Communication perception integrated system security beam forming method for silent eavesdropper

Abstract

The invention discloses a silent eavesdropper-oriented communication perception integrated system security beam forming method. The method comprises the steps of constructing a security beam forming optimization problem; solving a noise projection matrix according to the legal user channel matrix, performing eigenvalue decomposition on the noise projection matrix, and constructing an artificial noise matrix; determining an optimal value of a scale factor in the beam pattern; auxiliary variables are introduced, quadratic transformation is applied, and an optimization problem is converted into an easy-to-solve form from minimum-maximization and multi-proportion fractional programming; converting the non-convex constraint in the converted optimization problem by using a successive convex approximation method, and introducing a penalty term to obtain a new optimization problem; solving a new optimization problem, and determining optimal values of a precoding matrix and a noise matrix through one-dimensional linear search; and the base station configures a beam directional diagram by using the optimal value of the scale factor, and performs signal emission by using the optimal values of the precoding matrix and the noise matrix.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more specifically to a secure beamforming method for an integrated communication and sensing system designed to detect silent eavesdroppers. Background Technology

[0002] In traditional wireless communication systems, artificial noise-assisted signal transmission can significantly degrade the received signal of eavesdroppers while having almost no impact on the signal reception of legitimate users, making it a representative technology for achieving physical layer security. To improve the security performance of Integrated Sensing and Communications (ISAC) systems, and drawing on traditional wireless communication techniques, this invention introduces artificial noise to enhance the physical layer security of ISAC systems. Specifically, targeting silent eavesdroppers, it further improves the communication and sensing quality of ISAC systems through the joint design of artificial noise and transmitted signal precoding, which is of great significance for promoting the practical application of ISAC technology.

[0003] Reference 1, "Deligiannis A, Daniyan A, Lambotharan S, et al. Secret rate optimizations for MIMO communication radar[J]. IEEE Transactions on Aerospace and Electronic Systems, 2018, 54(5): 2481-2492." To minimize the probability of intercepted confidential information, the base station additionally transmits a pseudo-random distorted signal. This distorted signal significantly reduces the eavesdropper's ability to decode confidential information, and it can also be used for target detection. The transmission covariance matrices of the communication signal and the distorted signal are designed to achieve the goals of maximizing the system's confidentiality rate, maximizing the target return signal-to-noise ratio, and minimizing the transmission power, respectively.

[0004] Reference 2, "Ren Z, Qiu L, Xu J. Optimal transmit beamforming for secrecy integrated sensing and communication [C] / / 2022-IEEE International Conference on Communications (ICC). IEEE, 2022: 5555-5560," states that to ensure sensing quality while preventing eavesdropping, base stations transmit a dedicated sensing signal in addition to a secure signal. This signal also functions as artificial noise. Furthermore, under the premise of meeting the minimum security rate requirements of communication users and the base station's transmit power constraints, the precoding of the transmitted information and the dedicated sensing signal at the base station were jointly optimized.

[0005] Reference 3, "Yang R, Du H. Joint precoding and artificial noise design for secure transmission in ISAC system[C] / / 2023 IEEE 24th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC).IEEE,2023:16-20," studies the joint beamforming and artificial noise design. It establishes an optimization problem with the objective function of maximizing the signal-to-interference-plus-noise ratio (SIR) of legitimate users, constrained by factors such as beam pattern matching error, SIR received by eavesdroppers, constant mode, and total power. The weighted least mean square error algorithm is used to solve for the beamforming matrix and the artificial noise vector.

[0006] Reference 4, "Su N, Liu F, Masouros C. Secure radar-communication systems with malicious targets: Integrating radar, communications and jamming functionalities[J]. IEEE Transactions on Wireless Communications, 2020, 20(1): 83-95," assumes the target is a potential eavesdropper and aims to minimize the eavesdropper's signal-to-interference-plus-noise ratio (SIR). Under performance constraints related to communication, sensing, and security, the precoding matrix and artificial noise vector are designed. Further research is conducted on the design method of the precoding matrix and artificial noise vector when the legitimate user channel state information obtained at the transmitter is imperfect, and when the location of the target (eavesdropper) is ambiguous, demonstrating greater universality and robustness.

