Optimization methods for maximizing security and rate in RIS-assisted uplink multi-user systems under non-ideal CSI conditions

Abstract

This invention discloses an optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI (Content Security Interference System), relating to the field of communication technology. The method includes: constructing a multi-user cooperative interference physical layer secure communication model under non-ideal CSI; constructing a system security rate maximization problem; introducing rate auxiliary variables and interference power auxiliary variables to decouple the objective function in the system security rate maximization problem and transforming the fractional constraints in the system security rate maximization problem; constructing an alternating optimization framework to decompose the system security rate maximization problem after introducing rate and interference power auxiliary variables into a first subproblem, a second subproblem, and a third subproblem, which are then solved separately; the subproblems converge iteratively, outputting a suboptimal system resource scheduling strategy. Compared with existing technologies, this invention achieves a dual improvement in performance and practicality through innovative model construction, problem reconstruction, and algorithm design.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and specifically to an optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI conditions. Background Technology

[0002] The upcoming 6G wireless network is evolving towards intelligence and software reconfigurability, aiming to achieve seamless ubiquitous communication between people and devices. Through the perception, control, and optimization of the wireless environment, 6G strives to achieve breakthroughs in multiple dimensions, including low power consumption, high throughput, high energy efficiency, massive connectivity, high reliability, and security. In the field of physical layer secure communication, system confidentiality and speed are core indicators for measuring security performance, defining the maximum secure transmission rate a system can achieve while ensuring information is not eavesdropped on. To achieve these stringent secure communication goals, Reconfigurable Intelligent Surface (RIS) technology has emerged and is considered a key enabling technology for 6G communication. By deploying a large number of passive reflective elements, it intelligently regulates the propagation environment of electromagnetic waves, providing a new paradigm for improving system performance.

[0003] Specifically, RIS (Radio Reflection System) can enhance the desired signal while suppressing interference without increasing transmit power, simply by optimizing the reflection phase. This significantly improves spectral and energy efficiency, opening a new path for physical layer security enhancement. However, the precise control of RIS is highly dependent on the accuracy of Channel State Information (CSI). In real-world wireless environments, factors such as channel estimation errors and feedback delays are common, making perfect CSI difficult to obtain. These uncertainties severely interfere with the beamforming effect of RIS, thereby affecting the system's security performance.

[0004] However, existing RIS optimization techniques still have significant shortcomings: First, most studies have not fully considered channel uncertainties in real-world communication, resulting in a significant reduction in optimization effectiveness when channel errors exist; second, in uplink communication scenarios, the existence of potential passive eavesdroppers (JNs) is often overlooked, which may lead to information leakage for legitimate users. Therefore, designing a robust joint anti-interference secure transmission scheme under channel uncertainty conditions has become a critical issue that urgently needs to be addressed for RIS-assisted communication systems to be applied in practice. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide an optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI conditions.

[0006] The objective of this invention is achieved through the following technical solution: This application discloses an optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI conditions, including the following steps: S1. Construct a multi-user cooperative interference physical layer secure communication model under non-ideal CSI; S2, maximizing the security rate of the construction system; S3. Introduce rate auxiliary variables and interference power auxiliary variables to decouple the objective function in the system security rate maximization problem and transform the fractional constraints in the system security rate maximization problem. S4. Construct an alternating optimization framework to decompose the problem of maximizing the system security rate after introducing rate auxiliary variables and interference power auxiliary variables into a first subproblem, a second subproblem, and a third subproblem, and then solve them respectively; the subproblems converge iteratively in sequence, and the suboptimal system resource scheduling strategy is output.

[0007] Preferably, step S1 specifically includes the following sub-steps: S11. Consider an uplink communication system consisting of a base station BS with N antennas, a passive intelligent reflector RIS with M reflector elements, K single-antenna legitimate users User, J single-antenna interference nodes JN, and E single-antenna eavesdroppers PE. The key optimization variables of the uplink communication system include: BS receiver beamforming vector. RIS passive beamforming matrix Transmission power and the transmission power of interfering nodes ;in This represents a diagonal matrix with the elements within the parentheses as diagonal elements and the rest as 0. This represents the reflection coefficient of the m-th reflecting element, where m represents the index of the reflecting element in the RIS passive beamforming matrix. j represents the imaginary unit. Let m represent the phase angle of the m-th reflecting unit, and k represent the user. Indicates the index of the interfering node; The BS receives the beamforming vector Satisfy the normalized power constraint, i.e. ,in Represents the 2-norm; Satisfying the passive phase modulation constraint, i.e. Transmission power Limited by the maximum transmit power of user equipment ,Right now Interference node transmit power Limited by the maximum transmit power of the interfering nodes ,Right now ; S12. Based on step S11, the uplink communication system defines channels, including the RIS to user k link, RIS to BS link, BS to user k direct link, eavesdropper to user k link, interfering node to RIS link, RIS to eavesdropper link, interfering node to BS link, and interfering node to eavesdropper link; each channel is decomposed using a norm-bounded error model, i.e. ; in, This represents the actual channel coefficients of the RIS-to-user k link. This represents the estimated channel coefficients of the RIS-to-user k link. This represents the estimation error coefficient of the RIS-to-user k link. This represents the upper limit of the estimation error coefficient for the RIS-to-user k link; This represents the actual channel coefficients of the RIS to BS link. This represents the estimated channel matrix coefficients of the RIS to BS link. This represents the estimation error coefficient of the RIS to BS link. This represents the upper limit of the estimation error coefficient for the RIS to BS link; This represents the actual channel coefficients of the direct link from BS to user k. This represents the estimated channel matrix coefficients for the direct link from BS to user k. This represents the estimation error coefficient of the direct link from BS to user k. This represents the upper limit of the estimation error coefficient for the direct link from BS to user k; This represents the actual channel coefficients of the k-link from the eavesdropper to the user. This represents the estimated channel matrix coefficients of the k-link from the eavesdropper to the user. This represents the estimation error coefficient of the k-link from the eavesdropper to the user. This represents the upper limit of the estimation error coefficient for the k-link from the eavesdropper to the user; This represents the actual channel coefficients of the link from the interfering node to the RIS. These represent the estimated channel matrix coefficients of the interfering node to the RIS link. This represents the estimation error coefficient of the link from the interfering node to the RIS. This represents the upper limit of the estimated error coefficient for the link from the interfering node to the RIS; This represents the actual channel coefficients of the RIS-to-eavesdropper link. These represent the estimated channel matrix coefficients of the RIS-to-eavesdropper link. This represents the estimation error coefficient of the RIS-to-eavesdropper link. This represents the upper limit of the estimation error coefficient for the RIS-to-eavesdropper link; This represents the actual channel coefficients of the link from the interfering node to the BS. These represent the estimated channel matrix coefficients of the interfering node to the BS link. This represents the estimation error coefficient of the link from the interfering node to the BS. This represents the upper limit of the estimation error coefficient of the link from the interfering node to the BS; This represents the actual channel coefficients of the link from the interfering node to the eavesdropper. These represent the estimated channel matrix coefficients of the link from the interfering node to the eavesdropper. This represents the estimation error coefficient of the link from the interfering node to the eavesdropper. This represents the upper limit of the estimation error coefficient of the link from the interfering node to the eavesdropper; Channel representation that integrates multiple links combines multiple cascaded channels into an equivalent integrated channel, including: BS to user. k equivalent channel for The equivalent channel from the interfering node to the BS for The equivalent channel from the user to the eavesdropper e for The equivalent channel from the interfering node to the eavesdropper for ;in, , , and They represent known estimated channels, These represent the channel estimation error, respectively. express The corresponding upper bound of error, express The corresponding upper bound of error, express The corresponding upper bound of error, express The corresponding upper bound of error, Describes the 2-norm of a vector. This represents the F-norm.

