Energy-saving and safety perception optimization method based on ISAC-IRS

Abstract

The invention discloses an energy-saving and safety perception optimization method based on ISAC-IRS, which comprises the following steps of: taking the condition of perception information leakage caused by a perception eavesdropper in an environment into consideration, and optimizing a correlation matrix of a beam forming matrix related to each communication user, a covariance matrix of a special radar signal and a phase shift matrix of the IRS; the transmitting power of the base station is minimized, the energy-saving effect is achieved, meanwhile, the sufficient communication rate is guaranteed, the detection probability of a sensing receiver on a radar target is as high as possible, and the detection probability of a sensing eavesdropper on the target is as low as possible; coupling exists among variables in optimization, so that the optimization problem is non-convexity, the original problem is solved by adopting a positive semi-definite formation, alternate optimization and iterative rank minimization method, and a local optimal solution is obtained through alternate optimization iteration; the method has the advantages that the security of the system is improved by considering the protection mechanism of the sensing information, the transmitting power of the base station is minimized and optimized, and resources are consumed as little as possible while the sensing data are protected.

Description

Technical Field

[0001] The present invention relates to communication perception integration (ISAC) and intelligent reflecting surface (IRS) technology, and in particular to an energy-saving and security perception optimization method based on ISAC-IRS (communication perception integration combined with intelligent reflecting surface), which takes into account the existence of perceptual eavesdroppers in the environment and aims to minimize the transmission power of the base station while meeting the constraints of communication rate, perception performance and perception security. Background Art

[0002] The rapid development of integrated communication and perception (ISAC) technology has laid the foundation for the sixth generation of wireless networks. Its core lies in achieving efficient resource utilization by coordinating communication and perception functions. In recent years, with the advancement of multi-antenna technology, ISAC has made remarkable achievements in improving communication rate and perception accuracy. The use of multi-antenna technology in ISAC not only enhances multiplexing and diversity gain, but also improves the resolution and target recognition capability of radar. However, the competitive relationship between communication and perception functions under limited resources has prompted researchers to explore joint beam design to achieve optimal coordination between the two, thereby improving the overall system performance.

[0003] At the same time, intelligent reflecting surface (IRS) as an emerging key technology is receiving more and more attention. IRS can provide a low-cost, high-efficiency solution to support large-scale connections and ultra-reliable transmission by optimizing wireless channels. Combining IRS with ISAC can further enhance the flexibility and performance of the system. The application of IRS can create multiple line-of-sight links, combined with multi-antenna configurations, to provide additional spatial degrees of freedom for communication and perception, thereby achieving more accurate target detection and data transmission. This combination is driving the in-depth development of ISAC research and has attracted widespread attention from academia and industry.

[0004] With the development of ISAC technology, the deep integration of communication and perception functions has improved the overall performance of the system, but also brought new security challenges, especially when there are perception eavesdroppers in the system. Perception eavesdroppers can silently obtain perception data by listening to the perception signals transmitted by the base station, and then infer the working status of the system, which may pose a security threat to the communication or perception process. This type of passive eavesdropping behavior not only increases the risk of information leakage in the system, but also puts higher requirements on the energy efficiency of the system.

[0005] In order to deal with this problem, the ISAC system design needs to take into account the security of communication and perception while achieving energy saving goals. By rationally designing the base station's transmit beam, it is possible to reduce power consumption and improve the system's energy efficiency while ensuring the system's perception and communication performance. Especially in the presence of a perceptual eavesdropper, minimizing the base station's transmit power can not only reduce the risk of the perception signal being eavesdropped, but also effectively save energy. Current research shows that optimizing the base station's transmit beam against the threat of perceptual eavesdroppers is an important means to achieve energy saving and security in the ISAC system. Therefore, in the ISAC system, how to optimize the base station's transmit beam to achieve energy saving while ensuring the reliability of perception and communication has become a technical problem that needs to be solved urgently in this field. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide an energy-saving and security perception optimization method based on ISAC-IRS, which takes into account the presence of perceived eavesdroppers in the environment and can minimize the transmission power of the base station to achieve energy-saving effects while satisfying the constraints of perceived security, communication rate and perceived performance.

[0007] The technical solution adopted by the present invention to solve the above technical problems is: an energy saving and security perception optimization method based on ISAC-IRS, characterized by comprising the following steps:

[0008] Step 1: Establish an ISAC-IRS system considering a perceptual eavesdropper, wherein the ISAC-IRS system is provided with multiple communication users, a radar target, a base station for providing services to the communication users and perceiving the radar target, an IRS for assisting the base station in working, a perceptual receiver for performing target detection on the radar target according to its received signal, and a perceptual eavesdropper attempting to monitor the transmission signal of the base station to silently obtain the perceptual information, wherein the transmission signal of the base station is composed of the superposition of multiple communication signals and a dedicated radar signal;

[0009] Step 2: Establish the communication performance index, radar perception performance index, and perception eavesdropping performance index of the ISAC-IRS system. The communication performance index is measured by the received signal-to-interference-noise ratio of each communication user, the radar perception performance index is measured by the detection probability of the perception receiver to the radar target, and the perception eavesdropping performance index is measured by the detection probability of the perception eavesdropper to the target.

[0010] Step 3: To achieve the purpose of energy saving, on the basis of ensuring reliable communication, perception and perception security, the base station's transmit power is minimized. Taking the received signal-to-interference-noise ratio of each communication user, the detection probability of the perception receiver to the radar target, and the detection probability of the perception eavesdropper to the target as constraints, the beamforming matrix related to each communication user, the covariance matrix of the dedicated radar signal and the correlation matrix of the phase shift matrix of the IRS are jointly optimized to construct an optimization problem, where the beamforming matrix related to each communication user is composed of the beam vector designed by the base station for the communication user;

[0011] Step 4: By rewriting the detection probability constraint of the sensing receiver to the radar target in the optimization problem into a form in which the detection probability is only related to the covariance matrix of the base station's transmission signal, rewriting the detection probability constraint of the sensing eavesdropper to the target in the optimization problem into a linear form, and ignoring the rank-one constraint of the correlation matrix of the IRS phase shift matrix and the rank-one constraint of the received signal-to-interference-noise ratio of each communication user, the optimization problem is converted into a semi-positive definite relaxation problem;

[0012] Step 5: Decompose the semi-definite relaxation problem into two sub-problems. The first sub-problem is about the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal. Given the correlation matrix of the phase shift matrix of the IRS, the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal are optimized. At this time, the first sub-problem is a convex problem. The second sub-problem is about the correlation matrix of the phase shift matrix of the IRS. Given the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal, the correlation matrix of the phase shift matrix of the IRS is optimized. At this time, the second sub-problem is a convex problem.

