CN113721198A - Physical layer security combined beam forming method for dual-function MIMO radar communication system - Google Patents

Physical layer security combined beam forming method for dual-function MIMO radar communication system Download PDF

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CN113721198A
CN113721198A CN202111055222.XA CN202111055222A CN113721198A CN 113721198 A CN113721198 A CN 113721198A CN 202111055222 A CN202111055222 A CN 202111055222A CN 113721198 A CN113721198 A CN 113721198A
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radar
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CN113721198B (en
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王伟
董福王
李欣
黄平
薛冰
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Harbin Engineering University
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    • 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
    • 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
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • 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
    • G01S7/28—Details of pulse systems
    • G01S7/282—Transmitters
    • 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
    • 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
    • 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
    • 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
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S2013/0236—Special technical features
    • G01S2013/029—Antistealth radar
    • 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

A dual-function MIMO radar communication system physical layer security united beam forming method relates to the technical field of radar communication, aiming at two design defects existing in the prior art, namely only AN AN covariance matrix is designed and a relaxation algorithm with poor performance is adopted to cause the problem of low system secrecy rate, the method firstly adds MIMO radar performance constraint, QoS (communication service quality constraint) and PLS (physical layer security constraint) in sequence by utilizing a cost function of a radar transmission beam pattern, constructs AN optimization problem by utilizing constraint of each antenna of the system and total power of the system, then utilizes SDR relaxation to realize the solution of the optimization problem, and proves that the optimized solution of the relaxation problem is also the optimal solution of the original problem. According to simulation analysis, under the condition that the multi-user communication safety problem of the dual-function radar and the communication system is considered, the radar performance of the original system can be better ensured and the system confidentiality rate is improved by using the SDRPLS algorithm and the ZFPLS algorithm.

Description

Physical layer security combined beam forming method for dual-function MIMO radar communication system
Technical Field
The invention relates to the technical field of radar communication, in particular to a physical layer security combined beam forming method of a dual-function MIMO radar communication system.
Background
The DFRC (dual function radar communication) technology has advantages in power consumption, physical hardware, spectrum utilization and the like, is a promising wireless communication scheme, and can support automatic driving, the internet of things and the like. The DFRC system transmits dual function signals from a single hardware platform for simultaneous target detection and communication, which can be used for joint sensing and signal manipulation through real-time collaboration. Generally, DFRC designs fall into two categories: information embedding and transmit beamforming. The former typically embeds the communication data into the radar waveform by means such as phase, frequency modulation, etc., but such methods suffer from a significant low information rate, which is on the order of the radar pulse repetition rate. Unlike information embedding, the main idea of transmit beamforming is to synthesize multiple beams for multiple communication users and targets using the associated spatial degrees of freedom.
The authors of the literature (MU-MIMO communications with MIMO radar: from co-existence to joint transmission, IEEE trans. wireless communication, vol.17, No.4, pp.2755-2770, apr.2018) consider the radar target to be the line-of-sight channel of the virtual downlink, and therefore design the beamforming matrix to closely match the required radar beam pattern while ensuring the SINR (signal to interference plus noise ratio) of the downstream communicating user. In addition, the design of a correlated waveform level detection Signal is researched in the literature (correlated waveform design for dual-functional MIMO radio-communication system, Signal process, vol.171, No.107530, pp.1-11, feb.2020), and similarity constraint and constant modulus constraint are applied to a radar waveform, so that multi-user interference energy is minimum. However, the above scheme implements target detection using only the communication waveform as the DFRC signal, resulting in a reduction in the degree of freedom in designing the radar signal, resulting in a reduction in radar performance. For this purpose, the document (Joint transmit beamforming for multiuser MIMO communications and MIMO radar, IEEE trans. signal process, vol.68, pp.3929-3944, jun.2020) proposes a Joint design scheme for communication signals and radar waveforms, in which a single communication waveform can be considered as a special case where the radar precoding is zero. Particularly, when downlink users are few, the combined precoding design scheme can effectively compensate the loss of the degree of freedom of radar waveform design, so that the target detection performance is improved.
Another key issue in DFRC systems is how to ensure privacy and security of information. The DFRC base station transmits the confidential information to be transmitted to the target in the process of transmitting the dual-function signal to detect the target. Clearly, serious information security issues are faced when the target is a potential eavesdropper. For this purpose, An AN (artificial noise) method is used in the document (QoS-based transmit beamforming in the presence of the eavesdropper: advanced noise addressed, IEEE trans. Signal Process, vol.59, No.3, pp.1202-1216, Mar.2011) to enhance physical layer security by applying AN to overwhelm eavesdropper channels. In particular, by carefully designing the transmitted signal with AN, the signal to interference and noise ratio of the signal received by AN eavesdropper can be reduced without affecting legitimate users. In recent years, the AN-aided concept has also been extended to DFRC security design and optimization problems such as secret rate maximization, target return SINR maximization and transmit power minimization have been proposed for DFRC systems for single targets and single communication receivers. In order to solve the non-convex problem of the secret expression, the literature (secret rate optimizations for MIMO communication-radar, IEEE trans. aerosp. electron. syst., vol.54, No.5, pp.2481-2492, oct.2018) proposes an approximation algorithm of first-order taylor difference expansion, which results in the performance of the solution of the original problem and the solution of the approximated problem. The literature (Performance radar in a unified system of communication and passive radar: a coherent capacity adaptive Digital Signal Processing, vol.82, pp.282-293,2018.) considers a unified combined passive radar and communication system that keeps the secret ratio above a given threshold while ensuring the maximum SINR for the passive radar receiver. In addition, the robust beamforming of the document (Secure radio-communication systems with multimedia targets: Integrating radio, communications and formatting functions, IEEE trans. wireless communication, vol.20, No.1, pp.83-95, jan.2021) also considers the practical problems of the reality of target direction estimation and the incompleteness of channel state, but both of the above algorithms have higher computational complexity. The existing DFRC system safety design method has two defects, one is to only design a covariance matrix of AN, and the influence on radar detection performance after AN is applied is not further analyzed; the other is that various relaxation algorithms such as taylor expansion or SDR (semi-positive relaxation) are often adopted without considering the performance loss of the problem after relaxation.