[0008] Preferably, step S2 specifically includes the following sub-steps: S21, Signal received by base station BS for ,in This represents the transmitted signal of user k. This indicates the transmitted signal of the interfering node. The additive white Gaussian noise at the BS end represents the received signal at the eavesdropper's location e. for ,in, This represents additive white Gaussian noise at the eavesdropping end; S22. The base station uses a linear receiver and employs a BS to receive beamforming vectors. Receiving users k The signal, user k The instantaneous signal-to-interference-plus-noise ratio at the BS end is ,in Indicates excluding users k Total transmit power of other users Indicates the first i The actual equivalent channel for each user Indicates the first i The channel estimation error term for each user, where H represents the conjugate transpose. This represents the variance of Gaussian white noise at the base station, and the user... k At the instantaneous signal-to-interference-plus-noise ratio of eavesdropper e, ,in, Indicates user i The equivalent channel to the eavesdropper, Indicates user i To the eavesdropper's channel estimation error, This represents the variance of the Gaussian white noise at the eavesdropping end; S23. Based on Shannon's formula, users k The achievable speed at the BS end is ,user k The achievable speed at the eavesdropping end is Based on physical layer security theory, in the presence of a passive eavesdropper, the achievable security rate for user k is: ,in This indicates that the safe rate is non-negative; S24. Under the premise that the channel has a bounded estimation error, jointly optimize the RIS phase shift matrix. BS receive beamforming vector User transmit power and the transmission power of interfering nodes To maximize the system's security rate under conditions of eavesdropping and uncertain channels, the first optimization problem is: ,in, Denotes the first objective function. Indicates the first constraint. Indicates the second constraint. Indicates a third constraint. This indicates the fourth constraint. Indicates the first The maximum transmit power of each interfering node.

[0009] Preferably, step S3 specifically includes the following sub-steps: S31, For users k Introduce rate auxiliary variables, including a lower bound on the achievable rate at the BS end. The upper bound of the achievable rate of the eavesdropping terminal Based on the introduced rate auxiliary variable, the first objective function is equivalently transformed into the second objective function. At the same time, a fifth constraint is added. and the sixth constraint , , ; S32. Introduce an interference power auxiliary variable to decouple the interference term in the denominator of the signal-to-interference-plus-noise ratio (SINR) expression at the BS end. The interference power auxiliary variable includes: user... i For users k Upper bound of interference power at the BS end , Upper bound of interference power of interfering node to user k at the BS end. , The lower bound of the interference power of user e to eavesdropper e. , , The lower bound of the interference power of the interfering node on the eavesdropper e eavesdropping on the user k. , ;user k eavesdropper e Total disturbance lower bound , ; S33, Assumption The constant of the previous iteration The first optimization problem is equivalently transformed into the second optimization problem: ,in This represents the seventh constraint. This indicates the eighth constraint. Indicates the ninth constraint. This indicates the tenth constraint. This indicates the eleventh constraint. This indicates the twelfth constraint. This represents the third objective function.

[0010] Preferably, solving the first subproblem specifically includes the following sub-steps: S401, Set the convergence threshold Maximum number of iterations and iterative index Initialize the RIS passive beamforming matrix for the current iteration. User transmit power Interference node transmission power Channel estimation value and Upper bound of error and Initial values ​​of auxiliary variables ; S402, Introducing a positive semidefinite matrix Processing BS receive beamforming vector The quadratic term temporarily relaxes the rank constraint. The first subproblem is transformed into a convex semidefinite programming problem; S403. Use the transformation tool S-procedure to transform the infinite-dimensional robust constraint caused by channel uncertainty into a finite-dimensional deterministic linear matrix inequality constraint. S404, Introduce nonnegative relaxation auxiliary variables , and Construct a first convex optimization problem with the objective of maximizing the BS receiver rate. S405. Call the convex optimization solver CVX to solve the first convex optimization problem and obtain the optimal solution set. ; S406. Regarding the optimal solution matrix Perform eigenvalue decomposition ,in Represents the eigenvector. Representing eigenvalues, taking the principal eigenvectors Normalization is performed to recover the rank-one beamforming vector. ; S407. Optimize the auxiliary variable based on the solution results. and Update , , ; S408, Update the iteration index t' = t + 1, if or , Let represent the BS receiver beamforming vector in the (t'-1)th iteration. If the BS receive beamforming vector for the t'th iteration is obtained, the iteration exits; otherwise, return to step S403. After the iteration update is complete, the final BS beamforming vector is output. and auxiliary variables .

[0011] Preferably, solving the second subproblem specifically includes: S411, Set the convergence threshold Maximum number of iterations Iterative index and penalty factor Initialize the BS receive beamforming vector for the current iteration. Interference node transmission power User transmit power Auxiliary variables and Channel estimation value and Upper bound of error and RIS phase shift initial vector ; S412, Define the RIS phase shift vector , T represents transpose, introducing the extended vector. , ; S413, Combined with BS receiver beamforming vector Calculate the equivalent channel matrix and ,vector and ; S414, Introducing Penalty Items Relax the unit modulus constraint and perform a first-order Taylor expansion of the penalty term to complete the SCA linearization; S415. Use the transformation tool S-procedure to transform robust constraints into finite-dimensional deterministic linear matrix inequalities, and introduce non-negative auxiliary variables. and Construct the second convex optimization problem; S416. Call the convex optimization solver CVX to solve the second convex optimization problem and obtain the optimal extension vector. Auxiliary variables and ; S417, From the optimal expansion vector Extracting the phase shift vector And construct the phase shift matrix For auxiliary variables and Update , , and This represents the updated auxiliary variable; S418, Update the iteration index t' = t + 1, if or , Let represent the RIS passive beamforming matrix for the (t'-1)th iteration. If the RIS passive beamforming matrix represents the value of iteration t', then the iteration exits; otherwise, the phase shift vector is used. Perform an update to obtain the updated phase shift vector. , Then return to step S414; after the iteration update is completed, output the final RIS passive beamforming matrix. Auxiliary variables and .