[0013] Step 6: Use the alternating optimization algorithm to iteratively solve the first and second subproblems to obtain the local optimal solutions of the correlation matrices of the beamforming matrix related to each communication user, the covariance matrix of the dedicated radar signal, and the phase shift matrix of the IRS.

[0014] In step 1, the number of communication users is N, each of which is equipped with a single antenna; the radar target is equipped with a single antenna; the base station, the sensing receiver, the IRS, and the sensing eavesdropper are all equipped with uniform linear arrays, and the number of their antennas is T, T, and T respectively. IRS and T e , where N≤T.

[0015] In step 2, the process of obtaining the received signal to interference and noise ratio of the nth communication user is as follows:

[0016] Step 2.a1: Transform the received signal y of the nth communication user into n (t) is expressed as Where n = 1, 2, ..., N, t is the time variable, g B,n represents the channel from the base station to the nth communication user, g r,n represents the channel from IRS to the nth communication user, G Br represents the channel from the base station to the IRS, the superscript "H" represents the conjugate transposition operation, s(t) represents the transmission signal of the base station, r n represents the beam vector designed by the base station for the nth communication user, x n (t) represents the communication signal transmitted by the base station to the nth communication user, r r (t) represents the dedicated radar signal transmitted by the base station to the radar target, represents the phase shift matrix of IRS, diag(·) represents the diagonal elements used to extract or construct the matrix, v represents the phase shift vector of IRS, e is a natural constant, j is an imaginary part, represents the phase shift of the lth antenna of IRS, l=1,2,y…,T IRS , z n (t) represents the Gaussian white noise at the nth communication user, which has an expected value of 0 and a variance of The complex Gaussian distribution of

[0017] Step 2.a2: According to y n (t), obtain the received signal-to-interference-and-noise ratio SINR of the nth communication user c,n , Among them, tr(·) means to find the trace of the matrix, Represents the phase shift matrix of IRS The correlation matrix of R n Indicated by r n The beamforming matrix associated with the nth communication user is constructed. represents the channel matrix composed of the direct channel from the base station to the nth communication user and the cascade channel from the base station to the IRS and then to the nth communication user,

[0018] In step 2, the process of acquiring the detection probability of the radar target by the perception receiver is as follows:

[0019] Step 2.b1: Transform the received signal y of the sensing receiver into R (t) is expressed as Where α is the complex reflection coefficient related to the cross-sectional area of ​​the radar target, represents the channel from the radar target to the perception receiver, represents the channel from the base station to the radar target, represents the channel from IRS to radar target, z R (t) represents the Gaussian white noise at the sensor receiver, which has a mean of 0 and a variance of The complex Gaussian distribution of , I represents the unit matrix;

[0020] Step 2.b2: According to y R (t), obtain the detection probability P of the radar target by the perception receiver R , Among them, Q() represents the right tail distribution function of Gaussian distribution, P FA represents a given constant false alarm probability, “|·|” is a modulo operator, S represents the channel matrix consisting of the direct channel from the base station to the radar target and the cascade channel from the base station to the IRS and then to the radar target, R represents the covariance matrix of the base station's transmitted signal s(t), represents the mathematical expectation, R r Denotes a dedicated radar signal r r The covariance matrix of (t),

[0021] In step 2, the process of acquiring the detection probability of the target by the perceived eavesdropper is as follows:

[0022] Step 2.c1: The received signal y of the perceived eavesdropper e (t) is expressed as

[0023]

[0024] ,in, represents the angle of the radar target relative to the sensing eavesdropper, Indicates the position of the perceived eavesdropper relative to The steering vector, α e represents the complex reflection coefficient related to the cross-sectional area of ​​the sensing eavesdropper, represents the channel from the radar target to the sensing eavesdropper, G Be represents the channel from the base station to the eavesdropper, G re represents the channel from IRS to the perceptual eavesdropper, z e (t) represents the Gaussian white noise at the perceived eavesdropper, which has a mean of 0 and a variance of The complex Gaussian distribution of

[0025] Step 2.c2: According to y e (t), obtain the detection probability P of the target by the perceptual eavesdropper e , in, B 1represents the channel matrix composed of the direct channel from the base station to the perceptual eavesdropper, the cascade channel from the base station to the IRS to the radar target and then to the perceptual eavesdropper, the cascade channel from the base station to the IRS and then to the perceptual eavesdropper, and the cascade channel from the base station to the radar target and then to the perceptual eavesdropper, assuming that the radar target exists. B 0 represents the channel matrix consisting of the direct channel from the base station to the perceptual eavesdropper and the cascade channel from the base station to the IRS and then to the perceptual eavesdropper when the radar target does not exist.

[0026] In step 3, the optimization problem is described as:

[0027]

[0028]

[0029] C2:P R ≥Γ R ,

[0030] C3:P e ≤Γ e ,

[0031]

[0032]

[0033] C6:R r ≥0,

[0034]

[0035] Where tr(R) represents the transmission power of the base station, ξ c represents the receiving signal-to-interference-noise ratio threshold of the communication user, Γ R represents the detection probability threshold of the sensing receiver, Γ e represents the detection probability threshold of the perceived eavesdropper, express The l'th row and l'th column element in , rank(·) means to find the rank of the matrix.

[0036] The specific process of step 4 is as follows:

[0037] Step 4.1: Rewrite constraint C2 in the optimization problem as constraint C2':

[0038]

[0039] Step 4.2: Rewrite constraint C3 in the optimization problem as constraint C3': Among them, Λ eThe equation f(x) = Γ e The root of time,

[0040] Step 4.3: Using the semi-positive definite programming method, ignore the constraint C7 in the optimization problem and transform the optimization problem into a semi-positive definite relaxation problem, which can be described as:

[0041]

[0042] The specific process of step 6 is as follows:

[0043] Step 6.1: Let iter represent the number of external iterations and the initial value of iter be 1; initialize R n ,n∈{1,2,…,N},R r ,

[0044] Step 6.2: Use the convex optimization solver to solve the first subproblem and obtain R at the iterth external iteration. n ,n∈{1,2,…,N} and R r The solution is denoted by R n (iter) ,n∈{1,2,…,N} and R r (iter) , where iter = 1 is given when solving the first subproblem The value is the initialization value, given when iter>1 The value of is obtained at the iter-1th external iteration Solution

[0045] Step 6.3: Use the convex optimization solver to solve the second subproblem and get the iter-th external iteration time The initial solution Among them, R given when solving the second sub-problem n , n∈{1,2,…,N} and R r The value corresponding to R n (iter) ,n∈{1,2,…,N} and R r (iter) ;

