ratio SINR value +.>
Figure BDA0003860130060000099
Lower bound constraint for guaranteeing SINR value of each communication user>
Figure BDA00038601300600000910
Greater than R k 。
Step 5: the precoder matrix W is converted into a vector W and the optimization problem P1 of the complex domain is converted into an equivalence problem P2 of the real domain.
Step 51, introducing a suitable phase bias to the precoder W, it is easy to make it satisfy:
Figure BDA00038601300600000911
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure BDA0003860130060000101
the representation takes the imaginary part;
step 52, converting the precoder W from a matrix form to a one-dimensional vector form W for easy calculation, using the following method:
Figure BDA0003860130060000102
step 53, splitting the real part and imaginary part of the parameters in the problem P1, and converting into corresponding real matrix or vector form,
step 531, constructing the following auxiliary variables:
Figure BDA0003860130060000103
Figure BDA0003860130060000104
Figure BDA0003860130060000105
wherein DIAG (·) represents the principal diagonal matrix made up of variables in function brackets;
step 532, based on the transformation of steps 51-531, the constraint C1 in step 42 can be converted into the following form:
Figure BDA0003860130060000106
in step 533, auxiliary variables are established, and complex matrix and vector are converted into corresponding real matrix and vector forms:
Y＝W,y＝[Y T (:，1),…,Y T (:,K)] T ，
Figure BDA0003860130060000107
Figure BDA0003860130060000108
Figure BDA0003860130060000111
Figure BDA0003860130060000112
Figure BDA0003860130060000113
in the method, in the process of the invention,
Figure BDA0003860130060000114
represents the Kronecker product,/>
Figure BDA0003860130060000115
Representing the real part;
in step 54, the complex matrix multiplication is equivalently replaced by the real matrix multiplication, so as to convert the objective function of the problem P1 and the constraint term thereof into a real form, and the specific method is as follows:
step 541, converting the complex matrix-vector multiplication in P1 to real multiplication using the following method:
Figure BDA0003860130060000116
step 542, further, P1 may be equivalently converted into P2:
P2:
Figure BDA0003860130060000117
s.t.C2:
Figure BDA0003860130060000118
C3:
Figure BDA0003860130060000119
C4:
Figure BDA00038601300600001110
C5:
Figure BDA00038601300600001111
wherein constraint C2 is an equivalent representation of step 532 and constraint C1, aboutBeam C4 is used to ensure the assumption in step 51
Figure BDA00038601300600001112
This is true.
Step 55, constructing an optimization problem P2 based on the results of steps 53 and 54.
Step 6: and combining the constraint C2 and the constraint C5 in the P2 into an objective function through a penalty function method, converting the objective function into a problem P3, converting the solution problem P3 into an iterative solution problem P4 through a distance optimization method, and finally obtaining a Lagrange dual problem P5 of the P4 and a KKT condition thereof.
Step 61, using the penalty function method, selecting an appropriate penalty coefficient ρ, adding constraints C2 and C5 to the objective function of P2, thereby constructing an optimization problem P3:
P3:
Figure BDA0003860130060000121
s.t.C3,C4,
wherein dist (·) is used to calculate the distance of the variable to its feasible region Ω, defined as
Figure BDA0003860130060000122
Figure BDA0003860130060000123
Whereas omega k And xi are defined as:
Figure BDA0003860130060000124
Figure BDA0003860130060000125
when rho in the problem P3 is →++infinity, solving the optimal solution of P3 to obtain the optimal solution of P2; however, the dist (·) is quite complex to calculate, so that the dist (·) is approximated by a distance optimization method;
step 62, performing iterative approximate solution to the problem P3 by using a distance optimization algorithm, wherein the ith iteration is equivalent to solving the following optimization problem P4:
P4：
Figure BDA0003860130060000126
Figure BDA0003860130060000127
s.t.C3,C4,
in the method, in the process of the invention,
Figure BDA0003860130060000131
representing the solution mapping to the feasible domain xi at the ith y iteration, ++>
Figure BDA0003860130060000132
And->
Figure BDA0003860130060000133
Respectively represents r at the ith iteration k And->
Figure BDA0003860130060000134
Mapping to feasible region Ω k And (5) performing subsequent solution.
