Safety perception and communication optimization method based on ISAC-IRS

Abstract

The invention discloses a security perception and communication optimization method based on ISAC-IRS, and aims to improve communication security and perception performance and confront a communication eavesdropper and a perception eavesdropper, the method establishes a system model comprising a base station, an IRS, multiple users, a target, a perception eavesdropper and a perception receiver, and comprehensively considers communication and perception performance indexes, so as to improve the communication security and perception performance. By optimizing a correlation matrix of a communication beam forming matrix, a covariance matrix of a special radar signal and a phase shift matrix of an IRS, the detection probability of a sensing receiver to a target is improved. By means of the positive semidefinite relaxation and alternating optimization algorithm, communication eavesdropping and sensing eavesdropping behaviors can be restrained while communication safety is guaranteed, and the detection accuracy of the sensing receiver is improved. The method has the advantages that the communication performance can be improved, communication eavesdropping and sensing eavesdropping are suppressed, and the detection probability of a sensing receiver to a target is improved.

Description

Technical Field

[0001] The present invention relates to communication perception integration (ISAC) and intelligent reflecting surface (IRS) technology, and in particular to a security perception and communication optimization method based on ISAC-IRS (communication perception integration combined with intelligent reflecting surface). The method takes into account the situation that perception eavesdroppers and communication eavesdroppers exist in the environment at the same time, aims to maximize the detection probability of a perception receiver to a target, and takes the received signal-to-interference-noise ratio at each user, the signal-to-interference-noise ratio of the communication signal of each user eavesdropper, and the detection probability of the perception eavesdropper to the target after performing energy detection on its received signal as constraints to jointly optimize the communication beamforming matrix related to each user, the covariance matrix of a dedicated radar signal, and the correlation matrix of a phase shift matrix of an IRS. Background Art

[0002] Integrated Communication and Sensing (ISAC) has been identified as one of the application scenarios of the sixth generation of wireless networks in the future. It has the ability to support a variety of new applications and is one of the hottest topics in the field of wireless communications today. In recent years, with the advancement of multi-antenna technology, the performance of ISAC has been greatly improved. In particular, the use of multi-antenna transmitters in ISAC systems can not only improve multiplexing and diversity gain, thereby improving communication rate and reliability, but also provide additional degrees of freedom for radar perception, thereby improving perception resolution and accuracy. However, under certain system resources, the two functions of communicating with users and perceiving targets inevitably have a competitive relationship for system resources. The joint design of communication and perception beams can effectively coordinate these two functions to achieve the required system performance. Therefore, the joint design of communication and perception beams has become a promising ISAC solution.

[0003] Intelligent Reflecting Surface (IRS) is one of the key enabling technologies for next-generation wireless systems, which can provide massive connections and ultra-reliable transmission, as well as improve target detection and parameter perception accuracy. Due to the low cost and easy deployment of IRS, deploying IRS in ISAC can create multiple line-of-sight links, and combined with multi-antenna technology, it can provide the system with additional spatial degrees of freedom, thereby further improving perception and communication performance. Therefore, the research on introducing IRS into ISAC for more sophisticated design has received widespread attention.

[0004] The emergence of ISAC coordinates and integrates communication and perception systems to achieve mutual performance gains, but also raises serious security issues. First, in order to facilitate perception, the ISAC system uses an optimized transmission information beam to aim at the sensing target to improve the perception performance, but it directly leads to the problem of information leakage when the sensing target is an information eavesdropper. In addition, the ISAC system also faces new perception security issues, because the perception information may be attacked by the perception eavesdropper, resulting in the leakage of perception information. The perception eavesdropper in the ISAC system can silently intercept the perception results without actively transmitting its own signal by listening to the perception signal transmitted by the ISAC transmitter. Based on the intercepted perception results, the behavior of the ISAC system is inferred, which may further initiate behaviors that endanger the performance of the system. This passive eavesdropping of the perception information by the perception eavesdropper brings additional privacy and security challenges to the design of the ISAC system, and advanced mechanisms are needed to ensure the confidentiality and security of the perception data. Today, there are few studies on the impact of perception eavesdroppers on the ISAC system. One study proposes to use perception mutual information to measure the degree of perception eavesdropping and combine it with artificial noise technology to combat perception eavesdroppers. Another study is aimed at jointly optimizing base station beamforming in cell-free ISAC systems to counter perception and communication eavesdroppers. However, the existence of perception eavesdropping in ISAC-IRS systems has not received much attention and research. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide an optimization method for security perception and communication based on ISAC-IRS, which takes into account the situation where both perception eavesdroppers and communication eavesdroppers exist in the environment, and jointly optimizes the communication beamforming matrix related to each user, the covariance matrix of the dedicated radar signal, and the correlation matrix of the IRS phase shift matrix, so as to achieve the improvement of communication performance, the suppression of communication eavesdropping and perception eavesdropping, and the improvement of the detection probability of the perception receiver for the target.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: an optimization method for security perception and communication based on ISAC-IRS, characterized by comprising the following steps:

[0007] Step 1: Establish a system model based on ISAC-IRS with both communication eavesdroppers and perceptual eavesdroppers. The model contains a base station, an IRS, multiple users, a target, a perceptual eavesdropper, and a perceptual receiver. The target also acts as a communication eavesdropper. The base station transmits signals to each user and target with the assistance of the IRS. The signal transmitted by the base station is composed of multiple communication signals and a special radar signal. The target, which acts as a communication eavesdropper, attempts to eavesdrop on the communication signals transmitted by the base station to each user. The target reflects its received signal to the perceptual eavesdropper and the perceptual receiver. The perceptual eavesdropper attempts to silently detect the target based on its received signal and attempts to perceive the target's location. The perceptual receiver detects the target based on its received signal and perceives the target's location.