[0046] Step 6.4: R n (iter) ,n∈{1,2,…,N},R r (iter) and As the initial value, the iterative rank minimization method is used to Perform rank-one recovery to obtain the iter-th external iteration Solution The specific process is:

[0047] Step 6.4.1: Let k represent the number of internal iterations, and the initial value of k is 1;

[0048] Step 6.4.2: The rank-one constraint Convert to Among them, p is the auxiliary variable introduced, I TIRS Indicates dimension T IRS ×T IRS The identity matrix, when k = 1, Z (k-1) Indicated by T obtained by eigendecomposition IRS +1 eigenvalue in T IRS The characteristic matrix consists of the eigenvectors corresponding to the small eigenvalues. When k>1, Z (k-1) Indicates that in the k-1th internal iteration The internal iteration value of T obtained by eigendecomposition IRS +1 eigenvalue in T IRS The characteristic matrix consists of the eigenvectors corresponding to the small eigenvalues;

[0049] Step 6.4.3: Change the objective function of the second sub-problem to the penalty term ηp, and the second sub-problem is transformed into:

[0050]

[0051] stC1,C2',C3',C4,

[0052]

[0053] Among them, η represents a variable weight;

[0054] Step 6.4.4: Use a convex optimization solver to solve the problem in step 6.4.3 and obtain the kth inner iteration time The internal iteration value of Among them, R given in the solution process n ,n∈{1,2,…,N} and R r The value corresponding to R n (iter) ,n∈{1,2,…,N} and R r (iter) , during the solution process, the value of η in the kth internal iteration is increased so that the value of p approaches 0;

[0055] Step 6.4.5: Judgement T obtained by eigendecomposition IRS+1 eigenvalue in T IRS Is the maximum value among the small eigenvalues ​​less than the internal iteration threshold? If so, the iteration ends and As the iterth external iteration Solution Otherwise, set k = k + 1 and return to step 6.4.2 to continue;

[0056] Step 6.5: According to R n (iter) ,n∈{1,2,…,N},R r (iter) , Calculate the objective function in the semi-positive definite relaxation problem and obtain the objective function value of the iter-th external iteration; then make the difference between the objective function value of the iter-th external iteration and the objective function value of the iter-1-th external iteration; then determine whether the ratio of the difference to the objective function value of the iter-1-th external iteration is greater than the set threshold, then set iter = iter + 1, and then return to step 6.2 to continue execution; otherwise, the iteration ends and R n (iter) ,n∈{1,2,…,N},R r (iter) , Corresponding to R n ,n∈{1,2,…,N},R r , The local optimal solution of each; among them, when iter=1, the objective function value of the iter-1th external iteration is based on R n ,n∈{1,2,…,N},R r , The initial value of is used to calculate the objective function in the semi-positive definite relaxation problem.

[0057] Compared with the prior art, the advantages of the present invention are:

[0058] 1) The method of the present invention performs communication and perception functions simultaneously by deploying IRS in the ISAC system, and performs comprehensive optimization in terms of resource allocation, power control and beamforming. Traditionally, perception systems (such as radars, sensors) and communication systems are often designed and optimized separately. This separate design mode not only increases the complexity of the system, but may also lead to repeated configuration of resources and mutual interference of performance. The introduction of IRS can provide more propagation paths for the ISAC system to perform communication and perception functions to improve system performance, but it also increases the difficulty of solving the optimization problem. The present invention decomposes the original problem into two sub-problems of optimizing the beamforming of the base station and the phase shift of the IRS by adopting alternating optimization and semi-definite relaxation methods, which effectively reduces the complexity of the solution and has good accuracy.

[0059] 2) Traditional communication systems mainly focus on protecting the security of data transmission, that is, preventing the intrusion of communication eavesdroppers, while in ISAC systems, another problem of perception information leakage should also be considered. In ISAC, since the perception performance and base station transmission power are generally proportional, a larger transmission power will certainly prompt the perception performance, but it also increases the risk of perception information leakage. Therefore, in the present invention, perception security is taken into consideration and optimized, that is, by optimizing the base station beam and IRS phase shift to counter attackers who try to obtain base station perception information by receiving signals, the base station transmission power is minimized while meeting perception and communication requirements. Traditional technology may compromise between security and perception performance, while the present invention achieves the best balance between the two through an optimization algorithm based on alternating optimization and semi-definite relaxation, greatly improving the overall performance of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 It is a flowchart of the overall implementation process of the method of the present invention;

[0061] Figure 2 A simple schematic diagram of the ISAC-IRS system built for the method of the present invention taking into account the perception of eavesdroppers;

[0062] Figure 3 is the detection probability threshold Γ of the eavesdropper detected by the method of the present invention and the comparative method e is 0.29, the detection probability threshold of the perceptual receiver is Γ R is 0.88, and the communication rate threshold R c =log 2 (1+ξ c ) A schematic diagram of a comparison curve of a base station's transmit power change when the bit rate changes from 4.5 bps / Hz to 6.5 bps / Hz;

[0063] Figure 4 The communication rate threshold R of the communication user in the method of the present invention and the comparative method c =log 2 (1+ξ c ) is 5.5 bps / Hz, the detection probability threshold of the sensing receiver is Γ R is 0.88, and the detection probability threshold of the perceived eavesdropper is Γ e A schematic diagram of a comparison curve of the change in the base station's transmit power when the power changes from 0.28 to 0.34;

[0064] Figure 5 The communication rate threshold R of the communication user in the method of the present invention and the comparative method c =log 2 (1+ξ c) is 5.5 bps / Hz, the detection probability threshold of the perceived eavesdropper is Γ e is 0.29, and the detection probability threshold of the sensing receiver is Γ R Schematic diagram of a comparison curve of the change in the base station's transmit power when it changes from 0.8 to 0.9. DETAILED DESCRIPTION

[0065] The present invention is further described in detail below with reference to the accompanying drawings.

[0066] The present invention proposes an energy-saving and security perception optimization method based on ISAC-IRS, which optimizes the correlation matrix of the beamforming matrix related to each communication user, the covariance matrix of the dedicated radar signal and the phase shift matrix of the IRS in an ISAC-IRS system with a perception eavesdropper. In the ISAC-IRS system, the base station transmits a signal composed of a plurality of communication signals and a dedicated radar signal superimposed to serve multiple single-antenna communication users and perceive specific radar targets. The IRS is deployed in the space between the base station and the communication users and the radar targets, providing an additional line-of-sight link between the base station and the objects it serves. There is a multi-antenna perception eavesdropper in the environment trying to steal perception information. The goal of the method of the present invention is to optimize the correlation matrix of the beamforming matrix related to each communication user, the covariance matrix of the dedicated radar signal and the phase shift matrix of the IRS under the premise of ensuring reliable communication and perception security, so as to minimize the transmission power of the base station. Since the variables in the optimization problem are coupled with each other, the optimization problem presents a non-convex property, and the original problem is decomposed into two sub-problems. The alternating optimization (AO) method is adopted to alternately optimize these sub-problems and gradually approach the local optimal solution.

