A physical layer security enhancement method based on intelligent reflective surface and full-duplex communication

Abstract

The present invention discloses a physical layer security enhancement method based on intelligent reflective surface and full-duplex communication, which comprises the following steps: step 1, determining the number of antennas of source nodes and eavesdroppers and the number of IRS passive devices; step 2, determining the received signals of the source node and the eavesdropper; step 3, determining the range of the channel error set by the imperfect CSI of the eavesdropper; step 4, introducing a proxy function to convert non-convex items into convex items; step 5, decoupling the original problem into three sub-problems; step 6, fixing irrelevant variables, iterative alternating optimization, and updating variables; step 7, the original problem finally converges to a finite value. The present invention relaxes the problem by adding slack variables so that it can be violated by non-convex unit modulus constraints, and then punishes the sum of the violations. When converged, the solution returned by P‑CCP is the first-order approximate optimal solution of the original sub-problem.

Description

Technical Field

[0001] The invention relates to the field of communication security, and in particular to a physical layer security enhancement method based on an intelligent reflection surface and full-duplex communication. Background Art

[0002] With the rise of mobile Internet, wireless networks have become widely popular. Due to the omnidirectional broadcast characteristics of wireless channels, the communication between senders and receivers is very easy to be eavesdropped by potential third parties. How to ensure the security of wireless communications has increasingly attracted the attention of the industry and academia.

[0003] Due to the open nature of the wireless environment, data transmission is extremely vulnerable to eavesdropping. To improve the security of the physical layer, beamforming technology is used to navigate the information beam to the ID receiver, thereby mitigating the information leakage to the eavesdropper. Artificial noise (AN) is also commonly used to improve physical layer security. Artificial noise is an artificially generated interference signal designed to damage the eavesdropping channel. Full-duplex systems assisted by smart reflectors have rarely been considered, except for a few works. It turns out that the corresponding transmission optimization problem is quite difficult even for point-to-point systems, more specifically, the sum rate maximization problem for full-duplex multiple-input multiple-output (MIMO) systems assisted by smart reflectors.

[0004] The existing technology currently only considers the case of imperfect channel state information of the eavesdropping channel. The channel between two source nodes is a perfect channel state information channel, but it is usually difficult to obtain perfect channel state information, especially for channels reflected by smart reflective surfaces. The number of user settings is small. Therefore, how to design a new physical layer security enhancement method based on smart reflective surfaces and full-duplex communication is a technical problem that technicians in this field need to solve urgently. Summary of the invention

[0005] In view of the above problems, the present invention proposes a physical layer security enhancement method based on smart reflective surface and full-duplex communication, which solves the above problems by adopting penalty convex-concave process (P-CCP) and adding relaxation variables to relax.

[0006] The present invention provides the following technical solutions:

[0007] A physical layer security enhancement method based on intelligent reflective surface and full-duplex communication, characterized by comprising the following steps:

[0008] Step 1: Determine the number of source nodes, eavesdropper antennas, and IRS passive devices;

[0009] Step 2: Determine the received signals of the source node and the eavesdropper;

[0010] Step 3: Determine the range of the channel error set by the eavesdropper's imperfect CSI;

[0011] Step 4: Introduce a proxy function to convert non-convex items into convex items;

[0012] Step 5: Decouple the original problem into three sub-problems;

[0013] Step 6: Fix irrelevant variables, iterate and optimize alternately, and update variables;

[0014] Step 7: The original problem eventually converges to a finite value.

[0015] Preferably, in step 2, The received signals of the source node and the eavesdropper are determined by the following formula:

[0016]

[0017]

[0018]

