Physical layer security optimization method assisted by smart reflective surfaces under conditions of inaccurate channel state information

Abstract

This invention discloses a physical layer security optimization method assisted by smart reflective surfaces under conditions of inaccurate channel state information. This method utilizes smart reflective surfaces to reflect signals transmitted by base stations, thereby enabling signal transmission from base stations to users. Furthermore, to optimize the physical layer security performance of multi-user systems, the beamforming vectors for base station transmitted information signals and artificial noise, as well as the phase shift matrix of the smart reflective surface, are jointly optimized with the goal of maximizing the system confidentiality rate under the worst-case scenario, under the condition that the base station's eavesdropping channel state information contains errors. The method utilizes slack variables, penalty functions, Charnes-Cooper transforms, and alternating iterative optimization methods to transform the original non-convex semidefinite programming problem into a convex optimization problem, which is then solved using standard convex optimization problem solving methods.

Description

Technical Field

[0001] The present invention relates to the field of information communication, and in particular to a design method for a physical layer security solution assisted by an intelligent reflective surface under conditions of inaccurate channel state information. Background Art

[0002] With the commercialization of 5G technology and the research and development of 6G technology, the transmission rate of wireless communications continues to increase. However, wireless communication networks still have many problems to solve in terms of hardware costs, resource allocation, and information security [Zhang Shunqing, Wu Qingqing, Xu Shugong, et al. Fundamental green tradeoffs: progresses, challenges, and impacts on 5G networks [J]. IEEE Communications Surveys & Tutorials, 2017, 19(1): 33-56. doi: 10.1109 / COMST.2016.2594120.]. Physical layer security technology improves system transmission security by utilizing the randomness, time-varying nature, and spatial uniqueness of wireless channels. In physical layer security, multi-antenna beamforming and artificial noise technology are important technical means. Among them, multi-antenna beamforming technology [Lei Weijia, Zhou Yang. Optimization of average confidentiality and rate in MIMO full-duplex two-way communication systems [J]. Journal of Electronics, 2020, 48(06): 1041-1051. doi: 10.3969 / j.issn.0372-2112.2020.06.001.] uses spatial degrees of freedom to achieve directional information transmission, weakening the eavesdropper's ability to intercept information. Artificial noise technology [Lei Weijia, Lin Xiuzhen, Yang Xiaoyan, et al. A physical layer security scheme using artificial noise to improve the performance of legitimate receivers [J]. Journal of Electronics and Information Technology, 2016, 38(11): 2887-2892. doi: 10.11999 / JEIT160054.] adds appropriate noise when sending information, reducing the quality of the signal received by the eavesdropper without significantly affecting the reception quality of the legitimate receiver. Intelligent Reflecting Surface (IRS) is a low-cost passive device that does not have a radio frequency unit and baseband processing circuit. It only reflects wireless signals. By adjusting the phase and amplitude of the reflecting unit, intelligent control of the wireless environment can be achieved [Wu Qingqing, Zhang Rui. Towards smart and reconfigurable environment: intelligent reflecting surface aided wireless network[J]. IEEE Communications Magazine, 2020, 58(1): 106-112. doi: 10.1109 / MCOM.001.1900107.].In recent years, the use of IRS technology to enhance the physical layer security of wireless communications has attracted widespread attention from scholars at home and abroad [Chen Jie, Liang Yingchang, Pei Yiyang, et al. Intelligent reflecting surface: a programmable wireless environment for physical layer security [J]. IEEE Access, 2019, 7: 82599-82612. doi: 10.1109 / ACCESS.2019.2924034.]. Currently, in the research of IRS-assisted secure wireless communications, most of the work focuses on the optimization of base station beamforming vectors, power allocation, and IRS phase shift matrix with the goal of improving the secure transmission rate. Reference [Guan Xinrong, Wu Qqingqing, Zhang Rui. Intelligent reflecting surface assisted secrecy communication: is artificial noise helpful or not? [J].IEEE Wireless Communications Letters,2020,9(6):778-782.doi:10.1109 / LWC.2020.2969629.]For the IRS-assisted MISO (Multiple-Input Single-Output, MISO) communication system, with the goal of maximizing the confidentiality rate, the base station transmit beamforming matrix, artificial noise covariance matrix and IRS phase shift matrix are jointly optimized using the alternating iterative optimization algorithm and the semidefinite relaxation (SDR) method.Reference [Hong Sheng, Pan Cunhua, Ren Hong, et al. Artificial-noise-aided secure MIMO wireless communications via intelligent reflecting surface[J]. IEEE Transactions on Communications, 2020, 68(12): 7851-7866. doi: 10.1109 / TCOMM.2020.3024621.] For the Multiple-Input Multiple-Output (MIMO) communication system, with the goal of maximizing the confidentiality rate, the Block Coordinate Descent (BCD) and Majorization-Minimization algorithms are used to jointly optimize the design of the transmitter precoding matrix and the IRS phase shift matrix. The literature [Yu Xianghao, Xu Dongfang, Schober Robert. Enabling secure wireless communications via intelligent reflecting surfaces [C] / / 2019 IEEE Global Communications Conference (GLOBECOM). Waikoloa, HI, USA, 2019: 1-6. doi: 10.1109 / GLOBECOM38437.2019.9014322.] and [Cui Miao, Zhang Guangchi, Zhang Rui. Secure wireless communication via intelligent reflecting surface [J]. IEEE Wireless Communications Letters, 2019, 8 (5): 1410-1414. doi: 10.1109 / LWC.2019.2919685.] respectively use the BCD and minimum maximization algorithms to solve the confidentiality rate maximization problem. The latter also uses the SDR algorithm and linear fractional transform to transform the optimization problem into a convex problem.Reference [Huang Chong, Chen Gaojie, Wang Kaikit. Multi-agent reinforcement learning-based buffer-aided relay selection in IRS-assisted secure cooperative networks[J]. IEEE Transactions on Information Forensics and Security, 2021, 16: 4101-4112. doi: 10.1109 / TIFS.2021.3103062.] For a wireless communication system in which IRS and multiple cache-assisted relays exist between the base station and users and eavesdroppers, a cache-aided relay selection scheme in an IRS-assisted secure cooperative network is proposed. In the scenario where the phase shift and amplitude of the IRS reflected signal can only be discrete, and under the delay constraint caused by the cache-assisted relay, with the goal of maximizing the system confidentiality rate, the deep learning method is used to solve the joint optimization problem of cache-assisted relay selection and IRS phase shift matrix.