[0067] The present invention proposes an energy-saving and security perception optimization method based on ISAC-IRS, and its overall implementation flow chart is as follows: Figure 1 As shown, it includes the following steps:

[0068] Step 1: Establish an ISAC-IRS (intelligent reflective surface assisted integrated communication perception) system considering a perceptual eavesdropper, wherein the ISAC-IRS system is provided with multiple communication users, a radar target, a base station for providing services to the communication users and perceiving the radar target, an IRS for assisting the base station in working, a perceptual receiver for detecting the radar target according to its received signal, and a perceptual eavesdropper attempting to monitor the base station's transmission signal to silently obtain the perceptual information, wherein the base station's transmission signal is composed of a superposition of multiple communication signals and a dedicated radar signal. An IRS is deployed in the environment to assist the base station, provide additional virtual line-of-sight links, broaden the coverage of the system, and further improve the performance of perception and communication; assuming that the base station and the legitimate perception receiver are in a collaborative relationship, the base station transmits a signal to perceive the radar target, and the perception receiver detects the radar target based on its received signal combined with the understanding of the base station's transmission signal and environmental information; the perception eavesdropper is assumed to be unaware of the base station's transmission signal, making the perception technology that requires the base station's transmission signal not applicable. Therefore, it is assumed that the perception eavesdropper detects the transmission power from a specific direction, performs target detection, and uses receive beamforming related to the radar target direction to assist detection.

[0069] Here, the number of communication users is N, each of which is equipped with a single antenna; the radar target is equipped with a single antenna; the base station, sensing receiver, IRS, and sensing eavesdropper are all equipped with uniform linear arrays, and the number of their antennas is T, T, and T respectively. IRS and T e , where N≤T. In this embodiment, N=3, T=9, T IRS =18, T e =8.

[0070] Step 2: Establish the communication performance index, radar perception performance index, and perception eavesdropping performance index of the ISAC-IRS system. The communication performance index is measured by the received signal-to-interference-and-noise ratio (SINR) of each communication user, the radar perception performance index is measured by the detection probability of the perception receiver to the radar target, and the perception eavesdropping performance index is measured by the detection probability of the perception eavesdropper to the target.

[0071] Preferably, in step 2, the process of obtaining the received signal to interference and noise ratio of the nth communication user is as follows:

[0072] Step 2.a1: Transform the received signal y of the nth communication user into n (t) is expressed as Where n = 1, 2, ..., N, t is the time variable, g B,n represents the channel from the base station to the nth communication user, g r,n represents the channel from IRS to the nth communication user, GBr represents the channel from the base station to the IRS, the superscript "H" represents the conjugate transposition operation, s(t) represents the transmission signal of the base station, r n represents the beam vector designed by the base station for the nth communication user, x n (t) represents the communication signal transmitted by the base station to the nth communication user, r r (t) represents the dedicated radar signal transmitted by the base station to the radar target. The base station transmits the communication signal with the dedicated radar signal to provide additional spatial freedom for system design. represents the phase shift matrix of IRS, diag(·) represents the diagonal elements used to extract or construct the matrix, v represents the phase shift vector of IRS, e is a natural constant, e=2.71…, j is the imaginary part, represents the phase shift of the lth antenna of IRS, l=1,2,y…,T IRS , z n (t) represents the Gaussian white noise at the nth communication user, which has an expected value of 0 and a variance of The complex Gaussian distribution is taken in this embodiment.

[0073] Step 2.a2: According to y n (t), obtain the received signal-to-interference-and-noise ratio SINR of the nth communication user c,n , Among them, tr(·) means to find the trace of the matrix, Represents the phase shift matrix of IRS The correlation matrix of R n Indicated by r n The beamforming matrix associated with the nth communication user is constructed. R i represents the beam vector r designed by the base station for the i-th, i≠n communication user i The beamforming matrix associated with the i-th, i≠n-th communication user is constructed. There are direct links between the base station and the communication user and cascade links between the base station, IRS and the communication user. represents the channel matrix composed of the direct channel from the base station to the nth communication user and the cascade channel from the base station to the IRS and then to the nth communication user, Will Replace n with i, i≠n to get

[0074] Preferably, in step 2, the process of acquiring the detection probability of the radar target by the perception receiver is as follows:

[0075] Step 2.b1: Transform the received signal y of the sensing receiver into R (t) is expressed as Where α is the complex reflection coefficient related to the cross-sectional area of ​​the radar target, represents the channel from the radar target to the perception receiver, represents the channel from the base station to the radar target, represents the channel from IRS to radar target, z R (t) represents the Gaussian white noise at the sensor receiver, which has a mean of 0 and a variance of The complex Gaussian distribution, I represents the unit matrix, in this embodiment,

[0076] Step 2.b2: According to y R (t), obtain the detection probability P of the radar target by the perception receiver R , Among them, Q() represents the right tail distribution function of Gaussian distribution, P FA represents a given constant false alarm probability, in this embodiment, P FA = 0.0001, "|·|" is the modulo operator, S represents the channel matrix composed of the direct channel from the base station to the radar target and the cascade channel from the base station to the IRS and then to the radar target, R represents the covariance matrix of the base station's transmitted signal s(t), represents the mathematical expectation, R r Denotes a dedicated radar signal r r The covariance matrix of (t),

[0077] The perceptual eavesdropper attempts to silently obtain the perceptual information of the base station through its received signal, so as to further perform dangerous actions on the system. The behavior of stealing perceptual information is now characterized as detecting radar targets. Since the perceptual eavesdropper is an illegal node in the system, it does not have information about the transmitted signal, so it will use the receiving beam forming method to detect the receiving power along the direction of the incoming wave, similar to the passive radar technology. The receiving beam it constructs is the steering vector at the perceptual eavesdropper relative to the arrival angle, and the arrival angle is the angle of the radar target relative to the perceptual eavesdropper. Preferably, in step 2, the process of obtaining the detection probability of the target by the perceptual eavesdropper is:

[0078] Step 2.c1: The received signal y of the perceived eavesdropper e (t) is expressed as

[0079] ,

[0080] in, represents the angle of the radar target relative to the sensing eavesdropper, Indicates the position of the perceived eavesdropper relative to The steering vector, α e represents the complex reflection coefficient related to the cross-sectional area of ​​the sensing eavesdropper, represents the channel from the radar target to the sensing eavesdropper, G Be represents the channel from the base station to the eavesdropper, G re represents the channel from IRS to the perceptual eavesdropper, z e (t) represents the Gaussian white noise at the perceived eavesdropper, which has a mean of 0 and a variance of The complex Gaussian distribution is taken in this embodiment.