Disclosure of Invention
The purpose of the invention is: aiming at the two design defects in the prior art, namely the problem of low system secrecy rate caused by only designing AN AN covariance matrix and adopting a relaxation algorithm with poor performance, the method for forming the physical layer security combined beam of the dual-function MIMO radar communication system is provided.
The technical scheme adopted by the invention to solve the technical problems is as follows:
a physical layer security combined beam forming method of a dual-function MIMO radar communication system comprises the following steps:
the method comprises the following steps: firstly, establishing a transmitting and receiving signal model of a dual-function radar-communication system, and then establishing a corresponding MIMO radar target detection index, a multi-user communication service quality index and a physical layer safety transmission index according to the model;
step two: the method comprises the steps of detecting a target position by transmitting an omnidirectional beam through an MIMO radar, obtaining angle information theta of the target, obtaining an expected beam transmitting directional diagram by using the angle information theta of the target, uniformly sampling within an angle variation range of [ -90 degrees and 90 degrees ] at a resolution of 0.1 degree to obtain a set of space direction grids, constructing a predicted beam transmitting directional diagram with a signal covariance matrix as an unknown number according to the set of the space direction grids, and constructing a cross-correlation beam diagram with the signal covariance matrix as the unknown number;
step three: acquiring the mean square error of a predicted beam transmitting directional diagram and an expected beam transmitting directional diagram, then constructing an original optimization problem by taking the weighted sum of the obtained mean square error and a cross-correlation beam diagram as an objective function, carrying out maximum transmitting power constraint on a dual-function radar-communication system, carrying out constraint on multi-user communication service quality indexes and carrying out constraint on physical layer safety indexes, converting the original optimization problem into a convex-semi-definite optimization problem by using a semi-definite relaxation method, and finally solving the convex-semi-definite optimization problem by using a CVX tool bag to obtain the solution of the convex-semi-definite optimization problem;
step four: and constructing an optimal solution of the original optimization problem by using the solution of the convex semi-definite optimization problem, and obtaining a precoding matrix corresponding to the dual-function radar and the communication system according to the optimal solution of the original optimization problem.
Further, the dual-function radar and communication system transmitting and receiving signal model is represented as:
x[n]＝Wrs[n]+Wcc[n],n＝0,1,…，N-1
wherein, s [ n ]]＝[s1[n],…,sM[n]]T∈CM×1For individual radar signals, c [ n ]]＝[c1[n],…,cK[n]]TFor the communication data streams of K communication users,
Figure BDA0003254358180000031
and
Figure BDA0003254358180000032
respectively representing a radar beam forming matrix and a communication precoding matrix, wherein N is the number of symbols.
Further, the signal covariance matrix is expressed as:
Figure BDA0003254358180000033
wherein, E { xxHThe expectation of the transmitted signal is that,
Figure BDA0003254358180000034
and
Figure BDA0003254358180000035
respectively representing the conjugate of the radar beamforming matrix and the communication precoding matrix.
Further, the third step also includes constraining zero-forcing precoding,
and constructing an original optimization problem by performing maximum transmission power constraint on the dual-function radar and the communication system, performing constraint on multi-user communication service quality indexes, performing constraint on physical layer safety indexes and performing constraint on zero forcing precoding through a target function.
Further, the convex-concave optimization problem is expressed as:
Figure BDA0003254358180000036
subject to
Figure BDA0003254358180000037
[R][m,m]＝Pt/M,m＝1,2,…,M,
HRHH＝diag(ρ),
HRcomHH＝diag(ρ),
Figure BDA0003254358180000038
Figure BDA0003254358180000039
wherein ,Lr(R, α) is a weighted least squares cost function, R represents the covariance matrix of the entire signal, RcomA communication signal covariance matrix, a is a scaling factor, p is the signal power of the user,
Figure BDA0003254358180000041
represents an M-dimensional semi-positive definite matrix,
Figure BDA0003254358180000042
[R][m,m]for power constraints on each antenna, PtRepresenting the total transmitted power, pkFor the signal power of the kth user, H denotes a communication channel matrix, ΓcRepresenting a user received signal to interference plus noise ratio threshold,
Figure BDA0003254358180000043
representing the user noise power, ΓeSignal to interference plus noise ratio threshold, a, representing the signal received by an eavesdropper0The vector is directed at the target location and,
Figure BDA0003254358180000044
representing the power of the eavesdropper receiving noise, beta representing the complex path loss coefficient, K being the number of communication users,
Figure BDA0003254358180000045
representing an M x M dimensional complex matrix.
Further, the precoding matrix obtaining step is as follows:
optimal solution using convex optimization problem
Figure BDA0003254358180000046
And
Figure BDA0003254358180000047
recovering the precoding matrix from the optimal solution
Figure BDA0003254358180000048
And
Figure BDA0003254358180000049
the semi-positive property of (a) is decomposed by Cholesky into the following form:
Figure BDA00032543581800000410
wherein LcFor M × M lower triangular matrix, and then for HLcLine QR decomposition, expressed as:
HLc＝[Lh,0K×(M-K)]Q
wherein LhThe matrix is a triangular matrix under K multiplied by K, Q is an M multiplied by M unitary matrix, and the communication precoding matrix is expressed as:
Wc＝Lc[QH][:,1:K]
the radar precoding matrix may be represented as:
Figure BDA00032543581800000411
wherein ,[·][:,1:K]To take from 1 to K columns of the matrix,
Figure BDA00032543581800000412
a covariance matrix of the radar signal.
