A method for RIS-aided MIMO secure communication based on subarray division

Abstract

The present application relates to a kind of RIS assisted MIMO security communication methods based on subarray division, comprising: constructing RIS assisted MIMO security communication system based on subarray division;Security secrecy rate of RIS assisted MIMO security communication system is calculated;Subarray number minimization optimization model P1 is constructed;Subarray number minimization optimization model P1 is solved by the method that bisection method and alternating optimization method are combined, and the optimal solution of transmission covariance matrix and RIS reflection coefficient is sought.RIS element is divided into multiple subarrays, the complexity and overhead of RIS architecture are simplified, and the number of optimizing RIS reflection coefficient is reduced;Bisection method and alternating optimization combined method are used to jointly optimize subarray number, transmission covariance matrix and RIS reflection coefficient, so as to reduce the calculation complexity of system optimization, while guaranteeing system security transmission performance, reduce calculation complexity and system overhead, also applicable to RIS assisted MISO security communication system, and the considered hardware loss has important significance in actual security communication system.

Description

Technical Field

[0001] This invention relates to the field of physical layer secure communication technology, and in particular to a RIS-assisted MIMO secure communication method based on subarray partitioning. Background Technology

[0002] Physical Layer Security (PLS) technology, as a novel security measure, can effectively address issues such as line-of-sight obstacles and eavesdropping in wireless communication, improving the security and confidentiality of information during communication. Reconfigurable Intelligent Surfaces (RIS) are planar arrays composed of numerous low-cost, low-power passive reflective elements, each capable of independently and controllably reflecting incident signals with adjustable amplitude and phase shift. As a successor to massively multi-input multiple-output (MIMO) and relay technologies, RIS can improve wireless link throughput and reliability, showing broad application prospects in the field of physical layer secure communication. However, in practical applications, passive RIS-assisted communication systems typically require very large surfaces; otherwise, they may be outperformed by traditional relays. Furthermore, increasing the number of RIS elements leads to high overhead and non-negligible power consumption in channel acquisition, while also increasing the computational complexity of joint transmit beamforming and RIS reflection coefficient optimization. Therefore, it is essential to research how to improve the security performance of RIS-assisted secure communication systems while reducing system complexity and hardware costs.

[0003] To simplify system complexity and improve efficiency, subarray partitioning is a promising approach. The basic idea is to divide the entire RIS into several subarrays, each containing elements with the same reflection coefficient. This significantly reduces the RIS reflection coefficient that needs optimization, greatly simplifying the RIS architecture's complexity and overhead. However, while existing subarray-based RIS-assisted wireless communication schemes reduce computational complexity and system overhead, they all assume system security, the absence of eavesdroppers, and are mostly multiple-input single-output (MISO) communication systems. In the presence of eavesdroppers, it's necessary to consider the eavesdropping channel and how to improve system security. Furthermore, the system still suffers from high computational complexity and overhead. Therefore, existing subarray partitioning methods are no longer applicable, necessitating a redesigned subarray partitioning method specifically for RIS-assisted MIMO secure communication under eavesdropping scenarios. Summary of the Invention

[0004] To address the issues of high computational complexity and overhead in existing RIS-assisted secure communication technologies, the present invention aims to provide a RIS-assisted MIMO secure communication method based on subarray partitioning that reduces computational complexity and overhead while ensuring secure transmission performance.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a RIS-assisted MIMO secure communication method based on subarray partitioning, the method comprising the following sequential steps:

[0006] (1) Construct a RIS-assisted MIMO secure communication system based on subarray partitioning: The RIS-assisted MIMO secure communication system consists of a base station, legitimate users, eavesdroppers, and a RIS with subarray partitioning. Subarray partitioning refers to dividing the RIS element into multiple subarrays. The same subarray element is connected to the same phase shifter. The channel coefficients of each link, the subarray partitioning matrix, and the RIS reflection coefficient are defined.

[0007] (2) Calculate the security rate of the RIS-assisted MIMO secure communication system: Based on the signal expressions received by legitimate users and eavesdroppers, calculate the channel capacity C of the effective link between the base station and the legitimate user. B Channel capacity C of the effective link between the base station and the eavesdropper E Calculate the security and confidentiality rate C s ;

[0008] (3) Construct a subarray number minimization optimization model P1: The objective function of the subarray number minimization optimization model P1 is to minimize the number of subarrays. The constraints of the subarray number minimization optimization model P1 include security rate constraint C1, transmission power constraint C2, RIS reflection coefficient constraint C3, and subarray partitioning matrix constraint C4.

[0009] (4) Solve the subarray number minimization optimization model P1 by combining the bisection method and the alternating optimization method: The bisection method is used to optimize the number of subarrays. In the bisection method, the number of subarrays and the partition matrix are fixed. The subarray number minimization optimization model P1 is transformed into the security maximization optimization model P2. The alternating optimization method is used to solve the optimal solutions of the emission covariance matrix and the RIS reflection coefficient. The optimal solution of the RIS reflection coefficient is obtained by the coordinate descent method. Then, the feasibility of the solution of the security maximization optimization model P2 is checked by iteration, and the optimal solution of the subarray number minimization optimization model P1 is obtained.