[0003] The premise of the optimization of beamforming, IRS phase shift, artificial noise, etc. in the above literature is that the base station perfectly knows the state information (Channel State Information, CSI) of all channels. Whether the CSI of the channel can be obtained has an important impact on the design of the transmission scheme and system performance in the wireless communication system. In actual scenarios, due to channel estimation errors, channel time variations, etc., the obtained channel CSI inevitably has errors. The literature [Zheng Beixiong, Zhang Rui. Intelligent reflecting surface-enhanced OFDM: channel estimation and reflection optimization [J]. IEEE Wireless Communications Letters, 2020, 9 (4): 518-522. doi: 10.1109 / LWC.2019.2961357.] proposes a transmission protocol for channel estimation of IRS enhanced orthogonal frequency division multiplexing system. The literature [Zhao Mingming, Liu An, Zhang Rui. Outage-constrained robust beamforming for intelligent reflecting surface aided wireless communication [J]. IEEE Transactions on Signal Processing, 2021, 69: 1301-1316. doi: 10.1109 / TSP.2021.3056899.] The channel estimation method in the above literature is used to estimate the CSI error in the IRS-assisted multi-user downlink communication system. Under the constraints of the probability that the user-side signal-to-interference-and-noise ratio is less than the threshold and the discrete value of the IRS phase, the continuous convex approximation (SCA) and other algorithms are used to jointly optimize the base station transmit signal beamforming vector and the IRS phase shift matrix to minimize the base station transmit power.The paper [Zhao Mingming, Wu Qingqing, Zhao Minjian, et al. Exploiting amplitude control in intelligent reflecting surface-aided wireless communication with imperfect CSI [J]. IEEE Transactions on Communications, 2021, 69(6): 4216-4231. doi: 10.1109 / TCOMM.2021.3064959.] aims to jointly optimize the base station transmit signal beamforming vector and the IRS phase shift matrix with the goal of maximizing the multi-user information weighted sum rate when the reflected signal amplitudes of the IRS reflection units are different. The paper adopts an iterative block continuous upper bound minimization algorithm to solve the optimization problem, and analyzes the impact of the reflected signal amplitude change on the multi-user information weighted sum rate through simulation.

[0004] In the study of physical layer security, it is generally assumed that the CSI of the legitimate channel is accurately known, while the CSI of the eavesdropping channel is divided into several situations, such as known, partially known, or unknown. Different security solutions need to be adopted for different situations. For example, the aforementioned literature assumes that the CSI of the eavesdropping channel is perfectly known. The above literature studies the physical layer security communication assisted by IRS in the scenario of imperfect channel CSI. For the downlink communication system with multiple users, multiple eavesdroppers, and multiple IRSs, the literature [Yu Xianghao, Xu Dongfang, Sun Ying, et al. Robust and secure wireless communications via intelligent reflecting surfaces [J]. IEEE Journal on Selected Areas in Communications, 2020, 38 (11): 2637-2652. doi: 10.1109 / JSAC.2020.3007043.] studies the optimization problem of improving system security performance when the CSI of the channel between the IRS obtained by the base station and the eavesdropper is imperfect. The literature assumes that there is an obstacle blocking the base station and the user, and uses a bounded CSI error model to characterize the CSI error. Under the constraint that the interception rate of the eavesdropper is less than a given value, the base station transmit beamforming matrix, artificial noise covariance matrix and IRS phase shift matrix are jointly optimized to maximize the system sum rate. The literature [Yu Xianghao, Xu Dongfang, Sun Ying, et al. Robust and secure wireless communications via intelligent reflecting surfaces [J]. IEEE Journal on Selected Areas in Communications, 2020, 38 (11): 2637-2652. doi: 10.1109 / JSAC.2020.3007043.] For a MISO system where there is an obstacle blocking the base station and the user, and signal reflection is required through the IRS to form a communication link, a statistical error model is used to describe the CSI error of the cascade channel between the base station, IRS and eavesdropper. Under the constraints of the legitimate user information transmission rate and the eavesdropper interception interruption probability, the base station transmit power is minimized.The paper [Dong Limeng, Wang Huiming and Xiao Haitao. Secure Cognitive Radio Communication via Intelligent Reflecting Surface [J]. IEEE Transactions on Communications, 2021, 69(7): 4678-4690. doi: 10.1109 / TCOMM.2021.3073028.] studies the optimization problem of improving system security performance in IRS-assisted cognitive radio communication systems under the conditions of imperfect CSI in the direct channel between base station and eavesdropper and the cascade channel between base station, IRS and eavesdropper. The paper uses a bounded CSI error model to characterize the CSI error and utilizes auxiliary variables and algorithms such as SCA to jointly optimize the base station transmit signal beamforming vector and the IRS phase shift matrix to maximize the confidentiality rate achievable by cognitive users. Summary of the Invention