In step 6, according to the strong dual, P4 is converted into its lagrangian dual problem P5, and its KKT condition is given, which is implemented as follows for step 63:
step 631, computing the Lagrangian dual function of the problem P4, and incorporating the constraints C3 and C4 into the objective function:
Figure BDA0003860130060000135
the method comprises the following steps:
Figure BDA0003860130060000136
λ k ,η,θ k is Lagrangian multiplier, τ, with constraint C3 in P3 k Is a Lagrangian multiplier corresponding to constraint C4 in P3;
step 632, according to the dual function of step 631, adding the total power constraint at the same time, and establishing an optimization problem P5:
P5：
Figure BDA0003860130060000141
s.t.C6:
Figure BDA0003860130060000142
in the formula, the constraint C6 represents total power constraint, and because of the existence of the constraint C5, the constraint C6 is required to be automatically satisfied when an optimal solution is achieved, so that the constraint C6 cannot shrink a feasible region of a problem, and the optimal solution of P2 can be obtained by the iterative solution problem P5;
step 633, based on the strong dual of P5, obtaining the optimal solution of the problem according to the KKT condition of P5, wherein the KKT condition of P5 is first
Figure BDA0003860130060000143
Figure BDA0003860130060000144
Figure BDA0003860130060000145
Figure BDA0003860130060000146
Figure BDA0003860130060000147
Figure BDA0003860130060000148
In the method, in the process of the invention,
Figure BDA0003860130060000149
representing the multiplier of constraint C6. Because P5 has strong dual, its optimal solution meets the above KKT condition, and the next step is to solve by using the KKT condition.
Step 71: and (3) carrying out iterative solution on the problem P5 according to the KKT condition of the step 633, and simultaneously introducing Nesterov algorithm acceleration to realize rapid iterative solution on the problem P2.
Step 711, initializing relevant parameters and variables.
Initializing a convergence threshold and an iteration counter:
∈＝10 -4 ,i＝1
initializing parameters:
ρ＝1,c＝2,ρ max ＝10 9 ,
Figure BDA0003860130060000151
step 712, iterating and outputting
Figure BDA0003860130060000152
Step 712.1, updating z (i), r of the i-th iteration k (i),f k (i) Y (i) is expressed as follows:
Figure BDA0003860130060000153
r k ＝g k,1 z(i),
Figure BDA0003860130060000154
step 712.2, updating the iteration of step i
Figure BDA0003860130060000155
And->
Figure BDA0003860130060000156
The expression is as follows:
Figure BDA0003860130060000157
Figure BDA0003860130060000158
the method comprises the following steps:
Figure BDA0003860130060000159
step 712.3, using dichotomy
Figure BDA00038601300600001510
Searching to obtain +.>
Figure BDA00038601300600001511
Value is according to->
Figure BDA00038601300600001512
The value may be calculated in the following manner:
Figure BDA00038601300600001513
Figure BDA00038601300600001514
Figure BDA0003860130060000161
because of
Figure BDA0003860130060000162
Is about->
Figure BDA0003860130060000163
Is thus necessarily searchable for the appropriate +.>
Figure BDA0003860130060000164
Step 713, using the obtained in step 712.3
Figure BDA0003860130060000165
Update +.1 in step i->
Figure BDA0003860130060000166
Figure BDA0003860130060000167
/>
Step 714, when the iteration number i reaches a certain threshold value, update ρ using:
ρ＝min(ρ max ,cρ)
step 715, update the iteration counter:
i＝i+1
step 716, stopping the iteration and letting the following conditions are satisfied
Figure BDA0003860130060000168
Outputting a final result, otherwise returning to step 712 for loop execution:
Figure BDA0003860130060000169
step 72, using the method of step 55 to compare the results obtained in step 716
Figure BDA00038601300600001610
Restoring back to w * Then referring to the method in step 52, further reverts back to W * 。
The effect of the invention can be further illustrated by the following simulation experiment:
1. and (5) setting simulation parameters.