[0019] in represents the self-interference channel of S1, H 11 Conjugate transpose, represents the channel from S1 to IRS, H 1r Conjugate transpose, represents the channel from S1 to Eve, H 1e Conjugate transpose, represents the self-interference channel of S2, H 22 Conjugate transpose, represents the channel from S2 to IRS, H 2r Conjugate transpose, represents the channel from S2 to Eve, H 2e Conjugate transpose, represents the channel from IRS to S1, H r1 Conjugate transpose, represents the channel from IRS to S2, H r2 Conjugate transpose, represents the channel from IRS to Eve, H reConjugate transpose, IRS reflection phase shift matrix Θ = diag (θ1, ..., θ n ,...,θ M ),in where ω M ∈(0,2π] represents the phase shift range, β M ∈[0,1] represents the amplitude reflection coefficient, and the sending signals of the two nodes are x i =w i s i , where i = 1, 2, where s i is a data symbol with unit power, w i is the precoding matrix, Represents a dimension of N rows and N columns, denote the additive Gaussian noise at S1, S2 and Eve respectively, and are circularly symmetric complex Gaussian vectors representing the covariance matrices of S1 and S3, respectively, represents the circularly symmetric complex Gaussian vector of the covariance matrix of the eavesdropper e, and I represents the identity matrix.

[0020] Preferably, in step 3, the range of the channel error set by the imperfect CSI of the eavesdropper is determined by the following formula:

[0021]

[0022]

[0023] in, and Respectively represent G3, G4, H 1e and H 2e Estimated values ​​of; ΔG3, ΔG4, ΔH 1e and ΔH 2e Respectively represent G3, G4, H 1e and H 2e Channel error; v3, δ4, δ 1e and δ 2e Respectively represent G3, G4, H 1e and H 2e The uncertainty radius.

[0024] Preferably, in step 4, the proxy function expression is as follows:

[0025]

[0026] in, And A>0, f(ψ)=-tr(ψA)+ln|Ψ|+N, N is a constant, tr() represents the trace of the matrix, and Ψ is a positive definite matrix.

[0027] Preferably, in step 5, the three sub-problems are respectively the sub-problem of maximizing the worst-case optimized transmission power, the sub-problem of maximizing the worst-case optimized reflection IRS phase shift matrix, and the closed-form solution of the iterated ψ (n+1) .

[0028] Preferably, in step 6, the irrelevant variables include ψ2, ψ4, ψ5, Θ, X1 and X2, wherein Θ is the reflection phase shift matrix of IRS, and X1 and X2 are the transmission powers of S1 and S2 respectively.

[0029] Preferably, in step 7, after the original problem is replaced by a convex problem, an upper bound exists and the overall algorithm eventually converges to a finite value.

[0030] Since the objective function of the original problem has an upper bound, the solved sub-problems can gradually approach the convergence value of the original problem through iteration, and the overall algorithm eventually converges to a finite value.

[0031] The beneficial effects of the present invention are:

[0032] The physical layer security enhancement method based on smart reflective surface and full-duplex communication proposed in the present invention adopts the penalty convex-concave process (P-CCP) method to solve the optimization design problem of the phase shift matrix of the smart reflective surface, relaxes the problem by adding slack variables so that it can be violated by non-convex unit modulus constraints, and then punishes the sum of the violations. When converged, the solution returned by P-CCP is the first-order approximate optimal solution of the original subproblem. Simulation results show that compared with the non-robust scheme, the proposed robust scheme has better performance; compared with the scheme of single antenna node and all perfect channel state information, it considers the more practical scenarios of multi-antenna source nodes and eavesdropper's imperfect channel state information, which is more in line with the actual situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] The present invention is further described using the accompanying drawings, but the embodiments in the accompanying drawings do not constitute any limitation to the present invention. A person skilled in the art can obtain other drawings based on the following drawings without creative work.

[0034] Figure 1 It is a flow chart of a physical layer security enhancement method based on an intelligent reflective surface and full-duplex communication according to an embodiment of the present invention;

[0035] Figure 2 It is a schematic diagram of a communication model of a preferred embodiment of the present invention. DETAILED DESCRIPTION

[0036] A physical layer security enhancement method based on an intelligent reflective surface and full-duplex communication is further described in detail below in conjunction with specific embodiments. These embodiments are only used for comparison and explanation purposes, and the present invention is not limited to these embodiments.

