Non-ideal ISAC system beam forming method with anti-eavesdropping capability

Abstract

The invention discloses a non-ideal ISAC system beam forming method with an anti-eavesdropping capability, which is characterized in that a base station is intelligently optimized to transmit beam forming so as to ensure that radar sensing requirements are met under the condition of limited power resources, and attacks of potential eavesdroppers and guards are effectively resisted, so that the anti-eavesdropping capability of the non-ideal ISAC system is improved. Therefore, the safety communication and covert communication performance of system communication users is obviously improved. Specifically, according to the method, a safe ISAC scene which has potential eavesdroppers and guards at the same time, legal nodes of a system have hardware damage, and CSI of illegal nodes cannot be obtained perfectly is considered, and in order to guarantee safe communication and sensing performance, a legal signal energy minimization optimization problem is established. And then, the original problem is converted into a convex optimization problem by utilizing a positive semidefinite relaxation technology and an S process technology, and the convex optimization problem is solved by utilizing a CVX toolbox, so that the strategy effectively ensures the safety communication and target sensing performance of the system under limited power resources, and the complexity of the problem is reduced.

Description

Technical Field

[0001] The present invention relates to a security beamforming technology for a communication and perception integrated system, and in particular to a beamforming method for a non-ideal ISAC (Integrated Sensing and Communication) system with anti-eavesdropping capability. When there is hardware impairment (HWI) at the transceiver end of the ISAC system, it is a non-ideal ISAC system. Background Art

[0002] With the rise of emerging application scenarios such as the Internet of Things, intelligent transportation, and smart cities, traditional communication systems have been unable to meet the dual needs of information transmission and environmental perception. The deep integration of communication and perception not only improves the functionality and flexibility of the system, but also effectively responds to complex environmental challenges. In this context, Integrated Communication and Sensing (ISAC) technology has received increasing attention. ISAC technology organically combines perception and communication equipment to collect surrounding environmental data in real time, thereby enhancing the system's intelligent decision-making capabilities and meeting the needs of modern society for efficient and reliable communication.

[0003] Although the development of ISAC technology has improved communication efficiency and environmental perception capabilities, it has also brought about wireless security issues. In an open wireless environment, communication data is vulnerable to eavesdroppers, resulting in information leakage and threatening user privacy and data security. Therefore, it is particularly important to ensure that the ISAC system can achieve effective secure communication. In this context, secure communication and covert communication have become two important strategies. The purpose of secure communication is to ensure that information is not obtained by unauthorized persons during transmission, while covert communication aims to reduce the risk of communication activities being monitored by suspicious guards. In order to meet the security challenges in the ISAC system, physical layer security (PLS) technology has emerged. PLS technology uses the characteristics of wireless signal propagation and implements security strategies through channel conditions, such as beamforming and signal interference, to effectively enhance the information transmission quality of legitimate users while suppressing the signal reception ability of potential eavesdroppers. This method provides security for users at the physical level, reduces dependence on traditional encryption technology, simplifies system complexity, and improves communication efficiency.

[0004] However, ISAC systems are often faced with complex operating environments and unforeseen hardware failures in applications such as intelligent transportation, unmanned driving, and environmental monitoring. In practical applications, hardware damage at the transceiver end may cause signal distortion and attenuation, directly affecting communication quality and data reliability. In addition, since illegal nodes in the system generally do not easily leak their information, their channel state information (CSI) cannot be perfectly obtained by the system, making the system at a disadvantage in resisting eavesdropping.

[0005] Although some technical studies have considered secure ISAC systems, they have only considered the situation where eavesdroppers or guards exist unilaterally, that is, they have not fully considered the situation where the above two illegal nodes exist at the same time in the ISAC system; secondly, previous technical studies have mostly considered ideal ISAC systems, for example, assuming that the hardware of the ISAC system's transceiver is perfect or that the CSI of illegal nodes in the ISAC system can be perfectly obtained, which cannot be guaranteed in the actual ISAC system and will overestimate the performance of the actual ISAC system. Therefore, it is necessary to design strategies that can adapt to hardware damage and handle imperfect CSI in the ISAC system where eavesdroppers and guards exist at the same time, so as to improve the system's adaptability to environmental changes and enhance its protection against malicious attacks. These strategies should be able to ensure the security and reliability of data while ensuring the quality of communication. Summary of the invention

[0006] The technical problem to be solved by the present invention is to provide a non-ideal ISAC system beamforming method with anti-eavesdropping capability, which jointly designs the transmission beamforming of the base station under the condition that potential eavesdroppers and guards exist at the same time, the legal node has hardware damage, and the illegal node has imperfect CSI, so that the ISAC system can ensure secure communication, covert communication and radar perception performance under limited energy resources.

[0007] The technical solution adopted by the present invention to solve the above technical problems is: a non-ideal ISAC system beamforming method with anti-eavesdropping capability, characterized by comprising the following steps:

[0008] Step 1: Establish a downlink secure ISAC system model with potential eavesdroppers and guards. In the model, there is a base station with dual functions of communication and radar, a secure communication user, a covert communication user, a guard, and K radar targets. The transmitting end of the base station is equipped with a uniform linear array with half-wavelength intervals. The number of array elements in the uniform linear array is N. The secure communication user, the covert communication user, the guard, and each radar target are equipped with a single antenna. The K radar targets also play the role of potential eavesdroppers. The base station communicates with the secure communication user and the covert communication user and senses the radar target in one transmission block. The radar target, as a potential eavesdropper, attempts to eavesdrop on the legitimate communication information between the base station and the secure communication user in real time. The guard attempts to detect in real time whether the base station and the covert communication user are communicating; wherein, 1<K≤N;

[0009] Step 2: Construct the communication service quality model, covert communication model, channel error model and radar target perception model as follows:

[0010] Communication service quality model: Assuming that the base station and the covert communication user are in a covert communication state, the base station communicates with the secure communication user and the covert communication user simultaneously in one transmission block. The radar target, as a potential eavesdropper, attempts to eavesdrop on the legitimate communication information between the base station and the secure communication user in real time. The base station's transmitted signal x is expressed as The receiving signal y of the secure communication user b Expressed as The received signal y of the concealed communication user g Expressed as The received signal y of the kth potential eavesdropper k Expressed as in, represents the secure communication data flow between the base station and the secure communication user, represents the covert communication data flow between the base station and the covert communication user, w s express The corresponding communication beamforming vector, w c express The corresponding communication beamforming vector, w s and w c The dimensions of s are all N×1. r represents the radar signal with mean 0 and covariance matrix S for sensing radar targets, s r The dimension of is N×1, the dimension of S is N×N, and the rank of S determines the number of sensing beams, z t Indicates the transmission distortion noise caused by hardware damage to the base station. represents a circularly symmetric complex Gaussian distribution, λ trepresents the hardware damage factor of the base station, diag{} represents the reconstruction of the diagonal matrix into a vector, (·) H represents the Hermitian conjugate transpose operation, h ab represents the channel from the base station to the secure communication user, h ag represents the channel from the base station to the covert communication user, h ab and h ag The dimensions are all N×1, n b means that the mean is 0 and the covariance is The receiving noise of the safety communication user, n g means that the mean is 0 and the covariance is The receiving noise of the covert communication user, z b It represents the receiving distortion noise caused by hardware damage to the secure communication user, z g It represents the receiving distortion noise caused by hardware damage to the covert communication user. λ r represents the hardware damage factor of secure communication users and covert communication users, It means to find the mathematical expectation, |·| is the modulus operator,