[0081] Step 2.c2: The sensing eavesdropper performs energy detection on its received signal to sense the radar target, according to y e (t), obtain the detection probability P of the target by the perceptual eavesdropper e , in, B 1 represents the channel matrix composed of the direct channel from the base station to the perceptual eavesdropper, the cascade channel from the base station to the IRS to the radar target and then to the perceptual eavesdropper, the cascade channel from the base station to the IRS and then to the perceptual eavesdropper, and the cascade channel from the base station to the radar target and then to the perceptual eavesdropper, assuming that the radar target exists. B 0 represents the channel matrix consisting of the direct channel from the base station to the perceptual eavesdropper and the cascade channel from the base station to the IRS and then to the perceptual eavesdropper when the radar target does not exist.

[0082] Above, g B,n , g r,n , G Br , G Be , G re All are modeled as Rice channel models. B,n For example, ρ represents the Rice factor, and here ρ=3, represents the line-of-sight link channel from the base station to the nth communication user, specifically in the form of the path loss coefficient multiplied by the steering vector, represents the non-line-of-sight link channel from the base station to the nth communication user, All terms in obey a complex Gaussian distribution with mean 0 and variance 1, that is, Another example: G Br For example,

[0083] represents the line-of-sight link channel from the base station to the IRS, specifically in the form of the path loss coefficient multiplied by the steering vector, represents the non-line-of-sight link channel from the base station to the IRS, All terms in obey a complex Gaussian distribution with a mean of 0 and a variance of 1. For example,

[0084] represents the line-of-sight link channel from the base station to the radar target, specifically in the form of the path loss coefficient multiplied by the steering vector, represents the non-line-of-sight link channel from the base station to the radar target, All terms in obey a complex Gaussian distribution with mean 0 and variance 1, that is,

[0085] Step 3: To achieve the purpose of energy saving, on the basis of ensuring reliable communication, perception and perception security, the base station's transmit power is minimized. Taking the received signal-to-interference-noise ratio of each communication user, the detection probability of the perception receiver for the radar target, and the detection probability of the perception eavesdropper for the target as constraints, the beamforming matrix related to each communication user, the covariance matrix of the dedicated radar signal and the correlation matrix of the phase shift matrix of the IRS are jointly optimized to construct an optimization problem, where the beamforming matrix related to each communication user is composed of the beam vector designed by the base station for the communication user.

[0086] Further limiting, the optimization problem is described as:

[0087]

[0088] C2:P R ≥Γ R ,

[0089] C3:P e ≤Γ e ,

[0090]

[0091] C6:R r ≥0,

[0092]

[0093] Among them, min means taking the minimum value of the objective function, st means "constrained by...", tr(R) represents the transmission power of the base station, c represents the receiving signal-to-interference-noise ratio threshold of the communication user, To define the symbol, Γ R represents the detection probability threshold of the sensing receiver, Γ erepresents the detection probability threshold of the perceived eavesdropper. In this embodiment, c =2 4.5 -1, Γ R =0.88,Γ e =0.3, express The l'th row and l'th column element in the matrix, rank(·) represents the rank of the matrix. Constraint C1 is used to ensure a certain communication performance, which is measured by the received signal-to-interference-noise ratio of the communication user; constraint C2 is used to ensure reliable perception, in the form of the perception receiver's detection probability of the radar target is greater than or equal to the threshold Γ R ; Constraint C3 is used to ensure the security of perception. The specific form is to make the detection probability of the radar target by the perception eavesdropper not exceed the threshold Γ e ; Since this system uses a passive IRS, that is, it does not have a power amplification function, constraint C4 ensures that the phase shift modulus of each array element, i.e., antenna, in the optimized IRS is 1; constraints C5 and C6 ensure that the beamforming matrix R related to each communication user is n , n = {1, 2, ..., N} and the covariance matrix R of the dedicated radar signal r is a semi-positive definite matrix; constraint C7 ensures that the correlation matrix of the IRS phase shift matrix is The beamforming matrix R associated with each communication user n , the rank of n={1,2,...,N} is 1.

[0094] Step 4: By rewriting the constraints on the detection probability of the radar target by the perceptual receiver in the optimization problem into a form in which the detection probability is only related to the covariance matrix of the base station's transmitted signal, rewriting the constraints on the detection probability of the target by the perceptual eavesdropper in the optimization problem into a linear form, and ignoring the rank-one constraint of the correlation matrix of the IRS phase shift matrix and the rank-one constraint of the received signal-to-interference-noise ratio of each communication user, the optimization problem is converted into a semi-positive definite relaxation problem.

[0095] Further defined, the specific process of step 4 is:

[0096] Step 4.1: In the optimization problem, to ensure a certain degree of reliable perception, the detection probability P of the perception receiver for the radar target is set to R Set to be greater than or equal to a given threshold Γ R In the form of constraint C2, given a constant false alarm probability P FA and the complex reflection coefficient α related to the cross-sectional area of ​​the radar target, P R It is only related to the covariance matrix R of the base station's transmitted signal. Therefore, after some processing of the known quantities, the constraint C2 in the optimization problem is rewritten as constraint C2':

[0097] Step 4.2: Perceive the detection probability P of the eavesdropper to the radar target e There is an obvious nonlinear relationship, but it is found that As a whole, the original formula has the same properties as the equation The same mathematical form, and it has the property of monotonically increasing in the interval 0<x<1 and x>1, so the constraint C3 in the optimization problem is rewritten as constraint C3': Among them, Λ e The equation f(x) = Γ e The root of time, If we take Γ e = 0.3, we get Λ e =0.6815.

[0098] Step 4.3: Using the semi-positive definite programming method, ignore the constraint C7 in the optimization problem and transform the optimization problem into a semi-positive definite relaxation problem, which can be described as:

[0099]

[0100] Here, ignoring the rank-one constraint and looking for a method to restore the rank-one in the subsequent process, a better solution can be obtained.