[0037] Example

[0038] See attached Figure 1-2 In the design of the embodiment of the present invention, the robust security performance of a full-duplex MIMO system assisted by a smart reflector is considered, in which two legitimate nodes exchange information in full-duplex mode in the presence of a passive eavesdropper. It is assumed that the channel state information of the eavesdropping channel is not ideal, and the channel uncertainty is modeled using a worst-case model. Both users and the eavesdropper are equipped with multiple antennas. In the proposed system, through the smart reflector, the two legitimate nodes can communicate simultaneously and work at the same frequency, thereby greatly improving the spectrum efficiency. On this basis, the problem of maximizing the system's achievable secrecy rate (ASR) by jointly designing robust transmit precoding and smart reflector phase shift is proposed, and the impact of smart reflectors on full-duplex robust secure communication in MIMO systems is revealed. Due to the non-convexity of the objective function, the coupling of optimization variables and the worst-case constraints, the established optimization problem is highly non-convex. In order to solve this problem, a surrogate function is first introduced to deal with the non-convexity in the objective function, and then the optimization problem is decoupled into sub-problems, in which S-Procedure is used to transform the worst-case constraints. By alternately optimizing these three groups of sub-problems, a local optimal solution can be obtained. The simulation results demonstrate the effectiveness of the proposed robust full-duplex scheme. In addition, another innovation of our work lies in the optimal design of the smart reflector phase shift matrix. A penalized convex-concave process (P-CCP) approach is proposed for this subproblem. The core idea of ​​P-CCP is to relax the problem by adding slack variables so that it can be violated by non-convex unit modulus constraints, and then penalize the sum of the violations. When converged, the solution returned by P-CCP is a first-order approximate optimal solution to the original subproblem. Simulation results show that the proposed robust scheme has better performance compared to the non-robust scheme.

[0039] Specific as Figure 1 As shown, the physical layer security enhancement method based on the smart reflective surface and full-duplex communication provided in this embodiment includes the following steps:

[0040] Step 1: Determine the number of source nodes, eavesdropper antennas, and IRS passive devices;

[0041] Step 2: Determine the received signals of the source node and the eavesdropper;

[0042] Step 3: Determine the range of the channel error set by the eavesdropper's imperfect CSI;

[0043] Step 4: Introduce a proxy function to convert non-convex items into convex items;

[0044] Step 5: Decouple the original problem into three sub-problems;

[0045] Step 6: Fix irrelevant variables, iterate and optimize alternately, and update variables;

[0046] Step 7: The original problem eventually converges to a finite value.

[0047] Preferably, in step 2, The received signals of the source node and the eavesdropper are determined by the following formula:

[0048]

[0049]

[0050]

[0051] in represents the self-interference channel of S1, H 11 Conjugate transpose, represents the channel from S1 to IRS, H 1r Conjugate transpose, represents the channel from S1 to Eve, H 1e Conjugate transpose, represents the self-interference channel of S2, H 22 Conjugate transpose, represents the channel from S2 to IRS, H 2r Conjugate transpose, represents the channel from S2 to Eve, H 2e Conjugate transpose, represents the channel from IRS to S1, H r1 Conjugate transpose, represents the channel from IRS to S2, H r2 Conjugate transpose, represents the channel from IRS to Eve, H re Conjugate transpose, IRS reflection phase shift matrix Θ = diag (θ1, ..., θ n ,...,θM ),in where ω M ∈(0,2π] represents the phase shift range, β M ∈[0,1] represents the amplitude reflection coefficient, and the sending signals of the two nodes are x i =w i s i , where i = 1, 2, where s i is a data symbol with unit power, w i is the precoding matrix, Represents a dimension of N rows and N columns, denote the additive Gaussian noise at S1, S2 and Eve respectively, and are circularly symmetric complex Gaussian vectors representing the covariance matrices of S1 and S3, respectively, represents the circularly symmetric complex Gaussian vector of the covariance matrix of the eavesdropper e, and I represents the identity matrix.

[0052] Preferably, in step 3, the range of the channel error set by the imperfect CSI of the eavesdropper is determined by the following formula:

[0053]

[0054]

[0055] in, and Respectively represent G3, G4, H 1e and H 2e Estimated values ​​of; ΔG3, ΔG4, ΔH 1e and ΔH 2e Respectively represent G3, G4, H 1e and H 2e Channel error; δ3, δ4, δ 1e and δ 2e Respectively represent G3, G4, H 1e and H 2e The uncertainty radius.