[0005] The present invention aims to optimize physical layer security in an IRS-assisted multi-user downlink system. In the absence of direct transmission links between the base station and users, IRS reflection is used to form transmission links. Information between multiple users must be kept confidential. In each time slot, users not transmitting information are considered eavesdroppers. Due to the time-varying nature of the channel, the base station's CSI of the eavesdropped channel is outdated and differs from the actual CSI. Under these conditions, the beamforming vectors for the base station's transmitted information signal and artificial noise, as well as the IRS phase shift matrix, are jointly optimized to maximize the worst-case confidentiality rate.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: first, an optimization problem is constructed based on the system model. Then, the non-convex optimization problem is transformed into a two-layer optimization problem, wherein the solution of the first-layer optimization problem includes the solution of the second-layer optimization problem. The first-layer optimization problem is further solved using a one-dimensional search algorithm. The second-layer optimization problem is then decomposed into two non-convex sub-problems that are optimized alternately and solved separately. Finally, the maximum system confidentiality rate is obtained. Specifically, the following steps are included:

[0007] (1) Construct a communication system model, and obtain the information transmission rate between the legitimate user and the eavesdropping user based on the constructed system model, and then obtain the system confidentiality rate;

[0008] (2) Taking the maximization of the system confidentiality rate as the optimization goal, a mathematical model is constructed to jointly optimize the base station transmitted information signal and artificial noise beamforming vector, as well as the phase shift matrix of the smart reflective surface, under the constraints of the base station's total transmit power and the unit mode of the smart reflective surface's reflective unit.

[0009] (3) The mathematical model in step (2) is a non-convex optimization problem, which is converted into a two-layer optimization problem, wherein the solution of the first-layer optimization problem includes the solution of the second-layer optimization problem;

[0010] (4) The first-level optimization problem is a single-variable optimization problem, which is solved using a one-dimensional search algorithm;

[0011] (5) Decompose the second-level optimization problem into two non-convex sub-problems of alternating iterative optimization and solve them separately.

[0012] Furthermore, the specific algorithm for solving the two-layer optimization problem in step (3) is as follows: set the initial number of iterations i=1, and the relaxation variable β (1) =1, β increases by step δ, the optimal solution The set Ω; the fixed β (i) Substitute it into the second-level optimization problem to obtain the optimal solution, which is the fixed β (i) Corresponding Will Merge into the set Ω; increase β according to the step size δ (i) Repeat the above steps until β (i) Until the value of exceeds its value range; obtain an optimal value β from the set Ω opt Make The value of is the largest in the set. This is the maximum confidentiality rate of the system.

[0013] Furthermore, the alternating iterative optimization algorithm for solving the second-level optimization problem in step (5) is specifically as follows: in the first iteration, the initial number of iterations m=0 is set, Φ (0) , error tolerance ζ; fixed Φ = Φ (m-1) , solve the first sub-problem and get W1 (m) With W2 (m) ; Given W1 = W1 (m) and Solve the second subproblem and get Φ (m) ; Compare the system confidentiality rate obtained in this iteration with the system confidentiality rate obtained in the previous iteration to determine whether the iteration has converged. If not, proceed to the next round of iteration, otherwise end the iteration.

[0014] Compared with the existing research on the design of IRS-assisted wireless communication system security solutions under imperfect CSI scenarios, the present invention has the following beneficial technical effects: (1) When the goal of the optimization problem is to maximize the system confidentiality rate, the objective function and constraints are complex and difficult to solve, so the literature often uses a certain security performance indicator of the system as a constraint, and takes maximizing the legitimate user rate and minimizing the base station transmission power as the optimization goals. The system confidentiality rate is the most direct and important performance indicator for evaluating the physical layer security transmission performance. Maximizing the confidentiality rate is the optimization goal, which has higher theoretical and practical value. (2) Reference [Dong Limeng, Wang Huiming and Xiao Haitao. Secure Cognitive Radio Communication via Intelligent Reflecting Surface [J]. IEEE Transactions on Communications, 2021, 69 (7): 4678-4690. doi: 10.1109 / TCOMM.2021.3073028.] When the CSI of the eavesdropping channel is partially known, artificial noise is not used to enhance the confidentiality performance. Under the same CSI conditions, the present invention uses artificial noise, which can further improve the confidentiality rate of the system, but the complexity of the optimization problem is also higher. Simulation experiments show that compared with the benchmark scheme, the optimization algorithm proposed in the present invention can effectively improve the confidentiality rate of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is the communication system model of the present invention;

[0016] Figure 2 A communication system simulation model of the present invention;

[0017] Figure 3 The impact of base station transmission power on system confidentiality rate;

[0018] Figure 4 The impact of the number of base station transmitting antennas on the system security rate;

[0019] Figure 5 The impact of the number of IRS reflection units on the system confidentiality rate. DETAILED DESCRIPTION

[0020] The downlink multi-user system model studied in this invention is as follows: Figure 1As shown. The system consists of a base station (Alice), an IRS (Rose) and K users. Alice uses a time-division method to send information to these K users in turn. The information sent to each user needs to be kept confidential. Without loss of generality, the target user of the information at the current moment is called Bob, and other users are regarded as eavesdroppers (Eves). Alice is equipped with M antennas, Rose contains N reflection units, and the user is equipped with a single antenna. There are obstacles between Alice and the user, and the transmission link can only be formed through the reflection of Rose. Assume that all channels are quasi-static flat fading channels. The channel coefficient matrices or vectors between Alice and Rose, Rose and Bob, and Rose and Eves are respectively denoted as in Rose's phase shift matrix is Among them A n ∈[0,1],θ n ∈[0,2π] represents the reflection amplitude and reflection phase of the nth reflection unit of Rose, n=1,2,…,N.