[0008] Step 2: Establish the communication performance index, perception performance index, communication eavesdropping performance index, and perception eavesdropping performance index of the system model based on ISAC-IRS and with both communication eavesdroppers and perceptual eavesdroppers. The communication performance index is measured by the received signal-to-interference-to-noise ratio at each user, the perception performance index is measured by the detection probability of the target by the perception receiver, the communication eavesdropping performance index is measured by the signal-to-interference-to-noise ratio of the communication signal of each user eavesdropped by the target acting as a communication eavesdropper, and the perception eavesdropping performance index is measured by the detection probability of the target by the perception eavesdropper after performing energy detection on its received signal;

[0009] Step 3: Taking the received signal-to-interference-noise ratio at each user, the signal-to-interference-noise ratio of the communication signal of each user eavesdropped by the target acting as a communication eavesdropper, and the detection probability of the target by the perceptual eavesdropper after performing energy detection on its received signal as constraints, jointly optimize the communication beamforming matrix related to each user, the covariance matrix of the dedicated radar signal, and the correlation matrix of the phase shift matrix of the IRS, with the goal of maximizing the detection probability of the perceptual receiver to the target, and construct an optimization problem, wherein the communication beamforming matrix related to each user is composed of the beamforming vector designed by the base station for the user;

[0010] Step 4: The optimization problem is transformed into a semi-definite relaxation problem by simplifying the objective function in the optimization problem, rewriting the constraints on the detection probability of the target after the sensing eavesdropper performs energy detection on its received signal, and ignoring the rank-one constraint;

[0011] Step 5: Decompose the semi-definite relaxation problem into two sub-problems. The first sub-problem is about the communication beamforming matrix related to each user and the covariance matrix of the dedicated radar signal. Given the correlation matrix of the phase shift matrix of the IRS, the communication beamforming matrix related to each 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 communication beamforming matrix related to each 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.

[0012] Step 6: Use the alternating optimization algorithm to iteratively solve the first and second subproblems to obtain the local optimal solutions of the communication beamforming matrix related to each user, the covariance matrix of the dedicated radar signal, and the correlation matrix of the IRS phase shift matrix.

[0013] In step 1, the number of users is K, each of which is equipped with a single antenna; the 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 with half-wavelength intervals, and the number of their antennas is N, N, M, and N, respectively. e .

[0014] In step 2, the process of obtaining the received signal to interference and noise ratio at the kth user is as follows:

[0015] Step 2.a1: Substitute the received signal y at the kth user at time t k (t) is expressed as Where k = 1, 2, ..., K, h B,k represents the channel from the base station to the kth user, h r,k represents the channel from IRS to the kth user, represents the channel from the base station to the IRS, Θ represents the phase shift matrix of the IRS, Θ = diag(θ H ), diag(·) is used to extract or construct the diagonal elements of a matrix, e is a natural constant, j is the imaginary part, φ m represents the phase shift of the mth antenna of IRS, m=1,2,…,M, x(t) represents the signal transmitted by the base station at time t, w k represents the beamforming vector designed by the base station for the kth user, s k (t) represents the communication signal transmitted by the base station to the kth user at time t, w r (t) represents the dedicated radar signal transmitted by the base station at time t, n k (t) represents the Gaussian white noise at the kth user at time t, which has an expectation of 0 and a variance of The complex Gaussian distribution of Indicates n k (t) The noise power, the superscript “H” indicates the conjugate transpose operation;

[0016] Step 2.a2: According to y k (t), and obtain the received signal-to-interference-and-noise ratio SINR at the kth user c,k , Among them, tr(·) means to find the trace of the matrix, represents the correlation matrix of Θ, v H =[θ H ,1],U k represents the channel matrix composed of the direct channel from the base station to the kth user and the cascade channel from the base station to the IRS and then to the kth user, Indicated by w k The communication beamforming matrix formed by

[0017] In step 2, the process of acquiring the detection probability of the target by the perception receiver is as follows:

[0018] Step 2.b1: The received signal y at the sensing receiver at time t R (t) is expressed as Where β represents the complex reflection coefficient of the target reflected to the sensing receiver, represents the channel from the target to the sensing receiver, represents the channel from the base station to the target, represents the channel from IRS to the target, n R (t) represents the Gaussian white noise at the receiver at time t, which has a mean of 0 and a variance of The complex Gaussian distribution of Indicates n R (t) is the noise power, I represents the unit matrix;

[0019] Step 2.b2: According to y R (t), and obtain the detection probability P of the target by the sensing receiver R , Among them, Q() represents the right tail distribution function of Gaussian distribution, P FA represents the false alarm probability, "|·|" is the modulo operator, G represents the channel matrix composed of the direct channel from the base station to the target and the cascade channel from the base station to the IRS and then to the target, R represents the covariance matrix of x(t), It means to find the mathematical expectation. Indicates w rThe covariance matrix of (t),

[0020] In step 2, the process of obtaining the signal to interference noise ratio of the communication signal of the kth user by the target eavesdropper acting as a communication eavesdropper is as follows:

[0021] Step 2.c1: The received signal at the target of the communication eavesdropper at time t Expressed as in, represents the Gaussian white noise at the target of the communication eavesdropper at time t, which has an expected value of 0 and a variance of The complex Gaussian distribution of express The noise power;

[0022] Step 2.c2: According to Get the signal-to-interference-noise ratio of the communication signal of the kth user that acts as a communication eavesdropper

[0023] In step 2, the process of acquiring the detection probability of the target by the perceptual eavesdropper after performing energy detection on the received signal is as follows:

[0024] Step 2.d1: The received signal y at the eavesdropper at time t is sensed e (t) is expressed as ,

[0025] in, represents the angle of the target relative to the sensing eavesdropper, Indicates the position of the perceived eavesdropper relative to The steering vector, β e represents the complex reflection coefficient reflected from the target to the sensing eavesdropper, represents the channel from the target to the sensing eavesdropper, represents the channel from the base station to the sensing eavesdropper, represents the channel from IRS to the sensing eavesdropper, n e (t) represents the Gaussian white noise perceived by the eavesdropper at time t, which has a mean of 0 and a variance of The complex Gaussian distribution of Indicates n e (t) noise power;

[0026] Step 2.d2: According to y e (t), and obtain the detection probability P of the target after the perceptual eavesdropper performs energy detection on the received signal e , in,

[0027] In step 3, the communication beamforming matrix associated with the kth user is: The covariance matrix of the dedicated radar signal is The correlation matrix of the IRS phase shift matrix is The optimization problem is described as:

[0028]

[0029] C3:P e ≤Λ,

[0030]

[0031] in, γ c represents the lower threshold of the user's received signal-to-interference-noise ratio, γ e represents the upper threshold of the eavesdropping signal-to-interference-to-noise ratio, γ c >γ e , Λ represents the maximum detection probability of the perceived eavesdropper, P max represents the total transmission power of the base station, rank(·) represents the rank of the matrix, express The element at the m'th row and m'th column in .