[0012] Preferably, solving the third subproblem specifically includes: S421. Set the convergence threshold. Maximum number of iterations Iterative index Maximum transmit power of user equipment and the maximum transmit power of the interfering node Initialize the BS receive beamforming vector for the current iteration. RIS passive beamforming matrix Auxiliary variables , , , , , ; S422, Based on a fixed BS receiver beamforming vector and RIS passive beamforming matrix Calculate all equivalent channel constant terms. , , , ; S423, Construct a system to maximize overall security rate The objective is a third convex optimization problem, where the constraints involved include power constraints. Transformed finite-dimensional deterministic linear matrix inequality constraints and auxiliary variable association constraints ; S424. Call the convex optimization solver CVX to solve the third convex optimization problem and obtain the power-optimal solution. , The obtained power-optimal solution is then updated to obtain the updated power-optimal solution. , , Synchronous lower bound of base station rate Update; S425, Update the iteration index t' = t + 1, if or , This represents the transmit power of user k in the t'-th iteration. This represents the transmit power of user k in the (t'-1)th iteration. This represents the transmit power of the interfering node in the t'-th iteration. If the transmit power of the interfering node is expressed as t'-1, then the iteration exits; otherwise, return to step S423. After the iteration update is completed, the final user transmit power is output. Interference node transmission power and base station rate lower bound .

[0013] The beneficial effects of this invention are: 1) Compared with existing physical layer security optimization techniques for RIS-assisted uplink communication, this invention achieves a dual improvement in performance and practicality through innovative model construction, problem reconstruction, and algorithm design. Attached Figure Description

[0014] Figure 1 This is a schematic diagram illustrating the steps of an optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI conditions, according to an embodiment of the present invention. Figure 2 The simulation diagram shows the convergence performance of the optimization method for maximizing security and rate of RIS-assisted uplink multi-user system under non-ideal CSI in this embodiment of the invention under different system parameter configurations. Figure 3 This is a comparison chart of the system security rate of the optimization method and benchmark scheme for maximizing security and rate of RIS-assisted uplink multi-user system under non-ideal CSI conditions in this invention, with different numbers of RIS units. Figure 4 This is a comparison chart of the security rate of the optimization method and benchmark scheme for maximizing security and rate of RIS-assisted uplink multi-user system under non-ideal CSI in an embodiment of the present invention at different transmit powers. Figure 5 This is a comparison chart of the security rate of the optimization method for maximizing security and rate of a RIS-assisted uplink multi-user system under non-ideal CSI conditions and the benchmark scheme under different interference node transmit powers, according to an embodiment of the present invention. Detailed Implementation

[0015] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0016] This application discloses an optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI conditions, the steps of which are illustrated in the diagram below. Figure 1 As shown, it includes the following steps: S1. Construct a multi-user cooperative interference physical layer secure communication model under non-ideal CSI; S2, maximizing the security rate of the construction system; S3. Introduce rate auxiliary variables and interference power auxiliary variables to decouple the objective function in the system security rate maximization problem and transform the fractional constraints in the system security rate maximization problem. S4. Construct an alternating optimization framework to decompose the problem of maximizing the system security rate after introducing rate auxiliary variables and interference power auxiliary variables into a first subproblem, a second subproblem, and a third subproblem, and then solve them respectively; the subproblems converge iteratively in sequence, and the suboptimal system resource scheduling strategy is output.

[0017] Specifically, step S1 includes the following sub-steps: S11. Consider an uplink communication system consisting of a base station (BS) with N antennas, a passive intelligent surface (RIS) with M reflector elements, K single-antenna legitimate users (User), J single-antenna jamming nodes (JN), and K single-antenna eavesdroppers (PE). The key optimization variables of the uplink communication system include: the BS receive beamforming vector. (Used to detect users) k The signal satisfies the normalized power constraint, that is... ), Represents an N x 1 complex vector space, the RIS passive beamforming matrix. ,in, It is a complex matrix space of M rows and M columns. This represents a diagonal matrix with the elements within the parentheses as diagonal elements and the rest as 0. This represents the reflection coefficient of the m-th reflecting element, where m represents the index of the reflecting element in the RIS passive beamforming matrix. , This represents the phase angle of the m-th reflecting unit; Satisfying the passive phase modulation constraint, i.e. User transmit power (Limited by the maximum transmit power of the user equipment) Interference node transmit power (Limited by the maximum transmit power of the interfering nodes) ), j represents the imaginary unit, This represents the index of the interfering node, and k represents the user; S12. In the uplink communication system, legitimate users send information to the BS via direct links and links reflected by the RIS. To enhance the physical layer security of communication, the system introduces multiple controllable single-antenna interference nodes (JNs) that collaboratively transmit artificial noise to interfere with potential single-antenna eavesdroppers (PEs). Simultaneously, the passive RIS intelligently enhances the received signal quality of legitimate users and suppresses eavesdropping channels by dynamically adjusting the phase of its reflecting units. Channels are defined, including the RIS-to-user k link, RIS-to-BS link, BS-to-user k direct link, eavesdropper-to-user k link, interference node-to-RIS link, RIS-to-eavesdropper link, interference node-to-BS link, and interference node-to-eavesdropper link. In actual communication scenarios, obtaining perfect channel state information is unrealistic due to factors such as channel estimation errors, feedback delays, and dynamic environmental changes. To model channel uncertainty, a norm-bounded error model is used to decompose each channel, i.e. ,in, This represents the actual channel coefficients of the RIS-to-user k link. This represents the estimated channel coefficients of the RIS-to-user k link. This represents the estimation error coefficient of the RIS-to-user k link. This represents the upper limit of the estimation error coefficient for the RIS-to-user k link; This represents the actual channel coefficients of the RIS to BS link. This represents the estimated channel matrix coefficients of the RIS to BS link. This represents the estimation error coefficient of the RIS to BS link. This represents the upper limit of the estimation error coefficient for the RIS to BS link; This represents the actual channel coefficients of the direct link from BS to user k. This represents the estimated channel matrix coefficients for the direct link from BS to user k. This represents the estimation error coefficient of the direct link from BS to user k. This represents the upper limit of the estimation error coefficient for the direct link from BS to user k; This represents the actual channel coefficients of the k-link from the eavesdropper to the user. This represents the estimated channel matrix coefficients of the k-link from the eavesdropper to the user. This represents the estimation error coefficient of the k-link from the eavesdropper to the user. This represents the upper limit of the estimation error coefficient for the k-link from the eavesdropper to the user; This represents the actual channel coefficients of the link from the interfering node to the RIS. These represent the estimated channel matrix coefficients of the interfering node to the RIS link. This represents the estimation error coefficient of the link from the interfering node to the RIS. This represents the upper limit of the estimated error coefficient for the link from the interfering node to the RIS; This represents the actual channel coefficients of the RIS-to-eavesdropper link. These represent the estimated channel matrix coefficients of the RIS-to-eavesdropper link. This represents the estimation error coefficient of the RIS-to-eavesdropper link. This represents the upper limit of the estimation error coefficient for the RIS-to-eavesdropper link; This represents the actual channel coefficients of the link from the interfering node to the BS. These represent the estimated channel matrix coefficients of the interfering node to the BS link. This represents the estimation error coefficient of the link from the interfering node to the BS. This represents the upper limit of the estimation error coefficient of the link from the interfering node to the BS; This represents the actual channel coefficients of the link from the interfering node to the eavesdropper. These represent the estimated channel matrix coefficients of the link from the interfering node to the eavesdropper. This represents the estimation error coefficient of the link from the interfering node to the eavesdropper. This represents the upper limit of the estimation error coefficient of the link from the interfering node to the eavesdropper; To simplify the formulation of the subsequent robust optimization problem, the channel representations of multiple links are integrated, and multiple cascaded channels are merged into an equivalent integrated channel, including: BS to user. k equivalent channel , The equivalent channel from the interfering node to the BS , The equivalent channel from the user to the eavesdropper e , The equivalent channel from the interfering node to the eavesdropper , ;in, , , and They represent known estimated channels, These represent the channel estimation error, respectively. express The corresponding upper bound of error, express The corresponding upper bound of error, express The corresponding upper bound of error, express The corresponding upper bound of error, Describes the 2-norm of a vector. This represents the F-norm.