Further, the original optimization problem is expressed as:
Figure BDA0003254358180000051
subject to
Figure BDA0003254358180000052
Figure BDA0003254358180000053
rank(Rk)＝1,k＝1,…,K,
[R][m,m]＝Pt/M,m＝1,…,M,
Figure BDA0003254358180000054
Figure BDA0003254358180000055
wherein ,RKDenotes the kth covariance matrix, hkRepresenting the channel from the base station to the k-th user.
Further, the convex-concave optimization problem is expressed as:
Figure BDA0003254358180000056
subject to
Figure BDA0003254358180000057
Figure BDA0003254358180000058
[R][m,m]＝Pt/M,m＝1,…,M,
Figure BDA0003254358180000059
Figure BDA00032543581800000510
further, the precoding matrix is represented as:
Figure BDA00032543581800000511
Figure BDA00032543581800000512
wherein ,
Figure BDA00032543581800000513
for the purpose of a radar pre-coding matrix,
Figure BDA00032543581800000514
a covariance matrix representing the optimal overall signal,
Figure BDA00032543581800000515
represents the optimal solution of the overall convex-semi-definite optimization problem,
Figure BDA00032543581800000516
a precoding vector representing the k-th user,
Figure BDA00032543581800000517
represents the optimal solution of the kth convex-semi-definite optimization problem.
Further, the second step and the third step are replaced by:
step two: transmitting an omnidirectional beam through an MIMO radar to detect a target position, obtaining a rough angle interval [ theta-delta theta, theta + delta theta ], and obtaining a 3dB low side lobe beam transmitting directional diagram by utilizing the rough angle interval [ theta-delta theta, theta + delta theta ];
then sampling uniformly in the angle variation range of [ -90 degrees, 90 degrees ] with the resolution of 0.1 degree to obtain a set of space direction grids, constructing a predicted beam emission directional diagram with a signal covariance matrix as an unknown number according to the set of space direction grids, and constructing a cross-correlation beam diagram with the signal covariance matrix as the unknown number;
step three: obtaining the mean square error of the predicted beam emission directional diagram and the expected beam emission directional diagram, then taking the weighted sum of the obtained mean square error and the cross-correlation beam diagram as a target function, and carrying out maximum emission power constraint on the dual-function radar-communication system, constraint on the multi-user communication service quality index and the whole angle interval [ theta ] through the target function0-Δθ,θ0+Δθ]The original optimization problem is constructed by applying safety constraint in the interior, and the original optimization problem is converted into the original optimization problem by using a semi-positive definite relaxation methodChanging the convex-semi-definite optimization problem into a convex-semi-definite optimization problem, and finally solving the convex-semi-definite optimization problem by utilizing a CVX tool kit to obtain a solution of the convex-semi-definite optimization problem;
the 3dB low sidelobe beam emission pattern is obtained by solving the following problem:
Figure BDA0003254358180000061
subject to
Figure BDA0003254358180000062
Figure BDA0003254358180000063
Figure BDA0003254358180000064
Figure BDA0003254358180000065
wherein aiIs a (theta)i) Omega is a set of discrete angles that divides the side lobe region, theta1 and θ2For controlling the 3dB main lobe width, here taken as θ1＝θ0-Δθ，θ2＝θ0+ delta theta, delta is a small constant which plays a role in relaxing 3dB constraint and increasing the probability of obtaining a feasible solution of the optimization problem;
the convex half fixed optimization problem is expressed as:
Figure BDA0003254358180000066
subject to
Figure BDA0003254358180000067
Figure BDA0003254358180000068
[R][m,m]＝Pt/M,m＝1,…,M,
Figure BDA0003254358180000069
Figure BDA00032543581800000610
wherein
Figure BDA00032543581800000611
Is a discrete set of angles that encompasses all possible directions for an eavesdropper.
The invention has the beneficial effects that:
the application is based on the SDRPLS (semi-positive relaxed physical layer security) and ZFPLS (zero-forcing physical layer security) algorithms. The method comprises the steps of firstly, sequentially adding MIMO radar performance constraint, QoS (quality of service) constraint and PLS (physical layer security constraint) constraint to each antenna constraint of a system and total power constraint of the system by using a cost function of a radar transmission beam pattern, constructing an optimization problem, then, utilizing SDR relaxation to realize the solution of the optimization problem, and proving that the optimization solution of the relaxation problem is also the optimal solution of the original problem. Because the SDR has overhigh calculation complexity, ZF constraint is further added to the optimization problem, the optimization problem is solved by using a ZF algorithm, and the algorithm complexity is greatly reduced while the reasonable performance is ensured. According to simulation analysis, under the condition that the multi-user communication safety problem of the dual-function radar and the communication system is considered, the radar performance of the original system can be better ensured and the system confidentiality rate is improved by using the SDRPLS algorithm and the ZFPLS algorithm.