In the DFRC system model, the number of base station receiving antennas N is assumed r =10. Noise power
Figure BDA00038601300600001611
The fixed interference signal has 3 sources, the horizontal angles of which are respectively psi 1 ＝10°,ψ 2 ＝-60°,ψ 3 =60°, the signal amplitudes of which are |β respectively 1 | 2 ＝|β 2 | 2 ＝|β 3 | 2 =0.1. Base station antenna number N t Base station power budget P tot SINR lower bound R of user k The number of users K and the positions of the users are all variables in the simulation.
2. Simulation experiment contents and results
Simulation 1 mainly verifies the beam pattern of the present invention under a single target, using the above simulation parameters, the present invention is used to optimize the precoder of the base station under two conditions in table 1, the optimization result of the precoder is obtained first, then the corresponding airspace waveform diagram is calculated, and compared with the conventional SDR-based method, and the result is shown in fig. 3. Wherein, the power P (theta) = |t in the angle theta direction in the airspace waveform diagram H A(v)w| 2 。
Figure BDA0003860130060000171
TABLE 1 partial parameter settings for Emulation 1
Simulation 2 mainly verifies the airspace waveform of the invention under the multi-perception target, the invention is used for optimizing the precoder of the base station under the two conditions in table 2 by utilizing the simulation parameters, the optimization result of the precoder is obtained first, then the corresponding airspace waveform diagram is calculated, and compared with the traditional SDR-based method, and the result is shown in fig. 4.
Figure BDA0003860130060000172
Table 2, partial parameter settings for simulation 2
As can be seen from fig. 3 and 4, the precoder designed by the method of the present invention and the existing SDR-based method has similar beam patterns-similar main beam and null beam positions under the same parameters. Meanwhile, the power of the main beam position is higher than that of the existing method, and the position of the null beam is lower, so that the perception target direction and the interference direction have larger distinction degree.
Simulation 3 mainly verifies that the radar perceived signal-to-interference-and-noise ratio SINR of the present invention at different total transmit powers adjusts the total transmit power P under three conditions in Table 3 using the above simulation parameters tot The invention optimizes the precoder of the base station to obtain different P of the precoder tot The following optimization results are compared with SNIR comparison results of the prior radar perception signal-to-interference-plus-noise ratio designed based on SDR method, as shown in FIG. 5.
Figure BDA0003860130060000181
TABLE 3 partial parameter settings for Emulation 3
As can be seen from fig. 4, as the total transmit power increases, the radar perceived signal to interference plus noise ratio SINR increases, and the method of the present invention is superior to the SDR-based design method under the same parameter setting.
The above description is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that are not creatively contemplated by those skilled in the art within the technical scope of the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope defined by the claims.

Claims (4)

1. The low-complexity general sense integrated transmitting precoding optimization method is characterized by comprising the following steps of:
step 1, constructing a dual-function radar communication system model, wherein the model comprises the following steps: one is provided with N t Root transmit antenna and N r A dual-function radar communication base station of a root receiving antenna, K single-antenna users;
step 2, building a corresponding channel model according to the system model built in the step 1;
selecting Rayleigh channel model to construct channel h between difunctional radar communication base station and kth user k Constructing a radar sensing channel model A (v) with an azimuth angle v by using a line-of-sight propagation model, and modeling an interference signal c by using a complex Gaussian signal irrelevant to a transmitting signal;
step 3, calculating the SINR value of the kth user in the dual-function radar communication system model
Figure FDA0004255993780000011
And a radar perceived signal-to-interference-plus-noise ratio (SINR) value omega (t, W), wherein W and t are a precoder and a receiving filter respectively; calculating an optimal solution t of a radar receiving filter given a precoder W from an optimal solution of a minimum variance distortion-free response problem * Then bringing the signal to interference plus noise ratio SINR value into the expression of omega (t, W) to obtain the radar perception SINR value under the optimal receiving filter>