[0018] Specifically, step S2 includes the following sub-steps: S21, Signal received by base station BS The summation of signals from all legitimate users, interfering nodes, and additive white Gaussian noise, i.e. ,in This represents the transmitted signal of user k. This indicates the transmitted signal of the interfering node. The additive white Gaussian noise at the BS end represents the received signal at the eavesdropper's location e. for ,in, This represents additive white Gaussian noise at the eavesdropping end; S22. The base station uses a linear receiver and employs a BS to receive beamforming vectors. Receiving users k The signal, user k The instantaneous signal-to-interference-plus-noise ratio (SINR) at the BS end is: ,in, This represents the total transmit power of all users except user k. Indicates the first i The actual equivalent channel for each user Indicates the first i The channel estimation error term for each user, where H represents the conjugate transpose. This represents the variance of Gaussian white noise at the base station, and the user... k At the instantaneous signal-to-interference-plus-noise ratio of eavesdropper e, ,in, Indicates user i The equivalent channel to the eavesdropper, Indicates user i To the eavesdropper's channel estimation error, This represents the variance of the Gaussian white noise at the eavesdropping end; S23. Based on Shannon's formula, users k The achievable speed at the BS end is ,user k The achievable speed at the eavesdropping end is Based on physical layer security theory, in the presence of a passive eavesdropper, the achievable security rate for user k is: ,in This indicates that the security rate is non-negative; the overall performance index of the system is the sum of the confidentiality and security rates of all users under this system. S24. Under the premise that the channel has a bounded estimation error, jointly optimize the RIS phase shift matrix. BS receive beamforming vector User transmit power and the transmission power of interfering nodes To maximize the system's security rate under conditions of eavesdropping and uncertain channels, the first optimization problem is: ,in, Denotes the first objective function. Indicates the first constraint. Indicates the second constraint. Indicates a third constraint. This indicates the fourth constraint. Indicates the first The maximum transmit power of each interfering node. This optimization problem is a complex non-convex optimization problem, and the challenges mainly come from three aspects: the unity modulus constraint C1 of RIS is non-convex; both the objective function and the constraints contain optimization variables and complex fractional forms; and channel uncertainty leads to the constraints being infinite-dimensional robust constraints.

[0019] Specifically, step S3 includes the following sub-steps: S31, For users k Introduce rate auxiliary variables, including a lower bound on the achievable rate at the BS end. (satisfy ) and the upper bound of the achievable rate of the eavesdropping end (satisfy Based on the introduced rate auxiliary variable, the first objective function is equivalently transformed into the second objective function. At the same time, a fifth constraint is added. and the sixth constraint , , ; S32. Introduce an interference power auxiliary variable to decouple the interference term in the denominator of the signal-to-interference-plus-noise ratio (SINR) expression at the BS end. The interference power auxiliary variable includes: user... i For users k Upper bound of interference power at the BS end , Upper bound of interference power of interfering node to user k at the BS end. , The lower bound of the interference power of user e to eavesdropper e. , , The lower bound of the interference power of the interfering node on the eavesdropper e eavesdropping on the user k. , ;user k eavesdropper e Total disturbance lower bound , The introduction of these auxiliary variables is crucial for improving safety performance under robustness constraints: and These represent the worst-case interference from other users and interfering nodes on the BS side, respectively. , and This quantifies the minimum interference experienced by the eavesdropping device; S33, and also to further address the sixth constraint Assuming The constant of the previous iteration The first optimization problem is equivalently transformed into the second optimization problem: ,in This represents the seventh constraint (ensuring safe rate non-negativity). This indicates the eighth constraint. Indicates the ninth constraint. Indicates the tenth constraint (establishment) and , The relationship between them makes it easy to see that this is a convex constraint. This indicates the eleventh constraint. This indicates the twelfth constraint. Let represent the third objective function. Although the second optimization problem is still non-convex, its structure has been significantly simplified: the objective function becomes linear, and the types of constraints are more clearly defined, laying the foundation for subsequent alternating optimization decomposition.

[0020] For example, this application proposes a three-stage transformation framework: Auxiliary variable introduction and problem reconstruction: By introducing rate auxiliary variables and interference power auxiliary variables, the logarithmic term in the objective function is decoupled, and the fractional constraint is transformed into a quadratic inequality; Alternating optimization decomposition: The coupled multivariate optimization problem is decomposed into three sub-problems—BS beamforming optimization, RIS phase shift matrix optimization, and user transmit power and interference node transmit power optimization, which converge gradually through iterative solutions; Handling non-convex constraints and robust constraints: Based on the specific characteristics of each sub-problem, techniques such as continuous convex approximation (SCA), penalty function method, and S-procedure are used to transform non-convex robust constraints into solvable convex optimization problems.

[0021] Specifically, the optimization variables in the objective optimization problem are highly coupled and difficult to solve directly. This paper adopts the Alternating Optimization (AO) framework, decomposing the second optimization problem into three relatively independent subproblems, solving each subproblem optimally, and then updating the solution through an iterative framework until convergence. First subproblem: Optimize the BS receiving beamforming vector among the key optimization variables of the fixed uplink communication system, excluding the BS receiving beamforming vector. The second subproblem is to optimize the RIS passive beamforming matrix by fixing the vectors other than the RIS passive beamforming matrix among the key optimization variables of the fixed uplink communication system. The third subproblem: Optimize the transmit power by fixing the vectors of the key optimization variables of the uplink communication system, except for the transmit power; All three subproblems involve non-convex and robust constraints, requiring different mathematical processing methods or equivalent approaches for convex optimization. Here, several mathematical transformation tools are introduced: S-procedure transforms quadratic constraints into easily tractable matrix forms, used to convert infinite-dimensional robust constraints into finite-dimensional LMIs; Schur's complement lemma simplifies block matrix inequalities; Continuous Convex Approximation (SCA) handles non-convex functions through iterative linearization; Kronecker product and vectorization unify the handling of the coupling between beamforming and RIS phase shift; semidefinite programming relaxation and Gaussian randomization jointly handle rank-one constraints. These tools work together to provide a systematic mathematical framework for solving the convexity of the three subproblems.