[0010] Step (1) specifically refers to: the number of antennas equipped at the base station, the legitimate user, and the eavesdropper are respectively N. A N B N EThe RIS is configured with N reflective elements. The RIS controller divides these N reflective elements into M subarrays, each subarray containing N / M elements. Elements in the same subarray are connected to the same phase shifter, meaning elements in the same group have the same reflection coefficient. Each link includes base station-RIS, RIS-legitimate user, RIS-eavesdropper, base station-legitimate user, and base station-eavesdropper links. The channel coefficients for these links are defined as follows: and The RIS reflection coefficient of the m-th subarray is m = 1, 2, ..., M, where θ m ∈[0,2π] and α m ∈[0,1] represents the phase shift and amplitude, respectively. Let α m =1, then β m Satisfy |β m | = 1; Define the m-th subarray partition matrix as a diagonal matrix V m =diag(v m,1 ,v m,2 ,…,v m,N V m V represents the location and number of elements contained in the subarray. m diagonal element v m,n =0 or 1, n = 1, 2, ..., N, and satisfying I N Let N be the identity matrix, then the diagonal matrix of reflection coefficients at RIS is...

[0011] Step (2) specifically refers to: Let the transmitted signal vector at the base station be s, and let the average transmitted power at the base station satisfy... P A Let y represent the maximum transmit power at the base station, then the signal y received at a legitimate user's location is... B The signal y received at the eavesdropper E They are represented as follows:

[0012] y B =(H RB ΘH AR +H AB )s+n b =H B s+n b (1)

[0013] y E =(H RE ΘH AR +H AE )s+ne =H E s+n e (2)

[0014] In the formula, H AR For the channel coefficients of the base station-RIS link, H RB For the channel coefficients of the RIS-legitimate user link, H RE For the channel coefficients of the RIS-eavesdropper link, H AB For the channel coefficients of the base station-legitimate user link, H AE Let n be the channel coefficient of the base station-eavesdropper link. b and n e The additive Gaussian noise at the legitimate user and the eavesdropper, respectively. and The average noise power at legitimate users and eavesdroppers, H, are respectively. B H represents the channel coefficients of the effective link between the base station and the legitimate user. E Let Θ be the channel coefficient of the effective link between the base station and the eavesdropper, and let Θ be the diagonal matrix of the reflection coefficients at RIS. Equations (1) and (2) are the expressions for the received signals of the legitimate user and the eavesdropper, respectively.

[0015] Assumption The channel capacity C of the effective link between the base station and the legitimate user B The channel capacity C of the effective link between the base station and the eavesdropper. E They are respectively:

[0016]

[0017]

[0018] in, N represents B An identity matrix of order 1. H represents B The conjugate transpose of . H represents E The conjugate transpose of the emission covariance matrix Satisfying tr(Q)≤P A tr(Q) is the trace of the emission covariance matrix Q, s H Let s be the conjugate transpose of s, then the security and confidentiality rate C s for:

[0019] C s =[C B -C E ] + =max(C B -C E ,0) (5).

[0020] The step (3) specifically refers to the objective function of the subarray number minimization optimization model P1 being the minimum subarray number M: minM;

[0021] The constraints of the subarray number minimization optimization model P1 include:

[0022] Confidentiality constraint C1:

[0023] C s ≥C smin

[0024] Among them, C smin This represents the minimum security level requirement for the system.

[0025] Transmit power constraint C2:

[0026]

[0027] In the formula, tr(Q) is the trace of the emission covariance matrix Q, and P A This represents the maximum transmit power at the base station, and Q is the transmit covariance matrix.

[0028] RIS reflection coefficient constraint C3:

[0029] |β m |=1,m=1,2,...,M

[0030] In the formula, β m Let be the RIS reflection coefficient of the m-th subarray;

[0031] Subarray partitioning matrix constraint C4:

[0032]

[0033] In the formula, V m The matrix to partition the m-th subarray is a diagonal matrix, v m,n For V m The diagonal element, I N This represents an N-order identity matrix.

[0034] Step (4) specifically refers to: in each step of the bisection method, the number of subarrays M is fixed, let {V m If the number of subarrays is determined in a predefined manner and no optimization is required, then the optimization model P1 for minimizing the number of subarrays is transformed into the optimization model P2 for maximizing the security rate.

[0035] The objective function of the confidentiality maximization optimization model P2 is to maximize the security confidentiality rate, i.e., max C. s ;

[0036] The constraints of the security maximization optimization model P2 include transmit power constraint C2 and RIS reflection coefficient constraint C3:

[0037] Transmit power constraint C2:

[0038]

[0039] In the formula, tr(Q) is the trace of the emission covariance matrix Q, and P A This represents the maximum transmit power at the base station, and Q is the transmit covariance matrix.

[0040] RIS reflection coefficient constraint C3:

[0041] |β m |=1,m=1,2,...,M

[0042] In the formula, β m Let be the RIS reflection coefficient of the m-th subarray;

[0043] The emission covariance matrix Q and the RIS reflection coefficient {β} are optimized using the alternating optimization method. m Solving the confidentiality maximization optimization model P2 yields the optimal security confidentiality rate. Then, by iteratively verifying the feasibility of the solution of the security maximization optimization model P2, the optimal number of subarrays M*, the optimal emission covariance matrix Q*, and the optimal RIS reflection coefficient are obtained. The steps are as follows:

[0044] (4a) Initialization: Let the range of the number of subarrays M be [l, u], t be the threshold, and C smin To achieve the lowest system security and confidentiality rate, randomize {β} m};

[0045] (4b) Using the bisection method, let M = (l + u) / 2, given the subarray partitioning matrix {V m};

[0046] (4c) Using the alternating optimization method, given the RIS reflection coefficient {β} m}, optimize the emission covariance matrix Q;

[0047] (4d) Given the emission covariance matrix Q, optimize the RIS reflection coefficients {β} using the coordinate descent method. m};

[0048] (4e) Calculate the security and confidentiality rate C s It then determines whether convergence has occurred; if convergence has occurred, the optimal security and confidentiality rate is obtained. Proceed to step (4f); otherwise, repeat steps (4c) to (4e).