[0007] In the physical layer security designs of ISAC systems in references 1-4, the target of detection is assumed to be a potential eavesdropper, and prior information about the eavesdropper's location is utilized. However, in reality, especially when dealing with silent eavesdroppers, it is impossible to detect them, and prior information such as their location is difficult to obtain. Furthermore, these designs do not consider the fairness of the achievable safe rate for legitimate users, resulting in a lower achievable safe rate for users with poor channel conditions, thus reducing the quality of service for some legitimate users. Summary of the Invention

[0008] The purpose of this invention is to provide a secure beamforming method for a communication sensing integrated system for silent eavesdroppers, in order to overcome the shortcomings of existing ISAC secure beamforming methods, such as relying on the eavesdropper's prior information and not considering the fairness of the secure rate achievable by legitimate users.

[0009] To achieve the above objectives, the present invention employs the following technical solution:

[0010] A secure beamforming method for an integrated communication sensing system targeting silent eavesdroppers, including:

[0011] The optimization problem of constructing secure beamforming is described. The optimization objective of the problem is to maximize the minimum generalized secure channel capacity. The constraints are: sensing beam pattern error constraint, constant modulus constraint, rank-1 constraint and positive semi-definite constraint of artificial noise matrix and legal user precoding matrix.

[0012] The noise projection matrix is ​​solved based on the legitimate user channel matrix. The noise projection matrix is ​​then decomposed into eigenvalues, and the eigenvectors corresponding to the non-zero eigenvalues ​​are taken. These eigenvectors constitute the artificial noise matrix.

[0013] Determine the optimal value of the scale factor in the beam pattern;

[0014] By introducing auxiliary variables and using a quadratic transformation, the optimization problem is transformed from minimax and multiproportional fractional programming into a form that is easier to solve.

[0015] The non-convex constraints in the transformed optimization problem are transformed using the successive convex approximation method and a penalty term is introduced to obtain a new optimization problem;

[0016] Solve the new optimization problem and determine the optimal values ​​of the precoding matrix and the noise matrix through a one-dimensional linear search;

[0017] The base station uses the optimal value of the scaling factor to configure the beam pattern and uses the optimal values ​​of the precoding matrix and noise matrix to transmit signals.

[0018] Furthermore, the sensing beam pattern error constraint is: the mean square error between the beam pattern of the transmitted signal x and the ideal beam pattern. Less than the error threshold μ; constant modulus constraint: the total power of the transmitted signal x does not exceed the system power budget P. t Furthermore, the average power of each antenna is the same.

[0019] Furthermore, the optimization problem of secure beamforming is expressed as follows:

[0020]

[0021] Where ψ is the scaling factor, i represents the i-th legitimate user, and II = {1, 2, ..., M} r}, M r GSR represents the number of legitimate users. i Represents the capacity of a generalized secure channel. R represents the mean square error between the beam pattern of the transmitted signal x and the ideal beam pattern, where μ is the error threshold and R is the mean square error. x (n,n) represents the covariance matrix R of the transmitted signal x. x The diagonal element, P t M represents the total power of the system. t The number of antennas in a uniform linear array antenna; Q≥0 and Z i ≥0 represent the artificial noise matrix Q and the legal user precoding matrix Z, respectively. i Let be a positive semi-definite matrix, and Rank(·) denotes the rank of the matrix.

[0022] Furthermore, the noise projection matrix is ​​solved based on the legitimate user channel matrix. Eigenvalue decomposition is then performed on the noise projection matrix, and the eigenvectors corresponding to the non-zero eigenvalues ​​are taken. These eigenvectors constitute the artificial noise matrix, including:

[0023] The noise projection matrix is ​​represented as:

[0024]

[0025] Where I is the identity matrix and the channel matrix of the legitimate users. h b,i Let M be the channel vector from the base station to the i-th legitimate user, where i = 1, 2, ..., M. r The superscript T indicates transpose, and the superscript H indicates conjugate transpose;

[0026] Further eigenvalue decomposition of the noise projection matrix P is expressed as:

[0027] P=GΣG H

[0028] Where Σ is a diagonal matrix, its diagonal elements are the eigenvalues ​​of P, and the columns of the unitary matrix G are the eigenvectors of P; the artificial noise matrix is ​​represented as:

[0029] Q = [e1, e2, ..., e K ] T

[0030] Among them, e k Let P be the eigenvector corresponding to the non-zero eigenvalues ​​of P, and K be the number of non-zero eigenvalues.

[0031] Further, determining the optimal value of the scale factor in the beam pattern includes:

[0032]

[0033] Where, θ l Let d(θ) be the l-th sampling angle, and L be the number of sampling angles. l ) represents the ideal beam pattern, a(θ) l ) represents the steering vector of the antenna at the ISAC base station. This represents the optimal value of the scaling factor.