[0021] Alice transmits information to each user in turn. Before the information transmission begins, Alice will send a pilot sequence to the user. The user performs channel estimation based on the received pilot sequence and sends the result back to Alice. Therefore, it is assumed that Alice can obtain the accurate CSI of the channel between her and the target user of this transmission, that is, Bob. The CSI of the channel between Rose owned by Alice and other users, that is, possible eavesdroppers, will have errors compared with the current actual channel CSI because the channel estimation time is early and the channel is a time-varying fading channel. The earlier the estimation time, the greater the error. Therefore, it is assumed that in the process of transmitting information to Bob, Alice has perfect CSI for the Alice-Rose and Rose-Bob channels, but has errors in the CSI of the Rose-Eves channel. The bounded CSI error model is used to characterize the channel CSI error, that is, the true channel coefficient vector is the sum of the estimated channel coefficient vector and a random error:

[0022]

[0023] Among them, h RE,k represents the channel coefficient vector between IRS and the kth eavesdropper, They represent the outdated channel coefficient vector between Rose and the kth eavesdropper obtained by Alice, and the error between it and the current true channel coefficient vector. k Characterizes the uncertainty of Alice's CSI of the kth eavesdropper. The longer the time since the last communication, the greater the corresponding uncertainty.

[0024] In order to improve the security of information transmission, Alice sends artificial noise to interfere with the eavesdropper's eavesdropping while sending information to Bob. Alice's sending signal is expressed as

[0025] x=w1s+w2a

[0026] in, represent information signal and artificial noise respectively; are the beamforming vectors of information signal and artificial noise respectively, satisfying the power constraint Tr(w1w1 H )+Tr(w2w2 H )≤P, where P is Alice’s maximum transmission power. The received signals at Bob and the kth eavesdropper can be expressed as

[0027]

[0028]

[0029] in, Denote the additive complex Gaussian white noise at Bob and the kth eavesdropper respectively. Substituting Alice’s transmitted signal into the above equation and expanding it, we can get

[0030]

[0031]

[0032] According to the above formula, the information transmission rates at Bob and the kth eavesdropper are

[0033]

[0034]

[0035] represent the noise power at Bob and the kth eavesdropper respectively.

[0036] Assuming that each eavesdropper obtains information independently, the system confidentiality rate is the minimum difference between Bob's information transmission rate and the information transmission rate of all eavesdroppers:

[0037]

[0038] Since the CSI of the eavesdropping channel is not perfectly known, With the real h RE,k There is a random error between Base Station and IRS Setting the beamforming vector and phase shift matrix will reduce the system security rate compared to setting it based on accurate CSI. The degree of reduction is related to random errors. With the goal of maximizing the system security rate under the most severe error conditions that lead to performance degradation, the Alice information signal beamforming vector w1, the artificial noise beamforming vector w2, and the IRS phase shift matrix Φ are jointly optimized. The optimization problem is:

[0039]

[0040] stC1:Tr(w1w1 H +w2w2 H )≤P,

[0041] C2:|Φ n,n |=1,n=1,2,…,N.

[0042] In the question, It represents the maximum information transmission rate between Alice-Rose-Eves under random error conditions. Φ represents the range of the true Rose-Eves channel coefficient; the two constraints are Alice's maximum transmit power constraint and the IRS reflection amplitude constraint of 1. n,n Represents the value of the nth row and nth column in the matrix Φ, Tr(X) represents the trace of the matrix X, and the superscript H represents the conjugate transpose of the matrix.

[0043] The objective function and constraints in the optimization problem are non-convex functions, multiple optimization variables are coupled with each other, and the possible h RE,k There are infinite numbers of these three variables, and it is very difficult to solve the optimization problem directly. The problem needs to be transformed first. First, a slack variable is introduced to transform the maximum value part of the objective function into an equivalent infinite number of inequality constraints. Then, these infinite constraints are transformed into a finite number of inequality constraints, and then the transformed problem is transformed into a two-level optimization problem. The solution to the first-level optimization problem includes the solution to the second-level optimization problem, where the first-level optimization problem is a single-variable optimization problem and is solved using a one-dimensional search algorithm; the second-level optimization problem contains three optimization variables, and the algorithm is used to decompose it into two non-convex sub-problems of alternating iterative optimization. The two non-convex sub-problems are transformed into convex problems using the Charnes-Cooper transformation method and the penalty function method for solution.

[0044] The objective function of the optimization problem can be written as

[0045]

[0046] Substitution variables and in The above formula can be transformed into

[0047]

[0048] In order to simplify the objective function, the slack variable β is introduced and the problem is transformed into an equivalent problem.

[0049]

[0050] stC1:Tr(w1w1 H +w2w2 H )≤P,

[0051] C2:|Φ n,n |=1,n=1,2,...,N,

[0052]

[0053]

[0054]

[0055] Where log2β represents the maximum value of the eavesdropping channel information rate in all cases. They respectively indicate that the information signal power and artificial noise power sent by the base station are both positive values.

[0056] The maximum value part of the objective function in the problem is transformed into the infinite number of inequality constraints C3 in the above formula, which needs to be transformed into a finite number of inequality constraints. Rewrite C3 of the above problem as

[0057]

[0058] Substituting the eavesdropping channel error into the above formula, we can get

[0059]

[0060]

[0061] Expand the above formula and combine like terms to get

[0062]

[0063]

[0064] The formula still contains infinite quadratic inequalities. We will use the method given in the literature to transform these infinite inequalities into a finite number of inequalities.