[0022] Specifically, solving the first subproblem includes the following sub-steps: S401, Set the convergence threshold Maximum number of iterations and iterative index Initialize the RIS passive beamforming matrix for the current iteration. User transmit power Interference node transmission power Channel estimation value and Upper bound of error and Initial values ​​of auxiliary variables ; S402, Introducing a positive semidefinite matrix Processing BS receive beamforming vector The quadratic term temporarily relaxes the rank constraint. The first subproblem is transformed into a convex semidefinite programming problem; S403. Use the transformation tool S-procedure to transform the infinite-dimensional robust constraint caused by channel uncertainty into a finite-dimensional deterministic linear matrix inequality constraint. S404, Introduce nonnegative relaxation auxiliary variables , and Construct a first convex optimization problem with the objective of maximizing the BS receiver rate. S405. Call the convex optimization solver CVX to solve the first convex optimization problem and obtain the optimal solution set. ; S406. Regarding the optimal solution matrix Perform eigenvalue decomposition ,in Represents the eigenvector. Representing eigenvalues, taking the principal eigenvectors Normalization is performed to recover the rank-one beamforming vector. ; S407. Optimize the auxiliary variable based on the solution results. and Update , , ; S408, Update the iteration index t' = t + 1, if or , Let represent the BS receiver beamforming vector in the (t'-1)th iteration. If the BS receive beamforming vector for the t'th iteration is obtained, the iteration exits; otherwise, return to step S403. After the iteration update is complete, the final BS beamforming vector is output. and auxiliary variables .

[0023] For example, in the alternating optimization framework, when the RIS phase shift matrix, user transmit power, interfering node power, and other auxiliary variables besides the BS-side SINR are fixed, the first subproblem focuses on optimizing the base station receive beamforming vector, since it fixes all transmit powers (user transmit power). and the transmission power of interfering nodes ) and channel environment (RIS passive beamforming matrix) The signal and interference strength received by the eavesdropper are determined, and at this point, the upper limit of the eavesdropping terminal's rate is... constant Therefore, the objective function of the first subproblem is: Based on monotonicity, maximize This is equivalent to maximizing the lower bound of the worst-case signal-to-interference-plus-noise ratio (SINR). Introducing auxiliary variables Then the fifth constraint (Considering the reachability rate constraint of user k at the base station) is equivalent to Substitute it into In the expression: Using auxiliary variables and The above constraints are conservatively approximated as: This approximation separates multiple uncertainties while ensuring the feasibility and robustness of the solution, significantly simplifying the problem structure.

[0024] For example, for processing beamforming vectors To address the quadratic term, we introduce a positive semidefinite matrix variable. ,in and Then, we temporarily relax the rank-one constraint, thus transforming the problem into a convex semidefinite programming problem (SDP). For the quadratic constraint involving channel uncertainty, we use SProcedure to transform it into a deterministic linear matrix inequality (LMI), then the fifth constraint... Can be written as , , This represents the equivalent total interference plus noise power for user k; ,exist ; make: ; Let N×N be the identity matrix. Then the first subproblem is reconstructed into the first convex optimization problem: ; Indicates semidefinite relaxation constraints. The trace of the matrix is ​​used to find a set of beamforming vectors that maximize signal enhancement of the legitimate link and suppress inter-user and artificial noise interference, while satisfying worst-case signal-to-noise ratio and interference constraints. This lays the foundation for optimizing the second subproblem. Solving the first convex optimization problem yields the optimal solution. Since the rank-one constraint has been relaxed, it is necessary to start from... Eigenvalue decomposition is performed to recover feasible BS receiver beamforming vectors. ; Take the principal feature vector As a beamforming direction estimate, and normalized to satisfy the unit mode constraint, the final solution is obtained: .

[0025] Specifically, solving the second subproblem includes: S411, Set the convergence threshold Maximum number of iterations Iterative index and penalty factor Initialize the BS receive beamforming vector for the current iteration. Interference node transmission power User transmit power Auxiliary variables and Channel estimation value and Upper bound of error and RIS phase shift initial vector ; S412, Define the RIS phase shift vector , T represents transpose, introducing the extended vector. , ; S413, Combined with BS receiver beamforming vector Calculate the equivalent channel matrix and ,vector and ; S414, Introducing Penalty Items Relax the unit modulus constraint and perform a first-order Taylor expansion of the penalty term to complete the SCA linearization; S415. Use the transformation tool S-procedure to transform robust constraints into finite-dimensional deterministic linear matrix inequalities, and introduce non-negative auxiliary variables. and Construct the second convex optimization problem; S416. Call the convex optimization solver CVX to solve the second convex optimization problem and obtain the optimal extension vector. Auxiliary variables and ; S417, From the optimal expansion vector Extracting the phase shift vector And construct the phase shift matrix For auxiliary variables and Update , , and This represents the updated auxiliary variable; S418, Update the iteration index t' = t + 1, if or , Let represent the RIS passive beamforming matrix for the (t'-1)th iteration. If the RIS passive beamforming matrix represents the value of iteration t', then the iteration exits; otherwise, the phase shift vector is used. Perform an update to obtain the updated phase shift vector. , Then return to step S414; after the iteration update is completed, output the final RIS passive beamforming matrix. Auxiliary variables and .

[0026] For example, with the BS receive beamforming vector, user transmit power, interfering node power, and all auxiliary variables fixed, the second subproblem focuses on optimizing the RIS passive beamforming matrix. The core objective of this problem is to maximize the system's security level by intelligently adjusting the RIS reflection phase, while satisfying the unit mode constraint and robust security requirements. The main challenges of this problem come from two aspects: the non-convex unit mode constraint. Non-convex constraints are difficult to handle directly; the infinite-dimensional property of robust constraints: the channel uncertainty in the constraints leads to the constraint set being infinite-dimensional, which needs to be transformed into a solvable finite-dimensional form.

[0027] For example, in order to overcome the above difficulties, the rate at the eavesdropper end is fixed at... The paper proposes the following: unifying the representation of RIS phase shift variables through vectorization and reformulating the optimization problem; relaxing the unit modulus constraint using the penalty function method and handling the non-convexity of the penalty term using the continuous convex approximation (SCA); and transforming the robust constraint containing channel uncertainty into a deterministic linear matrix inequality (LMI) using the S-procedure.

[0028] For example, a RIS phase shift vector is defined. And introduce extended vector To uniformly express the channel coupling term, the following equivalent channel matrix / vector is constructed: ; Represents the space of N rows (M+1) columns of complex matrices. To represent a (M+1)-row, 1-column complex vector space in a concise manner: To handle non-convex constraints Relax it and introduce a penalty term into the objective function: ; when When sufficiently large, the solution will approach the unity modulus constraint. Penalty term. It is non-convex. At the nth iteration point At this point, a first-order Taylor lower bound approximation is performed using SCA: ;in Since the value is a constant, the penalty term is linearized, and the objective function becomes convex. This is the LMI transformation of robust constraints (S-procedure). Its norm is bounded. Fifth constraint Equivalent to: ;in , , Given a k×k dimensional identity matrix, define the column vector corresponding to user k. ,but Define the error term satisfy ,but Using the generalized S-procedure, the above constraints are equivalent to the existence of Make Established; among them Represents a 1×1 dimensional identity matrix, with quadratic terms. about Non-convex, at the current point Perform a first-order lower bound approximation at [location]. Substituting this into the equation yields the convex approximation of LMI: Similarly, constraints C6, C11, and C12 can be treated in the same way, introducing auxiliary variables respectively. And use SCA to obtain the corresponding convex LMI form.