[0049] (4f) Iteratively verify the feasibility of the solution to the confidentiality maximization optimization model P2. If Let u = M, if Let l = M; if |ul| > t, we obtain the optimal number of subarrays M*, the optimal emission covariance matrix Q*, and the optimal RIS reflection coefficient. If |ul|≤t, repeat steps (4b) to (4f).

[0050] In step (4c), the optimized emission covariance matrix Q specifically refers to:

[0051] When the number of subarrays M and the subarray partitioning matrix {V} m When determined, given the RIS reflection coefficient {β} m Let the optimization model for Q be P3;

[0052] The objective function of the optimization model P3 is to maximize the security and confidentiality rate, i.e., max C. s ;

[0053] The constraint condition for optimizing model P3 is the transmit power constraint C2:

[0054]

[0055] In the formula, tr(Q) is the trace of the emission covariance matrix Q, and P A This indicates the maximum transmit power at the base station;

[0056] In optimization model P3, the optimal solution of Q has a rank of 1, and Q = FF. H F is the optimal transmit beamforming vector, tr(Q)≤P A Equivalent to ||F|| 2 ≤P A And Q satisfies The optimal solution for F is:

[0057]

[0058] in, H B H represents the channel coefficients of the effective link between the base station and the legitimate user. E For the effective link between the base station and the eavesdropper, the channel coefficients are... N represents A σ is an identity matrix of order 1. 2 The average noise power, Indicates parameters If the normalized eigenvector corresponds to the largest eigenvalue, then the optimal solution for Q is:

[0059] Q * =F * (F* ) H (7).

[0060] In step (4d), the RIS reflection coefficient {β} is optimized using the coordinate descent method. m Specifically, it refers to:

[0061] When the number of subarrays M and the subarray partitioning matrix {V} m When determined, given the emission covariance matrix Q, let the reflection coefficients {β} of RIS be determined. m The optimization model for} is P4;

[0062] The objective function of optimization model P4 is to maximize the security and confidentiality rate, i.e., max C. s ;

[0063] The constraint condition for the optimization model P4 is the RIS reflection coefficient constraint C3:

[0064] |β m |=1,m=1,2,...,M

[0065] In the formula, β m Let be the RIS reflection coefficient of the m-th subarray;

[0066] Using the coordinate descent method, {β} m The optimization is performed by transforming the high-dimensional optimization problem into multiple one-dimensional optimization subproblems for solution, i.e., given Q and... Optimize β m First, the channel coefficient H of the effective link between the base station and the legitimate user is... B Decompose as follows:

[0067]

[0068] Among them, H B,-m For H B In and β m Irrelevant parts, H AR and H RB V represents the channel coefficients for the base station-RIS link and the RIS-legitimate user link, respectively. m The matrix for dividing the m-th subarray is a diagonal matrix;

[0069] Substituting equation (8) into the channel capacity C of the base station-legitimate user effective link... B From:

[0070]

[0071] in, For β m conjugate, N represents BAn identity matrix of order 1. For H B,-m The conjugate transpose of . For q Bm The conjugate transpose of σ 2 X is the average noise power. Bm p Bm and q Bm The expression is as follows:

[0072]

[0073]

[0074]

[0075] It can be known p Bm,i and p Bm and The i-th element, i = 1, 2, ..., N;

[0076] The same logic applies to the effective link between the base station and the eavesdropper:

[0077]

[0078] in, For q Em The conjugate transpose of p Em,i and p Em and The i-th element, i = 1, 2, ..., N, X Em p Em and q Em The expression is as follows:

[0079]

[0080] Among them, H E,-m Channel coefficient H of the effective link between base station and eavesdropper E In and β m Irrelevant parts N represents E An identity matrix of order 1. For H E,-m The conjugate transpose of H RE For the RIS-eavesdropper link, the channel coefficients are used.

[0081] Let the equivalent optimization model for the m-th subproblem be P5;

[0082] The objective function of the equivalent optimization model P5 is:

[0083]

[0084] Among them, |a Bm |<1,|a Em |<1, and a Bm and a Em The conjugate of a Bm and a Em The expression is as follows:

[0085]

[0086] In the formula, and They are respectively and The conjugate of the parameter, where the subscript i or j represents the i-th or j-th element in the parameter, i = 1, 2, ..., N, j = 1, 2, ..., N;

[0087] The constraints of the equivalent optimization model P5 are: RIS reflection coefficient constraint C3:

[0088] |β m |=1,

[0089] In the formula, β m Let be the RIS reflection coefficient of the m-th subarray;

[0090] Based on Cauchy's inequality, the optimal solution for optimization model P5 is derived as follows:

[0091]

[0092] The expression for ρ is as follows:

[0093]

[0094] Then, using the coordinate descent method, for β m We perform optimization solutions for each m = 1, 2, ..., M.

[0095] As can be seen from the above technical solution, the beneficial effects of the present invention are as follows: First, compared with the prior art, the RIS-assisted MIMO secure communication system of the present invention divides the RIS element into multiple subarrays, simplifying the complexity and overhead of the RIS architecture and reducing the number of RIS reflection coefficients to be optimized; Second, the present invention is the first to construct an optimization problem that minimizes the number of subarrays while ensuring the system's security and confidentiality rate. It uses a combination of bisection method and alternating optimization to jointly optimize the number of subarrays, the transmission covariance matrix, and the RIS reflection coefficients. The optimal solutions for the transmission covariance matrix and the RIS reflection coefficients are derived by combining the coordinate descent method, thereby reducing the computational complexity of the system optimization; Third, compared with the prior art, the present invention reduces computational complexity and system overhead while ensuring the system's secure transmission performance. It is also applicable to RIS-assisted MISO secure communication systems, and the hardware losses considered are of great significance in practical secure communication systems. Attached Figure Description

[0096] Figure 1 This is a flowchart of the method of the present invention;

[0097] Figure 2 This is a block diagram of a RIS-assisted MIMO secure communication system based on subarray partitioning.