Drawings
FIG. 1 is a block diagram of a DFRC-based multi-probe target and multi-channel credit user system;
fig. 2 shows that the number K of users is 2 and the threshold value Γ of communication SINRc10dB, the eavesdropper SINR threshold is ΓeWhen the number of users is 0dB (all the users are legal users), based on Radar-Only, SDRPLS, ZFPLS, SDR and ZF algorithms, simulating the Radar transmission beam mode in the target direction with theta equal to 0 degrees;
FIG. 3 shows an eavesdropper SINR threshold of ΓeWhen the communication SINR is equal to 0dB, based on SDRPLS, ZFPLS, SDR and ZF algorithms, the MSE of the radar transmission beam mode follows the communication SINR threshold value gammacChanging a simulation comparison result;
FIG. 4 is a diagram of an eavesdropper SINR threshold of ΓeWhen the communication SINR is equal to 0dB, based on SDRPLS, ZFPLS, SDR and ZF algorithms, the system communication sum rate is along with the communication SINR threshold value gammacChanging a simulation comparison result;
FIG. 5 shows an eavesdropper SINR threshold of ΓeWhen the communication SINR is equal to 0dB, under the action of the number of different communication users, based on SDRPLS, ZFPLS, SDR and ZF algorithms, the system secret ratio is dependent on a communication SINR threshold value gammacChanging a simulation result;
FIG. 6 shows communication SINR threshold ΓcAt a certain time, based on SDRPLS, ZFPLS, SDR and ZF algorithms, the MSE of the radar transmission beam mode is gamma along with the SINR threshold of the eavesdroppereChanging a simulation result;
FIG. 7 shows communication SINR threshold ΓcWhen the number of communication users is different, the system communication sum rate is dependent on the SINR threshold gamma of the eavesdropper on the basis of SDRPLS, ZFPLS, SDR and ZF algorithmseChanging a simulation result;
FIG. 8 shows communication SINR threshold ΓcWhen the number of communication users is different, the system privacy rate is dependent on the SINR threshold gamma of the eavesdropper on the basis of SDRPLS, ZFPLS, SDR and ZF algorithmseChanging a simulation result;
FIG. 9 shows communication SINR threshold Γc10dB, eavesdropper SINR threshold ΓeWhen uncertainty exists in different target directions, comparing results of Radar transmission beam mode simulation based on Radar-Only, ZFPLS and SDRPLS algorithms when the uncertainty exists in the different target directions;
FIG. 10 is a diagram showing an eavesdropper SINR threshold value of Γe0dB, different uncertainty exists in the target angleIn the time of measurement, based on ZFPLS and SDRPLS algorithms, the MSE of the radar transmission beam mode is along with the threshold value gamma of communication SINRcAnd changing and simulating comparison results.
Detailed Description
It should be noted that, in the present invention, the embodiments disclosed in the present application may be combined with each other without conflict.
The first embodiment is as follows: specifically, referring to fig. 1, the method for jointly beamforming physical layer security of a dual-function MIMO radar communication system in the present embodiment is characterized by including the following steps:
step 1: establishing a model of a signal transmitted and received by the DFRC system and performance indexes;
the DFRC system transmits and receives signal models, establishes corresponding MIMO radar target detection indexes, and the multi-user communication QoS (quality of service) and PLS (physical layer security) transmission indexes are as follows:
(1) DFRC system transmit and receive signal model:
x[n]＝Wrs[n]+Wcc[n],n＝0,1,…，N-1
wherein ,
Figure BDA0003254358180000081
for individual radar signals, c [ n ]]＝[c1[n],…,cK[n]]TCommunication data streams for K communication users.
Figure BDA0003254358180000082
And
Figure BDA0003254358180000083
respectively representing a radar beamforming matrix and a communication precoding matrix. The radar signal and the communication signal are zero-mean, time domain white signal and generalized stationary random process, the radar waveform and the communication symbol are statistically independent,
Figure BDA0003254358180000084
m radar waveforms are mutually orthogonal
Figure BDA0003254358180000085
The transmission of the communication symbols to different users is not relevant,
Figure BDA0003254358180000086
the signal power is normalized to unity power, and therefore, the covariance matrix of the transmitted signal can be expressed as:
Figure BDA0003254358180000087
the receiving vector of the communication user is y ═ y1,y2,…,yK]，
y＝Hx+nc,
wherein
Figure BDA0003254358180000088
Is a channel matrix of which hkIndicating the channel from the base station to the communication user,
Figure BDA0003254358180000089
for additive white gaussian noise, assuming H is known, the signal received by the kth target is represented as:
rk＝βkaH(θk)x+ne
wherein ,βkIs the complex path loss coefficient, neIs an additive white gaussian noise, and is,
Figure BDA00032543581800000810
for covariance, a (θ) is the array steering vector for the ULA, which can be expressed as:
Figure BDA00032543581800000811
where d is the inter-antenna spacing, λ is the signal wavelength, and θ is the target angle obtained by different DoA (target direction of arrival) algorithms.
(2) MIMO radar target detection index
The composite radar beam pattern for the target angle θ direction can be expressed as:
Figure BDA0003254358180000091
target angle theta1 and θ2The cross-correlation radar beam pattern between can be expressed as:
Pc(θ1,θ2；R)＝aH(θ2)Ra(θ1)
the mean square error between the transmit beam pattern and the desired beam pattern can be expressed as:
Figure BDA0003254358180000092
where alpha is a scaling factor, phi (theta) represents the desired transmit beam pattern,
Figure BDA0003254358180000093
are fine grid points covering the object of interest. The cross-correlation root mean square beam, can be expressed as:
Figure BDA0003254358180000094
wherein ,
Figure BDA0003254358180000095
is a given target angle.
In the least squares sense, to account for the characteristics of the transmission pattern matching the desired pattern in each direction, the weighted least squares cost function can be expressed as:
Lr(R,α)＝Lb(R,α)+ηLc(R)
where η is a weighting factor that adjusts the importance of these two terms according to actual needs.
(3) Multi-user communication QoS (quality of service)
The achievable transmission rate related to the SINR of the downlink user received signal is a standard performance indicator of a multi-user communication system, and for convenience, W ═ W is expressedc,Wr], wherein wiFor the low i column of W, i ═ 1, …, K + M, the corresponding covariance matrix can be expressed as:
Figure BDA0003254358180000096
wherein
Figure BDA0003254358180000097
For a rank 1 matrix, i is 1, …, K + M for a traffic symbol, and i is K +1, …, K + M for a radar waveform, so the SINR of the kth communication user can be expressed as:
Figure BDA0003254358180000101
therefore, the communication reachable rate of the kth communication user is as follows:
Ck＝log2(1+γk).
the system throughput, system communication and rate are:
Figure BDA0003254358180000102
the minimum SINR maximization per communication user can be expressed as:
max min{γ1,…,γK}
(4) PLS (physical layer Security) Transmission metrics
The jth target received SINR may be expressed as:
Figure BDA0003254358180000103
the jth target achievable transmission rate may be expressed as:
Figure BDA0003254358180000104
the typical system worst-case privacy rate is defined as the difference in the achievable rate between the communicating user and the target, which can be expressed as
Figure BDA0003254358180000105
wherein [·]+Represents max {. 0 }.