[0056] Preferably, in step 4, the proxy function expression is as follows:

[0057]

[0058] in, And A>0, f(ψ)=-tr(ψA)+ln|Ψ|+N, N is a constant, tr() represents the trace of the matrix, and Ψ is a positive definite matrix.

[0059] Preferably, in step 5, the three sub-problems are respectively the sub-problem of maximizing the worst-case optimized transmission power, the sub-problem of maximizing the worst-case optimized reflection IRS phase shift matrix, and the closed-form solution of the iterated ψ (n+1) .

[0060] Preferably, in step 6, in S6, the irrelevant variables include ψ2, ψ4, ψ5, Θ, X1 and X2, wherein Θ is the reflection phase shift matrix of IRS, and X1 and X2 are the transmission powers of S1 and S2 respectively.

[0061] Preferably, in step 7, after the original problem is replaced by a convex problem, an upper bound exists and the overall algorithm eventually converges to a finite value.

[0062] Since the objective function of the original problem has an upper bound, the solved sub-problems can gradually approach the convergence value of the original problem through iteration, and the overall algorithm eventually converges to a finite value.

[0063] In one embodiment, if Figure 2 As shown, the number of source nodes S is 2, the number of antennas of the eavesdropper Eve is 1, and the number of IRS passive devices is 1; represents the self-interference channel of S1, H 11 Conjugate transpose, represents the channel from S1 to IRS, H 1r Conjugate transpose, represents the channel from S1 to Eve, H 1e Conjugate transpose, represents the self-interference channel of S2, H 22 Conjugate transpose, represents the channel from S2 to IRS, H 2r Conjugate transpose, represents the channel from S2 to Eve, H 2e Conjugate transpose, represents the channel from IRS to S1, H r1 Conjugate transpose, represents the channel from IRS to S2, H r2 Conjugate transpose, represents the channel from IRS to Eve, H re Conjugate transpose, IRS reflection phase shift matrix Θ = diag (θ1, ..., θn ,...,θ M ),in where ω M ∈(0,2π] represents the phase shift range, β M ∈[0,1] represents the amplitude reflection coefficient. In this embodiment, β M =1, the sending signals of the two nodes are x i =w i s i , where i = 1, 2, and the received signals of S1, S2 and Eve are y1, y2 and y e Given, where s i is a data symbol with unit power, w i is the precoding matrix, represents a dimension of N rows and N columns, that is,

[0064]

[0065]

[0066]

[0067] denote the additive Gaussian noise at S1, S2 and Eve respectively, represents the circularly symmetric complex Gaussian vector of the covariance matrix, and I represents the identity matrix. Path loss ratio is much larger and can be omitted, then the receiving signals of S1 and S2 can be updated as

[0068]

[0069]

[0070] make get:

[0071]

[0072]

[0073]

[0074] Furthermore, it is assumed that the eavesdropper's CSI is imperfect and the channel uncertainty is bounded by an elliptical region.

[0075] ΔG i ,ΔH ie and is bounded by an elliptical area, i.e.,

[0076]

[0077]

[0078] in, and Respectively represent G3, G4, H 1e and H 2e Estimated values ​​of; ΔG3, ΔG4, ΔH 1e and ΔH 2e Respectively represent G3, G4, H 1e and H 2e Channel error; δ3, δ4, δ 1e and δ 2e Respectively represent G3, G4, H 1e and H 2e The uncertainty radius.

[0079] The original problem is the robust security beamforming problem of maximizing the worst-case confidentiality rate under different transmit power constraints in a MIMO full-duplex secure communication system. It can be expressed as follows:

[0080]

[0081] sttr(X i )≤P,i=1,2

[0082] (11b)

[0083]

[0084]

[0085] Where P is the transmit power limit, R is the achievable confidentiality rate, M is the number of IRS components, and X is the transmit power.

[0086] Then the surrogate function is introduced to convert the non-convex term into a convex term. The expression of the surrogate function is as follows:

[0087]

[0088] in, And A>0, f(ψ)=-tr(ψA)+ln|Ψ|+N, N is a constant, tr() represents the trace of the matrix, and Ψ is a positive definite matrix.