Figure FDA0004255993780000012
Step 4, regarding the radar perception signal-to-interference-plus-noise ratio SINR value under the optimal receiving filter constructed in the step 3
Figure FDA0004255993780000013
Performing approximation and simplification, and then constructing an optimization problem P1 of the precoder W based on the approximation and the simplification;
progressively increasing with the information length L, and
Figure FDA0004255993780000014
wherein (1)>
Figure FDA0004255993780000015
For the user information matrix, L is the information length, +.>
Figure FDA0004255993780000016
Can gradually approach +>
Figure FDA0004255993780000017
Simultaneously constructing a precoder W optimization problem P1, progressive results +.>
Figure FDA0004255993780000018
The formula can be expressed as:
Figure FDA0004255993780000021
P1：max W Tr(ΘWW H )
Figure FDA0004255993780000022
Figure FDA0004255993780000023
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA0004255993780000024
R c covariance matrix representing interference signal c, I representing total number of interference sources, σ c Is the standard deviation of communication noise, A H (v) Is the conjugate transpose of A (V), A (V) is the radar sensing channel model, P tot Represents the total emission power, R k Representing the lower bound of SINR required by the kth user, diag (·) representing diagonal matrix, "s.t." representing the optimization problem is constrained, "C0" and "C1" representing two constraints to be satisfied, where constraintsC0 is a limiting condition of single antenna power, ensures that each antenna adopts maximum signal transmitting power, and constrains C1 to be communication signal-to-interference-plus-noise ratio SINR value of each communication user +.>
Figure FDA0004255993780000025
Lower bound constraint for guaranteeing SINR value of communication signal to interference plus noise ratio of each communication user
Figure FDA0004255993780000026
Greater than R k ；
Step 5, constructing a feasible optimization problem by carrying out equivalent transformation on the optimization problem P1, namely converting the precoder W into a vector W, and converting the optimization problem P1 of a complex number domain into an equivalent problem P2 of a real number domain;
specifically, the method comprises the steps of 51-55,
step 51, introducing an additional phase bias to the precoder W to satisfy:
Figure FDA0004255993780000027
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA0004255993780000031
representing the imaginary part->
Figure FDA0004255993780000032
Representing a precoding vector of a kth user in the precoding matrix;
step 52, converting the precoder W from a matrix form to a vector form W, as follows:
Figure FDA0004255993780000033
step 53, splitting the real part and the imaginary part of the parameter in the problem P1, and converting the real part and the imaginary part into a corresponding real matrix or vector form;
in the step 53, the real part and the imaginary part of the parameter in the problem P1 are split and converted into corresponding real matrix or vector form:
step 531, constructing auxiliary variables, and the method is as follows
Figure FDA0004255993780000034
Figure FDA0004255993780000035
Figure FDA0004255993780000036
Step 532, based on steps 51 to 531, converts constraint C1 of problem P1 into the following form:
Figure FDA0004255993780000037
in step 533, an auxiliary variable is constructed, and the complex matrix and the vector are converted into a corresponding real matrix and vector, and the method is as follows:
Y＝W，y＝[Y T (：，1)，...，Y T (：，K)] T ，
Figure FDA0004255993780000038
Figure FDA0004255993780000041
Figure FDA0004255993780000042
Figure FDA0004255993780000043
Figure FDA0004255993780000044
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA0004255993780000045
represents the Kronecker product,/>
Figure FDA0004255993780000046
Representing the real part;
step 54, performing equivalence replacement on complex matrix multiplication by using real matrix multiplication, and converting the objective function of the problem P1 and the constraint term thereof into a real form; the specific method comprises the following steps:
step 541, converting the complex matrix-vector multiplication in P1 to real multiplication using the following method:
Figure FDA0004255993780000047
step 542, further, P1 may be equivalently converted into P2:
P2：
Figure FDA0004255993780000048
Figure FDA0004255993780000049
Figure FDA00042559937800000410