[0101] Step 5: Due to the high coupling of variables, the semi-definite relaxation problem is non-convex, so the semi-definite relaxation problem is decomposed into two sub-problems. The first sub-problem is about the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal. Given the correlation matrix of the phase shift matrix of the IRS, the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal are optimized. At this time, the first sub-problem is a convex problem; the second sub-problem is about the correlation matrix of the phase shift matrix of the IRS. Given the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal, the correlation matrix of the phase shift matrix of the IRS is optimized. At this time, the second sub-problem is a convex problem.

[0102] Step 6: Use the alternating optimization algorithm to iteratively solve the first and second subproblems to obtain the local optimal solutions of the correlation matrices of the beamforming matrix related to each communication user, the covariance matrix of the dedicated radar signal, and the phase shift matrix of the IRS.

[0103] Further defined, the specific process of step 6 is:

[0104] Step 6.1: Let iter represent the number of external iterations and the initial value of iter be 1; initialize R n ,n∈{1,2,…,N},R r ,

[0105] Step 6.2: Use a convex optimization solver such as CVX in MATLAB to solve the first subproblem and obtain R at the iterth external iteration. n ,n∈{1,2,…,N} and R r The solution is denoted by R n (iter) ,n∈{1,2,…,N} and R r (iter) , where iter = 1 is given when solving the first subproblem The value is the initialization value, given when iter>1 The value of is obtained at the iter-1th external iteration Solution

[0106] Step 6.3: Use a convex optimization solver such as CVX in MATLAB to solve the second subproblem and obtain the iter-th external iteration time The initial solution Among them, R given when solving the second sub-problem n ,n∈{1,2,…,N} and R r The value corresponding to R n (iter) ,n∈{1,2,…,N} and R r (iter) .

[0107] Step 6.4: R n (iter) ,n∈{1,2,…,N},R r (iter) and As the initial value, the iterative rank minimization (IRM) method is used to Perform rank-one recovery to obtain the iter-th external iteration Solution The specific process is:

[0108] Step 6.4.1: Let k represent the number of internal iterations and the initial value of k is 1.

[0109] Step 6.4.2: The rank-one constraint Convert to Among them, p is the introduced auxiliary variable, Indicates dimension T IRS ×T IRS The identity matrix, when k = 1, Z (k-1) Indicated by T obtained by eigendecomposition IRS +1 eigenvalue in TIRS Small eigenvalues ​​(i.e., T IRS +1 eigenvalues ​​except the largest one among the remaining T IRS eigenvalues), the characteristic matrix is ​​composed of the eigenvectors corresponding to the eigenvalues. When k>1, Z (k-1) Indicates that in the k-1th internal iteration The internal iteration value of T obtained by eigendecomposition IRS +1 eigenvalue in T IRS The characteristic matrix consists of the eigenvectors corresponding to the small eigenvalues.

[0110] Step 6.4.3: Change the objective function of the second sub-problem to the penalty term ηp, and the second sub-problem is transformed into:

[0111]

[0112] stC1,C2',C3',C4,

[0113]

[0114] Here, η represents a variable weight, and the initial value of η is set to 50.

[0115] Step 6.4.4: Use a convex optimization solver such as CVX to solve the problem in step 6.4.3 and obtain the kth inner iteration time The internal iteration value of Among them, R given in the solution process n ,n∈{1,2,…,N} and R r The value corresponding to R n (iter) ,n∈{1,2,…,N} and R r (iter) , during the solution process, the value of η in the kth internal iteration is increased so that the value of p approaches 0. Here, η increases at a speed of 3.5 steps, that is, η k =3.5×η k-1 , η k represents the value of η in the kth internal iteration, and η is 1 when k=1 k-1 is the initial value, when k>1,η k-1 represents the value of η in the k-1th inner iteration.

[0116] Step 6.4.5: Judgement T obtained by eigendecomposition IRS +1 eigenvalue in T IRS Is the maximum value among the small eigenvalues ​​less than the internal iteration threshold? If so, the iteration ends and As the iterth external iteration Solution Otherwise, set k = k + 1 and return to step 6.4.2 to continue execution; the internal iteration threshold is 10 -3 , the “=” in k=k+1 is an assignment symbol.

[0117] Here, the Iterative Rank Minimization (IRM) method is a prior art method for restoring the rank of the matrix optimization variables in the semi-positive definite relaxation problem to 1.

[0118] Step 6.5: According to R n (iter) ,n∈{1,2,…,N},R r (iter) , Calculate the objective function in the semi-positive definite relaxation problem and obtain the objective function value of the iter-th external iteration; then make the difference between the objective function value of the iter-th external iteration and the objective function value of the iter-1-th external iteration; then determine whether the ratio of the difference to the objective function value of the iter-1-th external iteration is greater than the set threshold, then set iter = iter + 1, and then return to step 6.2 to continue execution; otherwise, the iteration ends and R n (iter) ,n∈{1,2,…,N},R r (iter) , Corresponding to R n ,n∈{1,2,…,N},R r , The local optimal solution of each; among them, when iter=1, the objective function value of the iter-1th external iteration is based on R n ,n∈{1,2,…,N},R r , The initial value of is used to calculate the objective function in the semi-positive definite relaxation problem. Here, the threshold value is set to 0.0001, and the “=” in iter=iter+1 is the assignment symbol.

[0119] The feasibility and effectiveness of the method of the present invention are further illustrated by the following simulation.

[0120] In the simulation, the 2D coordinates of the base station are set to (30,0), the 2D coordinates of the IRS are set to (0,15), the 2D coordinates of the N communication users are randomly selected within a circle with a center of (25,22) and a radius of 2, the 2D coordinates of the radar target are set to (30,50), the 2D coordinates of the sensing eavesdropper are set to (10,40), and the 2D coordinates of the sensing receiver are set to (30,70).

[0121] In the simulation, the comparison methods include the random value method of the IRS phase shift matrix and the ISAC method without IRS deployment. The random value method of the IRS phase shift matrix refers to the phase shift matrix of the IRS deployed in the environment. The diagonal elements of are randomly selected, and the base station beam is optimized according to the phase shift of the random values; the ISAC method without IRS deployment means that the IRS is not deployed in the environment, and the optimization goal is achieved only by optimizing the base station beam.

[0122] Figure 3 The difference between the proposed method and the comparative method in the detection probability threshold Γ of the eavesdropper is given. e is 0.29, the detection probability threshold of the perceptual receiver is Γ R is 0.88, and the communication rate threshold R c =log 2 (1+ξ c ) is a comparison curve of the base station's transmission power change when the bit rate changes from 4.5bps / Hz to 6.5bps / Hz. Figure 3 It can be seen that as the communication rate threshold of the communication user increases, the transmission power of the base station increases, which reflects that when the communication demand in the ISAC increases, more transmission power needs to be consumed to meet it. Moreover, under the same conditions, the required transmission power of the method of the present invention is much lower than that of the two comparison methods. This shows that the method of the present invention gives full play to the role of IRS and can achieve better system performance under the same conditions.