[0089] Using the alternating optimization method, (11a) is decoupled into three subproblems, which are the subproblem of maximizing the worst-case optimized transmission power, the subproblem of maximizing the worst-case optimized reflected IRS phase shift matrix, and the closed-form solution of the iterative ψ (n+1) question.

[0090] The three sub-questions are:

[0091] (1) Maximizing the worst-case optimization transmission power subproblem:

[0092]

[0093] sttr(X1)≤P,tr(X2)≤P (13b)

[0094]

[0095] (2) Maximizing the worst-case optimized reflection IRS phase shift matrix subproblem

[0096]

[0097]

[0098] (3) Closed-form solution for the iterative ψ (n+1) question:

[0099]

[0100]

[0101]

[0102] Then, {ψ2, ψ4, ψ5}, {X1, X2} and Θ are optimized alternately. First, given the optimal n-th iteration Θ (n) , solve (fix irrelevant variables). After that, solve When getting Then, solve Θ (n+1) At this point, the convex optimization transformation of the original problem has been completed, laying the foundation for the subsequent processing of the active precoding matrix and the reflected IRS phase shift.

[0103] First, fix Θ. Due to the semi-infinite nature of the channel error, the constraint part of the optimization problem is non-convex. To solve the non-convexity in the constraints, we use S-Procedure to convert the constraints into linear matrix inequalities (LMI). The converted problem is a convex optimization problem, which can be obtained using CVX.

[0104] Since the non-convex strict equation (11d) is difficult to solve, a P-CCP method is proposed to optimize θ in (11). The key idea is to relax the problem by adding slack variables. In PCCP, the non-convex (11d) is relaxed to convex, so the optimized θ minfinitely close to 1. By introducing an auxiliary real vector t=[t1,t2,...,t M ] T , and q=[q1,q2,...,q M ] T , where t m and q m Greater than 0. The following constraints are established:

[0105]

[0106] Make |θ m |The feasible set changes to a continuous region. Although the unit modulus constraint is violated, the total number of violations can be penalized in each iteration l so that t m and q m is guaranteed to converge to zero, so |θ m |The returned value is infinitely close to 1. It is further divided into convex constraints |θ m | 2 ≤1+q m and the non-convex constraint |θ m | 2 ≥1-t m , in order to approximate |θ m | 2 ,

[0107] In another embodiment, The Hermitian matrix, for any point x H The upper bound of Ax is

[0108]

[0109] Using this lemma, for any complex number x and have

[0110]

[0111] According to formula (17), |θ m | 2 ≥1-t m It can also be approximated as in is a feasible point. Based on the key concept of P-CCP, a penalty parameter β is introduced. Given β, this problem is a convex problem and can be solved directly through CVX.

[0112] Since the objective function of the original problem has an upper bound, the solved sub-problems can gradually approach the convergence value of the original problem through iteration, and the overall algorithm eventually converges to a finite value.

[0113] In the above-mentioned embodiment of the present invention, a proxy function is first introduced to deal with the non-convexity in the objective function, and then the optimization problem is decoupled into sub-problems, and S-Procedure is used in the sub-problems to transform the constraints in the worst case. By alternately optimizing these three groups of sub-problems, a local optimal solution can be obtained. The simulation results prove the effectiveness of the proposed robust full-duplex scheme. A penalty convex-concave process (P-CCP) method is proposed for the optimal design of the phase shift matrix of the smart reflection surface. The problem is relaxed by adding slack variables so that it can be violated by the non-convex unit modulus constraint, and then the sum of the violations is penalized. When converged, the solution returned by P-CCP is a first-order approximate optimal solution to the original sub-problem.

[0114] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention, rather than to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the essence and scope of the technical solution of the present invention.