[0098] Figure 3 This is a flowchart illustrating the overall process of combining the dichotomy method with alternating optimization.

[0099] Figure 4 This is a convergence trend graph for the alternating optimization method.

[0100] Figure 5 This is a graph showing the relationship between maximum transmission power and average security level.

[0101] Figure 6 This is a graph showing the relationship between the number of subarrays and the average security level. Detailed Implementation

[0102] like Figure 1 As shown, a RIS-assisted MIMO secure communication method based on subarray partitioning includes the following sequential steps:

[0103] (1) Construct a RIS-assisted MIMO secure communication system based on subarray partitioning: The RIS-assisted MIMO secure communication system consists of a base station, legitimate users, eavesdroppers, and a RIS with subarray partitioning. Subarray partitioning refers to dividing the RIS element into multiple subarrays. The same subarray element is connected to the same phase shifter. The channel coefficients of each link, the subarray partitioning matrix, and the RIS reflection coefficient are defined.

[0104] (2) Calculate the security rate of the RIS-assisted MIMO secure communication system: Based on the signal expressions received by legitimate users and eavesdroppers, calculate the channel capacity C of the effective link between the base station and the legitimate user. B Channel capacity C of the effective link between the base station and the eavesdropper E Calculate the security and confidentiality rate C s ;

[0105] (3) Construct a subarray number minimization optimization model P1: The objective function of the subarray number minimization optimization model P1 is to minimize the number of subarrays. The constraints of the subarray number minimization optimization model P1 include security rate constraint C1, transmission power constraint C2, RIS reflection coefficient constraint C3, and subarray partitioning matrix constraint C4.

[0106] (4) Solve the subarray number minimization optimization model P1 by combining the bisection method and the alternating optimization method: The bisection method is used to optimize the number of subarrays. In the bisection method, the number of subarrays and the partition matrix are fixed. The subarray number minimization optimization model P1 is transformed into the security maximization optimization model P2. The alternating optimization method is used to solve the optimal solutions of the emission covariance matrix and the RIS reflection coefficient. The optimal solution of the RIS reflection coefficient is obtained by the coordinate descent method. Then, the feasibility of the solution of the security maximization optimization model P2 is checked by iteration, and the optimal solution of the subarray number minimization optimization model P1 is obtained.

[0107] like Figure 2 As shown, step (1) specifically refers to: the number of antennas equipped at the base station, the legitimate user, and the eavesdropper are respectively N. A N B N E The RIS is configured with N reflective elements. The RIS controller divides these N reflective elements into M subarrays, each subarray containing N / M elements. Elements in the same subarray are connected to the same phase shifter, meaning elements in the same group have the same reflection coefficient. Each link includes base station-RIS, RIS-legitimate user, RIS-eavesdropper, base station-legitimate user, and base station-eavesdropper links. The channel coefficients for these links are defined as follows: and The RIS reflection coefficient of the m-th subarray is m = 1, 2, ..., M, where θ m ∈[0,2π] and α m ∈[0,1] represents the phase shift and amplitude, respectively. Let α m =1, then β m Satisfy |β m| = 1; Define the m-th subarray partition matrix as a diagonal matrix V m =diag(v m,1 ,v m,2 ,…,v m,N V m V represents the location and number of elements contained in the subarray. m diagonal element v m,n =0 or 1, n = 1, 2, ..., N, and satisfying I N Let N be the identity matrix, then the diagonal matrix of reflection coefficients at RIS is...

[0108] Step (2) specifically refers to: Let the transmitted signal vector at the base station be s, and let the average transmitted power at the base station satisfy... P A Let y represent the maximum transmit power at the base station, then the signal y received at a legitimate user's location is... B The signal y received at the eavesdropper E They are represented as follows:

[0109] y B =(H RB ΘH AR +H AB )s+n b =H B s+n b (1)

[0110] y E =(H RE ΘH AR +H AE )s+n e =H E s+n e (2)

[0111] In the formula, H AR For the channel coefficients of the base station-RIS link, H RB For the channel coefficients of the RIS-legitimate user link, H RE For the channel coefficients of the RIS-eavesdropper link, H AB For the channel coefficients of the base station-legitimate user link, H AE Let n be the channel coefficient of the base station-eavesdropper link. b and n e The additive Gaussian noise at the legitimate user and the eavesdropper, respectively. , and The average noise power at legitimate users and eavesdroppers, H, are respectively. BH represents the channel coefficients of the effective link between the base station and the legitimate user. E Let Θ be the channel coefficient of the effective link between the base station and the eavesdropper, and let Θ be the diagonal matrix of the reflection coefficients at RIS. Equations (1) and (2) are the expressions for the received signals of the legitimate user and the eavesdropper, respectively.

[0112] Assumption The channel capacity C of the effective link between the base station and the legitimate user B Channel capacity C of the effective link between the base station and the eavesdropper E They are respectively:

[0113]

[0114]

[0115] in, N represents B An identity matrix of order 1. H represents B The conjugate transpose of . H represents E The conjugate transpose of the emission covariance matrix Satisfying tr(Q)≤P A tr(Q) is the trace of the emission covariance matrix Q, s H Let s be the conjugate transpose of s, then the security and confidentiality rate C s for:

[0116] C s =[C B -C E ] + =max(C B -C E ,0) (5).

[0117] The step (3) specifically refers to the objective function of the subarray number minimization optimization model P1 being the minimum subarray number M: minM;

[0118] The constraints of the subarray number minimization optimization model P1 include:

[0119] Confidentiality constraint C1:

[0120] C s ≥C smin

[0121] Among them, C smin This represents the minimum security level requirement for the system.