[0123] Figure 4 The communication rate threshold R of the communication user of the method of the present invention and the comparative method is given. c =log 2 (1+ξ c ) is 5.5 bps / Hz, the detection probability threshold of the sensing receiver is Γ R is 0.88, and the detection probability threshold of the perceived eavesdropper is Γ e The comparison curve of the base station's transmission power change when it changes from 0.28 to 0.34. Figure 4 It can be seen from the figure that the transmission power of the base station decreases as the detection probability threshold of the perceived eavesdropper increases, and the transmission power required by the method of the present invention is much smaller than that of the two comparative methods under the same conditions.

[0124] Figure 5 The communication rate threshold R of the communication user of the method of the present invention and the comparative method is given. c =log 2 (1+ξ c ) is 5.5 bps / Hz, the detection probability threshold of the perceived eavesdropper is Γ e is 0.29, and the detection probability threshold of the sensing receiver is Γ RThe comparison curve of the base station's transmission power change when the power changes from 0.8 to 0.9. Figure 5 It can be seen that the transmission power of the base station increases with the increase of the detection probability threshold of the perception receiver, indicating that the transmission power required to ensure higher perception performance is also greater, and the transmission power required by the method of the present invention under the same conditions is much smaller than that of the two comparison methods.

Claims

1. An energy-saving and security-aware optimization method based on ISAC-IRS, characterized in that The following steps are involved: Step 1: Establish an ISAC-IRS system considering a perceptual eavesdropper, wherein the ISAC-IRS system is provided with multiple communication users, a radar target, a base station for providing services to the communication users and perceiving the radar target, an IRS for assisting the base station in working, a perceptual receiver for performing target detection on the radar target according to its received signal, and a perceptual eavesdropper attempting to monitor the transmission signal of the base station to silently obtain the perceptual information, wherein the transmission signal of the base station is composed of the superposition of multiple communication signals and a dedicated radar signal; Step 2: Establish the communication performance index, radar perception performance index, and perception eavesdropping performance index of the ISAC-IRS system. The communication performance index is measured by the received signal-to-interference-noise ratio of each communication user, the radar perception performance index is measured by the detection probability of the perception receiver to the radar target, and the perception eavesdropping performance index is measured by the detection probability of the perception eavesdropper to the target. Step 3: To achieve the purpose of energy saving, on the basis of ensuring reliable communication, perception and perception security, the base station's transmit power is minimized. Taking the received signal-to-interference-noise ratio of each communication user, the detection probability of the perception receiver to the radar target, and the detection probability of the perception eavesdropper to the target as constraints, the beamforming matrix related to each communication user, the covariance matrix of the dedicated radar signal and the correlation matrix of the phase shift matrix of the IRS are jointly optimized to construct an optimization problem, where the beamforming matrix related to each communication user is composed of the beam vector designed by the base station for the communication user; Step 4: By rewriting the detection probability constraint of the sensing receiver to the radar target in the optimization problem into a form in which the detection probability is only related to the covariance matrix of the base station's transmission signal, rewriting the detection probability constraint of the sensing eavesdropper to the target in the optimization problem into a linear form, and ignoring the rank-one constraint of the correlation matrix of the IRS phase shift matrix and the rank-one constraint of the received signal-to-interference-noise ratio of each communication user, the optimization problem is converted into a semi-positive definite relaxation problem; Step 5: Decompose the semi-definite relaxation problem into two sub-problems. The first sub-problem is about the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal. Given the correlation matrix of the phase shift matrix of the IRS, the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal are optimized. At this time, the first sub-problem is a convex problem. The second sub-problem is about the correlation matrix of the phase shift matrix of the IRS. Given the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal, the correlation matrix of the phase shift matrix of the IRS is optimized. At this time, the second sub-problem is a convex problem. Step 6: Use the alternating optimization algorithm to iteratively solve the first and second subproblems to obtain the local optimal solutions of the correlation matrices of the beamforming matrix related to each communication user, the covariance matrix of the dedicated radar signal, and the phase shift matrix of the IRS.

2. The energy saving and security perception optimization method based on ISAC-IRS according to claim 1 is characterized in that In step 1, the number of communication users is N, and each communication user is equipped with a single antenna; The radar target is equipped with a single antenna; the base station, sensing receiver, IRS, and sensing eavesdropper are all equipped with uniform linear arrays, and the number of their antennas is T, T, T IRS and T e , where N≤T.