[0029] in:

[0030] in, It is a linearized approximation function of the i-th legal link of user k with respect to the RIS phase vector. It is used to perform a first-order Taylor expansion on the non-convex SINR constraint and transform the non-convex term into a linear convex constraint. It is a linearized approximation function of the link from user k to the eavesdropper, used to linearize the non-convex quadratic terms in the eavesdropper SINR constraint; It is a linearized approximation function of the link from the interfering node to the eavesdropper, used to linearize the non-convex constraints of the artificial noise interference link; It is a linearized approximation function of the j-th cross-user interference link for user k, used to linearize multi-user interference constraints; It is a linearized approximation function of the link from the interfering node to the target node, used to linearize the non-convex constraints of the artificial noise link from the interfering node. , and An equivalent intermediate variable constructed to simplify the channel uncertainty coupling term; This indicates that the complex number inside the parentheses is represented by its real part. It represents a (M+1)×(M+1) dimensional identity matrix.

[0031] For the ninth constraint Essentially, it's about The convex constraint should be directly transformed into an exact linear matrix inequality (LMI) through the S-procedure and Schur's complement lemma, by using the upper bound of the interference power of the interference node on user k at the BS end. and concise representation of equivalent channels The upper bound of this constraint can be expressed as: According to the generalized definition of S-procedure, there exist non-negative slack variables. Make Converting it to LMI means that there exists a non-negative slack variable. Make Using Schur's complement lemma, it can be transformed into: For the eighth constraint Perform a similar transformation: According to the S-procedure and Schur's complement lemma, there exist slack variables. Make Valid. Combining all the above processing steps, in the nth iteration, the second subproblem transforms into: The objective of this problem is the sum of a linear function and a linear penalty term. The constraints are all LMI or linear inequalities, so it is convex and can be solved efficiently using standard convex optimization tools (such as CVX).

[0032] For example, solving the third subproblem specifically includes: S421. Set the convergence threshold. Maximum number of iterations Iterative index Maximum transmit power of user equipment and the maximum transmit power of the interfering node Initialize the BS receive beamforming vector for the current iteration. RIS passive beamforming matrix Auxiliary variables , , , , , ; S422, Based on a fixed BS receiver beamforming vector and RIS passive beamforming matrix Calculate all equivalent channel constant terms. , , , ; S423, Construct a system to maximize overall security rate The objective is a third convex optimization problem, where the constraints involved include power constraints. Transformed finite-dimensional deterministic linear matrix inequality constraints and auxiliary variable association constraints ; S424. Call the convex optimization solver CVX to solve the third convex optimization problem and obtain the power-optimal solution. , The obtained power-optimal solution is then updated to obtain the updated power-optimal solution. , , Synchronous lower bound of base station rate Update; S425, Update the iteration index t' = t + 1, if or , This represents the transmit power of user k in the t'-th iteration. This represents the transmit power of user k in the (t'-1)th iteration. This represents the transmit power of the interfering node in the t'-th iteration. If the transmit power of the interfering node is expressed as t'-1, then the iteration exits; otherwise, return to step S423. After the iteration update is completed, the final user transmit power is output. Interference node transmission power and base station rate lower bound .

[0033] For example, see Figures 2-5To verify the performance of the proposed robust alternating optimization algorithm based on S-procedure and SCA in environments with eavesdroppers and interfering nodes, simulation experiments were conducted using MATLAB. Consider a communication scenario in a three-dimensional coordinate system. The base station (BS) is located at (0, 0, 0), and the RIS is deployed at (50, 10, 0). Legitimate users are randomly distributed within an area centered at (40, -10, 0) with a radius of 5m. The eavesdropper (PE) is deployed near (35, -5, 0), while the interfering node (JN) is deployed at (32, 2, 0) to be close to the eavesdropper and implement precise interference. The link fading model includes large-scale path loss and small-scale Rayleigh fading. The path loss model is defined as... ,in Reference distance Path loss at each location, path loss index of each link The settings are as follows: BS-User link is 3.5 (simulated non-line-of-sight), BS-RIS and RIS User links are 2.2 (simulated near-line-of-sight). Under the default configuration, the number of legitimate users K=2, the number of base station antennas N=4, the number of eavesdroppers E=1, the number of interfering nodes J=1, and the channel estimation error bound... The noise power spectral density is -174 dBm / Hz, and the bandwidth is 1 MHz, meaning the noise power... (Normalization processing in simulation). To compare and verify the effectiveness of the proposed algorithm, the following two benchmark schemes were introduced: RandomPhase: Other variables are optimized using the algorithm in this paper, but the RIS passive beamforming matrix is... Internally randomly generated, not participating in joint optimization. No RIS (No RIS Scheme): No RIS is deployed in the system; legitimate users and interfering nodes communicate and interfere solely through direct links. Figure 2The convergence performance of this application under different system parameter configurations (average of 100 simulation iterations) is demonstrated. It can be seen that all curves reach a stable convergence state after approximately 10 to 15 iterations. This is attributed to the efficiency of the Continuous Convex Approximation (SCA) and penalty function method used in solving subproblems, proving that the algorithm has low computational latency in practical applications. Furthermore, comparing the curves with different parameters shows that when the number of base station antennas is increased (from N=4 to N=12) or the number of users (from K=2 to K=4), the system gains more spatial degrees of freedom and multi-user diversity gain, significantly improving the overall average security rate. Particularly noteworthy is the precipitous drop in the system's security rate when the interfering node is removed (J=0, No Jammer). This phenomenon intuitively and powerfully confirms the original intention of the system model design in this paper: introducing controlled interfering nodes (JN) to emit artificial noise is an indispensable key means to suppress passive eavesdroppers and ensure physical layer security.

[0034] For example, Figure 2 evaluates the relationship between the system's average security rate and the number of RIS reflector units M. Clearly, the No RIS scheme performs the worst and remains constant. When RIS is introduced, the security rate of both schemes increases with increasing M. However, the Proposed Robust scheme exhibits a significant, almost linear, increase, far outperforming the Random Phase scheme. This indicates that simply physically deploying RIS is insufficient. This application achieves this by intelligently adjusting the RIS passive beamforming matrix. This not only achieves passive beamforming gain (enhancing useful signals) on the link from legitimate users to the base station, but also forms "intelligent nulls" (suppressing signal leakage) for eavesdropping links. As the value increases, the ability of RIS to control electromagnetic waves is enhanced, and the algorithm in this paper can more perfectly adapt to complex channel uncertainty environments, thereby maximizing the security rate.