[0122] Transmit power constraint C2:

[0123]

[0124] In the formula, tr(Q) is the trace of the emission covariance matrix Q, and P A This represents the maximum transmit power at the base station, and Q is the transmit covariance matrix.

[0125] RIS reflection coefficient constraint C3:

[0126] |β m |=1,m=1,2,...,M

[0127] In the formula, β m Let be the RIS reflection coefficient of the m-th subarray;

[0128] Subarray partitioning matrix constraint C4:

[0129]

[0130] In the formula, V m The matrix to partition the m-th subarray is a diagonal matrix, v m,n For V m The diagonal element, I N This represents an N-order identity matrix.

[0131] like Figure 3 As shown, step (4) specifically refers to: in each step of the bisection method, the number of subarrays M is fixed, let {V m If the number of subarrays is determined in a predefined manner and no optimization is required, then the optimization model P1 for minimizing the number of subarrays is transformed into the optimization model P2 for maximizing the security rate.

[0132] The objective function of the confidentiality maximization optimization model P2 is to maximize the security confidentiality rate, i.e., max C. s ;

[0133] The constraints of the security maximization optimization model P2 include transmit power constraint C2 and RIS reflection coefficient constraint C3:

[0134] Transmit power constraint C2:

[0135]

[0136] In the formula, tr(Q) is the trace of the emission covariance matrix Q, and P A This represents the maximum transmit power at the base station, and Q is the transmit covariance matrix.

[0137] RIS reflection coefficient constraint C3:

[0138] |β m |=1,m=1,2,...,M

[0139] In the formula, β mLet be the RIS reflection coefficient of the m-th subarray;

[0140] The emission covariance matrix Q and the RIS reflection coefficient {β} are optimized using the alternating optimization method. m Solving the confidentiality maximization optimization model P2 yields the optimal security confidentiality rate. Then, by iteratively verifying the feasibility of the solution of the security maximization optimization model P2, the optimal number of subarrays M*, the optimal emission covariance matrix Q*, and the optimal RIS reflection coefficient are obtained. The steps are as follows:

[0141] (4a) Initialization: Let the range of the number of subarrays M be [l, u], t be the threshold, and C smin To achieve the lowest system security and confidentiality rate, randomize {β} m};

[0142] (4b) Using the bisection method, let M = (l + u) / 2, given the subarray partitioning matrix {V m};

[0143] (4c) Using the alternating optimization method, given the RIS reflection coefficient {β} m}, optimize the emission covariance matrix Q;

[0144] (4d) Given the emission covariance matrix Q, optimize the RIS reflection coefficients {β} using the coordinate descent method. m};

[0145] (4e) Calculate the security and confidentiality rate C s It then determines whether convergence has occurred; if convergence has occurred, the optimal security and confidentiality rate is obtained. Proceed to step (4f); otherwise, repeat steps (4c) to (4e).

[0146] (4f) Iteratively verify the feasibility of the solution to the confidentiality maximization optimization model P2. If Let u = M, if Let l = M; if |ul| > t, we obtain the optimal number of subarrays M*, the optimal emission covariance matrix Q*, and the optimal RIS reflection coefficient. If |ul|≤t, repeat steps (4b) to (4f).

[0147] In step (4c), the optimized emission covariance matrix Q specifically refers to:

[0148] When the number of subarrays M and the subarray partitioning matrix {V} m When determined, given the RIS reflection coefficient {β} m Let the optimization model for Q be P3;

[0149] The objective function of the optimization model P3 is to maximize the security and confidentiality rate, i.e., max C. s ;

[0150] The constraint condition for optimizing model P3 is the transmit power constraint C2:

[0151]

[0152] In the formula, tr(Q) is the trace of the emission covariance matrix Q, and P A This indicates the maximum transmit power at the base station;

[0153] In optimization model P3, the optimal solution of Q has a rank of 1, and Q = FF. H F is the optimal transmit beamforming vector, tr(Q)≤P A Equivalent to ||F|| 2 ≤P A And Q satisfies The optimal solution for F is:

[0154]

[0155] in, H B H represents the channel coefficients of the effective link between the base station and the legitimate user. E For the effective link between the base station and the eavesdropper, the channel coefficients are... N represents A σ is an identity matrix of order 1. 2 The average noise power, Indicates parameters If the normalized eigenvector corresponds to the largest eigenvalue, then the optimal solution for Q is:

[0156] Q * =F * (F * ) H (7).

[0157] In step (4d), the RIS reflection coefficient {β} is optimized using the coordinate descent method. m Specifically, it refers to:

[0158] When the number of subarrays M and the subarray partitioning matrix {V} m When determined, given the emission covariance matrix Q, let the reflection coefficients {β} of RIS be determined. m The optimization model for} is P4;

[0159] The objective function of optimization model P4 is to maximize the security and confidentiality rate, i.e., max C. s ;

[0160] The constraint condition for the optimization model P4 is the RIS reflection coefficient constraint C3:

[0161] |β m |=1,m=1,2,...,M

[0162] In the formula, β m Let be the RIS reflection coefficient of the m-th subarray;

[0163] Using the coordinate descent method, {β} m The optimization is performed by transforming the high-dimensional optimization problem into multiple one-dimensional optimization subproblems for solution, i.e., given Q and... Optimize β m First, the channel coefficient H of the effective link between the base station and the legitimate user is... B Decompose as follows:

[0164]

[0165] Among them, H B,-m For H B In and β m Irrelevant parts, H AR and H RB V represents the channel coefficients for the base station-RIS link and the RIS-legitimate user link, respectively. m The matrix for dividing the m-th subarray is a diagonal matrix;