Figure FDA00042559937800000411
Figure FDA00042559937800000412
where constraint C2 is an equivalent representation of step 532 and constraint C1, constraint C4 is used to ensure the assumptions in step 51
Figure FDA0004255993780000051
Is true, v k Is the arrival angle of the kth direct user signal to the base station;
step 55, constructing an optimization problem P2 based on the results of the steps 53 and 54;
step 6, converting P2 into a problem P3 by a penalty function method, then converting the solution problem P3 into an iteration solution problem P4 by a distance optimization method, and finally obtaining a Lagrange dual problem P5 of the P4 and KKT conditions thereof;
in the step 6, the inequality constraint in P2 is combined into an objective function through a penalty function method, and is converted into a problem P3, and the implementation is as follows:
step 61, using the penalty function method, selecting an appropriate penalty coefficient ρ, adding constraints C2 and C5 to the objective function of P2, thereby constructing an optimization problem P3:
P3：
Figure FDA0004255993780000052
s.t.C3，C4，
wherein dist (·) is used to calculate the distance of the variable to its feasible region Ω, defined as
Figure FDA0004255993780000053
Whereas omega k And xi are defined as:
Figure FDA0004255993780000054
Figure FDA0004255993780000055
when rho in the problem P3 is →++infinity, the optimal solution of P3 can be solved to obtain the optimal solution of P2, but at the moment, the computation of dist (&) is quite complex, so that the optimal solution is approximated by adopting a distance optimization method;
in the step 6, the solution problem P3 is converted into an iterative solution problem P4 by using a distance optimization method, and the following implementation is realized:
step 62, the ith iteration corresponds to solving the following optimization problem P4:
P4：
Figure FDA0004255993780000061
s.t.C3，C4，
in the method, in the process of the invention,
Figure FDA0004255993780000062
representing the solution mapping to the feasible domain xi at the ith y iteration, ++>
Figure FDA0004255993780000063
And->
Figure FDA0004255993780000064
Respectively represents r at the ith iteration k And->
Figure FDA0004255993780000065
Mapping to feasible region Ω k A subsequent solution;
in step 6, according to the strong dual, P4 is converted into its lagrangian dual problem P5, and its KKT condition is given, which is implemented as follows for step 63:
step 631, computing the lagrangian dual function of the problem P4, and merging the constraints C3, C4 into the objective function:
Figure FDA0004255993780000066
the method comprises the following steps:
Figure FDA0004255993780000071
λ k ，η，θ k is Lagrangian multiplier, τ, constrained to C3 in P3 k Is a Lagrangian multiplier corresponding to constraint C4 in P3;
step 632, according to the dual function of step 631, adding the total power constraint term at the same time, and establishing an optimization problem P5:
P5：
Figure FDA0004255993780000072
Figure FDA0004255993780000073
wherein constraint C6 represents the total power constraint;
step 633, based on the strong dual of P5, writing its KKT condition to solve:
Figure FDA0004255993780000074
Figure FDA0004255993780000075
Figure FDA0004255993780000081
Figure FDA0004255993780000082
Figure FDA0004255993780000083
Figure FDA0004255993780000084
wherein θ represents the multiplier of constraint C6, solved with KKT conditions;
step 7, obtaining a closed solution of the optimization problem according to the KKT condition of step 6, and further iteratively solving the problem P5 to obtain an optimal precoder W * The method comprises the steps of carrying out a first treatment on the surface of the Specific:
step 71, using closed-form solution iteration to solve problem P5 according to KKT condition of step 633 to obtain precoder optimization result in real number vector form
Figure FDA0004255993780000085
The low complexity solution to problem P2 is realized as follows:
step 711, initializing related parameters and variables;
initializing a convergence threshold and an iteration counter:
∈＝10 -4 ，i＝1，
initializing parameters:
ρ＝1，c＝2，ρ max ＝109，
Figure FDA0004255993780000086
step 712 performs an iteration and outputs
Figure FDA0004255993780000087
Step 712.1, updating z (i), r of the i-th iteration k (i)，f k (i) Y (i) is expressed as follows:
Figure FDA0004255993780000088
r k ＝g k，1 z(i)，
Figure FDA0004255993780000089
Figure FDA0004255993780000091
step 712.2, updating the iteration of step i
Figure FDA0004255993780000092
And->
Figure FDA0004255993780000093
The expression is as follows:
Figure FDA00042559937800000914
Figure FDA0004255993780000095