[0035] For example, Figure 3 This demonstrates the maximum transmit power for the user when the fixed number of RIS units M=30. Impact on Security Rate. Overall, as the capacity of the legitimate channel increases from 10 dBm to 30 dBm, the system security rate monotonically increases. Throughout the entire power range, the robust algorithm proposed in this application maintains optimal performance. This is because, without precise beam and phase joint optimization (such as No RIS or Random Phase schemes), increasing the user's transmit power, while enhancing the base station's received signal, also leads to a proportional increase in the signal power intercepted by eavesdroppers, resulting in a slow increase in the security rate. This application, however, utilizes the worst-case boundary of the uncertain channel to highly focus energy towards the base station while increasing transmit power, thus achieving efficient conversion of the security rate.

[0036] For example, Figure 4 It reveals the maximum power of the interfering node. The complex physical relationship between M and the system's security rate (assuming M=30, , =30dBm). When no jammer is deployed, the rate remains at a low level. When a jamming signal is introduced and At low levels, interference can effectively reduce the signal-to-noise ratio of an eavesdropper. However, for random phase schemes, when the interference power is too high ( At >22dBm, the system's security rate not only failed to improve but actually decreased sharply. This is because strong interference is a double-edged sword. Without precise phase control, the enormous interference energy undergoes disordered reflection through the RIS (Receptor Signal Processor), causing severe interference leakage and significantly impairing the reception of legitimate signals at the base station. In contrast, the robust algorithm proposed in this application perfectly resolves this contradiction. As the density increases, its security rate not only does not collapse but steadily increases and tends towards high-level saturation. This proves that the alternating optimization framework in this application successfully achieves the BS (Base Station) receiver beamforming vector through strict S-procedure LMI constraints. With RIS passive beamforming matrix The deep collaboration—constructing precise spatial nulling for strong interference signals at the base station while accurately reflecting interference energy towards the eavesdropper's location—fully demonstrates the absolute necessity and outstanding advantages of joint robust optimization in noisy and error-prone real-world communication systems.

[0037] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. An optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI conditions, characterized in that, Includes the following steps: S1. Construct a multi-user cooperative interference physical layer secure communication model under non-ideal CSI; S2, maximizing the security rate of the construction system; S3. Introduce rate auxiliary variables and interference power auxiliary variables to decouple the objective function in the system security rate maximization problem and transform the fractional constraints in the system security rate maximization problem. S4. Construct an alternating optimization framework to decompose the problem of maximizing the system security rate after introducing rate auxiliary variables and interference power auxiliary variables into a first subproblem, a second subproblem, and a third subproblem, and then solve them respectively; the subproblems converge iteratively in sequence, and the suboptimal system resource scheduling strategy is output.

2. The optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI conditions as described in claim 1, characterized in that, Step S1 specifically includes the following sub-steps: S11. Consider an uplink communication system consisting of a base station BS with N antennas, a passive intelligent reflector RIS with M reflector elements, K single-antenna legitimate users User, J single-antenna interference nodes JN, and E single-antenna eavesdroppers PE. The key optimization variables of the uplink communication system include: BS receiver beamforming vector. RIS passive beamforming matrix Transmission power and the transmission power of interfering nodes ;in This represents a diagonal matrix with the elements within the parentheses as diagonal elements and the rest as 0. This represents the reflection coefficient of the m-th reflecting element, where m represents the index of the reflecting element in the RIS passive beamforming matrix. j represents the imaginary unit. Let m represent the phase angle of the m-th reflecting unit, and k represent the user. Indicates the index of the interfering node; The BS receives the beamforming vector Satisfy the normalized power constraint, i.e. ,in Represents the 2-norm; Satisfying the passive phase modulation constraint, i.e. Transmission power Limited by the maximum transmit power of user equipment ,Right now Interference node transmit power Limited by the maximum transmit power of the interfering nodes ,Right now ; S12. Based on step S11, the uplink communication system defines channels, including the RIS to user k link, RIS to BS link, BS to user k direct link, eavesdropper to user k link, interfering node to RIS link, RIS to eavesdropper link, interfering node to BS link, and interfering node to eavesdropper link; each channel is decomposed using a norm-bounded error model, i.e. ; in, This represents the actual channel coefficients of the RIS-to-user k link. This represents the estimated channel coefficients of the RIS-to-user k link. This represents the estimation error coefficient of the RIS-to-user k link. This represents the upper limit of the estimation error coefficient for the RIS-to-user k link; This represents the actual channel coefficients of the RIS to BS link. This represents the estimated channel matrix coefficients of the RIS to BS link. This represents the estimation error coefficient of the RIS to BS link. This represents the upper limit of the estimation error coefficient for the RIS to BS link; This represents the actual channel coefficients of the direct link from BS to user k. This represents the estimated channel matrix coefficients for the direct link from BS to user k. This represents the estimation error coefficient of the direct link from BS to user k. This represents the upper limit of the estimation error coefficient for the direct link from BS to user k; This represents the actual channel coefficients of the k-link from the eavesdropper to the user. This represents the estimated channel matrix coefficients of the k-link from the eavesdropper to the user. This represents the estimation error coefficient of the k-link from the eavesdropper to the user. This represents the upper limit of the estimation error coefficient for the k-link from the eavesdropper to the user; This represents the actual channel coefficients of the link from the interfering node to the RIS. These represent the estimated channel matrix coefficients of the interfering node to the RIS link. This represents the estimation error coefficient of the link from the interfering node to the RIS. This represents the upper limit of the estimated error coefficient for the link from the interfering node to the RIS; This represents the actual channel coefficients of the RIS-to-eavesdropper link. These represent the estimated channel matrix coefficients of the RIS-to-eavesdropper link. This represents the estimation error coefficient of the RIS-to-eavesdropper link. This represents the upper limit of the estimation error coefficient for the RIS-to-eavesdropper link; This represents the actual channel coefficients of the link from the interfering node to the BS. These represent the estimated channel matrix coefficients of the interfering node to the BS link. This represents the estimation error coefficient of the link from the interfering node to the BS. This represents the upper limit of the estimation error coefficient of the link from the interfering node to the BS; This represents the actual channel coefficients of the link from the interfering node to the eavesdropper. These represent the estimated channel matrix coefficients of the link from the interfering node to the eavesdropper. This represents the estimation error coefficient of the link from the interfering node to the eavesdropper. This represents the upper limit of the estimation error coefficient of the link from the interfering node to the eavesdropper; Channel representation that integrates multiple links combines multiple cascaded channels into an equivalent integrated channel, including: BS to user. k equivalent channel for The equivalent channel from the interfering node to the BS for The equivalent channel from the user to the eavesdropper e for The equivalent channel from the interfering node to the eavesdropper for ;in, , , and They represent known estimated channels, These represent the channel estimation error, respectively. express The corresponding upper bound of error, express The corresponding upper bound of error, express The corresponding upper bound of error, express The corresponding upper bound of error, Describes the 2-norm of a vector. This represents the F-norm.