[0011] z b Variance for

[0012] z g Variance for

[0013]

[0014] k=1,2,…,K,h ak represents the channel from the base station to the kth radar target, h ak The dimension is N×1, n k means that the mean is 0 and the covariance is The received noise of the kth potential eavesdropper is,

[0015] The SINR of the received signal to interference and noise ratio of the secure communication user b Expressed as The received signal interference plus noise ratio SINR of the covert communication user g Expressed as The received signal interference plus noise ratio SINR of the kth potential eavesdropper is k Expressed as Then the achievable rate R of secure communication users is b Represented as R b =log2 (1+SINR b ), the achievable rate R of the concealed communication user g Represented as R g =log 2 (1+SINR g ), the eavesdropping rate R of the kth potential eavesdropper k Represented as R k =log 2 (1+SINR k ), where the interference term I b Expressed as

[0016] Interference I g Expressed as Interference I k Expressed as

[0017] Covert communication model: The guard attempts to detect in real time whether the base station and the covert communication user are communicating, and transmits the guard's received signal y w Expressed as Among them, h aw represents the channel from the base station to the guard, h aw The dimension is N×1, It represents the transmission distortion noise caused by the base station being affected by hardware damage under the assumption that the base station and the covert communication user are not conducting covert communication. n w means that the mean is 0 and the covariance is The guard's receiving noise, Indicates that the base station and the covert communication user do not assume a covert communication state. It indicates that the base station and the covert communication user are assumed to be in a covert communication state;

[0018] y w exist The likelihood function p under the state 0 (y w ) to y w exist The likelihood function p under the state 1 (y w )’s KL divergence D(p 0 ||p 1 ) is expressed as Among them, λ 0 and λ 1 are the intermediate quantities introduced,

[0019] According to D(p 0||p 1 ) determines a tractable covert communication constraint, described as: D(p 0 ||p 1 )≤2ξ 2 , where ξ is a given small constant, ξ∈(0,1];

[0020] Channel error model: h ak Modeled as in, λ is the carrier wavelength, d ak represents the distance between the base station and the kth radar target, θ ak represents the departure angle from the base station to the kth radar target, a(θ ak ) indicates that the base station is at θ ak The steering vector in the direction, e is a natural constant, j is an imaginary part, (·) T Indicates the transpose operation; h ab 、h ag 、h aw The respective small-scale fading parts are modeled as the Rice fading model, and h ab The large-scale fading part L(d ab ) is modeled as h ag The large-scale fading part L(d ag ) is modeled as h aw The large-scale fading part L(d aw ) is modeled as Among them, L 0 represents the path loss at a reference distance of one meter, d ab represents the distance between the base station and the secure communication user, d ag represents the distance between the base station and the covert communication user, d aw represents the distance between the base station and the guard, α ab represents the path loss index of the communication link between the base station and the secure communication user, α ag represents the path loss index of the communication link between the base station and the covert communication user, α aw represents the path loss index of the communication link between the base station and the guard;

[0021] Using an uncertain model with a certain bound on θ ak The error is modeled as: in, Represents θ ak The estimated value of Represents θ ak The uncertainty of is a set, Δθ represents the sensing beam width of the illuminated area of ​​the base station sensing radar target, is θ ak The estimated error bounds; using an uncertain model with a certain bound for d ak The error is modeled as: in, Indicates d ak The estimated value of Indicates d ak The uncertainty of is a set, D is d ak The estimated error bounds; using an uncertain model with a certain bound for h aw The error is modeled as: in, Indicates h aw The estimated value of Indicates h aw The uncertainty of is a set, ||·|| is the 2-norm operator, and ε is h aw Error bounds on estimates;

[0022] Radar target perception model: The base station communicates with both secure communication users and covert communication users in one transmission block and perceives radar targets. ISMR is used as a performance indicator to describe the perception performance, which reflects the ratio of sidelobe energy to mainlobe energy. Among them, Θ m represents the set containing the main lobe directions, The symbol ∪ represents the union, Θ s represents the set containing the sidelobe directions, the radar operating range of the base station minus Θ m Get Θ s , θ represents the departure angle independent variable from the base station to the radar target, a(θ) represents the guidance vector of the base station in the direction of θ, a(θ)=[1,e j πsinθ ,...,e jπ(N-1)sinθ ] T , R xx represents the covariance matrix of the base station's transmitted signal x, Then define the intermediate variable and Will Rewrite as Where Tr(·) means finding the trace of the matrix;

[0023] Step 3: Construct the joint optimization w s 、w c and S, minimizing the power of the combined communication signal ||w s || 2 +||wc || 2 The optimization problem is described as:

[0024]

[0025] stC1:log 2 (1+SINR b )≥R t ,

[0026] C2:log 2 (1+SINR g )≥R t ,

[0027] C3:

[0028] C4:D(p 0 ||p 1 )≤2ξ 2 ,

[0029] C5:ISMR≤ζ,

[0030] C6:

[0031] Among them, R t represents the minimum achievable rate requirement for secure communication users and covert communication users, R q represents the maximum eavesdropping rate requirement of a potential eavesdropper, satisfying R t >R q , ζ represents the maximum ISMR threshold, P max Indicates the maximum transmit power of the base station;

[0032] Step 4: Use the semi-definite relaxation technique and the S-process technique to transform the optimization problem constructed in step 3 into a convex optimization problem;

[0033] Step 5: Solve the convex optimization problem in step 4 and get and the solution of S, where

[0034] Step 6: If The rank of is 1, then w is obtained by eigenvalue decomposition s An approximate solution of If the rank is not 1, then w is obtained by Gaussian randomization technique. s The approximate solution of The rank of is 1, then w is obtained by eigenvalue decomposition c An approximate solution of If the rank is not 1, then w is obtained by Gaussian randomization technique. c The approximate solution of .