[0032] The specific process of step 4 is as follows:

[0033] Step 4.1: In P R The false alarm probability P in the expression FA When the complex reflection coefficient β of the target reflected to the sensing receiver is a given fixed value, the objective function in the optimization problem is equivalent to

[0034] Step 4.2: For P e , which has the same equation as Similar mathematical form allows the use of equations The monotonically increasing property when 0<x<1 and x>1 will optimize the constraint P in the problem. e ≤Λ can be rewritten as Among them, Γ d It is the root of the equation when f(x) = Λ;

[0035] Step 4.3: Ignore the rank-one constraints C8 and C9;

[0036] Step 4.4: Describe the semi-positive definite relaxation problem of the optimization problem as:

[0037]

[0038] The specific process of step 6 is as follows:

[0039] Step 6.1: Let iter represent the number of iterations, and the initial value of iter is 1; initialize

[0040] Step 6.2: Use the convex optimization solver to solve the first subproblem and get the iterth iteration and The solution of and Among them, when iter = 1, the given The value is the initialization value, given when iter>1 The value is obtained at the iter-1th iteration Solution

[0041] Step 6.3: Use the convex optimization solver to solve the second subproblem and get the iterth iteration The initial solution Among them, the given and The value of and

[0042] Step 6.4: and As the initial value, the iterative rank minimization method is used to Perform rank-one recovery to obtain the iter-th iteration Solution The specific process is:

[0043] Step 6.4.1: Let e ​​represent the number of internal iterations and the initial value of l be 1;

[0044] Step 6.4.2: The rank-one constraint Convert to Among them, p is the auxiliary variable introduced, I M represents the identity matrix of dimension M×M, and Z is (l-1) Indicated by The characteristic matrix consists of the eigenvectors corresponding to the M small eigenvalues ​​among the M+1 eigenvalues ​​obtained by eigendecomposition. When l>1, Z (l-1) Indicates that in the l-1th internal iteration The internal iteration value of The characteristic matrix consists of the eigenvectors corresponding to the M small eigenvalues ​​among the M+1 eigenvalues ​​obtained by eigendecomposition;

[0045] Step 6.4.3: Add a penalty term ηp to the objective function of the second sub-problem and transform the second sub-problem into:

[0046]

[0047] stC1,C2,C3',C5,

[0048]

[0049] Among them, η represents a variable weight;

[0050] Step 6.4.4: Use the convex optimization solver to solve the problem in step 6.4.3 and obtain the l-th internal iteration time The internal iteration value of Among them, the given and The value of and During the solution process, increase the value of η in the lth internal iteration so that the value of p approaches 0;

[0051] Step 6.4.5: Judgement Is the maximum value of the M small eigenvalues ​​in the M+1 eigenvalues ​​obtained by eigendecomposition less than the internal iteration threshold? If so, the iteration ends and As the iterth iteration Solution Otherwise, set l = l + 1 and return to step 6.4.2 to continue;

[0052] Step 6.5: According to Calculate the objective function in the semi-positive definite relaxation problem and obtain the objective function value of the iter-th iteration; then make the difference between the objective function value of the iter-th iteration and the objective function value of the iter-1-th iteration; then determine whether the ratio of the difference to the objective function value of the iter-1-th 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 Corresponding as Their respective local optimal solutions; where iter = 1, the objective function value of the iter-1th iteration is based on The initial value of is used to calculate the objective function in the semi-positive definite relaxation problem.

[0053] Compared with the prior art, the advantages of the present invention are:

[0054] 1) The method of the present invention deploys IRS in the ISAC system to simultaneously perform communication and perception functions, 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. In addition, the method of the present invention takes into account the situation where the channel strength between nodes (base stations, IRS, users, targets, perception eavesdroppers, and perception receivers) is poor in a more complex propagation environment, and introduces IRS to provide more favorable channel conditions for each node. In the optimization solution of the problem, for the optimization of IRS phase shift, semi-positive relaxation and iterative rank minimization method are used to solve it, which can effectively and accurately obtain the optimal solution.

[0055] 2) Traditional communication systems mainly focus on protecting the security of data transmission, that is, preventing the intrusion of communication eavesdroppers. However, in the present invention, in addition to considering communication eavesdroppers, it is also necessary to protect against perception eavesdroppers, that is, attackers who try to obtain base station perception information by receiving signals. This dual protection mechanism improves the security of the overall system and ensures that both communication content and perception data are protected. Traditional technologies may compromise between security and perception performance, while the method of the present invention achieves the best balance between the two, greatly improving the overall performance of the system. In the method of the present invention, the eavesdropping behavior of the perception eavesdropper is characterized as an action of perceiving the target to perform the task of destroying the system perception, and the detection probability of the perception eavesdropper on the target is used to measure the degree of perception eavesdropping. In the subsequent optimization problem, the detection probability of the perception eavesdropper on the target is less than a certain threshold to ensure better perception security. By considering the influence of perception eavesdroppers and communication eavesdroppers, the method of the present invention can design a more efficient optimization strategy to maximize the transmission quality and security of perception data and communication data. Integrating perception and communication functions in one system and considering the security of both can promote the design and application of new multifunctional systems. The ISAC-IRS system proposed in the present invention can simultaneously meet the requirements of data transmission, environmental perception and communication and perception security assurance on a single platform, thereby reducing the complexity and cost of the system.

[0056] 3) The alternating optimization method is used to effectively transform the optimization problem into a convex problem, eliminating the tedious process of converting non-convex to convex; the iterative rank minimization method has the characteristics of low complexity and fast solution, and can quickly and effectively restore the rank-one solution. Combining these methods can quickly and easily obtain the solution to the original problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is a flowchart of the overall implementation process of the method of the present invention;

[0058] Figure 2It is a simple schematic diagram of the system model based on ISAC-IRS with both communication eavesdroppers and perception eavesdroppers.

[0059] Figure 3 The maximum detection probability Λ of the method of the present invention and the comparative method when the perceived eavesdropper is 0.29 and the user's communication rate threshold R c =log2(1+γ c ) changes, a comparison curve diagram of the detection probability change of the target by the perception receiver;

[0060] Figure 4 The communication rate threshold R of the user in the method of the present invention and the comparative method c =log2(1+γ c ) is 5.5 bps / Hz and the maximum detection probability Λ of the perceived eavesdropper changes, a comparison curve diagram of the detection probability change of the target by the perception receiver. DETAILED DESCRIPTION

[0061] The present invention is further described in detail below with reference to the accompanying drawings.