Step 2: taking a maximized radar performance index as a target function, adding a transmitter maximum transmitting power constraint, and constructing an optimization problem by QoS (quality of service) and PLS (partial least squares) constraints, designing a combined PSL (particle swarm optimization) beam forming algorithm by utilizing an improved SDR (semi-positive definite relaxation) method, and respectively obtaining radar and communication pre-coding matrixes corresponding to the dual-function system by combining a matrix optimization theory;
step 2.1: by taking the maximum radar performance index as an objective function and adding the maximum transmitting power constraint of a transmitter, the QoS and PLS constraint structure optimization problem is as follows:
Figure BDA0003254358180000111
Figure BDA0003254358180000112
Figure BDA0003254358180000113
rank(Ri)＝1,i＝1,…,K+M,
[R][m,m]＝Pt/M,m＝1,…,M,
γk≥Γc,SINRE≤Γe,k＝1,…,K.
wherein
Figure BDA0003254358180000114
Represents an M-dimensional semi-positive definite matrix,
Figure BDA0003254358180000115
Figure BDA0003254358180000116
and rank (R)i) 1, i-1, …, K + M, where [ R ] is equivalent][m,m]＝PtM, where M is 1, …, where M denotes the power constraint on each antenna, γk≥ΓcIndicating communication QoS constraints, SINRE≤ΓeThe system imposes PLS performance constraints.
The QoS constraints and PLS constraints described above are developed and collated to yield:
Figure BDA0003254358180000117
Figure BDA0003254358180000118
it can be seen that
Figure BDA0003254358180000119
There are M + K +1 matrix unknowns and the QoS constraints and PLS constraints are only related to the K covariance matrices to be determined. Therefore, in order to reduce the memory space occupied in the problem solving process, the original problem can be expressed as:
Figure BDA00032543581800001110
Figure BDA00032543581800001111
Figure BDA00032543581800001112
rank(Rk)＝1,k＝1,…,K,
[R][m,m]＝Pt/M,m＝1,…,M,
Figure BDA00032543581800001113
Figure BDA00032543581800001114
step 2.2: design of combined PSL beam forming algorithm by SDR (semi-positive definite relaxation) method
Due to the rank 1 constraint, the above optimization problem is non-convex, so using SDR relaxation results in a new optimization problem, which can be expressed as:
Figure BDA0003254358180000121
subject to
Figure BDA0003254358180000122
Figure BDA0003254358180000123
[R][m,m]＝Pt/M,m＝1,…,M,
Figure BDA0003254358180000124
Figure BDA0003254358180000125
the objective function is a quadratic form that is positive and semi-definite and all constraints are linear or semi-definite, so the problem is that
Figure BDA0003254358180000126
Is a standard quadratic semi-definite programming (QSDP) problem and can therefore be solved using the CVX convex optimization toolkit.
Step 2.3: by utilizing a matrix optimization theory, the SDR relaxation is proved to be tight, and a global optimal solution can still be obtained after the relaxation is solved. The following is the utilization of the convex problem
Figure BDA0003254358180000127
Of (2) an optimal solution
Figure BDA0003254358180000128
And
Figure BDA0003254358180000129
the specific process of constructing the corresponding communication precoding matrix and the radar precoding matrix and the proving process of SDR tightness. When the PLS constraints are not taken into account,
Figure BDA00032543581800001210
an optimized solution to the problem P2,
Figure BDA00032543581800001211
is a globally optimal solution to the problem P1, from which can be derived:
Figure BDA00032543581800001212
and (3) deducing: when in use
Figure BDA00032543581800001213
The problem is an optimized solution to P2,
Figure BDA00032543581800001214
also a globally optimal solution to the problem P1, will be for any angle θ
Figure BDA00032543581800001215
Is brought into the above formula because
Figure BDA00032543581800001216
So the right end of this expression can be expressed as:
Figure BDA00032543581800001217
according to the Cauchy-Schwarz inequality:
Figure BDA00032543581800001218
further, the method can be obtained as follows:
Figure BDA00032543581800001219
wherein (a)
Figure BDA0003254358180000131
Equality and sum (b) satisfy the inequality
Figure BDA0003254358180000132
Thus after adding PLS constraints
Figure BDA0003254358180000133
It is still a global optimal solution, and the result is tight after SDR relaxation.