[0035] In step 2, y w exist The likelihood function p under the state 0 (y w ) is expressed as y w exist The likelihood function p under the state 1 (y w ) is expressed as in,

[0036] In step 2, the covert communication constraint D(p 0 ||p 1 )≤2ξ 2 The determination process is:

[0037] Step 2.1: Express the total false detection probability ψ of the guard as

[0038] Step 2.2: Describe the initial covert communication constraint as: ψ ≥ 1-ξ; when the guard adopts the optimal decision, ψ = 1-V T (p 0 ,p 1 ), then according to Pinskil inequality: Among them, V T (p 0 ,p 1 ) represents y w exist The likelihood function p under the state 0 (y w ) and y w exist The likelihood function p under the state 1 (y w ) between the total variation distance, D(p 0 ||p 1 ) represents y w exist The likelihood function p under the state 0 (y w ) to y w exist The likelihood function p under the state 1 (y w )’s KL divergence; so far, ψ≥1-ξ is transformed into an easily tractable covert communication constraint D(p 0 ||p 1 )≤2ξ 2 .

[0039] In step 2.1, the process of obtaining the total error detection probability ψ of the guard is:

[0040] Step 2.1.1: Change the detection performance of the guard from the false alarm probability and the probability of missed alarm To describe, the total false detection probability ψ of the guard is expressed as in, Indicates compliance Binary decision for state assumptions, Indicates compliance binary decision making for state assumptions;

[0041] Step 2.1.2: In the settings State assumptions and Under the premise that the probabilities of the state hypotheses are equal, the Neyman-Pearson criterion is used to obtain the optimal decision that minimizes ψ. The optimal decision is the likelihood ratio test, that is, Further Among them, |y w | 2 represents the average received power of the guard, ν * represents the optimal detection threshold of the guard,

[0042] Step 2.1.3: Change |y w | 2 exist Cumulative density function of guards under state assumptions Expressed as |y w | 2 exist Cumulative density function of guards under state assumptions Expressed as Combined with the optimal detection threshold ν of the guard * ,have: and Finally got

[0043] The specific process of step 4 is as follows:

[0044] Step 4.1: Define intermediate variables and Using the semi-definite relaxation technique, we have: and Among them, ≥ indicates that the matrix is ​​semi-positive definite, and rank(·) indicates the rank of the matrix;

[0045] Step 4.2: Transform the constraint C1 in the optimization problem into constraint C1', which is described as: in,

[0046] The constraint C2 in the optimization problem is transformed into C2', which is described as: in,

[0047] For constraint C3 in the optimization problem, ak )exist Perform a first-order Taylor expansion at the point, and we can get the approximate value: Among them, a(θ ak ) ak Replace with get ⊙ represents the Hadamard product operation; then the auxiliary variable τ is introduced k ,k=1,2,…,K separation variables θ ak and d ak , split constraint C3 into sub-constraints

[0048] and sub-constraint 2 Among them, among them, Then, the S-process technique is used to transform sub-constraint 1 into linear matrix inequality constraint C3', and sub-constraint 2 into linear matrix inequality constraint C3'. Constraint C3' is described as: Constraint C3" is described as:

[0049] in, is the auxiliary variable introduced, U and Z are intermediate variables,

[0050] For the constraint C4 in the optimization problem, it is equivalent to Combining functions Monotonicity of x>0, when Established holds, where x is the independent variable, f(x) is the function of x, and x 1 ,x 2 (x 1 <x 2 ) is the equation The two roots of Transformed into linear matrix inequality constraint C4', the constraint Transformed into linear matrix inequality constraint C4", constraint C4' is described as: Constraint C4" is described as: Among them, T 1 and T 2 is the intermediate variable, I is the identity matrix, κ 1 and κ 2is the introduced non-negative auxiliary variable;

[0051] The constraint C5 in the optimization problem is transformed into constraint C5', which is described as: Tr(AQ s )≤ζTr(AQ m );

[0052] The constraint C6 in the optimization problem is transformed into constraint C6', which is described as: Tr(A) = P max ;

[0053] Step 4.3: Convert the optimization problem constructed in step 3 into a convex optimization problem, which can be described as:

[0054]

[0055] stC1',C2',C3',C3",C4',C4",C5',C6',

[0056] S≥0.

[0057] in, represents the set of optimization variables,

[0058] Compared with the prior art, the advantages of the present invention are:

[0059] 1) The method of the present invention simultaneously considers two types of communication users (secure communication users and covert communication users) and two types of illegal nodes (potential eavesdroppers and guards) in the system. By optimizing the transmission beamforming of the base station, it ensures the secure communication of secure communication users and effectively hides the information transmission of covert communication users, truly realizing the comprehensive protection of secure communication users and covert communication users. This two-pronged design concept enables the system to have higher security and flexibility in practical applications, meeting the increasing demand for security protection in modern communication environments; at the same time, considering the general situation of radar targets as potential eavesdroppers, multiplexing radar signals as AN signals effectively resists eavesdropping by external eavesdroppers. The dual role of radar signals not only reduces the deployment requirements of additional security equipment, reduces system complexity and cost, but also provides an additional layer of protection barrier for data transmission through physical interference strategies, enhancing the security line of defense beyond encryption technology.

[0060] 2) The method of the present invention fully considers the general reality that the hardware damage of the transceiver of the legitimate nodes of the system (base stations, secure communication users and covert communication users) and the CSI of the illegal nodes of the system (radar targets and guards) cannot be perfectly obtained, and completes the modeling of the imperfect CSI of the illegal nodes of the system. By using the existing S process technology to deal with the thorny problems introduced by imperfect CSI, the established optimization problem is easier to solve and optimize. By effectively responding to these realities, the system can still maintain stable secure communication performance in a more complex environment. This means that even under some unfavorable conditions, such as normal equipment damage or incomplete channel information acquisition, the communication system can maintain high security and data transmission quality. In addition, this design can significantly reduce the reliance on perfect CSI and improve the robustness of the system, making it more effective in a changing actual environment.

[0061] 3) The method of the present invention minimizes the power of the combined communication signal under the premise of meeting the system communication rate requirements and radar perception performance requirements, that is, maximizes the radar signal power under limited power conditions, so that the system can have enough radar signal power to achieve radar target perception and interfere with potential eavesdroppers from stealing secure communication information without consuming additional power. This means that the system under consideration can simultaneously achieve the triple functions of secure communication, covert communication and radar perception under limited resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a flowchart of the overall implementation process of the method of the present invention;

[0063] Figure 2 A simple schematic diagram of the established downlink secure ISAC system model with potential eavesdroppers and guards;

[0064] Figure 3 A base station transmission beam pattern curve designed for the method of the present invention;

[0065] Figure 4 The minimum achievable rate requirement (i.e., the communication rate threshold of the safety communication user) of the method of the present invention and the method without AN signal for comparison R t The comparison curve of the change of security communication rate of security communication users when the value changes. DETAILED DESCRIPTION

[0066] The present invention is further described in detail below with reference to the accompanying drawings.

