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

Abstract

The present invention discloses an energy-saving and security perception optimization method based on ISAC-IRS, which takes into account the situation where perception information is leaked by perception eavesdroppers in the environment, and minimizes the base station transmission power by optimizing 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, thereby achieving energy saving effect, while ensuring sufficient communication rate, the detection probability of the perception receiver for the radar target is as large as possible, and the detection probability of the perception eavesdropper for the target is as small as possible; due to the coupling between the variables in the optimization, the optimization problem is non-convex, and the semi-positive definite formation, alternating optimization and iterative rank minimization method are used to solve the original problem, and a local optimal solution is obtained through alternating optimization iteration; the advantage is that the protection mechanism of the perception information is taken into account to improve the security of the system, the base station transmission power is minimized and optimized, and the perception data is protected while consuming as few resources as possible.

Description

Technical Field

[0001] The present invention relates to integrated communication perception (ISAC) and intelligent reflecting surface (IRS) technologies, and in particular to an energy-saving and security perception optimization method based on ISAC-IRS (integrated communication perception combined with intelligent reflecting surface). The method takes into account the presence 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 Sensing (ISAC) technology has laid the foundation for sixth-generation wireless networks. Its core goal is to achieve efficient resource utilization by coordinating communication and sensing functions. In recent years, advances in multi-antenna technology have enabled ISAC to achieve significant improvements in communication rates and sensing accuracy. The use of multi-antenna technology in ISAC not only enhances multiplexing and diversity gain but also improves radar resolution and target recognition capabilities. However, the competitive relationship between communication and sensing functions under limited resources has prompted researchers to explore joint beam design to achieve optimal coordination between the two, thereby improving overall system performance.

[0003] At the same time, intelligent reflecting surfaces (IRS), as an emerging key technology, are attracting increasing attention. IRS can provide a low-cost, high-efficiency solution that supports large-scale connectivity and ultra-reliable transmission by optimizing wireless channels. Combining IRS with ISAC can further enhance system flexibility and performance. The application of IRS can create multiple line-of-sight links. Combined with multi-antenna configurations, it provides additional spatial degrees of freedom for communication and perception, enabling 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 overall system performance while also introducing new security challenges, particularly in the presence of perceptual eavesdroppers. By monitoring the perception signals transmitted by base stations, perceptual eavesdroppers can silently obtain perception data, infer the system's operating status, and potentially pose a security threat to the communication or perception processes. This type of passive eavesdropping not only increases the risk of information leakage but also places higher demands on system energy efficiency.

[0005] To address this issue, ISAC system design needs to balance communication and perception security while achieving energy conservation. By rationally designing the base station's transmit beam, power consumption can be reduced and system energy efficiency improved while ensuring system perception and communication performance. Especially in the presence of a perceptual eavesdropper, minimizing the base station's transmit power not only reduces the risk of perceived signals being eavesdropped, but also effectively saves energy. Current research indicates that optimizing the base station's transmit beam to address the threat of perceptual eavesdroppers is a key means of achieving energy conservation and security in ISAC systems. Therefore, optimizing the base station's transmit beam to achieve energy conservation while ensuring perception and communication reliability in ISAC systems has become a pressing technical challenge 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 existence of perceptual eavesdroppers in the environment and can minimize the transmission power of the base station to achieve energy saving while meeting the constraints of perceptual security, communication rate and perceptual 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 that considers a perceptual eavesdropper. The ISAC-IRS system is configured 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, a perceptual receiver for detecting the radar target based on its received signal, and a perceptual eavesdropper that attempts to monitor the base station's transmitted signal to silently obtain perceptual information. The base station's transmitted signal is composed of the superposition of multiple communication signals and a dedicated radar signal.