And step 3: taking a maximized radar performance index as a target function, adding the maximum transmitting power constraint, QoS constraint, PLS constraint and ZF constraint of a transmitter to construct an optimization problem, designing a low-complexity combined PSL beam forming algorithm by using an improved ZF (zero forcing precoding) method, and obtaining a radar and communication precoding matrix corresponding to the dual-function system by using a matrix decomposition theory;
step 3.1: adding a communication QoS constraint, a system PLS constraint and a ZF constraint by taking the least square weighted sum of the mean square error between the relevant angle beam pattern and the expected beam pattern and the mean square error of the cross-correlation angle beam pattern as an objective function, and optimizing the problem construction
The ZF constraint can be expressed as:
Figure BDA0003254358180000134
wherein ρkFor the signal power on the kth user, K is more than or equal to 1 and less than or equal to K, and W is [ W ]c,Wr]，R＝WWHAnd thus can be further expressed as:
HRHH＝diag(ρ)
wherein ρ＝[ρ1,…,ρK]，
Figure BDA00032543581800001312
K is more than or equal to 1 and less than or equal to K, and an auxiliary matrix variable is introduced
Figure BDA0003254358180000135
Figure BDA0003254358180000136
Figure BDA0003254358180000137
The optimization problem can be expressed as:
Figure BDA0003254358180000138
Figure BDA0003254358180000139
[R][m,m]＝Pt/M,m＝1,2,…,M,
HRHH＝diag(ρ),
HRcomHH＝diag(ρ),
Figure BDA00032543581800001310
Figure BDA00032543581800001311
the objective function of the optimization problem is a semi-orthodefinite quadratic form, all constraint conditions are either linear or semi-definite, and the optimal optimization tool box is used for obtaining the optimal constraint conditions in polynomial time
Figure BDA0003254358180000141
And
Figure BDA0003254358180000142
step 3.2: optimization of utilization
Figure BDA0003254358180000143
And
Figure BDA0003254358180000144
recovering the pre-coding matrix, and obtaining the pre-coding matrix corresponding to the dual-function system by using Cholesky decomposition or square root method according to the semi-positive definite characteristic of the matrix, wherein the matrix decomposition is expressed as:
Figure BDA0003254358180000145
for HLcLine QR decomposition, expressed as:
HLc＝[Lh,0K×(M-K)]Q
wherein LhIs a triangular matrix under K multiplied by K, and Q is an M multiplied by M unitary matrix, so the communication precoding matrix considering the case of PLS is expressed as:
Wc＝Lc[QH][:,1:K]
the radar precoding matrix may be represented as:
Figure BDA0003254358180000146
when the MIMO radar carries out target detection, an accurate target angle theta cannot be obtained, but a rough angle interval [ theta ] is obtained0-Δθ,θ0+Δθ]It is now necessary to broaden the main lobe of the radar beam emission pattern to avoid target loss. The difference here from the previous precoding design approach is that the desired beam transmit pattern is replaced by a 3dB low sidelobe beam transmit pattern and over the entire angular interval theta0-Δθ,θ0+Δθ]Security constraints are imposed.
The method comprises the following specific steps:
widening the main lobe width by using a 3dB low sidelobe beam emission directional diagram, and inhibiting sidelobes, wherein the optimization problem can be expressed as:
Figure BDA0003254358180000147
subject to
Figure BDA0003254358180000148
Figure BDA0003254358180000149
Figure BDA00032543581800001410
Figure BDA00032543581800001411
wherein aiIs a (theta)i) Omega is a set of discrete angles that divides the side lobe region. Theta1 and θ2For controlling the 3dB main lobe width, here taken as θ1＝θ0-Δθ，θ2＝θ0+ Δ θ. Delta is a small constantThe 3dB constraint is relaxed to increase the effect of obtaining feasible solution probability of the optimization problem.
On the other hand, since the target is an eavesdropper, the eavesdropper may exist at any position in the angle interval, which requires that the security rate of each possible angle be guaranteed. Therefore, the privacy ratio constraint imposed in this case should be rewritten as:
Figure BDA0003254358180000151
wherein
Figure BDA0003254358180000152
Is a discrete set of angles that encompasses all possible directions for an eavesdropper.
Therefore, a joint beam forming design algorithm based on the physical layer security of the dual-function MIMO radar communication system is provided, a plurality of legal users are served, and the potential eavesdropper target can be detected. And jointly designing a radar and communication transmission precoding matrix, and ensuring the QoS (quality of service downlink) and PLS (physical layer security) levels while a desired radar beam pattern is closely matched. Modeling a combined radar and communication precoding design into a non-convex optimization problem, and taking a radar beam directional diagram, a communication user reachable rate and a privacy rate under the worst condition into consideration, providing a physical layer security design algorithm (SDRPLS) based on a semi-definite relaxation algorithm to obtain an optimal precoding matrix of radar and communication, and proving that SDR relaxation is tight. In addition, a low-complexity algorithm based on a zero forcing precoding method (ZFPLS) is provided, and a radar and communication precoding matrix is obtained through a construction algorithm after a solution of a low-complexity convex optimization problem is obtained by introducing an auxiliary matrix and ZF constraints.
The simulation experiment adopts (ULA) uniform linear array, the number of antennas M is 10, and the total transmission power PtThe set of grids with respect to the spatial direction is all 0.1 ° in resolution by uniform sampling, and the angular variation range [ -90 °,90 °]. Multiple user communication channels subject to Rayleigh fading, each H subject to a standard Gaussian distribution
Figure BDA0003254358180000153
The noise level of the eavesdropper is consistent with that of the downlink user
Figure BDA0003254358180000154
The individual radar waveform and communication symbols are generated as a random quadrature phase shift keying modulation sequence, and the total number of symbols N is 1024.
As can be seen from fig. 2, SDR (semi-positive definite relaxation) and ZF (zero forcing) represent relevant algorithms that form a beam pattern that fits well with the desired radar beam pattern, regardless of physical layer security. The SDRPLS and ZFPLS algorithms proposed herein form a transmit beam pattern that is substantially consistent with the desired radar beam pattern, while improving system privacy.
As can be seen from fig. 3, as the SINR of the communication user increases, the beam pattern MSE of all algorithms increases, when the number of users is 2 or 4, and especially when the SINR threshold of communication is small, the ZF algorithm and the proposed ZFPLS have substantially the same effect, and using ZF to remove interference can obtain a higher level of SINR, and the performance of the ZF-based method changes only when the SINR threshold is greater than the potential SINR value obtained by the ZF constraint. When the security secret ratio design of the physical layer is not considered, the SDR and ZF algorithms can realize better beam patterns, and the more the number of communication users is, the larger the mean square error between a transmission design beam pattern and an expected pattern is, namely the worse the radar performance is. Meanwhile, the influence of the change of the number of users on the mean square error of a radar beam pattern is larger than the change of a communication threshold, so that the radar performance is limited by serving more downlink users and improving the SINR level of the users.