[0067] The present invention proposes a non-ideal ISAC system beamforming method with anti-eavesdropping capability, in which the secure communication user and the base station will be eavesdropped by potential eavesdroppers (radar targets), and the covert communication user and the base station will be detected by the guard. At the same time, the radar target is illuminated by the communication and perception signals transmitted by the base station. Under the premise of not consuming additional power and limited total system power, the requirements of radar perception, secure communication and covert communication are achieved. On the one hand, considering the general situation that the radar target of the system is a potential eavesdropper, the radar signal transmitted by the base station is used as artificial noise (AN) and the AN signal power is maximized to interfere with the potential eavesdropper; on the other hand, considering the general situation that the system transceiver has hardware damage and the CSI of the illegal node cannot be perfectly obtained, the method of the present invention is proposed. The goal of the method of the present invention is to minimize the legal signal power of the system while satisfying the constraints of secure communication, covert communication, radar perception, etc. Due to the non-convex constraints of the established optimization problem, it is difficult to solve the optimization problem directly. The semi-positive relaxation technique and the S process technique are used here to transform the established optimization problem into a convex optimization problem, and finally the optimal solution is obtained through the CVX toolbox.

[0068] The present invention provides a non-ideal ISAC system beamforming method with anti-eavesdropping capability, and its overall implementation flow chart is as follows: Figure 1 As shown, it includes the following steps:

[0069] Step 1: Build a model of a downlink secure ISAC system with potential eavesdroppers and guards, such as Figure 2 As shown, the model is provided with a base station with dual functions of communication and radar, a secure communication user, a concealed communication user, a guard, and K radar targets. The transmitting end of the base station is equipped with a uniform linear array (ULA) with half-wavelength interval. The number of array elements in the uniform linear array is N. The secure communication user, the concealed communication user, the guard, and each radar target are equipped with a single antenna. The K radar targets also play the role of potential eavesdroppers. The base station communicates with the secure communication user and the concealed communication user and senses the radar target in one transmission block. The radar target, as a potential eavesdropper, attempts to eavesdrop on the legitimate communication information between the base station and the secure communication user in real time, and the guard attempts to detect in real time whether the base station and the concealed communication user are communicating. Among them, 1<K≤N, in this embodiment, K=2, N=10.

[0070] Step 2: Construct the communication service quality model, covert communication model, channel error model and radar target perception model as follows:

[0071] Communication service quality model: Assuming that the base station and the covert communication user are in a covert communication state, the base station communicates with the secure communication user and the covert communication user simultaneously in one transmission block. The radar target, as a potential eavesdropper, attempts to eavesdrop on the legitimate communication information between the base station and the secure communication user in real time. The base station's transmitted signal x is expressed as The receiving signal y of the secure communication user b Expressed as The received signal y of the concealed communication user g Expressed as For radar targets as potential eavesdroppers, since the base station cannot obtain all the information of potential eavesdroppers, the worst case is considered here, that is, the signal processing capability and hardware of the potential eavesdropper are perfect, then the received signal y of the kth potential eavesdropper is k Expressed as in, represents the secure communication data flow between the base station and the secure communication user, represents the covert communication data flow between the base station and the covert communication user, w s express The corresponding communication beamforming vector, w c express The corresponding communication beamforming vector, w s and w c The dimensions of s are all N×1. r represents the radar signal with mean 0 and covariance matrix S for sensing radar targets, s r The dimension of is N×1, the dimension of S is N×N, and the rank of S determines the number of sensing beams, z t It represents the transmission distortion noise caused by the hardware damage of the base station. t Obeys a circularly symmetric complex Gaussian distribution,

[0072] represents a circularly symmetric complex Gaussian distribution, λ t represents the hardware damage factor of the base station. In this embodiment, it is λ t = 0.03, diag{} means reconstructing a vector into a diagonal matrix or reconstructing a diagonal matrix into a vector, (·) H represents the Hermitian conjugate transpose operation, h ab represents the channel from the base station to the secure communication user, h ag represents the channel from the base station to the covert communication user, h ab and h ag The dimensions are all N×1, n b means that the mean is 0 and the covariance is The receiving noise of the safety communication user, n gmeans that the mean is 0 and the covariance is The receiving noise of the covert communication user, n b and n g All obey circularly symmetric complex Gaussian distribution, In this embodiment, z b It represents the receiving distortion noise caused by hardware damage to the secure communication user, z g represents the receiving distortion noise caused by the hardware damage of the covert communication user, z b and z g All obey circularly symmetric complex Gaussian distribution, λ r represents the hardware damage factor of the secure communication user and the concealed communication user. In this embodiment, λ r =0.03, It means to find the mathematical expectation, |·| is the modulus operator,

[0073] Based on the assumption that the variance of the received distortion noise generated by the hardware damage at the receiving end (secure communication user and covert communication user) is proportional to the signal power of the received signal at the receiving end (secure communication user and covert communication user), z can be calculated. b and z g The respective variance, z b Variance for z g Variance for

[0074]

[0075] k=1,2,…,K,h ak represents the channel from the base station to the kth radar target (kth potential eavesdropper), h ak The dimension is N×1, n k means that the mean is 0 and the covariance is The received noise of the kth potential eavesdropper is, In this embodiment,

[0076] The received signal-to-interference-plus-noise ratio (SINR) of the secure communication user is b Expressed as The received signal interference plus noise ratio SINR of the covert communication user g Expressed as The received signal interference plus noise ratio SINR of the kth potential eavesdropper isk Expressed as Then the achievable rate R of secure communication users is b Represented as R b =log 2 (1+SINR b ), the achievable rate R of the concealed communication user g Represented as R g =log 2 (1+SINR g ), the eavesdropping rate R of the kth potential eavesdropper k Represented as R k =log 2 (1+SINR k ), where the interference term I b Expressed as Interference I g Expressed as Interference I k Expressed as

[0077] Covert communication model: The purpose of the guard is to know whether the base station and the covert communication user are transmitting covert information. The guard attempts to detect whether the base station and the covert communication user are communicating in real time and transmits the guard's received signal y w Expressed as Among them, h aw represents the channel from the base station to the guard, h aw The dimension is N×1, It represents the transmission distortion noise caused by the base station being affected by hardware damage under the assumption that the base station and the covert communication user are not conducting covert communication. Obeys a circularly symmetric complex Gaussian distribution, n w means that the mean is 0 and the covariance is The guard's receiving noise, In this embodiment, Indicates that the base station and the covert communication user do not assume a covert communication state. It indicates that the base station and the covert communication user are assumed to be in a covert communication state.