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

[0010] Step 3: To achieve energy conservation, while ensuring reliable communication, perception, and perception security, the base station's transmit power is minimized. Using the received signal-to-interference-and-noise ratio (SINR) of each communication user, the probability of detecting a radar target by the perception receiver, and the probability of detecting a target by the perception eavesdropper as constraints, the beamforming matrix associated with each communication user, the covariance matrix of the dedicated radar signal, and the correlation matrix of the IRS phase shift matrix are jointly optimized to construct an optimization problem. The beamforming matrix associated with each communication user is composed of the beam vector designed by the base station for that communication user.

[0011] Step 4: The optimization problem is converted into a semi-definite relaxation problem by rewriting the detection probability constraint of the sensing receiver for the radar target into a form in which the detection probability is only related to the covariance matrix of the base station's transmitted signal, and rewriting the detection probability constraint of the sensing eavesdropper for the target into a linear form. 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-and-noise ratio of each communication user are ignored.

[0012] Step 5: Decompose the semidefinite relaxation problem into two subproblems. The first subproblem 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 IRS phase shift matrix, the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal are optimized. In this case, the first subproblem is a convex problem. The second subproblem is about the correlation matrix of the IRS phase shift matrix. Given the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal, the correlation matrix of the IRS phase shift matrix is ​​optimized. In this case, the second subproblem 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 transpose operation, s(t) represents the base station's transmitted signal, 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 the imaginary part, represents the phase shift of the lth antenna of the IRS, l=1,2,y…,T IRS , z n (t) represents the Gaussian white noise at the nth communication user, which has an expectation 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 finding 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 formed, represents the channel matrix consisting 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 represents 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, Indicates 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 Complex Gaussian distribution, 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 the 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), Indicates the mathematical expectation, R r Denotes the dedicated radar signal r r The covariance matrix of (t),

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

[0022] Step 2.c1: The received signal y of the eavesdropper is perceived 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 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, 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 the radar target exists. B0 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 Indicates the receiving signal-to-interference-and-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 e The equation f(x) = Γe The root of time,

[0040] Step 4.3: Using the semi-definite programming method, ignore the constraint C7 in the optimization problem and transform the optimization problem into a semi-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 is 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 get R at the iter-th 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 sub-problem The value is the initialization value, given when iter>1 The value 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 A preliminary solution Among them, R is 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 denote 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, and 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. 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 the 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, increase the value of η in the kth internal iteration so that the value of p approaches 0;

[0055] Step 6.4.5: Judgment T obtained by eigendecomposition IRS +1 eigenvalue in TIRS Is the maximum value among the small eigenvalues ​​less than the internal iteration threshold? If so, the iteration ends and the 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 、 Their respective local optimal solutions; where iter = 1, the objective function value of the iter-1th external iteration is based on R n ,n∈{1,2,…,N},R r 、 The objective function in the semi-definite relaxation problem is obtained by calculating the initial value of .

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

[0058] 1) The method of the present invention simultaneously performs communication and perception functions 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 duplicate 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, thereby improving 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, effectively reducing the complexity of the solution and having good accuracy.

[0059] 2) Traditional communication systems primarily focus on protecting the security of data transmission, that is, preventing intrusion by communication eavesdroppers. However, in ISAC systems, another issue of perception information leakage should also be considered. In ISAC, since perception performance is generally proportional to base station transmit power, a higher transmit power will certainly improve 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 attempt to obtain base station perception information through received signals, while minimizing base station transmit power while meeting perception and communication requirements. Traditional technologies may compromise between security and perception performance, but 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 This is a flowchart of the overall implementation 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 The detection probability threshold Γ of the present invention and the comparative method is e is 0.29, the detection probability threshold of the perceptual receiver Γ R is 0.88, and the communication rate threshold R c =log2(1+ξ c ) A schematic diagram showing a comparison curve of the 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 present invention and the comparative method c =log2(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 eavesdropper is Γ e Schematic diagram of the comparison curve of the base station's transmit power change from 0.28 to 0.34;

[0064] Figure 5 The communication rate threshold R of the communication user in the present invention and the comparative method c =log2(1+ξ c ) is 5.5 bps / Hz, the detection probability threshold of the eavesdropper is Γ e is 0.29, and the detection probability threshold of the sensing receiver is ΓR Schematic diagram of a comparison curve of the base station's transmit power change from 0.8 to 0.9. DETAILED DESCRIPTION

[0065] The present invention will be described in further detail below with reference to the accompanying drawings and embodiments.