[0065] Define f(X) = X H AX+X H B+B H X+C and The following equation is equivalent

[0066]

[0067] Perform the following variable substitutions: X=Δh RE,k , I N×N Represents the N×N dimensional identity matrix. Based on the above formula, the infinite number of constraints can be transformed into the following finite number of constraints:

[0068]

[0069] Among them, T k (W1,W2,Φ,β,t k )for t k is an auxiliary variable introduced.

[0070] Substituting the above formula into the optimization problem, it can be transformed into

[0071]

[0072] stC1:Tr(W1+W2)≤P,

[0073] C2:|Φ n,n |=1,n=1,2,...,N,

[0074]

[0075]

[0076] Although the number of constraints has been reduced from infinite to finite, the optimization problem still contains multiple mutually coupled variables, and it is still very difficult to solve the optimization problem directly. In order to solve the optimization problem more efficiently, β is separated and the optimization problem is converted into an equivalent two-layer optimization problem: the first layer is to find β that maximizes the objective function within the value range of β; the second layer optimization problem is to solve W1, W2 and Φ that maximize the objective function when β is given; the solution of the second layer optimization problem is included in the solution of the first layer problem. Let's first determine the value range of β. In order to remove the superscript + from the objective function of the optimization problem, it should be ensured that the legitimate channel rate is not lower than the eavesdropping channel rate, that is, it should satisfy

[0077]

[0078] because Can further obtain

[0079]

[0080] Due to the non-negativity of the transmission rate and the constraint of Tr(W1)≤P, the above formula can be simplified to

[0081]

[0082] ||X|| F Represents the Frobenius norm of the matrix X.

[0083] After obtaining the range of β values, the first-level optimization problem in the two-level optimization problem equivalent to the optimization problem is

[0084]

[0085]

[0086] in, For a given β, The maximum value of , and how to obtain this maximum value is the second-level optimization problem in the two-level optimization problem equivalent to the optimization problem:

[0087]

[0088] stC1:Tr(W1+W2)≤P,

[0089] C2:|Φ n,n |=1,n=1,2,…,N,

[0090]

[0091]

[0092] This is an SDP problem where the optimization variables W1, W2 and Φ are SDP. The solution of this problem will be described below.

[0093] The optimization problem is a single-variable optimization problem about β. The range of β is limited and can be solved using a one-dimensional search algorithm. The two-level solution algorithm for the optimization problem is summarized in Table 1 below. Among them, δ is the step size of the update β, and Ω is the optimal solution obtained by solving the second-level optimization problem after given β. The maximum value in the final set is the solution to the original optimization problem.

[0094] Algorithm 1: Algorithm for solving two-level optimization problems

[0095] (1) Initialization parameters: step size δ, i = 1, β (1) =1.

[0096] (2) Loop:

[0097] (3) Given β (i) , solve the second-level optimization problem and get the solution

[0098] (4)

[0099] (5) Update β (i) =β (i-1) +δ.

[0100] (6) Until

[0101] (7) Output the maximum value in Ω and its corresponding β opt .

[0102] The optimization variables W1, W2, and Φ in the second-level optimization problem are still coupled to each other, making joint solution very difficult. Therefore, an alternating iterative optimization method is used: (1) Fix the IRS phase shift matrix Φ and optimize W1 and W2 using methods such as the Charnes-Cooper transform; (2) Fix W1 and W2 and optimize the phase shift matrix Φ using methods such as the penalty function and the Charnes-Cooper transform. The two optimizations are performed alternately and iteratively until convergence.

[0103] When the IRS phase shift matrix Φ is fixed, the second-level optimization problem degenerates into

[0104]

[0105] stC1:Tr(W1+W2)≤P,

[0106]

[0107]

[0108] The objective function in this optimization problem is still a non-convex function. First, perform the following variable substitution: ξ>0, where ξ is the auxiliary variable introduced. Applying Charnes-Cooper transformation, the problem is transformed into

[0109]

[0110]

[0111] C2:Tr(Q+Z)≤Pξ,

[0112]

[0113]

[0114] Among them, the definition for Z, Q, λ W,k W1, W2 and t k The result after variable substitution.

[0115] The above questions are about Q, Z, λ W,k The convex problem of ξ can be solved using the CVX toolbox. The optimal solution of this problem is Q opt , Z opt 、 ξ opt , then the solution to the above problem is For W1 opt and Perform eigenvalue decomposition, and the eigenvector corresponding to the non-zero eigenvalue is the information signal beamforming vector Vector with artificial noise

[0116] After W1 and W2 are given, the second-level optimization problem degenerates into

[0117]

[0118] stC1:|Φ n,n |=1,n=1,2,…,N,

[0119]

[0120] The objective function and constraints of this problem are not convex functions and require certain form transformations. First, organize the diagonal elements of the phase shift matrix Φ into a vector in, Using the vector v, we can get

[0121]

[0122] Another definition is V = vv H , Perform singular value decomposition on G and get

[0123]

[0124] in a i , b i Respectively represent the column vector and row vector after the singular value decomposition of matrix G. In order to transform the problem into an SDP problem about V, using the definition of v, V and the singular value decomposition of G, we can get

[0125]

[0126] T k (W1,W2,Φ,β,t k ) in the definition use Substitution, the constraint C2 of the above problem has been transformed into a form with respect to V. Next, we further transform the objective function of the above problem into a function with respect to V. First, use and Expand the objective function of the above problem and separate the variable Φ to obtain

[0127] Redefine Substituting into, the above problem can be rewritten as

[0128]

[0129]

[0130] C2:|V n,n |=1,n=1,2,…,N.