[0062] The present invention proposes an optimization method for security perception and communication based on ISAC-IRS, which optimizes the base station beamforming vector and IRS phase shift in the ISAC-IRS system where both communication eavesdroppers and perception eavesdroppers exist. The goal of the method of the present invention is to optimize the base station beamforming vector and IRS phase shift under the premise of ensuring communication security and perception security, so as to maximize the detection probability of the perception receiver to the target. Since the variables in the optimization problem are coupled with each other, the optimization problem presents a non-convex property, so the original problem is decomposed into two sub-problems, and then the alternating optimization algorithm is used to iteratively solve the two sub-problems, gradually approaching the local optimal solution.

[0063] The present invention proposes an optimization method for security perception and communication based on ISAC-IRS, and its overall implementation flow chart is as follows: Figure 1 As shown, it includes the following steps:

[0064] Step 1: Establish a system model based on ISAC-IRS with both communication eavesdroppers and sensory eavesdroppers, such as Figure 2As shown, the model is provided with a base station, an IRS, multiple users, a target, a perceptual eavesdropper and a perceptual receiver. The target also acts as a communication eavesdropper. The base station transmits signals to each user and target with the assistance of the IRS. The signals transmitted by the base station are composed of multiple communication signals and a special radar signal superimposed. The target, which acts as a communication eavesdropper, attempts to eavesdrop on the communication signals transmitted by the base station to each user. The target reflects its received signals to the perceptual eavesdropper and the perceptual receiver. The perceptual eavesdropper attempts to silently detect the target based on its received signals and attempts to sense the position of the target. The perceptual receiver detects the target based on its received signals and senses the position of the target. Here, the number of users is K, each user is equipped with a single antenna, K>1, and K=3 in this embodiment; the target is equipped with a single antenna; the base station, perceptual receiver, IRS and perceptual eavesdropper are all equipped with uniform linear arrays (ULA) with half-wavelength intervals, and the number of their antennas is N, N, M and N respectively. e In this embodiment, N=9, M=18, N e =8.

[0065] Here, the number of communication signals in the signal transmitted by the base station is consistent with the number of users. The signal transmitted by the base station provides services to multiple users at the same time and senses specific targets to ensure communication security and provide additional spatial freedom for system design; IRS is usually deployed in the space between the base station and the users and targets to provide additional line-of-sight links between the base station and the objects served by the base station to further improve perception and communication performance; the perceptual eavesdropper can infer the behavior of the system after intercepting the perception results.

[0066] Step 2: Establish the communication performance index, perception performance index, communication eavesdropping performance index, and perception eavesdropping performance index of the system model based on ISAC-IRS and with both communication eavesdroppers and perceptual eavesdroppers. The communication performance index is measured by the received signal-to-interference-and-noise ratio (SINR) at each user. The perception performance index is measured by the detection probability of the target by the perception receiver. The communication eavesdropping performance index is measured by the signal-to-interference-and-noise ratio of the communication signal of each user eavesdropped by the target acting as a communication eavesdropper, that is, the eavesdropping signal-to-interference-and-noise ratio of the communication eavesdropper. The perception eavesdropping performance index is measured by the detection probability of the target by the perception eavesdropper after performing energy detection on its received signal. The perception eavesdropper is assumed to be unaware of the signal transmitted by the base station, so that the perception technology that requires the signal transmitted by the base station is not applicable. Therefore, it is assumed that the perception eavesdropper detects the transmission power from a specific direction, performs target detection, and uses the receiving beamforming related to the target direction to assist detection.

[0067] Preferably, in step 2, the process of obtaining the received signal to interference and noise ratio at the kth user is:

[0068] Step 2.a1: Substitute the received signal y at the kth user at time t k (t) is expressed as Where k = 1, 2, ..., K, h B,k represents the channel from the base station to the kth user, h r,k represents the channel from IRS to the kth user, represents the channel from the base station to the IRS, Θ represents the phase shift matrix of the IRS, Θ = diag(θ H ), diag(·) represents the diagonal elements used to extract or construct the matrix, e is a natural constant, e = 2.71…, j is the imaginary part, φ m represents the phase shift of the mth antenna of IRS, m=1,2,…,M, x(t) represents the signal transmitted by the base station at time t, w k represents the beamforming vector designed by the base station for the kth user, s k (t) represents the communication signal transmitted by the base station to the kth user at time t, w r (t) represents the dedicated radar signal transmitted by the base station at time t, n k (t) represents the Gaussian white noise at the kth user at time t, which has an expectation of 0 and a variance of The complex Gaussian distribution of Indicates n k The noise power of (t) is taken as The superscript "H" indicates the conjugate transpose operation.

[0069] Step 2.a2: According to y k (t), and obtain the received signal-to-interference-and-noise ratio SINR at the kth user c,k , Among them, tr(·) means to find the trace of the matrix, represents the correlation matrix of Θ, v H =[θ H ,1],U k represents the channel matrix composed of the direct channel from the base station to the kth user and the cascade channel from the base station to the IRS and then to the kth user, Will Substituting the subscript k in U with i gives i , Indicated by w k The communication beamforming matrix formed by Will Substituting the subscript k in the equation with i yields

[0070] Preferably, in step 2, the process of acquiring the detection probability of the target by the perception receiver is as follows:

[0071] Step 2.b1: The received signal y at the sensing receiver at time t R (t) is expressed as Where β represents the complex reflection coefficient of the target reflected to the sensing receiver, represents the channel from the target to the sensing receiver, represents the channel from the base station to the target, represents the channel from IRS to the target, n R (t) represents the Gaussian white noise at the receiver at time t, which has a mean of 0 and a variance of The complex Gaussian distribution of Indicates n R The noise power of (t) is taken as I represents the identity matrix.