[0034] Furthermore, by introducing auxiliary variables and employing a quadratic transformation, the optimization problem is transformed from a minimax and multiproportional fractional programming problem into a more easily solvable form, including:

[0035] Using a quadratic transformation, the optimization problem (P1) is transformed as follows:

[0036]

[0037] Where z is the quadratic transformation reconstruction function.

[0038] Z n This represents the precoding matrix of the nth legal user. This represents the noise variance at legitimate user locations. Z represents the equivalent noise variance at the eavesdropper's location, and tr(·) is the trace of the matrix; q Let γ be the beamforming matrix of the artificial noise, and γ be an auxiliary variable in the one-dimensional linear search.

[0039] proportionality coefficient ρ i Iterate according to the following rules:

[0040]

[0041] in, ρ is obtained in the kth iteration i , Z is obtained in the (k-1)th iteration i Given initialization Then, by solving the optimization problem (P1.1), we obtain... and Next calculation Repeat the iteration until convergence or the set number of iterations is reached.

[0042] Furthermore, the non-convex constraints in the transformed optimization problem are transformed using a successive convex approximation method, and a penalty term is introduced to obtain a new optimization problem, as follows:

[0043]

[0044] in, Let ξ represent the penalty term, and ξ be the penalty factor. Let ||Q||2 represent the lower bound, which is obtained by successive convex approximation. Let ||·||2 represent the L2 norm.

[0045] Furthermore, a new optimization problem is solved, and the optimal values ​​of the precoding matrix and noise matrix are determined through a one-dimensional linear search, including:

[0046] Given different values ​​of the auxiliary variable γ, the new optimization problem P(1.2) is solved, and its solution is defined as f(γ). Then, problem (P1.3) and P(1) have the same optimal solution. The optimal values ​​of the precoding matrix and the noise matrix are obtained by performing a one-dimensional linear search on different γ and f(γ).

[0047]

[0048] A terminal device includes a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, it implements the secure beamforming method for the integrated communication and sensing system for silent eavesdroppers.

[0049] A computer-readable storage medium storing a computer program; when executed by a processor, the computer program implements the secure beamforming method for an integrated communication and sensing system for silent eavesdroppers.

[0050] Compared with the prior art, the present invention has the following technical features:

[0051] First, the ISAC physical layer security design proposed in this invention does not require any prior information about the eavesdropper, making it more suitable for real-world scenarios. Second, it considers the fairness of the achievable security rate for legitimate communication users, ensuring the achievable security rate for legitimate users with poor channel conditions. Third, it develops an algorithm framework of set quadratic transformation and successive convex approximation for beamforming design of ISAC systems. Attached Figure Description

[0052] Figure 1 This is a schematic diagram illustrating an application scenario of the method of the present invention;

[0053] Figure 2 This is a convergence analysis diagram of the method in one embodiment of the present invention;

[0054] Figure 3 This invention provides a one-dimensional search for finding the optimal value in one embodiment.

[0055] Figure 4 This is a beam pattern in one embodiment of the present invention;

[0056] Figure 5 This illustrates the effect of beam pattern error on average safe rate in one embodiment of the present invention.

[0057] Figure 6 This invention illustrates the effect of beam pattern error on the average minimum safe rate in one embodiment of the invention. Detailed Implementation

[0058] This invention aims to utilize the null space of the user channel in the ISAC system and proposes a secure beamforming scheme that combines precoding with null space artificial noise design. It also considers the fairness of the user's achievable secure rate, enabling the system to achieve fair and secure transmission of private communication information in scenarios facing silent eavesdroppers (i.e., where no prior information about the eavesdropper can be obtained).

[0059] This invention provides a secure beamforming method for an integrated communication and sensing system designed to combat silent eavesdroppers. The method is applied to a scenario involving an ISAC base station equipped with a uniform linear array antenna, where the element spacing is half the signal wavelength, and the number of antennas is M. t M r A number of legal users with a single antenna (assuming the number of users is less than the number of antennas, i.e., M) t >Mr There are K targets in the system that need to be detected. It is assumed that the channel from the base station to the legitimate user and the eavesdropper is quasi-static block fading, meaning the channel remains unchanged during a single information transmission. The legitimate user estimates the channel state information from the base station to itself and feeds it back to the base station via the uplink. Further assuming the estimation is error-free and the feedback is timely, the base station obtains the accurate channel state information of the legitimate communication user. Simultaneously, there exists a non-cooperative silent eavesdropper equipped with a single antenna in the system, intercepting the legitimate user's confidential information, and it is assumed that the eavesdropper possesses multi-user detection capabilities.