[0166] Substituting equation (8) into the channel capacity C of the base station-legitimate user effective link... B From:

[0167]

[0168] in, For β m conjugate, N represents B An identity matrix of order 1. For H B,-m The conjugate transpose of . For q Bm The conjugate transpose of σ 2 X is the average noise power. Bm p Bm and q Bm The expression is as follows:

[0169]

[0170]

[0171]

[0172] It can be known p Bm,i and p Bm and The i-th element, i = 1, 2, ..., N;

[0173] The same logic applies to the effective link between the base station and the eavesdropper:

[0174]

[0175] in, For q Em The conjugate transpose of p Em,i and p Em and The i-th element, i = 1, 2, ..., N, X Em p Em and q Em The expression is as follows:

[0176]

[0177] Among them, H E,-m Channel coefficient H of the effective link between base station and eavesdropper E In and β m Irrelevant parts N represents E An identity matrix of order 1. For H E,-m The conjugate transpose of H RE For the RIS-eavesdropper link, the channel coefficients are used.

[0178] Let the equivalent optimization model for the m-th subproblem be P5;

[0179] The objective function of the equivalent optimization model P5 is:

[0180]

[0181] Among them, |a Bm |<1,|a Em |<1, and a Bm and a Em The conjugate of a Bm and a Em The expression is as follows:

[0182]

[0183] In the formula, and They are respectively and The conjugate of the parameter, where the subscript i or j represents the i-th or j-th element in the parameter, i = 1, 2, ..., N, j = 1, 2, ..., N;

[0184] The constraints of the equivalent optimization model P5 are: RIS reflection coefficient constraint C3:

[0185] |β m |=1,

[0186] In the formula, β m Let be the RIS reflection coefficient of the m-th subarray;

[0187] Based on Cauchy's inequality, the optimal solution for optimization model P5 is derived as follows:

[0188]

[0189] The expression for ρ is as follows:

[0190]

[0191] Then, using the coordinate descent method, for β m We perform optimization solutions for each m = 1, 2, ..., M.

[0192] The following simulation experiment demonstrates the effectiveness and feasibility of this invention. In the simulation, it is assumed that uniform linear arrays are deployed on the base station, the legitimate user, and the eavesdropper, and a uniform planar array is deployed on the RIS. Consider a two-dimensional topology network, where the base station, RIS, legitimate user, and eavesdropper are located at (0,0), (10,10), (140,0), and (150,0), respectively, and the number of antennas for the base station, legitimate user, and eavesdropper is N. A =8,N B =4 and N E =4, considering large-scale fading, the distance-dependent path loss model is L(d) = L0(d / d0). -λ Where L0 is the path loss at the reference distance d0 = 1m, d is the distance between the two locations, and λ is the path loss exponent. Assuming complete channel state information is available, for small-scale fading, the fading channel model is as follows: Where τ is the Rician factor, h LoS and h NLoS These represent the deterministic fading component and the Rayleigh fading component, respectively. All channels are the product of large-scale fading and small-scale fading. Parameter setting: σ 2 =-80dBm, L0=-30dB, λ AR =2, λ AB =λ AE =3.67, λ RB =λ RE=2.5, τ AR =τ AB =τ AE =0, τ RB =τ RE =1. Additionally, the convergence condition in the alternating iterations is that the confidentiality rate increment is less than 10. -4 The curve is set to bps / Hz and iterated a maximum of 100 times, with each point on the curve representing the average value after 100 Monte Carlo trials.

[0193] like Figure 4 As shown in the figure, the three curves correspond to different numbers of RIS reflector units and the number of segments, where the transmit power P A =30dBm. It can be seen that after 10 iterations, it gradually converges and tends to stabilize, indicating that iterative optimization has a relatively fast convergence speed.

[0194] like Figure 5 As shown, when N=M, it belongs to the case of no traditional subarray division. From Figure 5 As can be seen from this, when N and M are fixed, the average security rate increases with P. A It increases with the increase of N and P. A When fixed, the average security level increases with the increase of the number of subarrays M. When M and P A When N is constant, the average security level increases with increasing N. The average security level is the average of the security level over 100 Monte Carlo trials.

[0195] like Figure 6 As shown, the average security rate of the system without subarray division is used as the upper bound of performance. When the number of subarrays is small, the system performance is poor. As the number of subarrays increases, the average security rate gradually approaches the upper limit. When the system performance reaches the target security rate, a subarray division method with lower complexity can be selected.

[0196] Table 1 analyzes the complexity of the subarray partitioning, non-partitioning, and exhaustive search methods, where N is set to N. r =max(N) B N E K1 is the number of iterations when the reflection coefficient converges, and K2 is the number of iterations when the emission covariance matrix and the reflection coefficient converge together. As can be seen from Table 1, compared with the subarray partitioning method and the exhaustive search method, the subarray partitioning method can effectively reduce the complexity.

[0197] Table 1

[0198]

[0199] In summary, the RIS-assisted MIMO secure communication system of this invention divides the RIS element into multiple subarrays, simplifying the complexity and overhead of the RIS architecture and reducing the number of RIS reflection coefficients to be optimized. This invention is the first to construct an optimization problem that minimizes the number of subarrays while ensuring system security and confidentiality. It employs a combination of bisection and alternating optimization to jointly optimize the number of subarrays, the transmission covariance matrix, and the RIS reflection coefficients. Specifically, by incorporating coordinate descent, the optimal solutions for the transmission covariance matrix and the RIS reflection coefficients are derived, thereby reducing the computational complexity of system optimization. Compared with existing technologies, this invention reduces computational complexity and system overhead while ensuring secure transmission performance. It is also applicable to RIS-assisted MISO secure communication systems, and the hardware losses considered are of significant importance in practical secure communication systems.