As can be seen from fig. 4, the increasing trend is consistent with communication user threshold changes based on SDR and SDRPLS, since the optimal solution should reach the SINR boundary associated with a given threshold. And the wave beam forming based on ZF is at the cost of sacrificing the radar performance, so that higher communication reaching rate is realized. At high snr threshold, ZFPLS and SDRPLS algorithms tend to agree, where ZFPLS no longer suffers performance loss, as its advantage of low complexity is more pronounced.
As can be seen from fig. 5, no matter the number of users is 2 or 4, as the SINR of communication increases, the SDRPLS algorithm curve increases linearly, and no matter how other parameters change, the system secrecy rate reaches an extreme value as long as a feasible solution to the optimization problem exists, and the proposed PLS beamforming design can satisfy the security design level by selecting an appropriate threshold, and particularly when the number of users is large, the SDR and ZF algorithms cannot provide information protection.
As can be seen from fig. 6, the SDRPLS and ZFPLS algorithms cause the radar beam pattern MSE to decrease as the eavesdropper SINR increases, with a smooth curve when the eavesdropper SINR threshold is less than-12 dB, but with a sharp decrease in system performance when the eavesdropper SINR threshold is greater than-10 dB, illustrating the effect of the eavesdropper SINR threshold on system performance.
As can be seen from fig. 7, when the communication SINR threshold is constant, the system sum rate of the SDRPLS algorithm remains constant and approaches the optimal solution, and conversely, as the eavesdropper SINR threshold increases, the system sum rate of the ZFPLS algorithm increases, thereby indicating that as the eavesdropper SINR threshold increases, the ZFPLS beamforming design is less limited.
As can be seen from fig. 8, the privacy rate curve of the proposed algorithm is associated with the function g (x) -b-log when the SINR threshold of the communication user is 10dB2The curves of (1+ x) are identical. When K ═ 2, the privacy rate of the proposed ZFPLS algorithm is higher than other methods.
As can be seen from fig. 9, under the action of different algorithms, the synthesized radar beam pattern can detect and track a target with 3 directions and an uncertainty of 5 °, and can serve 3 legitimate users at the same time, and the SINR level of the ZFPLS algorithm is lower than that of the SDRPSL algorithm, which indicates that the performance of the ZFPLS algorithm is worse than that of the SDRPLS algorithm.
As can be seen from fig. 10, it is seen in the simulation result that adding uncertainty to the target direction when the SINR threshold of the user varies from 10dB to 18dB results in a loss of radar performance, and also causes a greater computational burden when the angle uncertainty is larger.
It should be noted that the detailed description is only for explaining and explaining the technical solution of the present invention, and the scope of protection of the claims is not limited thereby. It is intended that all such modifications and variations be included within the scope of the invention as defined in the following claims and the description.

Claims (10)

1. A physical layer security combined beam forming method of a dual-function MIMO radar communication system is characterized by comprising the following steps:
the method comprises the following steps: firstly, establishing a transmitting and receiving signal model of a dual-function radar-communication system, and then establishing a corresponding MIMO radar target detection index, a multi-user communication service quality index and a physical layer safety transmission index according to the model;
step two: the method comprises the steps of detecting a target position by transmitting an omnidirectional beam through an MIMO radar, obtaining angle information theta of the target, obtaining an expected beam transmitting directional diagram by using the angle information theta of the target, uniformly sampling within an angle variation range of [ -90 degrees and 90 degrees ] at a resolution of 0.1 degree to obtain a set of space direction grids, constructing a predicted beam transmitting directional diagram with a signal covariance matrix as an unknown number according to the set of the space direction grids, and constructing a cross-correlation beam diagram with the signal covariance matrix as the unknown number;
step three: acquiring the mean square error of a predicted beam transmitting directional diagram and an expected beam transmitting directional diagram, then constructing an original optimization problem by taking the weighted sum of the obtained mean square error and a cross-correlation beam diagram as an objective function, carrying out maximum transmitting power constraint on a dual-function radar-communication system, carrying out constraint on multi-user communication service quality indexes and carrying out constraint on physical layer safety indexes, converting the original optimization problem into a convex-semi-definite optimization problem by using a semi-definite relaxation method, and finally solving the convex-semi-definite optimization problem by using a CVX tool bag to obtain the solution of the convex-semi-definite optimization problem;
step four: and constructing an optimal solution of the original optimization problem by using the solution of the convex semi-definite optimization problem, and obtaining a precoding matrix corresponding to the dual-function radar and the communication system according to the optimal solution of the original optimization problem.
2. The method of claim 1, wherein the dual-function radar and communication system transmit and receive signal model is expressed as:
x[n]＝Wrs[n]+Wcc[n],n＝0,1,…，N-1
wherein, s [ n ]]＝[s1[n],…,sM[n]]T∈CM×1For individual radar signals, c [ n ]]＝[c1[n],…,cK[n]]TFor the communication data streams of K communication users,
Figure FDA0003254358170000011
and
Figure FDA0003254358170000012
respectively representing a radar beam forming matrix and a communication precoding matrix, wherein N is the number of symbols.
3. The method of claim 2, wherein the signal covariance matrix is expressed as:
Figure FDA0003254358170000013
wherein, E { xxHThe expectation of the transmitted signal is that,
Figure FDA0003254358170000014
and
Figure FDA0003254358170000015
respectively representing the conjugate of the radar beamforming matrix and the communication precoding matrix.
4. The method of claim 1, wherein the step three further comprises constraining zero-forcing precoding,
and constructing an original optimization problem by performing maximum transmission power constraint on the dual-function radar and the communication system, performing constraint on multi-user communication service quality indexes, performing constraint on physical layer safety indexes and performing constraint on zero forcing precoding through a target function.