[0060] In the sensing process of an ISAC system, if the system lacks prior information about the target's location, it emits an omnidirectional beam with equal power in all directions to scan the spatial domain and acquire target information. If the system possesses some prior information about the target's location, it designs a beam pattern to emit directional beams in the directions where the target is likely to appear, concentrating more energy to achieve a higher signal-to-noise ratio in the echo signal, thereby acquiring more target information. Therefore, the accuracy of the beam pattern design is crucial for the system's sensing function. This invention uses the error between the system's beam pattern and the ideal beam pattern as an indicator of sensing performance for optimization design.

[0061] This invention provides a secure beamforming method for an integrated communication and sensing system designed to combat silent eavesdroppers, comprising the following steps:

[0062] In the design of the transmission signal during the communication process, in order to ensure that the communication information s sent to the i-th legitimate user is... i To prevent (confidential information) from being illegally obtained by eavesdroppers, this invention designs a beamforming scheme based on artificial noise, that is, to give the communication information s i Artificial noise q was added, and the communication information s was also modified. i And precoding designs are performed for artificial noise q; for communication information s i Its precoding vector z i The main goal is to suppress multi-user interference among legitimate users and improve fairness in achieving safe rates for each legitimate user. For artificial noise q, a precoding matrix Z is used. q Projecting it onto the null space of the legitimate user channel will not interfere with legitimate users, but will only interfere with eavesdroppers, reducing their ability to intercept and demodulate confidential information. Simultaneously, the artificial noise q also serves as a virtual sensing signal, enhancing the sensing capabilities of the ISAC system.

[0063] The transmitted signal of the ISAC system can be represented as:

[0064]

[0065] in, For the precoded vector of the communication information of the i-th legitimate user, Let J be the vector of artificial noise (where J is the dimension of the artificial noise). Beamforming matrix for artificial noise; Let s represent the complex space. i For communication information sent to the i-th legitimate user; M r Let be the number of legitimate users; the received signal of the i-th legitimate user can be represented as:

[0066]

[0067] in, Let n be the channel vector from the base station to the i-th legitimate user. b,i The noise at the i-th legal user location is additive white Gaussian noise with a mean of 0 and a variance of . This scheme assumes that the Gaussian white noise power is consistent at legitimate user locations; therefore, the user index of the Gaussian white noise is subsequently deleted, denoted as n. b .

[0068] For the received signal of a legitimate user, since artificial noise is in the null space of its channel, no artificial noise will be received. After passing through the base station to the i-th legitimate user's channel, the received signal includes the target signal h. b,i z i s i Multi-user interference and Gaussian white noise n b,i After passing through the channel from the base station to the eavesdropper, the eavesdropper's received signal includes target information h. e z i s i Artificial noise h e Z q q, and Gaussian white noise n e .

[0069] The received signal-to-interference-plus-noise ratio (SIN / N) of the i-th legitimate user is:

[0070]

[0071] in, Z represents the precoding matrix for the i-th legitimate user, where k represents the k-th legitimate user. k This represents the precoding matrix of the kth legitimate user; the superscript H in the parameter indicates the conjugate transpose, and the same applies below.

[0072] The eavesdropper's received signal can be represented as:

[0073]

[0074] in, Let n be the channel vector from the base station to the eavesdropper. e The noise at the eavesdropper's location is additive white Gaussian noise with a mean of 0 and a variance of . The receiver's signal-to-interference-plus-noise ratio is:

[0075]

[0076] in, To perform the expected operation, h e The elements in the set are independent and identically distributed, and follow a distribution with mean 0 and variance . Complex Gaussian distribution, This represents the channel noise variance.

[0077] Since the channel / location information of the eavesdropper is unknown, it is impossible to directly perform beamforming and calculate the eavesdropper's rate of interception, thereby failing to optimize the system's security rate. In this situation, the strategy designed in this scheme is to minimize the power of confidential information while increasing the power of artificial noise, while ensuring the quality of service for communication users. This is a suboptimal secure transmission scheme against silent eavesdroppers.

[0078] The power leakage ratio is defined as:

[0079]

[0080] Where tr(·) is the trace of the matrix, and Q = qq H This is the artificial noise matrix.

[0081] To unify the units of measurement during optimization, the generalized secure channel capacity is defined as:

[0082]

[0083] Meanwhile, regarding the sensing function of the ISAC system, if the system lacks prior information about the target's location during the sensing process, it will emit an omnidirectional beam with equal power in all directions in space to scan the spatial domain and acquire information about the target. If the ISAC system possesses some prior information about the target's location, it will design a beam pattern to emit directional beams in the directions where the target may appear, concentrating more energy to achieve a higher signal-to-noise ratio in the echo signal, thereby acquiring more target information.