3. The optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI conditions as described in claim 2, characterized in that... Step S2 specifically includes the following sub-steps: S21, Signal received by base station BS for ,in This represents the transmitted signal of user k. This indicates the transmitted signal of the interfering node. The additive white Gaussian noise at the BS end represents the received signal at the eavesdropper's location e. for ,in, This represents additive white Gaussian noise at the eavesdropping end; S22. The base station uses a linear receiver and employs a BS to receive beamforming vectors. Receiving users k The signal, user k The instantaneous signal-to-interference-plus-noise ratio at the BS end is ,in, Indicates excluding users k Total transmit power of other users Indicates the first i The actual equivalent channel for each user Indicates the first i The channel estimation error term for each user, where H represents the conjugate transpose. This represents the variance of Gaussian white noise at the base station, and the user... k At the instantaneous signal-to-interference-plus-noise ratio of eavesdropper e, ,in, Indicates user i The equivalent channel to the eavesdropper, Indicates user i To the eavesdropper's channel estimation error, This represents the variance of the Gaussian white noise at the eavesdropping end; S23. Based on Shannon's formula, users k The achievable speed at the BS end is ,user k The achievable speed at the eavesdropping end is Based on physical layer security theory, in the presence of a passive eavesdropper, the achievable security rate for user k is: ,in This indicates that the safe rate is non-negative; S24. Under the premise that the channel has a bounded estimation error, jointly optimize the RIS phase shift matrix. BS receive beamforming vector User transmit power and the transmission power of interfering nodes To maximize the system's security rate under conditions of eavesdropping and uncertain channels, the first optimization problem is: ,in, Denotes the first objective function. Indicates the first constraint. Indicates the second constraint. Indicates a third constraint. This indicates the fourth constraint. Indicates the first The maximum transmit power of each interfering node.

4. The optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI conditions as described in claim 3, characterized in that... Step S3 specifically includes the following sub-steps: S31, For users k Introduce rate auxiliary variables, including a lower bound on the achievable rate at the BS end. The upper bound of the achievable rate of the eavesdropping terminal Based on the introduced rate auxiliary variable, the first objective function is equivalently transformed into the second objective function. At the same time, a fifth constraint is added. and the sixth constraint , , ; S3 2. An interference power auxiliary variable is introduced to decouple the interference term in the denominator of the signal-to-interference-plus-noise ratio (SINR) expression at the BS end. This interference power auxiliary variable includes: user... i For users k Upper bound of interference power at the BS end , Upper bound of interference power of interfering node to user k at the BS end. , The lower bound of the interference power of user e to eavesdropper e. , , The lower bound of the interference power of the interfering node on the eavesdropper e eavesdropping on the user k. , ;user k eavesdropper e Total disturbance lower bound , ; S33, Assumption The constant of the previous iteration The first optimization problem is equivalently transformed into the second optimization problem: ,in This represents the seventh constraint. This indicates the eighth constraint. Indicates the ninth constraint. This indicates the tenth constraint. This indicates the eleventh constraint. This indicates the twelfth constraint. This represents the third objective function.

5. The optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI conditions as described in claim 4, characterized in that... Solving the first subproblem involves the following sub-steps: S401, Set the convergence threshold Maximum number of iterations and iterative index Initialize the RIS passive beamforming matrix for the current iteration. User transmit power Interference node transmission power Channel estimation value and Upper bound of error and Initial values ​​of auxiliary variables ; S402, Introducing a positive semidefinite matrix Processing BS receive beamforming vector The quadratic term temporarily relaxes the rank constraint. The first subproblem is transformed into a convex semidefinite programming problem; S403. Use the transformation tool S-procedure to transform the infinite-dimensional robust constraint caused by channel uncertainty into a finite-dimensional deterministic linear matrix inequality constraint. S404, Introduce nonnegative relaxation auxiliary variables , and ; Construct a first convex optimization problem with the objective of maximizing the BS receiver rate; S405. Call the convex optimization solver CVX to solve the first convex optimization problem and obtain the optimal solution set. ; S406. Regarding the optimal solution matrix Perform eigenvalue decomposition ,in Represents the eigenvector. Representing eigenvalues, taking the principal eigenvectors Normalization is performed to recover the rank-one beamforming vector. ; S407. Optimize the auxiliary variable based on the solution results. and Update , , ; S408, Update the iteration index t' = t + 1, if or , Let represent the BS receiver beamforming vector in the (t'-1)th iteration. If the BS receive beamforming vector for the t'th iteration is obtained, the iteration exits; otherwise, return to step S403. After the iteration update is complete, the final BS beamforming vector is output. and auxiliary variables .

6. The optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI conditions as described in claim 4, characterized in that... Solving the second subproblem specifically includes: S411, Set the convergence threshold Maximum number of iterations Iterative index and penalty factor Initialize the BS receive beamforming vector for the current iteration. Interference node transmission power User transmit power Auxiliary variables and Channel estimation value and Upper bound of error and RIS phase shift initial vector ; S412, Define the RIS phase shift vector , T represents transpose, introducing the extended vector. , ; S413, Combined with BS receiver beamforming vector Calculate the equivalent channel matrix and ,vector and ; S414, Introducing Penalty Items Relax the unit modulus constraint and perform a first-order Taylor expansion of the penalty term to complete the SCA linearization; S415. Use the transformation tool S-procedure to transform robust constraints into finite-dimensional deterministic linear matrix inequalities, and introduce non-negative auxiliary variables. and Construct the second convex optimization problem; S416. Call the convex optimization solver CVX to solve the second convex optimization problem and obtain the optimal extension vector. Auxiliary variables and ; S417, From the optimal expansion vector Extracting the phase shift vector And construct the phase shift matrix For auxiliary variables and Update , , and This represents the updated auxiliary variable; S418, Update the iteration index t' = t + 1, if or , Let represent the RIS passive beamforming matrix for the (t'-1)th iteration. If the RIS passive beamforming matrix represents the value of iteration t', then the iteration exits; otherwise, the phase shift vector is used. Perform an update to obtain the updated phase shift vector. , Then return to step S414; after the iteration update is completed, output the final RIS passive beamforming matrix. Auxiliary variables and .

7. The optimization method for maximizing security and rate in a RIS-assisted uplink multi-user system under non-ideal CSI conditions as described in claim 4, characterized in that, Solving the third subproblem specifically includes: S421. Set the convergence threshold. Maximum number of iterations Iterative index Maximum transmit power of user equipment and the maximum transmit power of the interfering node Initialize the BS receive beamforming vector for the current iteration. RIS passive beamforming matrix Auxiliary variables , , , , , ; S422, Based on a fixed BS receiver beamforming vector and RIS passive beamforming matrix Calculate all equivalent channel constant terms. , , , ; S423, Construct a system to maximize overall security rate The objective is a third convex optimization problem, where the constraints involved include power constraints. Transformed finite-dimensional deterministic linear matrix inequality constraints and auxiliary variable association constraints ; S424. Call the convex optimization solver CVX to solve the third convex optimization problem and obtain the power-optimal solution. , The obtained power-optimal solution is then updated to obtain the updated power-optimal solution. , , Synchronous lower bound of base station rate Update; S425, Update the iteration index t' = t + 1, if or , This represents the transmit power of user k in the t'-th iteration. This represents the transmit power of user k in the (t'-1)th iteration. This represents the transmit power of the interfering node in the t'-th iteration. If the transmit power of the interfering node is expressed as t'-1, then the iteration exits; otherwise, return to step S423. After the iteration update is completed, the final user transmit power is output. Interference node transmission power and base station rate lower bound .

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