[0066] This paper proposes an energy-saving and security-aware optimization method based on ISAC-IRS. It optimizes the correlation matrices of the beamforming matrix, the covariance matrix of the dedicated radar signal, and the phase-shift matrix of the IRS for each communication user in an ISAC-IRS system with a perceptual eavesdropper. In this ISAC-IRS system, a base station transmits a signal composed of multiple communication signals and a superimposed dedicated radar signal to simultaneously serve multiple single-antenna communication users and perceive specific radar targets. The IRS is deployed in the space between the base station, the communication users, and the radar targets, providing an additional line-of-sight link between the base station and the objects it serves. A perceptual eavesdropper with multiple antennas attempts to eavesdrop on perceptual information. The method aims to minimize the base station's transmit power by optimizing the beamforming matrix, the covariance matrix of the dedicated radar signal, and the phase-shift matrix of the IRS for each communication user while ensuring reliable communication and perceptual security. Because the variables in the optimization problem are coupled, making it non-convex, the original problem is decomposed into two subproblems. These subproblems are optimized alternately using an alternating optimization (AO) method to gradually approach a 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 that takes into account a perceptual eavesdropper. The ISAC-IRS system is equipped 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 its work, a perceptual receiver for detecting the radar target based on its received signal, and a perceptual eavesdropper that attempts to monitor the base station's transmitted signal to silently obtain perceptual information. The base station's transmitted signal is composed of the superposition of multiple communication signals and a dedicated radar signal. An IRS is deployed in the environment to assist the base station, providing additional virtual line-of-sight links, broadening the system's coverage, and further improving perception and communication performance. 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 its 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 perception technology that requires the base station's transmission signal inapplicable. Therefore, it is assumed that the perception eavesdropper detects the transmission power from a specific direction to perform target detection, and uses receive beamforming related to the radar target direction to assist in detection.

[0069] Here, the number of communication users is N, each 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 indicators, radar perception performance indicators, and perception eavesdropping performance indicators of the ISAC-IRS system. The communication performance indicator is measured by the received signal-to-interference-and-noise ratio (SINR) of each communication user. The radar perception performance indicator is measured by the detection probability of the radar target by the perception receiver. The perception eavesdropping performance indicator is measured by the detection probability of the target by the perception eavesdropper.

[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 transpose operation, s(t) represents the base station's transmitted signal, 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 dedicated radar signal along with the communication 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 the IRS, l=1,2,y…,T IRS , z n (t) represents the Gaussian white noise at the nth communication user, which has an expectation 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 finding 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 formed, R i represents the beam vector r designed by the base station for the i-th communication user, i≠n i The beamforming matrix associated with the i-th, i≠n-th communication user is formed, 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 consisting 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 represents 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, Indicates 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 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), Indicates the mathematical expectation, R r Denotes the dedicated radar signal r r The covariance matrix of (t),

[0077] The perceptual eavesdropper attempts to silently obtain the base station's perceptual information through its received signals in order to further perform dangerous actions on the system. Its behavior of stealing perceptual information is now characterized as detecting radar targets. Since the perceptual eavesdropper is an illegal node in the system and does not have information about the transmitted signal, it will use the receive beamforming method to detect the received power along the incoming wave direction, similar to passive radar technology. The receive 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 as follows:

[0078] Step 2.c1: The received signal y of the eavesdropper is perceived 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 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, 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 the radar target exists. B0 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. For example: B,n For example, ρ represents the Rice factor, here we take 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 the 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, Indicates the non-line-of-sight link channel from the base station to the IRS, All the terms in obey the complex Gaussian distribution with mean 0 and variance 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 the complex Gaussian distribution with mean 0 and variance 1, that is,

[0085] Step 3: To achieve energy conservation, while ensuring reliable communication, perception, and perception security, the base station's transmit power is minimized. Using the received signal-to-interference-and-noise ratio (SINR) of each communication user, the probability of detecting a radar target by the perception receiver, and the probability of detecting a target by the perception eavesdropper as constraints, the beamforming matrix associated with each communication user, the covariance matrix of the dedicated radar signal, and the correlation matrix of the IRS phase shift matrix are jointly optimized to construct an optimization problem. The beamforming matrix associated with each communication user is composed of the beam vector designed by the base station for that 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 "subject to the constraints...", tr(R) represents the transmission power of the base station, c Indicates the receiving signal-to-interference-and-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-and-noise ratio of the communication user; constraint C2 is used to ensure reliable perception, in the form of the perception receiver detecting the radar target with a probability greater than or equal to the threshold Γ. R Constraint C3 is used to ensure the security of perception. Specifically, it 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, which does not have a power amplification function, the constraint C4 ensures that the phase shift modulus of each element in the optimized IRS, i.e., the antenna, is 1; the constraints C5 and C6 ensure that the beamforming matrix R associated with 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 sensing 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 sensing 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-and-noise ratio of each communication user, the optimization problem is converted into a semi-definite relaxation problem.

[0095] Further defining, 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 to 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 eavesdropper's detection probability P of 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 intervals 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-definite programming method, ignore the constraint C7 in the optimization problem and transform the optimization problem into a semi-definite relaxation problem, which can be described as:

[0099]

[0100] Here, ignoring the rank-one constraint and looking for a rank-one restoration method in the subsequent process can yield a better solution.

[0101] Step 5: Due to the high coupling of variables, the semi-definite relaxation problem is non-convex. Therefore, 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 IRS phase shift matrix, 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 IRS phase shift matrix. Given the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal, the correlation matrix of the IRS phase shift matrix 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 defining, 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 is 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 iter-th outer 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 sub-problem The value is the initialization value, given when iter>1 The value 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 outer iteration time. A preliminary solution Among them, R is 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 denote 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. 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 k-th 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) , in the process of solving, 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: Judgment 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 the 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 used to restore the rank of the matrix optimization variable in the semidefinite 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 、 Their respective local optimal solutions; where 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-definite relaxation problem. Here, the threshold is set to 0.0001, and the "=" in iter=iter+1 is an 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 two-dimensional coordinates of the base station are set to (30,0), the two-dimensional coordinates of the IRS are set to (0,15), the two-dimensional coordinates of the N communication users are randomly selected within a circle with a center of (25,22) and a radius of 2, the two-dimensional coordinates of the radar target are set to (30,50), the two-dimensional coordinates of the sensing eavesdropper are set to (10,40), and the two-dimensional coordinates of the sensing receiver are set to (30,70).

[0121] In the simulation, the comparison methods are the IRS phase shift matrix random value method and the ISAC method without IRS deployment. The IRS phase shift matrix random value method refers to the phase shift matrix of the IRS deployed in the environment. The diagonal elements of are randomly assigned values, and the base station beam is optimized based on the phase shift of the random values. The ISAC-only 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 Γ R is 0.88, and the communication rate threshold R c =log2(1+ξ c ) is a comparison curve of the base station's transmission power change when the data 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 shows 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 =log2(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 eavesdropper is Γ e The comparison curve of the base station's transmission power 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 =log2(1+ξ c ) is 5.5 bps / Hz, the detection probability threshold of the eavesdropper is Γ e is 0.29, and the detection probability threshold of the sensing receiver is Γ R The comparison curve of the base station's transmission power changes from 0.8 to 0.9. Figure 5It can be seen from the figure 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 is much smaller than that of the two comparison methods under the same conditions.