[0131] in, for

[0132]

[0133] The objective function of the above problem is still a non-convex function, so we can substitute the variables ξ>0, then apply Charnes-Cooper transformation, the above problem is transformed into

[0134]

[0135]

[0136]

[0137] C3:|Ε n,n |=ξ,n=1,2,…,N,

[0138]

[0139] in, for

[0140]

[0141] The optimization objective function in the above problem is already a convex function, but the constraint C3 is still a non-convex function. Rewrite the constraint C3 as the following equivalent constraint

[0142]

[0143] Among them, rank(Ε)=1 is a non-convex function, and it is necessary to construct a convex constraint equivalent to rank(Ε)=1.

[0144] For any positive semidefinite matrix A, the following inequality holds

[0145] |I+A|≥1+Tr(A)

[0146] The equality holds if and only if rank(A)≤1.

[0147] Applying the above formula, rank(Ε)=1 can be transformed into

[0148]

[0149] Applying the penalty function method, the constraint is added as a penalty to the objective function of the optimization problem. The objective function is rewritten as a penalty function, and the converted optimization problem is

[0150]

[0151]

[0152]

[0153] C3:vec(Ε)=ξ N ,

[0154]

[0155] Where κ is the penalty factor for rank(E)=1. When κ is small enough, the optimal solutions of the two optimization problems are the same. However, in the objective function of the optimization problem, log2det(I+E) is a non-convex function with respect to E. The solution of E obtained in the previous iteration can be converted into

[0156] log2det(I+Ε)≤(log2e)Tr{[(I+Ε) (m) ) -1 ] * (Ε-Ε (m) )}

[0157] +(log2e)log2det(I+Ε (m) )

[0158] Substituting the above formula into the optimization problem, we can get

[0159]

[0160]

[0161]

[0162] C3:vec(Ε)=ξ N ,

[0163]

[0164] Among them, E (m) The solution of E in the optimization problem at the mth iteration in the iterative solution of the second-level optimization problem (here we assume that the current iteration is the m+1th iteration). At this point, the optimization problem is converted into a convex problem, and the CVX toolkit can be used to solve it to obtain the optimal solution. The optimal solution of this problem is recorded as E opt 、 ξ opt , then the solution to the optimization problem is V opt Perform eigenvalue decomposition, the eigenvector corresponding to the non-zero eigenvalue is v opt , and then v opt Diagonalization can get the phase shift matrix Φ opt The solution algorithm of the optimization problem is summarized in Table 2. (0) For any diagonal matrix that satisfies the optimization problem constraint C2, ζ represents the error tolerance. The iteration ends when the absolute value of the relative difference in confidentiality rate obtained between two iterations is not greater than the error tolerance.

[0165] Algorithm 2: Algorithm for solving the second-level optimization problem

[0166] (1) Initialization parameters: number of iterations m = 0, Φ (0) ,ζ.

[0167] (2) Loop:

[0168] (3)m=m+1.

[0169] (4) Fixed Φ = Φ (m-1) , solve the first sub-problem and get W1 (m) With W2 (m) .

[0170] (5) Given W1 = W1 (m) and Solve the second subproblem and get Φ (m) .

[0171] (6) To W1 (m) 、 Perform eigenvalue decomposition to obtain w1 (m) 、w2 (m) .

[0172] (7) Until

[0173] (8) Output Φ opt =Φ (m) .

[0174] The performance of the optimization scheme given below is simulated. Unless otherwise specified, the number of users in the simulation is K = 4, and the positions of the base station, IRS and the four users are as follows: Figure 2 The unit is meter (m). The channel between each node is a Rice fading channel, and the channel fading includes path loss (large-scale fading) and small-scale fading. The channel matrix model from Alice to IRS is

[0175]

[0176] Where, is the path loss, where L0 = -30dB represents the path loss when the reference distance is 1 meter, α AR is the path loss exponent, d AR is the distance between Alice and Rose; is the small-scale fading part, where ρ AR is the Rice fading factor, is the channel coefficient matrix of the non-line-of-sight transmission part, and each element in the matrix is ​​a complex Gaussian random variable with zero mean and unit variance. The channel coefficient matrix representing the line-of-sight transmission between Alice and Rose is:

[0177]

[0178] in, and represents the azimuth and elevation of the transmitting antenna, and represents the azimuth and elevation of the IRS, and for

[0179]

[0180]

[0181] Where (x Alice ,y Alice ,z Alice ) and (x Rose ,y Rose ,z Rose ) represent the coordinates of Alice and Rose respectively, where for

[0182]

[0183] and Steering vector representing a uniform linear array

[0184]

[0185]

[0186] Wherein, d represents the distance between two adjacent antennas, λ is the wavelength of the center carrier, and d / λ=0.5 is set in the simulation.

[0187] The channel model between IRS and user is similar to that between base station and IRS. The channel coefficient matrix is:

[0188]

[0189]

[0190] In the simulation, the parameters of the channel model are set as: α AR =3.5,α RB =α RE,k =2.5, the Rice fading factor is ρ AR =1,ρ RB =ρ RE,k =5; the channel noise power is The channel error tolerance is ε1 = 0.1, ε2 = 0.15, ε3 = 0.2; the error tolerance in Algorithm 2 is γ = 10 -3 , the penalty factor is κ = 5 × 10 -6 .

[0191] In the simulation, the results of three benchmark schemes are given simultaneously for performance comparison. Benchmark scheme 1 - no artificial noise scheme: that is, the artificial noise vector w2 is a 0 vector, and the beamforming vector and the phase shift matrix of IRS are optimized using a method similar to the present invention. Benchmark scheme 2 - IRS random phase shift scheme: the phase shift matrix of IRS is randomly selected, and the signal beamforming vector w1 and the artificial noise beamforming vector w2 are obtained using a method similar to the present invention for solving the optimization problem. Benchmark scheme 3 - Maximum ratio transmission (MRT): The base station information signal beamforming vector is the conjugate of the Alice-Rose-Bob cascade channel, and artificial noise is sent in the orthogonal direction of the cascade channel. The signal beamforming vector and the artificial noise covariance matrix are respectively

[0192]

[0193]

[0194] in, and is the power Alice allocates to the information signal vector and artificial noise, represents the null space of the legal channel. The elements in the IRS phase shift matrix Φ are randomly selected between [0,2π]. With the confidentiality rate as the goal, optimize under the total power constraint and The confidentiality rates given in the simulation figures in this section are the average values ​​of the confidentiality rates under 1000 sets of channel samples.