Claims

1. A RIS-assisted MIMO secure communication method based on subarray partitioning, characterized in that: The method includes the following steps in sequence: (1) Construct a RIS-assisted MIMO secure communication system based on subarray partitioning: The RIS-assisted MIMO secure communication system consists of a base station, a legitimate user, an eavesdropper, and a RIS with subarray partitioning. The subarray partitioning refers to dividing the RIS element into multiple subarrays. The same subarray element is connected to the same phase shifter. The channel coefficients of each link, the subarray partitioning matrix, and the RIS reflection coefficient are defined. (2) Calculate the security confidentiality rate of the RIS-assisted MIMO secure communication system: Calculate the channel capacity of the effective link between the base station and the legitimate user based on the signal expressions received by the legitimate user and the eavesdropper. Channel capacity of the effective link between the base station and the eavesdropper Calculate the security and confidentiality rate ; (3) Construct a subarray number minimization optimization model P1: The objective function of the subarray number minimization optimization model P1 is to minimize the number of subarrays. The constraints of the subarray number minimization optimization model P1 include security rate constraint C1, transmission power constraint C2, RIS reflection coefficient constraint C3, and subarray partitioning matrix constraint C4. (4) Solve the optimization model P1 for minimizing the number of subarrays by combining the bisection method and the alternating optimization method: The bisection method is used to optimize the number of subarrays. In the bisection method, the number of subarrays and the partition matrix are fixed. The optimization model P1 for minimizing the number of subarrays is transformed into the optimization model P2 for maximizing the security rate. The optimal solution of the emission covariance matrix and the RIS reflection coefficient is obtained by the alternating optimization method. The optimal solution of the RIS reflection coefficient is obtained by the coordinate descent method. Then, the feasibility of the solution of the optimization model P2 for maximizing the security rate is checked by iteration. The optimal solution of the optimization model P1 for minimizing the number of subarrays is obtained. The step (4) specifically refers to: in each step of the bisection method, the number of subarrays M is fixed, let... If the number of subarrays is determined in a predefined manner and no optimization is required, the optimization model P1 for minimizing the number of subarrays is transformed into the optimization model P2 for maximizing the security rate. The objective function of the confidentiality maximization optimization model P2 is to maximize the security confidentiality rate, i.e. ; The constraints of the security maximization optimization model P2 include transmit power constraint C2 and RIS reflection coefficient constraint C3: Transmit power constraint C2: ； In the formula, tr(Q) is the emission covariance matrix. PA represents the maximum transmit power at the base station. For the emission covariance matrix; RIS reflection coefficient constraint C3: ； In the formula, Let be the RIS reflection coefficient of the m-th subarray; The emission covariance matrix Q and the RIS reflection coefficient were optimized using an alternating optimization method. Solving the confidentiality maximization optimization model P2 yields the optimal security confidentiality rate. Then, by iteratively verifying the feasibility of the solution of the security maximization optimization model P2, the optimal number of subarrays M*, the optimal emission covariance matrix Q*, and the optimal RIS reflection coefficient are obtained. The steps are as follows: (4a) Initialization: Let the number of subarrays M range from [l, u], t be the threshold, and Csmin be the minimum system security confidentiality rate. Randomization ; (4b) Using the bisection method, let M = (l + u) / 2, given the subarray partitioning matrix ; (4c) Using the alternating optimization method, given the RIS reflection coefficient Optimize the emission covariance matrix Q; (4d) Given the emission covariance matrix Q, optimize the RIS reflection coefficient using the coordinate descent method. ; (4e) Calculate the security ratio Cs and determine whether it converges. If it converges, the optimal security ratio is obtained. Proceed to step (4f); otherwise, repeat steps (4c) to (4e). (4f) Iteratively verify the feasibility of the solution to the confidentiality maximization optimization model P2. If Let u = M, if Let l = M; If |ul|>t, we obtain the optimal number of subarrays M*, the optimal emission covariance matrix Q*, and the optimal RIS reflection coefficient. If |ul|≤t, repeat steps (4b) to (4f).

2. The RIS-assisted MIMO secure communication method based on subarray partitioning according to claim 1, characterized in that: Step (1) specifically refers to the following: the number of antennas equipped at the base station, the legitimate user, and the eavesdropper are respectively NA, NB, and NE. The RIS is configured with N reflective elements, and the N reflective elements of the RIS are divided into M subarrays by the RIS controller. The number of elements in each subarray is N / M. Elements in the same subarray are connected to the same phase shifter, that is, the reflection coefficients of elements in the same group are the same. Each link includes the base station-RIS, RIS-legitimate user, RIS-eavesdropper, base station-legitimate user, and base station-eavesdropper links. The channel coefficients of the base station-RIS, RIS-legitimate user, RIS-eavesdropper, base station-legitimate user, and base station-eavesdropper links are defined as follows: , , , and ; The RIS reflection coefficient of the m-th subarray is Let m = 1, 2, ..., M, where θm ∈ [0, 2π] and αm ∈ [0, 1] represent phase shift and amplitude, respectively. Let αm = 1, then βm satisfies |βm| = 1. Define the partition matrix of the m-th subarray as a diagonal matrix Vm = diag(vm, 1, vm, 2, ..., vm, N), where Vm represents the position and number of elements contained in the subarray. The diagonal elements of Vm, vm, n = 0 or 1, n = 1, 2, ..., N, and satisfy... Let IN denote the N-order identity matrix, then the diagonal matrix of reflection coefficients at RIS is... .