[0072] Step 2.b2: According to y R (t), and obtain the detection probability P of the target by the sensing receiver R , Among them, Q() represents the right tail distribution function of Gaussian distribution, P FA Indicates the false alarm probability, here we take P FA = 0.0001, "|·|" is the modulo operator, G represents the channel matrix composed of the direct channel from the base station to the target and the cascade channel from the base station to the IRS and then to the target, R represents the covariance matrix of x(t), It means to find the mathematical expectation. Indicates w r The covariance matrix of (t),

[0073] Preferably, in step 2, the process of acquiring the signal to interference noise ratio of the communication signal of the k-th user by the target eavesdropper acting as a communication eavesdropper is as follows:

[0074] Step 2.c1: The received signal at the target of the communication eavesdropper at time t Expressed as in, represents the Gaussian white noise at the target of the communication eavesdropper at time t, which has an expected value of 0 and a variance of The complex Gaussian distribution of express The noise power is taken as

[0075] Step 2.c2: According to Get the signal-to-interference-noise ratio of the communication signal of the kth user that acts as a communication eavesdropper

[0076] Preferably, in step 2, the process of acquiring the detection probability of the target by the sensing eavesdropper after performing energy detection on the received signal is as follows:

[0077] Step 2.d1: Assume that the perceptual eavesdropper uses the steering vector As the receiving beam, the receiving power is detected along the target direction, similar to the passive radar technology, and the receiving signal y at the eavesdropper at time t is sensed e (t) is expressed as ,

[0078] in, represents the angle of the target relative to the sensing eavesdropper, Indicates the position of the perceived eavesdropper relative to The steering vector, β e represents the complex reflection coefficient reflected from the target to the sensing eavesdropper, represents the channel from the target to the sensing eavesdropper, represents the channel from the base station to the sensing eavesdropper, represents the channel from IRS to the sensing eavesdropper, n e (t) represents the Gaussian white noise perceived by the eavesdropper at time t, which has a mean of 0 and a variance of The complex Gaussian distribution of Indicates n e The noise power of (t) is taken as

[0079] Step 2.d2: According to y e (t), and obtain the detection probability P of the target after the perceptual eavesdropper performs energy detection on the received signal e , in,

[0080]

[0081] The above channels are all modeled as line-of-sight channel models, which are in the form of path loss coefficient multiplied by the steering vector. The path loss coefficient is modeled as in, Represents the reference path loss parameter per unit distance, where d represents the distance, α represents the path loss exponent, It is equal for each channel, so the path loss coefficient is only related to the distance and the path loss exponent.

[0082] Specifically, h B,k 、h r,k , Both are modeled as line-of-sight channel models, h B,k =ρ B,k a B (θ B,k ), h r,k =ρ r,k a r (θ r,k ), ρ B,k represents the path loss coefficient from the base station to the kth user, d B,k represents the distance from the base station to the kth user, α B,k Represents the path loss index from the base station to the kth user, where α is taken B,k =3.5,θ B,k represents the angle of the kth user relative to the base station, a B (θ B,k ) represents the base station relative to θ B,k The steering vector, ρ r,k represents the path loss coefficient from IRS to the kth user, a B (θ B,k ) has a dimension of N×1, d r,k represents the distance from IRS to the kth user, α r,k Represents the path loss index from IRS to the kth user, where α is taken r,k =2,θ r,k represents the angle of the kth user relative to the IRS, a r (θ r,k ) represents the IRS relative to θ r,k The steering vector, a r (θ r,k ) has a dimension of M×1, ρ Br represents the path loss coefficient from the base station to the IRS, d Br represents the distance from the base station to the IRS, α Br Represents the path loss index from the base station to the IRS, where α is taken Br =2,θ Br represents the angle of IRS relative to the base station, θ rB represents the angle of the base station relative to the IRS, a B (θ Br ) represents the base station relative to θ Br The steering vector, a B (θ Br ) has a dimension of N×1, ar (θ rB ) represents the IRS relative to θ rB The steering vector, a r (θ rB ) has a dimension of M×1.

[0083] Specifically, Both are modeled as line-of-sight channel models. in, represents the path loss coefficient from the target to the sensing receiver, represents the distance from the target to the sensing receiver, represents the path loss index from the target to the sensing receiver, where represents the angle of the sensing receiver relative to the target, Represents the sensing receiver relative to The guiding vector, represents the path loss coefficient from the base station to the target, Indicates the distance from the base station to the target. Represents the path loss index from the base station to the target, where represents the angle of the target relative to the base station, Indicates the base station relative to The guiding vector, represents the path loss coefficient from IRS to the target, represents the distance from IRS to the target, represents the path loss index from IRS to the target, where represents the angle of the target relative to the IRS, Indicates the IRS relative to The guiding vector.

[0084] Specifically, Both are modeled as line-of-sight channel models. in, represents the path loss coefficient from the target to the sensing eavesdropper, represents the distance from the target to the sensing eavesdropper, represents the path loss index from the target to the sensing eavesdropper, where ρ Be represents the path loss coefficient from the base station to the sensing eavesdropper, d Be represents the distance from the base station to the sensing eavesdropper, α BeRepresents the path loss index from the base station to the sensing eavesdropper, where α is taken Be =3.5,θ Be represents the angle of the perceived eavesdropper relative to the base station, a B (θ Be ) represents the base station relative to θ Be The steering vector, θ eB represents the angle of the base station relative to the sensing eavesdropper, a e (θ eB ) represents the position of the sensing eavesdropper relative to θ eB The steering vector, a e (θ eB ) dimension is N e ×1,ρ re represents the path loss coefficient from IRS to the sensing eavesdropper, d re represents the distance from IRS to the sensing eavesdropper, α re represents the path loss index from IRS to the sensing eavesdropper, where α is taken re =2,θ re represents the angle of the perceived eavesdropper relative to the IRS, a r (θ re ) represents the IRS relative to θ re The steering vector, θ er represents the angle of the IRS relative to the perceived eavesdropper, a e (θ er ) represents the position of the sensing eavesdropper relative to θ er The steering vector, a e (θ er ) dimension is N e ×1.

[0085] Step 3: Taking the received signal-to-interference-noise ratio at each user, the signal-to-interference-noise ratio of the communication signal of each user eavesdropped by the target acting as a communication eavesdropper, and the detection probability of the target by the perceptual eavesdropper after performing energy detection on its received signal as constraints, jointly optimize the communication beamforming matrix related to each user, the covariance matrix of the dedicated radar signal, and the correlation matrix of the phase shift matrix of the IRS, with the goal of maximizing the detection probability of the target by the perceptual receiver, and construct an optimization problem, where the communication beamforming matrix related to each user is composed of the beamforming vector designed by the base station for the user.