Claims

1. An energy-saving and security-aware optimization method based on ISAC-IRS, characterized by The following steps are involved: Step 1: Establish an ISAC-IRS system that considers a perceptual eavesdropper. The ISAC-IRS system is configured 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, a perceptual receiver for detecting the radar target based on its received signal, and a perceptual eavesdropper that attempts to monitor the base station's transmitted signal to silently obtain perceptual information. The base station's transmitted signal is composed of the superposition of multiple communication signals and a dedicated radar signal. Step 2: Establish the communication performance indicators, radar perception performance indicators, and perception eavesdropping performance indicators of the ISAC-IRS system. The communication performance indicator is measured by the received signal-to-interference-and-noise ratio of each communication user. The radar perception performance indicator is measured by the detection probability of the radar target by the perception receiver. The perception eavesdropping performance indicator is measured by the detection probability of the target by the perception eavesdropper. Step 3: To achieve energy conservation, while ensuring reliable communication, perception, and perception security, the base station's transmit power is minimized. Using the received signal-to-interference-and-noise ratio (SINR) of each communication user, the probability of detecting a radar target by the perception receiver, and the probability of detecting a target by the perception eavesdropper as constraints, the beamforming matrix associated with each communication user, the covariance matrix of the dedicated radar signal, and the correlation matrix of the IRS phase shift matrix are jointly optimized to construct an optimization problem. The beamforming matrix associated with each communication user is composed of the beam vector designed by the base station for that communication user. Step 4: The optimization problem is converted into a semi-definite relaxation problem by rewriting the detection probability constraint of the sensing receiver for the radar target into a form in which the detection probability is only related to the covariance matrix of the base station's transmitted signal, and rewriting the detection probability constraint of the sensing eavesdropper for the target into a linear form. 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-and-noise ratio of each communication user are ignored. Step 5: Decompose the semidefinite relaxation problem into two subproblems. The first subproblem 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 IRS phase shift matrix, the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal are optimized. In this case, the first subproblem is a convex problem. The second subproblem is about the correlation matrix of the IRS phase shift matrix. Given the beamforming matrix related to each communication user and the covariance matrix of the dedicated radar signal, the correlation matrix of the IRS phase shift matrix is ​​optimized. In this case, the second subproblem 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 transpose operation, and s(t) represents the base station's transmitted signal. 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 the imaginary part, represents the phase shift of the lth antenna of the IRS, l=1,2,…,T IRS , z n (t) represents the Gaussian white noise at the nth communication user, which has an expectation 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 finding 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 formed, represents the channel matrix consisting 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 represents 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, Indicates 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 Complex Gaussian distribution, 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 the modulo operator, and 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), Indicates the mathematical expectation, R r Denotes the 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 obtaining the detection probability of the target by the perceived eavesdropper is as follows: Step 2.c1: The received signal y of the eavesdropper is perceived 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 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 the radar target exists. B0 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.

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 Indicates the receiving signal-to-interference-and-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-definite programming method, ignore the constraint C7 in the optimization problem and transform the optimization problem into a semi-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 is 1; initialize R n ,n∈{1,2,…,N},R r 、 Step 6.2: Use the convex optimization solver to solve the first subproblem and get R at the iter-th 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 sub-problem 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 A preliminary solution Among them, R is 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 denote 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, and 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. The second sub-problem is transformed into: Among them, η represents a variable weight; Step 6.4.4: Use the 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, increase the value of η in the kth internal iteration so that the value of p approaches 0; Step 6.4.5: Judgment 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 the 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 、 Their respective local optimal solutions; where iter = 1, the objective function value of the iter-1th external iteration is based on R n ,n∈{1,2,…,N},R r 、 The objective function in the semi-definite relaxation problem is obtained by calculating the initial value of .

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