3. The RIS-assisted MIMO secure communication method based on subarray partitioning according to claim 1, characterized in that: Step (2) specifically refers to: Let the transmitted signal vector at the base station be s, and let the average transmitted power at the base station satisfy... PA represents the maximum transmit power at the base station, which is the signal received by a legitimate user. Signals received at the eavesdropper's location They are represented as follows: （1） （2） In the formula, HAR is the channel coefficient of the base station-RIS link, HRB is the channel coefficient of the RIS-legitimate user link, HRE is the channel coefficient of the RIS-eavesdropper link, HAB is the channel coefficient of the base station-legitimate user link, HAE is the channel coefficient of the base station-eavesdropper link, and n b and n e The additive Gaussian noise at the legitimate user and the eavesdropper, respectively. , , and The average noise power at legitimate users and eavesdroppers, respectively. For the effective link between the base station and the legitimate user, For the effective link between the base station and the eavesdropper, the channel coefficients are... Let be the diagonal matrix of reflection coefficients at RIS, and Equations (1) and (2) are the expressions for the received signals of the legitimate user and the eavesdropper, respectively; Assumption Then the channel capacity of the effective link between the base station and the legitimate user Channel capacity of the effective link between base station and eavesdropper They are respectively: （3） （4） in, Represents an NB-order identity matrix. express The conjugate transpose of . express The conjugate transpose of the emission covariance matrix The expression tr(Q) ≤ PA, where tr(Q) is the emission covariance matrix. Let sH represent the conjugate transpose of s, then the security and confidentiality rate is... for: （5）。 4. The RIS-assisted MIMO secure communication method based on subarray partitioning according to claim 1, characterized in that: The step (3) specifically refers to the objective function of the subarray number minimization optimization model P1 being the minimum subarray number M: minM; The constraints of the subarray number minimization optimization model P1 include: Confidentiality constraint C1: ； in, This represents the minimum security level requirement for the system. Transmit power constraint C2: ； In the formula, tr(Q) is the emission covariance matrix. PA represents the maximum transmit power at the base station. For the emission covariance matrix; RIS reflection coefficient constraint C3: ； In the formula, Let be the RIS reflection coefficient of the m-th subarray; Subarray partitioning matrix constraint C4: ； In the formula, The matrix to partition the m-th subarray is a diagonal matrix. IN represents the diagonal elements of Vm, and IN denotes the N-order identity matrix.

5. The RIS-assisted MIMO secure communication method based on subarray partitioning according to claim 1, characterized in that: In step (4c), the optimized emission covariance matrix Q specifically refers to: When the number of subarrays M and the subarray partitioning matrix When determined, given the RIS reflection coefficient Let the optimization model for Q be P3; The objective function of the optimization model P3 is to maximize the security and confidentiality rate, i.e. ; The constraint condition for optimizing model P3 is the transmit power constraint C2: ； In the formula, tr(Q) is the emission covariance matrix. PA represents the maximum transmit power at the base station; In the optimization model P3, the optimal solution of Q has a rank of 1, Q = FFH, F is the optimal transmitted beamforming vector, and tr(Q) ≤ PA is equivalent to And Q satisfies Then the optimal solution for F is: （6） in, , , For the effective link between the base station and the legitimate user, For the effective link between the base station and the eavesdropper, the channel coefficients are... Represents an NA-order identity matrix. Umax is the average noise power. Indicates parameters If the normalized eigenvector corresponds to the largest eigenvalue, then the optimal solution for Q is: （7）。 6. The RIS-assisted MIMO secure communication method based on subarray partitioning according to claim 1, characterized in that: In step (4d), the RIS reflection coefficient is optimized using the coordinate descent method. Specifically, it refers to: When the number of subarrays M and the subarray partitioning matrix Given the emission covariance matrix Q, let the reflection coefficients of RIS be determined. The optimization model is P4; The objective function of optimization model P4 is to maximize the security and confidentiality rate, i.e. ; The constraint condition for the optimization model P4 is the RIS reflection coefficient constraint C3: ； In the formula, Let be the RIS reflection coefficient of the m-th subarray; Using the coordinate descent method To optimize, the high-dimensional optimization problem is transformed into multiple one-dimensional optimization subproblems for solution, i.e., given Q and ,optimization First, the channel coefficient HB of the effective link between the base station and the legitimate user is decomposed as follows: （8） in, for China and The irrelevant parts are HAR and HRB, which are the channel coefficients for the base station-RIS link and the RIS-legal user link, respectively. The matrix for dividing the m-th subarray is a diagonal matrix; Substituting equation (8) into the channel capacity of the base station-legitimate user effective link From: （9） in, for conjugate, Represents an NB-order identity matrix. for The conjugate transpose of . for The conjugate transpose of . The average noise power, , and The expression is as follows: ； It can be known , and They are respectively and The i-th element, i = 1, 2, ..., N; The same logic applies to the effective link between the base station and the eavesdropper: ； in, for The conjugate transpose of . and They are respectively and The i-th element, i=1,2,…,N, , and The expression is as follows: （10） in, Channel coefficients for effective base station-eavesdropper links China and Irrelevant parts Denotes an NE-order identity matrix. for The conjugate transpose of HRE is the channel coefficient of the RIS-eavesdropper link; Let the equivalent optimization model for the m-th subproblem be P5; The objective function of the equivalent optimization model P5 is: ； in, , and They are respectively and conjugate, and The expression is as follows: （11） In the formula, and They are respectively and The conjugate of the parameter, where the subscript i or j represents the i-th or j-th element in the parameter, i=1,2,…,N, j=1,2,…,N; The constraints of the equivalent optimization model P5 are: RIS reflection coefficient constraint C3: ， In the formula, Let be the RIS reflection coefficient of the m-th subarray; Based on Cauchy's inequality, the optimal solution for optimization model P5 is derived as follows: （12） The expression for ρ is as follows: （13） Then, using the coordinate descent method, for We perform optimization and solution step by step.

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