[0086] Further defined, in step 3, the communication beamforming matrix associated with the kth user is The covariance matrix of the dedicated radar signal is The correlation matrix of the IRS phase shift matrix is The optimization problem is described as:

[0087]

[0088] C3:P e ≤Λ,

[0089]

[0090] Among them, max is the maximum value function, st means "subject to...", To define the symbol, γ c represents the lower threshold of the user's received signal-to-interference-noise ratio, γ e represents the upper threshold of the eavesdropping signal-to-noise ratio, and γ c >γ e To ensure communication security, Λ represents the maximum detection probability of the perceived eavesdropper, P max Represents the total transmission power of the base station, where γ c =2 4.5 -1, γ e =2 0.05 -1, Λ=0.3, P max =33dBm, rank(·) means to find the rank of the matrix, express The element in the m'th row and m'th column in . Constraint C1 ensures that the received signal-to-interference-noise ratio at each user is not less than γ c , constraint C2 ensures that the eavesdropper's signal-to-interference-to-noise ratio does not exceed γ e , constraint C3 ensures that the detection probability of the target by the sensing eavesdropper does not exceed Λ, and constraint C4 ensures that the transmission power of the base station is fixed to P max , constraint C5 ensures that the phase shift modulus of each antenna of the optimized IRS is 1, and constraints C6 and C7 ensure that the communication beamforming matrix and the covariance matrix of the dedicated radar signal is a semi-positive definite matrix, and constraints C8 and C9 ensure that the communication beamforming matrix The correlation matrix with the phase shift matrix of IRS The rank of is 1.

[0091] Step 4: Convert the optimization problem into a semi-definite relaxation problem by simplifying the objective function in the optimization problem, rewriting the constraints on the detection probability of the target after the sensing eavesdropper performs energy detection on its received signal, and ignoring the rank-one constraint.

[0092] Further defined, the specific process of step 4 is:

[0093] Step 4.1: In P R The false alarm probability P in the expression FAWhen the complex reflection coefficient β of the target reflected to the sensing receiver is a given fixed value, the objective function in the optimization problem is equivalent to

[0094] Step 4.2: For P e , which has the same equation as Similar mathematical form allows the use of equations The monotonically increasing property when 0<x<1 and x>1 will optimize the constraint P in the problem. e ≤Λ can be rewritten as Among them, Γ d It is the root of the equation when f(x) = Λ. According to Λ = 0.3, we can get Γ d =0.6815.

[0095] Step 4.3: Ignore the rank-one constraints C8 and C9.

[0096] Step 4.4: Describe the semi-positive definite relaxation problem of the optimization problem as:

[0097]

[0098] 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 communication beamforming matrix related to each user and the covariance matrix of the dedicated radar signal. Given the correlation matrix of the phase shift matrix of the IRS, the communication beamforming matrix related to each 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 communication beamforming matrix related to each 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.

[0099] Step 6: Use the alternating optimization algorithm to iteratively solve the first and second subproblems to obtain the local optimal solutions of the communication beamforming matrix related to each user, the covariance matrix of the dedicated radar signal, and the correlation matrix of the IRS phase shift matrix.

[0100] Further defined, the specific process of step 6 is:

[0101] Step 6.1: Let iter represent the number of iterations, and the initial value of iter is 1; initialize

[0102] Step 6.2: Use a convex optimization solver such as CVX to solve the first subproblem and get the iterth iteration and The solution of and Among them, when iter = 1, the given The value is the initialization value, given when iter>1 The value is obtained at the iter-1th iteration Solution

[0103] Step 6.3: Use a convex optimization solver such as CVX to solve the second subproblem and get the iterth iteration The initial solution Among them, the given and The value of and

[0104] Step 6.4: and As the initial value, the iterative rank minimization (IRM) method is used to Perform rank-one recovery to obtain the iter-th iteration Solution The specific process is:

[0105] Step 6.4.1: Let l represent the number of internal iterations and the initial value of l is 1.

[0106] Step 6.4.2: The rank-one constraint Convert to Among them, p is the auxiliary variable introduced, I M represents the identity matrix of dimension M×M, and Z is (l-1) Indicated by The characteristic matrix consists of the eigenvectors corresponding to the M small eigenvalues ​​(that is, the M eigenvalues ​​remaining except the largest eigenvalue) among the M+1 eigenvalues ​​obtained by eigendecomposition. When l>1, Z (l-1) Indicates that in the l-1th internal iteration The internal iteration value of The characteristic matrix consists of the eigenvectors corresponding to the M small eigenvalues ​​among the M+1 eigenvalues ​​obtained by eigendecomposition.

[0107] Step 6.4.3: Add a penalty term ηp to the objective function of the second sub-problem and transform the second sub-problem into:

[0108]

[0109] stC1,C2,C3',C5,

[0110]

[0111] Here, η represents a variable weight, and the initial value of η is set to 50.

[0112] Step 6.4.4: Use a convex optimization solver such as CVX to solve the problem in step 6.4.3 and obtain the l-th inner iteration time The internal iteration value of Among them, the given and The value of and During the solution process, the value of η in the lth internal iteration is increased so that the value of p approaches 0. Here, η increases at a step size of 3.5, that is, η l =3.5×η l-1 , η l represents the value of η in the lth internal iteration, and η is 1 when l=1 l-1 is the initial value, when l>1,η l-1 represents the value of η in the l-1th inner iteration.

[0113] Step 6.4.5: Judgement Is the maximum value of the M small eigenvalues ​​in the M+1 eigenvalues ​​obtained by eigendecomposition less than the internal iteration threshold? If so, the iteration ends and As the iterth iteration Solution Otherwise, set l = l + 1 and return to step 6.4.2 to continue execution; the internal iteration threshold is 10 -3 , the “=” in l=l+1 is the assignment symbol.

[0114] 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.

[0115] Step 6.5: According to Calculate the objective function in the semi-positive definite relaxation problem and obtain the objective function value of the iter-th iteration; then make the difference between the objective function value of the iter-th iteration and the objective function value of the iter-1-th iteration; then determine whether the ratio of the difference to the objective function value of the iter-1-th 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 Corresponding as Their respective local optimal solutions; where iter = 1, the objective function value of the iter-1th iteration is based on 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.

[0116] The feasibility and effectiveness of the method of the present invention are further illustrated by the following simulation.

[0117] 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 K users are randomly selected within a circle with a center of (25,22) and a radius of 2, the 2D coordinates of the 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).