[0084] The ISAC system at the sampling angle θ l The transmission power in the corresponding direction can be expressed as:

[0085] P(θ l )=a(θ l )R x aH (θ l (8)

[0086] in, Let x be the covariance matrix of the transmitted signal. Let M be the steering vector of the antenna at the ISAC base station, e be the natural constant, j be the imaginary unit, and M be the vector of the antenna. t d represents the number of antennas. a Indicates the antenna spacing, λ a The wavelength is the signal wavelength.

[0087] The mean square error between the beam pattern of the transmitted signal x and the ideal beam pattern As a metric for measuring the sensing performance of an ISAC system, it can be expressed as:

[0088]

[0089] Where, θ l Let L be the l-th sampling angle, and L be the number of sampling angles. The sampling interval is typically set to 1°. ψ is the scaling factor to be optimized, which can change the gain of the beam pattern; d(θ) l An ideal beam pattern can be represented as:

[0090]

[0091] Where, θ i Δ represents the location of the target to be detected. θ This is the beamwidth, typically set to 10°.

[0092] In the fair and secure beamforming scheme for the ISAC system targeting silent eavesdroppers, the specific steps of the joint design scheme of precoding and artificial noise are as follows:

[0093] Step 1: Construct an optimization problem for secure beamforming; the optimization problem is oriented towards fairness in achievable secure rates among users, and the optimization objective is to minimize the generalized secure channel capacity (GSR). i Maximize; the constraint is: the mean square error between the beam pattern of the transmitted signal x and the ideal beam pattern. Less than the error threshold μ; the total power of the transmitted signal x does not exceed the system power budget P. t The average power of each antenna is the same (constant modulus constraint ensures uniform signal power distribution, avoids distortion caused by amplitude fluctuations in nonlinear amplifiers, and improves transmission efficiency); the artificial noise matrix Q and the legal user precoding matrix Z i Rank 1 constraints and positive semidefinite constraints.

[0094] The objective of this invention is to jointly optimize the transmitted signal precoding vector and the artificial noise vector to maximize the minimum safe rate for legitimate users, achieving fairness in ensuring the safe rate achievable by legitimate users, while also considering the system's perception performance. Therefore, the optimization problem can be formulated as follows:

[0095]

[0096] Where, II = {1,2,...,M} r}, (11a) represents the sensing beam pattern error constraint, where μ is the error threshold (set according to the mean square error of the beam pattern; the smaller the error threshold, the closer the actual beam pattern is to the ideal beam pattern); (11b) represents the constant mode constraint. Since the radar system has a high transmit power, the constant mode constraint can ensure that the average transmit power of different antennas is the same, thereby improving the power efficiency of the system. At the same time, it constrains the total power of the system to P. t R x (n,n) represents matrix R x The diagonal elements, where n is any value on the diagonal; in (11c) and (11d), Q≥0 and Z... i ≥0 represents Q and Z respectively. i Let be a positive semi-definite matrix, and Rank(·) denotes the rank of the matrix.

[0097] Step 2: Solve for the noise projection matrix based on the legitimate user channel matrix, perform eigenvalue decomposition on the noise projection matrix, and take the eigenvectors corresponding to the non-zero eigenvalues. These eigenvectors constitute the artificial noise matrix.

[0098] The noise projection matrix can be represented as:

[0099]

[0100] Where I is the identity matrix and the channel matrix of the legitimate users. Further project the noise matrix Eigenvalue decomposition is performed, which is expressed as:

[0101] P=GΣG H (13)

[0102] in, It is a diagonal matrix whose diagonal elements are the eigenvalues ​​of P (where M is the eigenvalue of P). t -M r (with eigenvalues ​​of 0), unitary matrix The columns are the eigenvectors of P. The artificial noise matrix can be represented as:

[0103] Q = [e1, e2, ..., e K ] T (14)

[0104] in, Let P be the eigenvector corresponding to the non-zero eigenvalues ​​of P, and K be the number of non-zero eigenvalues.

[0105] Step 3: Determine the optimal value of the scale factor in the beam pattern.

[0106] Since the scale factor ψ depends only on constraint (11a), and constraint (11a) is a quadratic function of the scale factor ψ, the optimal value of the scale factor can be determined by taking its derivative.

[0107]

[0108] Step 4: Introduce auxiliary variables and apply a quadratic transformation to transform the optimization problem of safe beamforming from minimax and multi-proportional fractional programming into a form that is easier to solve.