the method comprises the following steps:
Figure FDA0004255993780000096
step 712.3, using dichotomy to θ * Searching to obtain the constraint C6
Figure FDA0004255993780000097
And further by the following:
Figure FDA0004255993780000098
Figure FDA0004255993780000099
Figure FDA00042559937800000910
step 713, using the obtained in step 712.3
Figure FDA00042559937800000911
Update +.1 in step i->
Figure FDA00042559937800000912
Figure FDA00042559937800000913
Step 714, when the iteration number i reaches a certain threshold value, update ρ using:
ρ＝min(ρ max ，cρ)，
step 715, update the iteration counter:
i＝i+1，
step 716, stopping the iteration and letting the following conditions are satisfied
Figure FDA0004255993780000101
Output final +.>
Figure FDA0004255993780000102
Otherwise, returning to step 712, the loop performs:
Figure FDA0004255993780000103
step 72, combining the rules obtained in step 716 according to the rules in step 53
Figure FDA0004255993780000104
Restoring back->
Figure FDA0004255993780000105
It is then further restored back to W according to the rules in step 52 * Obtaining the final optimal precoder W * 。
2. The low-complexity integrated transmitting and pre-coding optimization method according to claim 1, wherein the transmitting and receiving antennas of the dual-function radar communication base station in the step 1 adopt the same group of uniform linear arrays; communication signal noise n k Obeys complex gaussian distribution
Figure FDA0004255993780000106
Wherein sigma c Is the standard deviation of communication noise; />
Figure FDA0004255993780000107
For radar reception noise, each matrix element thereof obeys a complex Gaussian distribution +.>
Figure FDA0004255993780000108
Wherein sigma r Is the perceived noise standard deviation; user data is irrelevant, i.e.)>
Figure FDA0004255993780000109
Wherein->
Figure FDA00042559937800001010
The information matrix is a user information matrix, and L is the information length; interference signal is present at the radar receiver>
Figure FDA00042559937800001011
The signal y received by the kth user k And the signal x received by the radar 0 The respective expressions are as follows:
Figure FDA00042559937800001012
x 0 ＝t H y 0 ＝t H A(v)Ws+t H c+t H z 0
wherein, the liquid crystal display device comprises a liquid crystal display device,
Figure FDA0004255993780000111
represents a precoding matrix, wherein->
Figure FDA0004255993780000112
Precoding vector representing the kth user in the precoding matrix,/or->
Figure FDA0004255993780000113
Linear receive filter representing a base station +.>
Figure FDA0004255993780000114
Representing the echo of the signal received by the base station,/->
Figure FDA0004255993780000115
Figure FDA0004255993780000116
Represents a radar channel space steering vector, where v= [ v ] 1 ，...，v k ，...，v M ]A set of departure angles representing all table-aware targets, wherein the kth element v k Representing the departure angle from the base station to the kth perception target, M is the perception target number.
3. A low complexity integrated transmit precoding optimization method as defined in claim 2, wherein,the channel h constructed by utilizing the Rayleigh channel model in the step 2 k Obeys complex gaussian distribution
Figure FDA0004255993780000117
The radar-aware channel model a (v) is expressed as follows:
Figure FDA0004255993780000118
covariance matrix R of interference signal c c The expression of (2) is as follows:
Figure FDA0004255993780000119
wherein a is r (v) A spatial steering vector representing a signal having an angle of arrival v t (v) A guide vector, alpha, representing a signal with a departure angle v k And v k The signal amplitude of the kth user and the angle of arrival of the direct signal to the base station are respectively beta i Sum phi i The amplitude of the ith interference signal and the angle of arrival of the interference signal to the base station, respectively, I represents the total number of interference sources.
4. A low complexity, integrated transmit precoding optimization method as claimed in claim 3, characterized by the fact that: calculating the SINR value of the kth user in the communication system model in the step 3
Figure FDA00042559937800001110
Radar perceived signal-to-interference-plus-noise ratio SINR value ω (t, W), radar receiving filter optimal solution t given precoder W * Radar-aware signal-to-interference-plus-noise ratio SINR value at optimal receive filter>
Figure FDA00042559937800001111
The formula is as follows:
Figure FDA0004255993780000121
Figure FDA0004255993780000122
Figure FDA0004255993780000123
Figure FDA0004255993780000124
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