[0118] In the simulation, the comparison methods include the random value selection method of the IRS phase shift matrix and the ISAC method without IRS deployment. The random value selection method of the IRS phase shift matrix refers to randomly selecting values ​​for the diagonal elements of the phase shift matrix Θ of the IRS deployed in the environment, and then optimizing the base station beam according to the randomly selected phase shift; the ISAC method without IRS deployment refers to not deploying the IRS in the environment, and only achieving the optimization goal by optimizing the base station beam.

[0119] Figure 3 The results show that the maximum detection probability of the method of the present invention and the comparative method is 0.29 when the maximum detection probability of the eavesdropper is 0.29 and the user's communication rate threshold R c =log2(1+γ c ) changes, the comparison curve of the detection probability change of the target by the perception receiver, R c The unit is bps / Hz. Figure 3 It can be seen that as the user's communication rate threshold increases, the detection probability of the target by the perception receiver decreases, which reflects the trade-off between the communication and perception functions in ISAC. In addition, the detection probability of the target by the perception receiver of the method of the present invention is much higher 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.

[0120] Figure 4 The communication rate threshold R of the user is given by the method of the present invention and the comparative method. c =log2(1+γ c ) is 5.5bps / Hz and the maximum detection probability Λ of the perceived eavesdropper changes, the comparison curve of the detection probability change of the target by the perception receiver. Figure 4 It can be seen from the figure that the detection probability of the target by the sensing receiver increases with the increase of the maximum detection probability of the sensing eavesdropper, and the method of the present invention has a system performance far higher than the two comparative methods.

Claims

1. An optimization method for security perception and communication based on ISAC-IRS, characterized in that The following steps are involved: Step 1: Establish a system model based on ISAC-IRS with both communication eavesdroppers and perceptual eavesdroppers. The model contains a base station, an IRS, multiple users, a target, a perceptual eavesdropper, and a perceptual receiver. The target also acts as a communication eavesdropper. The base station transmits signals to various users and targets with the assistance of IRS. The signals transmitted by the base station are composed of multiple communication signals and a dedicated radar signal superimposed. The target, acting as a communication eavesdropper, attempts to eavesdrop on the communication signals in the signals transmitted by the base station to various users. The target reflects its received signals to the perceptual eavesdropper and the perceptual receiver. The perceptual eavesdropper attempts to silently detect the target based on its received signals and attempts to perceive the target's location. The perceptual receiver detects the target based on its received signals and perceives the target's location. Step 2: Establish the communication performance index, perception performance index, communication eavesdropping performance index, and perception eavesdropping performance index of the system model based on ISAC-IRS and with both communication eavesdroppers and perceptual eavesdroppers. The communication performance index is measured by the received signal-to-interference-to-noise ratio at each user, the perception performance index is measured by the detection probability of the target by the perception receiver, the communication eavesdropping performance index is measured by the signal-to-interference-to-noise ratio of the communication signal of each user eavesdropped by the target acting as a communication eavesdropper, and the perception eavesdropping performance index is measured by the detection probability of the target by the perception eavesdropper after performing energy detection on its received signal; Step 3: Taking the received signal-to-interference-noise ratio at each user, the signal-to-interference-noise ratio of the communication signal of each user eavesdropped by the target acting as a communication eavesdropper, and the detection probability of the target by the perceptual eavesdropper after performing energy detection on its received signal as constraints, jointly optimize the communication beamforming matrix related to each user, the covariance matrix of the dedicated radar signal, and the correlation matrix of the phase shift matrix of the IRS, with the goal of maximizing the detection probability of the perceptual receiver to the target, and construct an optimization problem, wherein the communication beamforming matrix related to each user is composed of the beamforming vector designed by the base station for the user; Step 4: The optimization problem is transformed into a semi-definite relaxation problem by simplifying the objective function in the optimization problem, rewriting the constraints on the detection probability of the target after the sensing eavesdropper performs energy detection on its received signal, and ignoring the rank-one constraint; Step 5: Decompose the semi-positive definite relaxation problem into two sub-problems. The first sub-problem is about the communication beamforming matrix related to each user and the covariance matrix of the dedicated radar signal. Given the correlation matrix of the IRS phase shift matrix, the communication beamforming matrix related to each 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 communication beamforming matrix related to each 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 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 communication beamforming matrix related to each user, the covariance matrix of the dedicated radar signal, and the correlation matrix of the IRS phase shift matrix.

2. The ISAC-IRS-based security perception and communication optimization method according to claim 1, characterized in that In step 1, the number of users is K, each of which is equipped with a single antenna; the 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 with half-wavelength intervals, and the number of their antennas is N, N, M, and N, respectively. e .