[0109] Using a quadratic transformation, the optimization problem (P1) is transformed as follows:

[0110]

[0111] Where z is the quadratic transformation reconstruction function. II = {1,2,…,M} r}, The beamforming matrix for artificial noise. This represents the noise variance at legitimate user locations. The equivalent noise variance at the eavesdropper's location is γ, which is an auxiliary variable in the one-dimensional linear search; the proportionality coefficient ρ i Iterate according to the following rules:

[0112]

[0113] Where k is the index of the iteration number. Given the initialization... Then, it can be obtained by solving the optimization problem (P1.1). and Then calculate according to (17). Repeat the above steps until convergence or the set number of iterations is reached.

[0114] Step 5: The non-convex constraints (11c) and (11d) in the transformed optimization problem are transformed using the successive convex approximation method and a penalty term is introduced to obtain a new optimization problem P(1.2).

[0115] For a positive semi-definite matrix Q with eigenvalues ​​λ greater than or equal to 0 and rank(Q) = 1, then:

[0116] λ1>0, λ2=λ3=…=λ K =0 (18)

[0117] ||Q||2=max(λ)=λ1 (19)

[0118] tr(Q)=λ1+λ2+…+λ K =λ1 (20)

[0119] Where, λ K This represents the Kth eigenvalue.

[0120] The rank-1 constraint can then be transformed as follows:

[0121]

[0122] However, -||Q||2 in the above equation is still non-convex. Therefore, this solution can use a successive convex approximation method to perform a first-order Taylor expansion on -||Q||2, obtaining its lower bound:

[0123]

[0124] Among them, Q (r) u represents the value of Q in the r-th iteration. m (Q (r) ) represents Q (r) The eigenvector corresponding to the largest singular value; in the successive convex approximation, given an initial Q... (r) According to (22), the lower bound of ||Q||2 can be obtained. Q is obtained by solving the optimization problem (P1.2). (r+1) Repeat the above steps until convergence.

[0125] Therefore, this scheme transforms the rank-1 constraint as follows:

[0126]

[0127] For Z i Perform the same operation; by introducing a penalty factor ξ, the optimization problem P(1.1) can be transformed into:

[0128]

[0129] in This is a penalty item that is introduced.

[0130] Step 6: Solve the new optimization problem P(1.2) and determine the optimal values ​​of the precoding matrix and noise matrix through a one-dimensional linear search; the base station uses the optimal value of the scale factor to configure the beam pattern and uses the optimal values ​​of the precoding matrix and noise matrix to transmit the signal.

[0131] Based on the CVX tool in MATLAB software, given different γ values ​​(with values ​​in the range of [-3dB, 3dB], with an interval of 0.1dB, and higher precision can be obtained by reducing the interval), the new optimization problem P(1.2) is solved, and its solution is defined as f(γ); then the problem (P1.3) has the same optimal solution as P(1), which can be obtained by performing a one-dimensional linear search on different γ and f(γ).

[0132]

[0133] Based on the obtained precoding matrix and noise matrix, the ISAC base station can complete the beamforming design of the transmitted signal, enabling the system to achieve good secure communication and sensing performance.

[0134] Example:

[0135] The effectiveness of this invention can be illustrated through simulations using Matlab R2018b. All simulated channels are modeled based on Rayleigh fading channels, and power amplification at the receiver is considered, thus path loss is ignored. The elements in the channel vectors from the base station to the legitimate user and the eavesdropper all follow a complex Gaussian random distribution with a mean of 0 and a variance of 1. A schematic diagram of the application scenario of this invention is shown below. Figure 1 As shown.

[0136] Figure 2 The convergence of the method of the present invention on a random channel is demonstrated (i.e., after a finite number of iterations, the average safe rate of the system converges to a certain value), wherein the number of transmit antennas M t =16, Number of valid users M r =3, beam matching error threshold μ = 0.05. As can be seen from the figure, the penalty term corresponding to each rank-1 constraint converges quickly to near 0, ensuring that the rank of the solved precoding matrix and noise matrix is ​​very close to 1. Simultaneously, the average security rate of legitimate users also rapidly increases and converges to a stable value. This demonstrates that the algorithm developed in this invention can efficiently perform ISAC secure beamforming design and possesses excellent convergence.