[0078] y w exist The likelihood function p under the state 0 (y w ) is expressed as y w exist The likelihood function p under the state 1 (y w ) is expressed as Among them, exp(·) is the natural exponential function, λ 0 and λ 1 are the intermediate quantities introduced, y w exist The likelihood function p under the state 0 (y w ) to y w exist The likelihood function p under the state 1 (y w )’s KL divergence D(p 0 ||p 1 ) is expressed as According to D(p 0 ||p 1 ) determines a tractable covert communication constraint, described as: D(p 0 ||p 1 )≤2ξ 2 , where ξ is a given small constant, ξ∈(0,1], and ξ=0.05 in this embodiment.

[0079] In this embodiment, the covert communication constraint D(p 0 ||p 1 )≤2ξ 2 The determination process is:

[0080] Step 2.1: Express the total false detection probability ψ of the guard as

[0081] Here, the process of obtaining the total error detection probability ψ of the guard is:

[0082] Step 2.1.1: Change the detection performance of the guard from the false alarm probability and the probability of missed alarm To describe, the total false detection probability ψ of the guard is expressed as ψ can be used to measure the stealth performance of the downlink secure ISAC system with potential eavesdroppers and guards, where Indicates compliance Binary decision for state assumptions, Indicates compliance Binary decision making for state assumptions.

[0083] Step 2.1.2: In the settings State assumptions and Under the premise that the probabilities of the state hypotheses are equal, the Neyman-Pearson criterion is used to obtain the optimal decision that minimizes ψ. The optimal decision is the likelihood ratio test, that is, Further Among them, |y w| 2 represents the average received power of the guard, ν * represents the optimal detection threshold of the guard, ln(·) represents the natural logarithm function.

[0084] Step 2.1.3: Change |y w | 2 exist Cumulative density function of guards under state assumptions Expressed as |y w | 2 exist Cumulative density function of guards under state assumptions Expressed as Combined with the optimal detection threshold ν of the guard * ,have: and Finally got

[0085] Step 2.2: For covert communication users, an effective covert communication should ensure that no matter what strategy the guard adopts, for any given small constant ξ∈(0,1], the covert communication constraint ψ≥1-ξ holds. However, the covert communication constraint ψ≥1-ξ is difficult to handle, so it is necessary to convert the covert communication constraint ψ≥1-ξ into an easily tractable form. The initial covert communication constraint is described as: ψ≥1-ξ; when the guard adopts the optimal decision, there is: ψ=1-V T (p 0 ,p 1 ), then according to Pinskil inequality: Among them, V T (p 0 ,p 1 ) represents y w exist The likelihood function p under the state 0 (y w ) and y w exist The likelihood function p under the state 1 (y w ) between the total variation distance, D(p 0 ||p 1 ) represents y w exist The likelihood function p under the state 0 (y w ) to y w exist The likelihood function p under the state 1 (y w)’s KL divergence; so far, ψ≥1-ξ is transformed into an easily tractable covert communication constraint D(p 0 ||p 1 )≤2ξ 2 .

[0086] Channel error model: Since the radar target (potential eavesdropper) is a point target in the low altitude with a good line-of-sight link, h ak Modeled as in, λ is the carrier wavelength. In this embodiment, λ=0.0107m (corresponding to the incident wave carrier frequency of 28GHz), d ak represents the distance between the base station and the kth radar target, θ ak represents the departure angle from the base station to the kth radar target. In this embodiment, when K=2, d a1 =d a2 =40m,θ a1 =-60°,θ a2 =60°, a(θ ak ) indicates that the base station is at θ ak The steering vector in the direction, e is a natural constant, j is an imaginary part, (·) T represents the transposition operation; for secure communication users, covert communication users, and guards, they are ground communication users, so h ab 、h ag 、h aw The respective small-scale fading parts are modeled as the Rice fading model, and h ab The large-scale fading part L(d ab ) is modeled as h ag The large-scale fading part L(d ag ) is modeled as h aw The large-scale fading part L(d aw ) is modeled as In this embodiment, the departure angle from the base station to the secure communication user in the Rice fading model is θ ab = 0°, the departure angle from the base station to the concealed communication user is θ ag =30°, the departure angle from the base station to the guard is θ aw =-30°, L 0 represents the path loss at a reference distance of one meter. In this embodiment, L 0 =-30dB, d ab represents the distance between the base station and the secure communication user, d ag represents the distance between the base station and the covert communication user, d awIndicates the distance between the base station and the guard. In this embodiment, d ab =d ag =30m,d aw =40m,α ab represents the path loss index of the communication link between the base station and the secure communication user, α ag represents the path loss index of the communication link between the base station and the covert communication user, α aw represents the path loss index of the communication link between the base station and the guard. In this embodiment, α is taken ab =α ag =α aw =2.5.

[0087] Since the base station cannot perfectly obtain the precise angle of the radar target (the departure angle θ ak ) and distance (d ak ), so an uncertain model with a certain bound is used to ak The error is modeled as: in, Represents θ ak The estimated value of Represents θ ak The uncertainty of is a set, Δθ represents the sensing beam width of the illuminated area of ​​the base station sensing radar target, and in this embodiment, Δθ=20°, is θ ak The estimated error bounds; using an uncertain model with a certain bound for d ak The error is modeled as: in, Indicates d ak The estimated value of Indicates d ak The uncertainty of is a set, D is d ak The estimated error bound is D = 4m in this embodiment; for the channels guarded by illegal nodes in the system, an uncertain model with a certain bound is also used to estimate h aw The error is modeled as: in, Indicates h aw The estimated value of Indicates h aw The uncertainty of is a set, ||·|| is the 2-norm operator, and ε is h aw The estimated error bound is taken as And ∈=0.1.

[0088] Radar target perception model: From a perception perspective, the integrated-sidelobe-to mainlobe ratio (ISMR) radar metric is used to optimize perception performance, making it possible to illuminate multiple radar targets (potential eavesdroppers) while leaking minimal communication information to the mainlobe specified within the ISMR. ISMR not only has a good effect on target detection, but also on positioning performance, where power focusing can be accomplished by pointing the mainlobe toward the radar target (potential eavesdropper) while keeping the sidelobe low to suppress unnecessary echoes such as signal-dependent interference and clutter. Therefore, the ISMR radar metric is very suitable for target positioning applications and tracking. The base station communicates with both secure communication users and covert communication users within one transmission block and perceives radar targets. ISMR is used as a performance indicator to describe the perception performance, which reflects the ratio of sidelobe energy to mainlobe energy. Among them, ∫(·) represents the integration operation, Θ m represents the set containing the main lobe directions, The symbol ∪ represents the union, Θ s Represents the set containing the sidelobe directions, the radar operating range of the base station (-90 degrees to 90 degrees) minus Θ m Get Θ s , θ represents the departure angle independent variable from the base station to the radar target, a(θ) represents the guidance vector of the base station in the direction of θ, a(θ)=[1,e jπsinθ ,...,e jπ(N-1)sinθ ] T , R xx represents the covariance matrix of the base station's transmitted signal x, Then define the intermediate variable and Will Rewrite as Where Tr(·) means finding the trace of the matrix.