3. The energy saving and security perception optimization method based on ISAC-IRS according to claim 2 is characterized in that In step 2, the process of obtaining the received signal to interference and noise ratio of the nth communication user is as follows: Step 2.a1: Transform the received signal y of the nth communication user into n (t) is expressed as Where n = 1, 2, ..., N, t is the time variable, g B,n represents the channel from the base station to the nth communication user, g r,n represents the channel from IRS to the nth communication user, G Br represents the channel from the base station to the IRS, the superscript "H" represents the conjugate transposition operation, s(t) represents the transmission signal of the base station, r n represents the beam vector designed by the base station for the nth communication user, x n (t) represents the communication signal transmitted by the base station to the nth communication user, r r (t) represents the dedicated radar signal transmitted by the base station to the radar target, represents the phase shift matrix of IRS, diag(·) represents the diagonal elements used to extract or construct the matrix, v represents the phase shift vector of IRS, e is a natural constant, j is an imaginary part, represents the phase shift of the lth antenna of IRS, l=1,2,…,T IRS , z n (t) represents the Gaussian white noise at the nth communication user, which has an expected value of 0 and a variance of The complex Gaussian distribution of Step 2.a2: According to y n (t), obtain the received signal-to-interference-and-noise ratio SINR of the nth communication user c,n , Among them, tr(·) means to find the trace of the matrix, Represents the phase shift matrix of IRS The correlation matrix of R n Indicated by r n The beamforming matrix associated with the nth communication user is constructed. represents the channel matrix composed of the direct channel from the base station to the nth communication user and the cascade channel from the base station to the IRS and then to the nth communication user, 4. The energy saving and security perception optimization method based on ISAC-IRS according to claim 3 is characterized in that In step 2, the process of acquiring the detection probability of the radar target by the perception receiver is as follows: Step 2.b1: Transform the received signal y of the sensing receiver into R (t) is expressed as Where α is the complex reflection coefficient related to the cross-sectional area of ​​the radar target, represents the channel from the radar target to the perception receiver, represents the channel from the base station to the radar target, represents the channel from IRS to radar target, z R (t) represents the Gaussian white noise at the sensor receiver, which has a mean of 0 and a variance of The complex Gaussian distribution of , I represents the unit matrix; Step 2.b2: According to y R (t), obtain the detection probability P of the radar target by the perception receiver R , Among them, Q() represents the right tail distribution function of Gaussian distribution, P FA represents a given constant false alarm probability, "|·|" is a modulo operator, S represents the channel matrix consisting of the direct channel from the base station to the radar target and the cascade channel from the base station to the IRS and then to the radar target, R represents the covariance matrix of the base station's transmitted signal s(t), represents the mathematical expectation, R r Denotes a dedicated radar signal r r The covariance matrix of (t), 5. The energy saving and security perception optimization method based on ISAC-IRS according to claim 4 is characterized in that In step 2, the process of acquiring the detection probability of the target by the perceived eavesdropper is as follows: Step 2.c1: The received signal y of the perceived eavesdropper e (t) is expressed as ， in, represents the angle of the radar target relative to the sensing eavesdropper, Indicates the position of the perceived eavesdropper relative to The steering vector, α e represents the complex reflection coefficient related to the cross-sectional area of ​​the sensing eavesdropper, represents the channel from the radar target to the sensing eavesdropper, G Be represents the channel from the base station to the eavesdropper, G re represents the channel from IRS to the perceptual eavesdropper, z e (t) represents the Gaussian white noise at the perceived eavesdropper, which has a mean of 0 and a variance of The complex Gaussian distribution of Step 2.c2: According to y e (t), obtain the detection probability P of the target by the perceptual eavesdropper e , in, B1 represents the channel matrix composed of the direct channel from the base station to the perceptual eavesdropper, the cascade channel from the base station to the IRS to the radar target and then to the perceptual eavesdropper, the cascade channel from the base station to the IRS and then to the perceptual eavesdropper, and the cascade channel from the base station to the radar target and then to the perceptual eavesdropper, assuming that the radar target exists. B0 represents the channel matrix composed of the direct channel from the base station to the perceptual eavesdropper and the cascade channel from the base station to the IRS and then to the perceptual eavesdropper when the radar target does not exist.

6. The energy saving and security perception optimization method based on ISAC-IRS according to claim 5 is characterized in that In step 3, the optimization problem is described as: Where tr(R) represents the transmission power of the base station, ξ c represents the receiving signal-to-interference-noise ratio threshold of the communication user, Γ R represents the detection probability threshold of the sensing receiver, Γ e represents the detection probability threshold of the perceived eavesdropper, express The l'th row and l'th column element in , rank(·) means to find the rank of the matrix.

7. The energy saving and security perception optimization method based on ISAC-IRS according to claim 6 is characterized in that The specific process of step 4 is as follows: Step 4.1: Rewrite constraint C2 in the optimization problem as constraint C2': Step 4.2: Rewrite constraint C3 in the optimization problem as constraint C3': Among them, Λ e The equation f(x) = Γ e The root of time, Step 4.3: Using the semi-positive definite programming method, ignore the constraint C7 in the optimization problem and transform the optimization problem into a semi-positive definite relaxation problem, which can be described as:

8. The energy saving and security perception optimization method based on ISAC-IRS according to claim 7 is characterized in that The specific process of step 6 is as follows: Step 6.1: Let iter represent the number of external iterations and the initial value of iter be 1; initialize R n ,n∈{1,2,…,N},R r , Step 6.2: Use the convex optimization solver to solve the first subproblem and obtain R at the iterth external iteration. n , n∈{1,2,…,N} and R r The solution is denoted by R n (iter) , n∈{1,2,…,N} and R r (iter) , where iter = 1 is given when solving the first subproblem The value is the initialization value, given when iter>1 The value is obtained at the iter-1th external iteration Solution Step 6.3: Use the convex optimization solver to solve the second subproblem and get the iter-th external iteration time The initial solution Among them, R given when solving the second sub-problem n , n∈{1,2,…,N} and R r The value corresponding to R n (iter) , n∈{1,2,…,N} and R r (iter) ; Step 6.4: R n (iter) ,n∈{1,2,…,N},R r (iter) and As the initial value, the iterative rank minimization method is used to Perform rank-one recovery to obtain the iter-th external iteration Solution The specific process is: Step 6.4.1: Let k represent the number of internal iterations, and the initial value of k is 1; Step 6.4.2: The rank-one constraint Convert to Among them, p is the auxiliary variable introduced, I TIRS Indicates dimension T IRS ×T IRS The identity matrix, when k = 1, Z (k-1) Indicated by T obtained by eigendecomposition IRS +1 eigenvalue in T IRS The characteristic matrix consists of the eigenvectors corresponding to the small eigenvalues. When k>1, Z (k-1) Indicates that in the k-1th internal iteration The internal iteration value of T obtained by eigendecomposition IRS +1 eigenvalue in T IRS The characteristic matrix consists of the eigenvectors corresponding to the small eigenvalues; Step 6.4.3: Change the objective function of the second sub-problem to the penalty term ηp, and the second sub-problem is transformed into: Among them, η represents a variable weight; Step 6.4.4: Use a convex optimization solver to solve the problem in step 6.4.3 and obtain the kth inner iteration time The internal iteration value of Among them, R given in the solution process n , n∈{1,2,…,N} and R r The value corresponding to R n (iter) , n∈{1,2,…,N} and R r (iter) , during the solution process, the value of η in the kth internal iteration is increased so that the value of p approaches 0; Step 6.4.5: Judgement T obtained by eigendecomposition IRS +1 eigenvalue in T IRS Is the maximum value among the small eigenvalues ​​less than the internal iteration threshold? If so, the iteration ends and As the iterth external iteration Solution Otherwise, set k = k + 1 and return to step 6.4.2 to continue; Step 6.5: According to R n (iter) ,n∈{1,2,…,N},R r (iter) , Calculate the objective function in the semi-positive definite relaxation problem and obtain the objective function value of the iter-th external iteration; then make the difference between the objective function value of the iter-th external iteration and the objective function value of the iter-1-th external iteration; then determine whether the ratio of the difference to the objective function value of the iter-1-th external iteration is greater than the set threshold, then set iter = iter + 1, and then return to step 6.2 to continue execution; otherwise, the iteration ends and R n (iter) ,n∈{1,2,y…,N},R r (iter) , Corresponding to R n ,n∈{1,2,y…,N},R r , The local optimal solution of each; among them, when iter=1, the objective function value of the iter-1th external iteration is based on R n ,n∈{1,2,…,N},R r , The initial value of is used to calculate the objective function in the semi-positive definite relaxation problem.

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