[0195] Figure 3 The system confidentiality rate of the present invention and three comparative schemes is given as the transmission power of Alice changes. In the simulation, the number of Alice's antennas M = 4, and the number of Rose's reflection units N = 8. Figure 3 It can be seen that the design scheme of the present invention is superior to other benchmark schemes. When Alice's transmission power is low, the performance of the scheme without artificial noise is relatively close to that of the scheme of the present invention. This is because when the transmission power is low, Alice allocates most of the power to the signal to ensure communication with the user, and only allocates a small amount of power to the artificial noise. As the transmission power increases, the system confidentiality rate growth rate of the scheme without artificial noise is significantly lower than that of the other schemes. This is because when Alice has a sufficiently large total transmission power, more power can be allocated to the artificial noise, interfering with eavesdroppers in the system and reducing the eavesdropper's receiving performance, thereby increasing the system confidentiality rate. This shows that adding artificial noise has a significant effect on improving the system confidentiality rate. The system confidentiality rate of the IRS random phase shift scheme has a similar change trend to that of the scheme of the present invention, but is always lower than the system confidentiality rate of the scheme of the present invention. This is because the IRS random phase shift scheme uses random phase values ​​and does not optimize the IRS phase shift matrix. This also shows that optimizing the IRS phase shift matrix can improve the system confidentiality rate. It can be noted that the system confidentiality rate of the maximum ratio transmission scheme is significantly lower than that of the scheme of the present invention and the IRS random phase shift scheme. This is because in the maximum ratio transmission scheme, the base station's beamforming is not optimized with the goal of maximizing the system confidentiality rate, and the IRS phase shift matrix also takes random values.

[0196] Figure 4 The system confidentiality rate is given as the number of transmitting antennas at Alice changes. In the simulation, Alice's transmit power P = 30dBm, and Rose's number of reflective units N = 8. Figure 4It can be seen that the system security rate of all schemes increases with the increase in Alice's transmit antennas. This is because as the number of antennas increases, the transmitter has greater spatial freedom, allowing for more precise control of the signal and noise beams. It can also be noted that the maximum ratio transmission scheme has the smallest increase in security rate with the increase in transmit antennas. This is because the MRT beam selected by the maximum ratio transmission scheme is not aimed at maximizing the system security rate and cannot effectively utilize the channel gain brought about by the increase in the number of transmit antennas on Alice's side.

[0197] Figure 5 The system's confidentiality rate is shown as it changes with the number of reflectors at the Rose. In the simulation, Alice's transmit power P = 30dBm and the number of antennas M = 4. It can be seen that the system confidentiality rate of all four schemes increases with the number of reflectors at the Rose. Among them, the confidentiality rate of the scheme without artificial noise increases very little after the number of reflectors increases to 8. This is because, compared to the other schemes, it does not introduce artificial noise, thereby preventing eavesdroppers from interfering with the system and reducing their reception performance. Furthermore, as the number of reflectors exceeds the number of transmitting antennas, the IRS cannot effectively utilize the spatial degrees of freedom and channel gain brought about by the increase in reflectors, resulting in a minimal improvement in the system confidentiality rate compared to the other three schemes.

Claims

1. A physical layer security optimization method assisted by a smart reflective surface under inaccurate channel state information conditions, characterized in that: The following steps are involved: (1) Construct a communication system model, and obtain the information transmission rate between the legitimate user and the eavesdropping user based on the constructed system model, and then obtain the system confidentiality rate; (2) Taking the maximization of the system confidentiality rate as the optimization goal, a mathematical model is constructed to jointly optimize the base station transmitted information signal and artificial noise beamforming vector, as well as the phase shift matrix of the smart reflective surface, under the constraints of the base station's total transmit power and the unit mode of the smart reflective surface's reflective unit. (3) The mathematical model in step (2) is a non-convex optimization problem, which is converted into a two-layer optimization problem, wherein the solution of the first-layer optimization problem includes the solution of the second-layer optimization problem; The transformation of the non-convex optimization problem into a two-level optimization problem specifically includes: introducing slack variables, transforming the maximum value part of the objective function into an infinite number of equivalent inequality constraints, then transforming the infinite number of constraints into a finite number of inequality constraints, and then transforming the transformed problem into a two-level optimization problem. The first-level optimization problem in the two-level optimization problem is: Among them, β is the introduced slack variable, For a given β, The maximum value of , and how to obtain this maximum value is the second-level optimization problem in the two-level optimization problem: stC1:Tr(W1+W2)≤P, C2:|Φ n,n |=1,n=1,2,…,N, C3: t k ≥0, C4: Where, and t k is the introduced variable, T k (W1,W2,Φ,β,t k )for I N×N represents the N×N dimensional identity matrix; represents the noise power of the legal user, P is the maximum transmit power of the base station, and the channel coefficient matrix or vector between the base station and IRS, and between the IRS and the legal user is recorded as H AR 、 in The phase shift matrix of IRS is Φ, Φ n,n represents the value of the nth row and nth column in the matrix Φ, N represents the number of reflection units of the IRS, w1 and w2 are the beamforming vectors of the information signal and artificial noise respectively, represents the channel coefficient vector of the channel between the IRS obtained by the base station and the kth eavesdropper, ε k Characterizes the uncertainty of the base station's CSI of the kth eavesdropper; (4) The first-level optimization problem is a single-variable optimization problem, which is solved using a one-dimensional search algorithm; (5) Decompose the second-level optimization problem into two non-convex sub-problems of alternating iterative optimization and solve them separately.