[0089] Step 3: Considering the radar signal s r It does not contain communication information, so it can be used as an artificial noise (AN) signal to interfere with potential eavesdroppers, ensuring system communication security while ensuring system perception performance. Covert communication data flow and radar signals r Therefore, the smaller the power of the communication signal, the larger the AN signal power. Therefore, under the achievable rate of secure communication users, the achievable rate of covert communication users, the eavesdropping rate of potential eavesdroppers, radar perception constraints and covert communication constraints, a joint optimization w is constructed. s 、w cand S, minimizing the power of the combined communication signal ||w s || 2 +||w c || 2 The optimization problem is described as:

[0090]

[0091] stC1:log 2 (1+SINR b )≥R t ,

[0092] C2:log 2 (1+SINR g )≥R t ,

[0093] C3:

[0094] C4:D(p 0 ‖p 1 )≤2ξ 2 ,

[0095] C5:ISMR≤ζ,

[0096] C6

[0097] Among them, min is the minimum function, st means "subject to...", R t represents the minimum achievable rate requirement for secure communication users and concealed communication users. In this embodiment, R t =4bps / Hz, R q represents the maximum eavesdropping rate requirement of a potential eavesdropper. In this embodiment, R q =0.1bps / Hz, in order to achieve safe communication, it is necessary to meet R t >R q ζ represents the maximum ISMR threshold. In this embodiment, ζ=0.2. max Indicates the maximum transmission power of the base station. In this embodiment, P max =20dBm, constraint C1 ensures the communication requirements of secure communication users, constraint C2 ensures the communication requirements of covert communication users, constraint C3 ensures the secure communication requirements of secure communication users, constraint C4 ensures the covert communication requirements of covert communication users, constraint C5 ensures the radar perception requirements of base station radar sensing radar targets, and constraint C6 ensures the total power requirements of the system.

[0098] Step 4: Use the semi-definite relaxation technique and the S-process technique to transform the optimization problem constructed in step 3 into a convex optimization problem.

[0099] In this embodiment, the specific process of step 4 is:

[0100] Step 4.1: Define intermediate variables and Using the semi-definite relaxation technique, we have: and Here, ≥ indicates that the matrix is ​​positive semidefinite, and rank(·) represents the rank of the matrix.

[0101] Step 4.2: Transform the constraint C1 in the optimization problem into constraint C1', which is described as: in,

[0102] The constraint C2 in the optimization problem is transformed into C2', which is described as: in,

[0103] For constraint C3 in the optimization problem, since a(θ ak ) is about is a nonlinear function, so here a(θ ak )exist Perform a first-order Taylor expansion at the point, and we can get the approximate value:

[0104] Among them, a(θ ak ) ak Replace with get ⊙ represents the Hadamard product operation; then the auxiliary variable τ is introduced k ,k=1,2,…,K separation variables θ ak and d ak , split constraint C3 into sub-constraints

[0105] and sub-constraint 2 Among them, among them, because and It contains two sets of infinite number of constraints, so here we use the S process technology to transform sub-constraint 1 into linear matrix inequality constraint C3', and sub-constraint 2 into linear matrix inequality constraint C3", constraint C3' is described as: Constraint C3" is described as:

[0106] in, is the auxiliary variable introduced, U and Z are intermediate variables,

[0107] For the constraint C4 in the optimization problem, it is equivalent to Combining functions Monotonicity of x>0, when Established holds, where x is the independent variable, f(x) is the function of x, and x 1 ,x 2 (x 1 <x 2 ) is the equation The two roots of contains an infinite number of constraints, so here we use the S process technology to constrain Transformed into linear matrix inequality constraint C4', the constraint Transformed into linear matrix inequality constraint C4", constraint C4' is described as: Constraint C4" is described as: Among them, T 1 and T 2 is the intermediate variable, I is the identity matrix, κ 1 and κ 2 is the introduced non-negative auxiliary variable.

[0108] The constraint C5 in the optimization problem is transformed into constraint C5', which is described as: Tr(AQ s )≤ζTr(AQ m ).

[0109] The constraint C6 in the optimization problem is transformed into constraint C6', which is described as: Tr(A) = P max .

[0110] Step 4.3: Convert the optimization problem constructed in step 3 into a convex optimization problem, which can be described as:

[0111]

[0112] stC1',C2',C3',C3",C4',C4",C5',C6',

[0113] S≥0.

[0114] in, represents the set of optimization variables,

[0115] Step 5: Use the CVX toolbox to solve the convex optimization problem in step 4 and obtain and the solution of S, where

[0116] Step 6: If The rank of is 1, then w is obtained by eigenvalue decomposition s An approximate solution of If the rank is not 1, then w is obtained by Gaussian randomization technique. s The approximate solution of The rank of is 1, then w is obtained by eigenvalue decomposition c An approximate solution of If the rank is not 1, then w is obtained by Gaussian randomization technique. c The approximate solution of .

[0117] The feasibility and effectiveness of the method of the present invention are further illustrated by the following simulation.

[0118] Figure 3 The base station transmission beam diagram curve designed by the method of the present invention. Figure 3 In the figure, the “ISAC signal” curve refers to the communication beam pattern curve of the total signal transmitted by the base station to the secure communication users, covert communication users and radar targets, the “safety signal” curve refers to the communication beam pattern curve of the secure communication data stream transmitted by the base station to the secure communication users, and the “covert signal” curve refers to the communication beam pattern curve of the covert communication data stream transmitted by the base station to the covert communication users. Figure 3 It can be seen that the ISAC signal beam pattern has a higher peak in the target direction (±60°) (main lobe) and a lower peak in other directions (side lobes), and the main lobe width is about 20°, which shows that the designed base station transmit beam can meet good perception performance and overcome the uncertainty of the target angle. The security signal beam pattern has a higher peak in the direction of the secure communication user (0°), and the covert signal beam pattern has a higher peak in the direction of the covert communication user (30°), and is well suppressed in the guard direction (-30°), which shows that the designed communication beamforming vector has good directivity to achieve the communication performance of the system. On the other hand, the peak value of the ISAC signal beam pattern in the target direction (±60°) is significantly higher than the peak value of the security signal and the covert signal. This is because the original intention of establishing the optimization problem is to maximize the radar signal to improve the perception performance and counter potential eavesdroppers while meeting the communication requirements of the system. At the same time, the communication signal can also be used for radar target perception. This shows that the method of the present invention has shown significant advantages and effects in improving the overall security communication performance and radar target perception performance of the system.