Claims

1. A physical layer security enhancement method based on intelligent reflective surface and full-duplex communication, characterized in that: The following steps are involved: Step 1: Determine the number of source nodes, eavesdropper antennas, and IRS passive devices; Step 2: Determine the received signals of the source node and the eavesdropper; In step 2, let The received signals of the source node and the eavesdropper are determined by the following formula: Among them, y1 represents the signal received by user 1, y2 represents the signal received by user 2, and y e Refers to the signal received by the eavesdropper Eve, S1 represents user 1, S2 represents user 2, and Eve represents Eavesdropper, the eavesdropper in the network. represents the self-interference channel of S1, Indicates H 11 The conjugate transpose of represents the channel from S1 to IRS, Indicates H 1r The conjugate transpose of represents the channel from S1 to Eve, Indicates H 1e The conjugate transpose of represents the self-interference channel of S2, Indicates H 22 The conjugate transpose of represents the channel from S2 to IRS, Indicates H 2r The conjugate transpose of represents the channel from S2 to Eve, Indicates H 2e The conjugate transpose of represents the channel from IRS to S1, Indicates H r1 The conjugate transpose of represents the channel from IRS to S2, Indicates H r2 The conjugate transpose of represents the channel from IRS to Eve, Indicates H re The conjugate transpose of , IRS reflection phase shift matrix Θ = diag (θ1, ..., θ M ),in Where n = {1, 2, ..., M}, ω M ∈(0, 2π] represents the phase shift range, β M ∈[0, 1] represents the amplitude reflection coefficient, and the transmission signals of the two nodes are x i =w i s i , where i = 1, 2, where s i is a data symbol with unit power, w i is the precoding matrix, Represents a dimension of N rows and N columns, denote the additive Gaussian noise at S1, S2 and Eve respectively, and are circularly symmetric complex Gaussian vectors representing the covariance matrices of S1 and S3, respectively, represents the circularly symmetric complex Gaussian vector of the covariance matrix of the eavesdropper e, and I represents the identity matrix; Step 3: Determine the range of the channel error set by the eavesdropper's imperfect CSI; In step 3, it is assumed that the eavesdropper's CSI is imperfect and the channel uncertainty is bounded by an elliptical region, ΔG3, ΔG4, ΔH 1e and ΔH 2e Defined by the elliptical area, i.e., the range of the channel error set by the eavesdropper's imperfect CSI is determined by the following formula: in, and Respectively represent G3, G4, H 1e and H 2e Estimated values ​​of; ΔG3, ΔG4, ΔH 1e and ΔH 2e Respectively represent G3, G4, H 1e and H 2e Channel error; δ3, δ4, δ 1e and δ 2e Respectively represent G3, G4, H 1e and H 2e The uncertainty radius of Step 4: Introduce a proxy function to convert non-convex items into convex items; In step 4, the original problem is the robust security beamforming problem of maximizing the worst-case confidentiality rate under different transmission power constraints in a MIMO full-duplex secure communication system, which can be expressed by the following formula: s.t.tr(X i )≤P,i=1,2 (11b) X i ≥0,i=1,2 (11c) Among them, P is the transmit power limit, R is the achievable confidentiality rate, M is the number of IRS components, and X is the transmit power. Then the proxy function is introduced to convert the non-convex term into a convex term. The proxy function expression is as follows: in, And A>0, f(ψ)=--tr(ψA)+ln|Ψ|+N, N is a constant, tr() represents the trace of the matrix, Ψ is a positive definite matrix; Step 5: Decouple the original problem into three sub-problems; In step 5, the alternating optimization method is used to decouple (11a) into three sub-problems, namely, the sub-problem of maximizing the worst-case optimized transmission power, the sub-problem of maximizing the worst-case optimized reflection IRS phase shift matrix, and the closed-form solution of the iterative ψ (n+1) , n is the number of iterations; Step 6: Fix irrelevant variables, iterate and optimize alternately, and update variables; In step 6, for the first sub-problem, variables Θ, ψ2, ψ4, ψ5 are fixed, and variables X1 and X2 are optimized and updated; for the second sub-problem, variables ψ2, ψ4, ψ5, X1 and X2 are fixed, and variable Θ is optimized and updated; for the third sub-problem, variables Θ, X1 and X2 are fixed, and ψ2, ψ4, ψ5 are optimized and updated; The irrelevant variables include ψ2, ψ4, ψ5, Θ, X1, and X2, where Θ is the reflection phase shift matrix of the IRS, and X1 and X2 are the transmit powers of S1 and S2, respectively; Step 7: After replacing the original problem with a convex problem, there is an upper bound and the overall algorithm eventually converges to a finite value.

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