[0137] Figure 3 The paper demonstrates the process of finding the optimal solution using a one-dimensional search. As the eavesdropper signal-to-interference-plus-noise ratio (SNR) threshold γ increases, the security rate initially increases, reaches its maximum value, and then begins to decrease. Furthermore, there exists a unique extreme point that maximizes the average security rate for legitimate users. This is because the transmit power is limited, and the power of the confidential information and the power of artificial noise are mutually constrained. Simultaneously, under the same power allocation scheme, a more relaxed SNR constraint on the eavesdropper increases the degree of freedom in system design, thus achieving a higher security rate. Simulation results verify that the optimal trade-off point that maximizes the average security rate of the system can be obtained through a one-dimensional linear search method.

[0138] Figure 4 The beam patterns designed in this invention and in references 3 and 4 are illustrated. In this scenario, there are three targets to be detected in a random channel, located in the [-40°, 0°, 40°] directions of the base station. The goal is to design the covariance matrix of the transmitted signal to align the main beam with the direction of the target, and the width of the main beam should be as small as possible (less than 10°). Simulation results show that all schemes can match the ideal beam pattern well. However, due to the embedding of communication information and the limitation of the number of base station transmit antennas, the designed beam patterns exhibit high sidelobes in some locations. These errors are tolerable in an ISAC system.

[0139] Figure 5 and Figure 6 The secure rate performance under different beam pattern mean square errors (μ values) is demonstrated. As μ increases, sensing performance gradually deteriorates while the secure rate improves, highlighting the trade-off between communication and sensing performance. When μ is small, the constraints on sensing performance are too strict, making it difficult to find feasible beamforming schemes, resulting in a sharp drop in the secure rate, even approaching zero.

[0140] exist Figure 5 In comparison, the average secure rate of our proposed scheme is lower than that of the Weighted Minimum Mean-Square Error (WMMSE) scheme based on precise prior information about the eavesdropper in Reference 3 and the Fractional Programming-Semi-definite Relaxation (FP-SDR) scheme in Reference 4. However, the performance of these two schemes degrades significantly when there is slight uncertainty regarding the eavesdropper's location. In contrast, our proposed scheme requires no prior information and mitigates covert eavesdroppers by allocating more power to artificial noise. While this limits the transmission rate for legitimate users, it exhibits greater robustness and achieves a satisfactory secure rate.

[0141] Furthermore, Figure 6 This demonstrates that our proposed scheme outperforms the WMMSE scheme (with / without precise location information) and the FP-SDR scheme (without precise location information) in terms of minimum user safety rate, reflecting its advantage in fairness design. Although our scheme is only slightly inferior to the FP-SDR scheme with precise location information (and the performance difference is not significant), it does not rely on any location information at all, thus making it more feasible in practical applications.

[0142] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A secure beamforming method for an integrated communication and sensing system designed to detect silent eavesdroppers, characterized in that: include: The optimization problem of constructing secure beamforming is described. The optimization objective of the problem is to maximize the minimum generalized secure channel capacity. The constraints are: sensing beam pattern error constraint, constant modulus constraint, rank-1 constraint and positive semi-definite constraint of artificial noise matrix and legal user precoding matrix. The noise projection matrix is ​​solved based on the legitimate user channel matrix. The noise projection matrix is ​​then decomposed into eigenvalues, and the eigenvectors corresponding to the non-zero eigenvalues ​​are taken. These eigenvectors constitute the artificial noise matrix. Determine the optimal value of the scale factor in the beam pattern; By introducing auxiliary variables and using a quadratic transformation, the optimization problem is transformed from minimax and multiproportional fractional programming into a form that is easier to solve. The non-convex constraints in the transformed optimization problem are transformed using the successive convex approximation method and a penalty term is introduced to obtain a new optimization problem; Solve the new optimization problem and determine the optimal values ​​of the precoding matrix and the noise matrix through a one-dimensional linear search; The base station uses the optimal value of the scaling factor to configure the beam pattern and uses the optimal values ​​of the precoding matrix and noise matrix to transmit signals.

2. The secure beamforming method for an integrated communication and sensing system for silent eavesdroppers according to claim 1, characterized in that, The sensing beam pattern error constraint is: the mean square error between the beam pattern of the transmitted signal x and the ideal beam pattern. Less than the error threshold μ; constant modulus constraint: the total power of the transmitted signal x does not exceed the system power budget P. t Furthermore, the average power of each antenna is the same.