[0119] Figure 4 The minimum achievable rate requirement (i.e., the communication rate threshold of the safety communication user) of the method of the present invention and the method without AN signal for comparison R t The comparison curve of the change of security communication rate of security communication users when the value changes. Figure 4In the AN-free signal method, the dual-function radar communication base station in the considered system only transmits the communication signal, and the countermeasures against potential eavesdroppers are not considered when establishing the optimization problem. Figure 4 The secure communication rate R of the secure communication user is s The calculation formula is in, max is the maximum value function, R b =log 2 (1+SINR b ) is the achievable rate of secure communication users, R k =log 2 (1+SINR k ) is the eavesdropping rate of the kth potential eavesdropper. Figure 4 It can be seen from the figure that the method of the present invention increases with the communication rate threshold R of the secure communication user. t The increase of the secure communication rate R of secure communication users s The communication rate threshold R of different secure communication users is t The secure communication rate under the condition is approximately equal to the secure communication user communication rate threshold R t This shows that the proposed method considers multiplexing radar signals into AN signals, which can suppress the eavesdropping rate of potential eavesdroppers to a lower level, thereby ensuring the security communication performance of the system. In contrast, the method without AN signals does not consider the impact of eavesdropping on the security communication of the system due to the lack of AN signals, which makes the security communication rate R of the secure communication users under this scheme s Maintained at a relatively low value (<0.25 bps / Hz). This shows that the method of the present invention has shown significant advantages and effects in improving the overall security of the communication system, and effectively ensures the confidentiality and integrity of data transmission.

Claims

1. A non-ideal ISAC system beamforming method with anti-eavesdropping capability, characterized in that The following steps are involved: Step 1: Establish a downlink secure ISAC system model with potential eavesdroppers and guards. In the model, there is a base station with dual functions of communication and radar, a secure communication user, a covert communication user, a guard, and K radar targets. The transmitting end of the base station is equipped with a uniform linear array with half-wavelength intervals. The number of array elements in the uniform linear array is N. The secure communication user, the covert communication user, the guard, and each radar target are equipped with a single antenna. The K radar targets also play the role of potential eavesdroppers. The base station communicates with the secure communication user and the covert communication user and senses the radar target in one transmission block. The radar target, as a potential eavesdropper, attempts to eavesdrop on the legitimate communication information between the base station and the secure communication user in real time. The guard attempts to detect in real time whether the base station and the covert communication user are communicating; wherein, 1<K≤N; Step 2: Construct the communication service quality model, covert communication model, channel error model and radar target perception model as follows: Communication service quality model: Assuming that the base station and the covert communication user are in a covert communication state, the base station communicates with the secure communication user and the covert communication user simultaneously in one transmission block. The radar target, as a potential eavesdropper, attempts to eavesdrop on the legitimate communication information between the base station and the secure communication user in real time. The base station's transmitted signal x is expressed as The receiving signal y of the secure communication user b Expressed as The received signal y of the concealed communication user g Expressed as The received signal y of the kth potential eavesdropper k Expressed as in, represents the secure communication data flow between the base station and the secure communication user, represents the covert communication data flow between the base station and the covert communication user, w s express The corresponding communication beamforming vector, w c express The corresponding communication beamforming vector, w s and w c The dimensions of s are all N×1. r represents the radar signal with mean 0 and covariance matrix S for sensing radar targets, s r The dimension of is N×1, the dimension of S is N×N, and the rank of S determines the number of sensing beams, z t Indicates the transmission distortion noise caused by hardware damage to the base station. represents a circularly symmetric complex Gaussian distribution, λ t represents the hardware damage factor of the base station, diag{} represents the reconstruction of the diagonal matrix into a vector, (·) H represents the Hermitian conjugate transpose operation, h ab represents the channel from the base station to the secure communication user, h ag represents the channel from the base station to the covert communication user, h ab and h ag The dimensions are all N×1, n b means that the mean is 0 and the covariance is The receiving noise of the safety communication user, n g means that the mean is 0 and the covariance is The receiving noise of the covert communication user, z b It represents the receiving distortion noise caused by hardware damage to the secure communication user, z g It represents the receiving distortion noise caused by hardware damage to the covert communication user. λ r represents the hardware damage factor of secure communication users and covert communication users, It means to find the mathematical expectation, |·| is the modulus operator, z b Variance for z g Variance for k=1,2,…,K,h ak represents the channel from the base station to the kth radar target, h ak The dimension is N×1, n k means that the mean is 0 and the covariance is The received noise of the kth potential eavesdropper is, The SINR of the received signal to interference and noise ratio of the secure communication user b Expressed as SINR g Expressed as The received signal interference plus noise ratio SINR of the kth potential eavesdropper is k Expressed as Then the achievable rate R of secure communication users is b Represented as R b =log2(1+SINR b ), the achievable rate R of the concealed communication user g Represented as R g =log2(1+SINR g ), the eavesdropping rate R of the kth potential eavesdropper k Represented as R k =log2(1+SINR k ); Among them, the interference term I b Expressed as Interference I g Expressed as Interference I k Expressed as Covert communication model: The guard attempts to detect in real time whether the base station and the covert communication user are communicating, and transmits the guard's received signal y w Expressed as Among them, h aw represents the channel from the base station to the guard, h aw The dimension is N×1, It represents the transmission distortion noise caused by the base station being affected by hardware damage under the assumption that the base station and the covert communication user are not conducting covert communication. n w means that the mean is 0 and the covariance is The guard's receiving noise, Indicates that the base station and the covert communication user do not assume a covert communication state. It indicates that the base station and the covert communication user are assumed to be in a covert communication state; y w exist The likelihood function p0(y w ) to y w exist The likelihood function p1(y w ) is expressed as Among them, λ0 and λ1 are introduced intermediate quantities. Then, we determine a tractable covert communication constraint based on D(p0‖p1), which is described as: D(p0‖p1)≤2ξ 2 , where ξ is a given small constant, ξ∈(0,1]; Channel error model: h ak Modeled as in, λ is the carrier wavelength, d ak represents the distance between the base station and the kth radar target, θ ak represents the departure angle from the base station to the kth radar target, a(θ ak ) indicates that the base station is at θ ak The steering vector in the direction, e is a natural constant, j is an imaginary part, (·) T Indicates the transpose operation; h ab 、h ag 、h aw The respective small-scale fading parts are modeled as the Rice fading model, and h ab The large-scale fading part L(d ab ) is modeled as h ag The large-scale fading part L(d ag ) is modeled as h aw The large-scale fading part L(d aw ) is modeled as Where L0 represents the path loss at a reference distance of one meter, d ab represents the distance between the base station and the secure communication user, d ag represents the distance between the base station and the covert communication user, d aw represents the distance between the base station and the guard, α ab represents the path loss index of the communication link between the base station and the secure communication user, α ag represents the path loss index of the communication link between the base station and the covert communication user, α aw represents the path loss index of the communication link between the base station and the guard; Using an uncertain model with a certain bound on θ ak The error is modeled as: in, Represents θ ak The estimated value of Represents θ ak The uncertainty of is a set, Δθ represents the sensing beam width of the illuminated area of ​​the base station sensing radar target, is θ ak The estimated error bounds; using an uncertain model with a certain bound for d ak The error is modeled as: in, Indicates d ak The estimated value of Indicates d ak The uncertainty of is a set, D is d ak The estimated error bounds; using an uncertain model with a certain bound for h aw The error is modeled as: in, Indicates h aw The estimated value of Indicates h aw The uncertainty of is a set, ||·|| is the operator for taking the 2-norm, and ε is h aw Error bounds on estimates; Radar target perception model: The base station communicates with both secure communication users and covert communication users in one transmission block and perceives radar targets. ISMR is used as a performance indicator to describe the perception performance, which reflects the ratio of sidelobe energy to mainlobe energy. Among them, Θ m represents the set containing the main lobe directions, The symbol ∪ represents the union, Θ s represents the set containing the sidelobe directions, the radar operating range of the base station minus Θ m Get Θ s , θ represents the departure angle independent variable from the base station to the radar target, a(θ) represents the guidance vector of the base station in the direction of θ, a(θ)=[1,e j πsinθ ,...,e jπ(N-1)sinθ ] T , R xx represents the covariance matrix of the base station's transmitted signal x, Then define the intermediate variable Will Rewrite as Where Tr(·) means finding the trace of the matrix; Step 3: Construct the joint optimization w s 、w c and S, minimizing the power of the combined communication signal ||w s || 2 +||w c || 2 The optimization problem is described as: s.t.C1:log2(1+SINR b )≥R t , C2:log2(1+SINR g )≥R t , C3: C4:D(p0||p1)≤2ξ 2 , C5:ISMR≤ζ, C6: Among them, R t represents the minimum achievable rate requirement for secure communication users and covert communication users, R q represents the maximum eavesdropping rate requirement of a potential eavesdropper, satisfying R t >R q , ζ represents the maximum ISMR threshold, P max Indicates the maximum transmit power of the base station; Step 4: Use the semi-definite relaxation technique and the S-process technique to transform the optimization problem constructed in step 3 into a convex optimization problem; Step 5: Solve the convex optimization problem in step 4 and get and the solution of S, where Step 6: If The rank of is 1, then w is obtained by eigenvalue decomposition s An approximate solution of If the rank is not 1, then w is obtained by Gaussian randomization technique. s The approximate solution of The rank of is 1, then w is obtained by eigenvalue decomposition c An approximate solution of If the rank is not 1, then w is obtained by Gaussian randomization technique. c The approximate solution of .