3. The ISAC-IRS-based security perception and communication optimization method according to claim 2, characterized in that In step 2, the process of obtaining the received signal to interference and noise ratio at the kth user is as follows: Step 2.a1: Substitute the received signal y at the kth user at time t k (t) is expressed as Where k = 1, 2, ..., K, h B,k represents the channel from the base station to the kth user, h r,k represents the channel from IRS to the kth user, represents the channel from the base station to the IRS, Θ represents the phase shift matrix of the IRS, diag(·) is used to extract or construct the diagonal elements of a matrix, e is a natural constant, j is the imaginary part, φ m represents the phase shift of the mth antenna of IRS, m=1,2,…,M, x(t) represents the signal transmitted by the base station at time t, w k represents the beamforming vector designed by the base station for the kth user, s k (t) represents the communication signal transmitted by the base station to the kth user at time t, w r (t) represents the dedicated radar signal transmitted by the base station at time t, n k (t) represents the Gaussian white noise at the kth user at time t, which has an expectation of 0 and a variance of The complex Gaussian distribution of Indicates n k (t) is the noise power. The superscript "H" indicates the conjugate transpose operation. Step 2.a2: According to y k (t), and obtain the received signal-to-interference-and-noise ratio SINR at the kth user c,k , Among them, tr(·) means to find the trace of the matrix, represents the correlation matrix of Θ, v H =[θ H ,1],U k represents the channel matrix composed of the direct channel from the base station to the kth user and the cascade channel from the base station to the IRS and then to the kth user, Indicated by w k The communication beamforming matrix formed by 4. The ISAC-IRS-based security perception and communication optimization method according to claim 3, characterized in that In step 2, the process of acquiring the detection probability of the target by the perception receiver is as follows: Step 2.b1: The received signal y at the sensing receiver at time t R (t) is expressed as Where β represents the complex reflection coefficient of the target reflected to the sensing receiver, represents the channel from the target to the sensing receiver, represents the channel from the base station to the target, represents the channel from IRS to the target, n R (t) represents the Gaussian white noise at the receiver at time t, which has a mean of 0 and a variance of The complex Gaussian distribution of Indicates n R (t) is the noise power, I represents the unit matrix; Step 2.b2: According to y R (t), and obtain the detection probability P of the target by the sensing receiver R , Among them, Q() represents the right tail distribution function of Gaussian distribution, P FA represents the false alarm probability, "|·|" is the modulo operator, G represents the channel matrix composed of the direct channel from the base station to the target and the cascade channel from the base station to the IRS and then to the target, R represents the covariance matrix of x(t), It means to find the mathematical expectation. Indicates w r The covariance matrix of (t), 5. The ISAC-IRS-based security perception and communication optimization method according to claim 4, characterized in that In step 2, the process of obtaining the signal to interference noise ratio of the communication signal of the kth user by the target eavesdropper acting as a communication eavesdropper is as follows: Step 2.c1: The received signal at the target of the communication eavesdropper at time t Expressed as in, represents the Gaussian white noise at the target of the communication eavesdropper at time t, which has an expected value of 0 and a variance of The complex Gaussian distribution of express The noise power; Step 2.c2: According to Get the signal-to-interference-noise ratio of the communication signal of the kth user that acts as a communication eavesdropper 6. The ISAC-IRS-based security perception and communication optimization method according to claim 5, characterized in that In step 2, the process of acquiring the detection probability of the target by the perceptual eavesdropper after performing energy detection on the received signal is as follows: Step 2.d1: The received signal y at the eavesdropper at time t is sensed e (t) is expressed as , in, represents the angle of the target relative to the sensing eavesdropper, Indicates the position of the perceived eavesdropper relative to The steering vector, β e represents the complex reflection coefficient reflected from the target to the sensing eavesdropper, represents the channel from the target to the sensing eavesdropper, represents the channel from the base station to the sensing eavesdropper, represents the channel from IRS to the sensing eavesdropper, n e (t) represents the Gaussian white noise perceived by the eavesdropper at time t, which has a mean of 0 and a variance of The complex Gaussian distribution of Indicates n e (t) noise power; Step 2.d2: According to y e (t), and obtain the detection probability P of the target after the perceptual eavesdropper performs energy detection on the received signal e , in, 7. The ISAC-IRS-based security perception and communication optimization method according to claim 6, characterized in that In step 3, the communication beamforming matrix associated with the kth user is: The covariance matrix of the dedicated radar signal is The correlation matrix of the IRS phase shift matrix is The optimization problem is described as: s.t.C1: C2: C3:P e ≤Λ, C4: C5: C6: C7: C8: C9: in, γ c represents the lower threshold of the user's received signal-to-interference-noise ratio, γ e represents the upper threshold of the eavesdropping signal-to-interference-to-noise ratio, γ c >γ e , Λ represents the maximum detection probability of the perceived eavesdropper, P max represents the total transmission power of the base station, rank(·) represents the rank of the matrix, express The element at the m'th row and m'th column in .

8. The ISAC-IRS-based security perception and communication optimization method according to claim 7, characterized in that The specific process of step 4 is as follows: Step 4.1: In P R The false alarm probability P in the expression FA When the complex reflection coefficient β of the target reflected to the sensing receiver is a given fixed value, the objective function in the optimization problem is equivalent to Step 4.2: For P e , which has the same equation as Similar mathematical form allows the use of equations The monotonically increasing property when 0<x<1 and x>1 will optimize the constraint P in the problem. e ≤Λ can be rewritten as Among them, Γ d It is the root of the equation when f(x) = Λ; Step 4.3: Ignore the rank-one constraints C8 and C9; Step 4.4: Describe the semi-positive definite relaxation problem of the optimization problem as:

9. The ISAC-IRS-based security perception and communication optimization method according to claim 8, characterized in that The specific process of step 6 is as follows: Step 6.1: Let iter represent the number of iterations, and the initial value of iter is 1; initialize Step 6.2: Use the convex optimization solver to solve the first subproblem and get the iterth iteration and The solution of and Among them, when iter = 1, the given The value is the initialization value, given when iter>1 The value is obtained at the iter-1th iteration Solution Step 6.3: Use the convex optimization solver to solve the second subproblem and get the iterth iteration The initial solution Among them, when solving the second sub-problem, and The value of and Step 6.4: and As the initial value, the iterative rank minimization method is used to Perform rank-one recovery to obtain the iter-th iteration Solution The specific process is: Step 6.4.1: Order represents the number of internal iterations, The initial value of is 1; Step 6.4.2: The rank-one constraint Convert to Among them, p is the auxiliary variable introduced, I M represents the identity matrix of dimension M×M, hour Indicated by The characteristic matrix consists of the eigenvectors corresponding to the M small eigenvalues ​​among the M+1 eigenvalues ​​obtained by eigendecomposition. hour Indicated by Internal iteration The internal iteration value of The characteristic matrix consists of the eigenvectors corresponding to the M small eigenvalues ​​among the M+1 eigenvalues ​​obtained by eigendecomposition; Step 6.4.3: Add a penalty term ηp to the objective function of the second sub-problem and transform the second sub-problem into: stC1,C2,C3',C5, C10: 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 Internal iterations The internal iteration value of Among them, the given and The value of and In the process of solving, the The value of η in the inner iteration makes the value of p approach 0; Step 6.4.5: Judgement Is the maximum value of the M small eigenvalues ​​in the M+1 eigenvalues ​​obtained by eigendecomposition less than the internal iteration threshold? If so, the iteration ends and As the iterth iteration Solution Otherwise, let Return to step 6.4.2 and continue; Step 6.5: According to Calculate the objective function in the semi-positive definite relaxation problem and obtain the objective function value of the iter-th iteration; then make the difference between the objective function value of the iter-th iteration and the objective function value of the iter-1-th iteration; then determine whether the ratio of the difference to the objective function value of the iter-1-th 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 Corresponding as Their respective local optimal solutions; where iter = 1, the objective function value of the iter-1th iteration is based on The initial value of is used to calculate the objective function in the semi-positive definite relaxation problem.

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