3. The secure beamforming method for an integrated communication and sensing system for silent eavesdroppers according to claim 1, characterized in that, The optimization problem of secure beamforming is expressed as follows: Where ψ is the scaling factor, i represents the i-th legitimate user, and II = {1, 2, ..., M} r }, M r GSR represents the number of legitimate users. i Represents the capacity of a generalized secure channel. R represents the mean square error between the beam pattern of the transmitted signal x and the ideal beam pattern, where μ is the error threshold and R is the mean square error. x (n,n) represents the covariance matrix R of the transmitted signal x. x The diagonal element, P t M represents the total power of the system. t The number of antennas in a uniform linear array antenna; Q≥0 and Z i ≥0 represent the artificial noise matrix Q and the legal user precoding matrix Z, respectively. i Let be a positive semi-definite matrix, and Rank(·) denotes the rank of the matrix.

4. The secure beamforming method for an integrated communication and sensing system for silent eavesdroppers according to claim 1, characterized in that, The noise projection matrix is ​​solved based on the legitimate user channel matrix. Eigenvalue decomposition is then performed on the noise projection matrix, and the eigenvectors corresponding to the non-zero eigenvalues ​​are taken. These eigenvectors constitute the artificial noise matrix, including: The noise projection matrix is ​​represented as: Where I is the identity matrix and the channel matrix of the legitimate users. h b,i Let M be the channel vector from the base station to the i-th legitimate user, where i = 1, 2, ..., M. r The superscript T indicates transpose, and the superscript H indicates conjugate transpose; Further eigenvalue decomposition of the noise projection matrix P is expressed as: P=GΣG H Where Σ is a diagonal matrix, its diagonal elements are the eigenvalues ​​of P, and the columns of the unitary matrix G are the eigenvectors of P; the artificial noise matrix is ​​represented as: Q=[e1,e2,...,e K ] T Among them, e k Let P be the eigenvector corresponding to the non-zero eigenvalues ​​of P, and K be the number of non-zero eigenvalues.

5. The secure beamforming method for an integrated communication and sensing system for silent eavesdroppers according to claim 1, characterized in that, Determining the optimal value of the scale factor in the beam pattern includes: Where, θ l Let d(θ) be the l-th sampling angle, and L be the number of sampling angles. l ) represents the ideal beam pattern, a(θ) l ) represents the steering vector of the antenna at the ISAC base station. This represents the optimal value of the scaling factor.

6. The secure beamforming method for an integrated communication and sensing system for silent eavesdroppers according to claim 1, characterized in that, By introducing auxiliary variables and applying quadratic transformations, the optimization problem is transformed from minimax and multiproportional fractional programming into a more easily solvable form, including: Using a quadratic transformation, the optimization problem (P1) is transformed as follows: Where z is the quadratic transformation reconstruction function. Z n This represents the precoding matrix of the nth legal user. This represents the noise variance at legitimate user locations. Z represents the equivalent noise variance at the eavesdropper's location, and tr(·) is the trace of the matrix; q Let γ be the beamforming matrix of the artificial noise, and γ be an auxiliary variable in the one-dimensional linear search. proportionality coefficient ρ i Iterate according to the following rules: in, ρ is obtained in the kth iteration i , Z is obtained in the (k-1)th iteration i Given initialization Then, by solving the optimization problem (P1.1), we obtain... and Next calculation Repeat the iteration until convergence or the set number of iterations is reached.

7. The secure beamforming method for an integrated communication and sensing system for silent eavesdroppers according to claim 1, characterized in that, The non-convex constraints in the transformed optimization problem are transformed using a successive convex approximation method, and a penalty term is introduced to obtain a new optimization problem, as follows: in, Let ξ represent the penalty term, and ξ be the penalty factor. Let ||Q||2 represent the lower bound, which is obtained by successive convex approximation. Let ||·||2 represent the L2 norm.

8. The secure beamforming method for an integrated communication and sensing system for silent eavesdroppers according to claim 1, characterized in that, Solve the new optimization problem and determine the optimal values ​​of the precoding matrix and noise matrix through a one-dimensional linear search, including: Given different values ​​of the auxiliary variable γ, the new optimization problem P(1.2) is solved, and its solution is defined as f(γ). Then, problem (P1.3) and P(1) have the same optimal solution. The optimal values ​​of the precoding matrix and the noise matrix are obtained by performing a one-dimensional linear search on different γ and f(γ).

9. A terminal device, comprising a processor, a memory, and a computer program stored in the memory; characterized in that, When the processor executes the computer program, it implements the secure beamforming method for a communication-sensing integrated system for silent eavesdroppers as described in any one of claims 1-8.

10. A computer-readable storage medium storing a computer program; characterized in that, When the computer program is executed by the processor, it implements the secure beamforming method for a communication-sensing integrated system for silent eavesdroppers as described in any one of claims 1-8.

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