2. The non-ideal ISAC system beamforming method with anti-eavesdropping capability according to claim 1, characterized in that In step 2, y w exist The likelihood function p0(y w ) is expressed as y w exist The likelihood function p1(y w ) is expressed as in, 3. The non-ideal ISAC system beamforming method with anti-eavesdropping capability according to claim 2, characterized in that In step 2, the covert communication constraint D(p0||p1)≤2ξ 2 The determination process is: Step 2.1: Express the total false detection probability ψ of the guard as Step 2.2: Describe the initial covert communication constraint as: ψ ≥ 1-ξ; when the guard adopts the optimal decision, ψ = 1-V T (p0,p1), then according to Pinskil inequality: Among them, V T (p0,p1) represents y w exist The likelihood function p0(y w ) and y w exist The likelihood function p1(y w ), D(p0||p1) represents the total variation distance between y w exist The likelihood function p0(y w ) to y w exist The likelihood function p1(y w ); So far, ψ≥1-ξ is transformed into an easily tractable covert communication constraint D(p0||p1)≤2ξ 2 .

4. The non-ideal ISAC system beamforming method with anti-eavesdropping capability according to claim 3, characterized in that In step 2.1, the process of obtaining the total error detection probability ψ of the guard is: Step 2.1.1: Change the detection performance of the guard from the false alarm probability and the probability of missed alarm To describe, the total false detection probability ψ of the guard is expressed as in, Indicates compliance Binary decision for state assumptions, Indicates compliance binary decision making for state assumptions; Step 2.1.2: In the settings State assumptions and Under the premise that the probabilities of the state hypotheses are equal, the Neyman-Pearson criterion is used to obtain the optimal decision that minimizes ψ. The optimal decision is the likelihood ratio test, that is, Further Among them, |y w | 2 represents the average received power of the guard, ν * represents the optimal detection threshold of the guard, Step 2.1.3: Change |y w | 2 exist Cumulative density function of guards under state assumptions Expressed as |y w | 2 exist Cumulative density function of guards under state assumptions Expressed as Combined with the optimal detection threshold ν of the guard * ,have: and Finally got 5. The non-ideal ISAC system beamforming method with anti-eavesdropping capability according to claim 1, characterized in that The specific process of step 4 is as follows: Step 4.1: Define intermediate variables and Using the semi-definite relaxation technique, we have: and in, indicates that the matrix is ​​semi-positive definite, and rank(·) indicates the rank of the matrix; Step 4.2: Transform the constraint C1 in the optimization problem into constraint C1', which is described as: in, The constraint C2 in the optimization problem is transformed into C2', which is described as: in, For constraint C3 in the optimization problem, ak )exist Perform a first-order Taylor expansion at the point, and we can get: Among them, a(θ ak ) ak Replace with get ⊙ represents the Hadamard product operation; then the auxiliary variable τ is introduced k ,k=1,2,…,K separation variables θ ak and d ak , split constraint C3 into sub-constraints and sub-constraint 2 Among them, among them, Then, the S-process technique is used to transform sub-constraint 1 into linear matrix inequality constraint C3', and sub-constraint 2 into linear matrix inequality constraint C3'. Constraint C3' is described as: Constraint C3" is described as: in, is the auxiliary variable introduced, U and Z are intermediate variables, For the constraint C4 in the optimization problem, it is equivalent to Combining functions Monotonicity of x>0, when Established holds, where x is the independent variable, f(x) is the function of x, and x1,x2 (x1<x2) is an equation The two roots of Transformed into linear matrix inequality constraint C4', the constraint Transformed into linear matrix inequality constraint C4", constraint C4' is described as: Constraint C4" is described as: Among them, T1 and T2 are intermediate variables. I is the identity matrix, κ1 and κ2 are introduced non-negative auxiliary variables; The constraint C5 in the optimization problem is transformed into constraint C5', which is described as: Tr(AQ s )≤ζTr(AQ m ); The constraint C6 in the optimization problem is transformed into constraint C6', which is described as: Tr(A) = P max ; Step 4.3: Convert the optimization problem constructed in step 3 into a convex optimization problem, which can be described as: stC1',C2',C3',C3",C4',C4",C5',C6', in, represents the set of optimization variables,

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