2. The method for physical layer security optimization using intelligent reflective surfaces under inaccurate channel state information according to claim 1, characterized in that: The system model described in step (1) consists of a base station, an IRS, and K users. The base station sends information to the K users in turn using a time-division method. The information sent to each user needs to be kept confidential. The base station is equipped with M antennas, the IRS contains N reflection units, and the user is equipped with a single antenna. There are obstacles between the base station and the user, and the transmission link can only be formed through the reflection of the IRS. All channels are quasi-static flat fading channels. The target user to whom the base station sends information at the current moment is defined as a legitimate user, and other users are eavesdroppers.

3. The method for physical layer security optimization using intelligent reflective surfaces under inaccurate channel state information according to claim 1, characterized in that: When the base station transmits information to legitimate users, it has perfect CSI in the base station-IRS and IRS-legitimate user channels. However, the CSI in the IRS-eavesdropping user channel has errors. A bounded CSI error model is used to characterize the channel CSI error. That is, the true channel coefficient vector is the sum of the estimated channel coefficient vector and a random error: Among them, h RE,k 、 Δh RE,k They represent the channel coefficient vector between IRS and the kth eavesdropper, the outdated channel coefficient vector between IRS and the kth eavesdropper obtained by the base station, and the error between them and the current true channel coefficient vector. ε k Characterizes the uncertainty of the base station's CSI of the kth eavesdropper. The longer the time since the last communication, the greater the corresponding uncertainty.

4. The method for physical layer security optimization using intelligent reflective surfaces under inaccurate channel state information according to claim 1 or 3, characterized in that: The information transmission rate between the legitimate user and the eavesdropping user in step (1) is calculated by the following method: the received signals at the legitimate user and the kth eavesdropper are expressed as Where, the channel coefficient matrices or vectors between the base station and IRS, IRS and legitimate users, and IRS and eavesdroppers are denoted as H AR 、 in The phase shift matrix of IRS is Among them A n ∈[0,1],θ n ∈[0,2π] represents the reflection amplitude and reflection phase of the nth reflection unit of IRS, n=1,2,…,N; n B 、n E,k They represent the additive complex Gaussian white noise at the legitimate user and the kth eavesdropper respectively; x is the signal sent by the base station, which is expressed as x=w1s+w2a Among them, s, a represent information signal and artificial noise respectively; w1, w2 are the beamforming vectors of information signal and artificial noise respectively; the information transmission rates at the legitimate user and the kth eavesdropper are The system confidentiality rate is the minimum difference between the information transmission rate of the legitimate user and the information transmission rate of all eavesdroppers:

5. The method for physical layer security optimization using intelligent reflective surfaces under inaccurate channel state information according to claim 4, characterized in that: The optimization mathematical model in step (2) is constrained by the total transmission power of the base station and the unit mode of the intelligent reflective surface reflection unit, with the maximization of the system confidentiality rate as the optimization goal. The optimization problem is constructed as follows: s.t.C1:Tr(w1w1 H +w2w2 H )≤P, C2:|Φ n,n |=1,n=1,2,…,N. in, represents the maximum information transmission rate between the base station, IRS and eavesdropper under random error conditions, where represents the range of the real IRS-eavesdropper channel coefficient; the two constraints are the maximum transmit power constraint of the base station and the constraint that the IRS reflection amplitude is 1; Φ n,n represents the value of the nth row and nth column in the matrix Φ, Tr(X) represents the trace of the matrix X, and P represents the maximum transmit power of the base station.

6. The design method of a physical layer security solution assisted by smart reflective surfaces under inaccurate channel state information conditions according to claim 1 is characterized by: The specific method for solving the two-layer optimization problem in step (3) is as follows: set the initial iteration number i=1, and the relaxation variable β (1) =1, β increases by step δ, the optimal solution The set Ω; the fixed β (i) Substitute it into the second-level optimization problem to obtain the optimal solution, which is the fixed β (i) Corresponding Will Merge into the set Ω; increase β according to the step size δ (i) Repeat the above steps until β (i) Until the value of exceeds its value range; obtain an optimal value β from the set Ω opt Make The value of is the largest in the set. This is the maximum confidentiality rate of the system.

7. The design method of a physical layer security solution assisted by smart reflective surfaces under inaccurate channel state information conditions according to claim 5, characterized in that: Step (5) decomposes the second-level optimization problem into two non-convex sub-problems of alternating iterative optimization. When the IRS phase shift matrix Φ is fixed, the first sub-problem is stC1:Tr(W1+W2)≤P, C2: t k ≥0, C3: After W1 and W2 are given, the second sub-problem is 8. The method for designing a physical layer security solution assisted by smart reflective surfaces under inaccurate channel state information conditions according to claim 7, characterized in that: The specific alternate iterative optimization algorithm for solving the second-level optimization problem in step (5) is as follows: in the first iteration, the initial number of iterations m=0 is set, Φ (0) , error tolerance ζ; fixed Φ = Φ (m-1) , solve the first sub-problem and get W1 (m) With W2 (m) ; Given W1=W1 (m) and Solve the second subproblem and get Φ (m) ; Compare the system confidentiality rate obtained in this iteration with the system confidentiality rate obtained in the previous iteration to determine whether the iteration has converged. If not, proceed to the next round of iteration, otherwise end the iteration.

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