5. The method of claim 4, wherein the convex semi-stationary optimization problem is expressed as:
Figure FDA0003254358170000021
subject to
Figure FDA0003254358170000022
[R][m,m]＝Pt/M,m＝1,2,…,M,
HRHH＝diag(ρ),
HRcomHH＝diag(ρ),
Figure FDA0003254358170000023
Figure FDA0003254358170000024
wherein ,Lr(R, α) is a weighted least squares cost function, R represents the covariance matrix of the entire signal, RcomA communication signal covariance matrix, a is a scaling factor, p is the signal power of the user,
Figure FDA0003254358170000025
represents an M-dimensional semi-positive definite matrix,
Figure FDA0003254358170000026
[R][m,m]for power constraints on each antenna, PtRepresenting the total transmitted power, pkFor the signal power of the kth user, H denotes a communication channel matrix, ΓcRepresenting a user received signal to interference plus noise ratio threshold,
Figure FDA0003254358170000027
representing the user noise power, ΓeSignal to interference plus noise ratio threshold, a, representing the signal received by an eavesdropper0The vector is directed at the target location and,
Figure FDA0003254358170000028
representing the power of the eavesdropper receiving noise, beta representing the complex path loss coefficient, K being the number of communication users,
Figure FDA0003254358170000029
representing an M x M dimensional complex matrix.
6. The method of claim 5, wherein the pre-coding matrix obtaining step comprises:
optimal solution using convex optimization problem
Figure FDA00032543581700000210
And
Figure FDA00032543581700000211
recovering the precoding matrix from the optimal solution
Figure FDA00032543581700000212
And
Figure FDA00032543581700000213
the semi-positive property of (a) is decomposed by Cholesky into the following form:
Figure FDA00032543581700000214
wherein LcFor M × M lower triangular matrix, and then for HLcLine QR decomposition, expressed as:
HLc＝[Lh,0K×(M-K)]Q
wherein LhThe matrix is a triangular matrix under K multiplied by K, Q is an M multiplied by M unitary matrix, and the communication precoding matrix is expressed as:
Wc＝Lc[QH][:,1:K]
the radar precoding matrix may be represented as:
Figure FDA0003254358170000031
wherein ,[·][:,1:K]To take from 1 to K columns of the matrix,
Figure FDA0003254358170000032
a covariance matrix of the radar signal.
7. The method of claim 1, wherein the original optimization problem is expressed as:
Figure FDA0003254358170000033
subject to
Figure FDA0003254358170000034
Figure FDA0003254358170000035
rank(Rk)＝1,k＝1,…,K,
[R][m,m]＝Pt/M,m＝1,…,M,
Figure FDA0003254358170000036
Figure FDA0003254358170000037
wherein ,RKDenotes the kth covariance matrix, hkRepresenting the channel from the base station to the k-th user.
8. The method of claim 7, wherein the convex semi-stationary optimization problem is expressed as:
Figure FDA0003254358170000038
subject to
Figure FDA0003254358170000039
Figure FDA00032543581700000310
[R][m,m]＝Pt/M,m＝1,…,M,
Figure FDA00032543581700000311
Figure FDA00032543581700000312
9. the method of claim 8, wherein the precoding matrix is expressed as:
Figure FDA0003254358170000041
Figure FDA0003254358170000042
wherein ,
Figure FDA0003254358170000043
for the purpose of a radar pre-coding matrix,
Figure FDA0003254358170000044
a covariance matrix representing the optimal overall signal,
Figure FDA0003254358170000045
represents the optimal solution of the overall convex-semi-definite optimization problem,
Figure FDA0003254358170000046
a precoding vector representing the k-th user,
Figure FDA0003254358170000047
represents the optimal solution of the kth convex-semi-definite optimization problem.
10. The method of claim 1, wherein the second and third steps are replaced with:
step two: transmitting an omnidirectional beam through an MIMO radar to detect a target position, obtaining a rough angle interval [ theta-delta theta, theta + delta theta ], and obtaining a 3dB low side lobe beam transmitting directional diagram by utilizing the rough angle interval [ theta-delta theta, theta + delta theta ];
then sampling uniformly in the angle variation range of [ -90 degrees, 90 degrees ] with the resolution of 0.1 degree to obtain a set of space direction grids, constructing a predicted beam emission directional diagram with a signal covariance matrix as an unknown number according to the set of space direction grids, and constructing a cross-correlation beam diagram with the signal covariance matrix as the unknown number;
step three: obtaining the mean square error of the predicted beam emission directional diagram and the expected beam emission directional diagram, then taking the weighted sum of the obtained mean square error and the cross-correlation beam diagram as a target function, and carrying out maximum emission power constraint on the dual-function radar-communication system, constraint on the multi-user communication service quality index and the whole angle interval [ theta ] through the target function0-Δθ,θ0+Δθ]Applying safety constraint to construct an original optimization problem, converting the original optimization problem into a convex-semi-definite optimization problem by using a semi-definite relaxation method, and finally solving the convex-semi-definite optimization problem by using a CVX tool kit to obtain a solution of the convex-semi-definite optimization problem;
the 3dB low sidelobe beam emission pattern is obtained by solving the following problem:
Figure FDA0003254358170000048
subject to
Figure FDA0003254358170000049
Figure FDA00032543581700000410
Figure FDA00032543581700000411
Figure FDA00032543581700000412
wherein aiIs a (theta)i) Omega is a set of discrete angles that divides the side lobe region, theta1 and θ2For controlling the 3dB main lobe width, here taken as θ1＝θ0-Δθ，θ2＝θ0+ delta theta, delta is a small constant which plays a role in relaxing 3dB constraint and increasing the probability of obtaining a feasible solution of the optimization problem;
the convex half fixed optimization problem is expressed as:
Figure FDA0003254358170000051
subject to
Figure FDA0003254358170000052
Figure FDA0003254358170000053
[R][m,m]＝Pt/M,m＝1,…,M,
Figure FDA0003254358170000054
Figure FDA0003254358170000055
wherein
Figure FDA0003254358170000056
Is aA discrete set of angles that contains all possible directions for an eavesdropper.
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