RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission system and optimization method

Abstract

The invention relates to the technical field of communication, and provides an RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission system and an optimization method, the system comprises a difunctional radar communication base station configured with Nt transmitting antennas; the reconfigurable intelligent surface is provided with M reflecting units; k single-antenna legal communication users; the eavesdropping target is located in a specific space direction; wherein the system cooperatively works with the reconfigurable intelligent surface through the base station, establishes a downlink multi-user communication link serving the K legal communication users, and performs radar sensing on the direction of the eavesdropping target by using a signal transmitted by the base station; according to the method, hardware damage of a transmitting end, a user end and an eavesdropping end is systematically modeled in an RIS-assisted ISAC secure communication model, and a corresponding joint robust optimization algorithm is provided; simulation results show that under the same non-ideal hardware condition, the reachable secrecy rate of the obtained system is obviously superior to that of all comparison reference schemes.

Description

Technical Field

[0001] This invention relates to the field of communication technology, specifically to a RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission system and optimization method. Background Technology

[0002] Integrated Sensing and Communication (ISAC), as a core enabling technology for 6G networks, achieves high-speed communication and high-precision perception of the surrounding environment by sharing hardware platforms and spectrum resources. This provides an efficient and low-cost integrated solution for emerging applications such as autonomous driving, smart cities, and the low-altitude economy. However, this functional integration also introduces unique and severe security challenges: the radar detection waveforms used for sensing naturally carry modulated communication symbols, and their wide beam or scanning characteristics allow malicious targets within the sensing range (such as unauthorized drones or nearby vehicles) to intercept and decipher confidential information during beam scanning, leading to the leakage of sensitive data. Therefore, physical layer security (PLS) technology, especially active jamming technology based on beamforming and artificial noise (AN), has become an indispensable means to ensure the confidentiality of information in ISAC systems.

[0003] In recent years, Reconfigurable Smart Surfaces (RIS) have emerged as a revolutionary technology, offering unprecedented controllability to wireless channels through their programmable electromagnetic property manipulation capabilities. Introducing RIS into ISAC systems theoretically allows for the creation of intelligent and controllable reflection links to overcome obstructions, enhance desired signals, and actively weaken the signal quality of eavesdropping links, opening new avenues for addressing these security challenges. Existing research has preliminarily explored the potential of RIS in improving communication rates or sensing accuracy in ISAC systems.

[0004] However, current research has two significant limitations: First, most work is based on the assumption of "ideal hardware," neglecting hardware impairments (HWIs) caused by the inherent nonlinear characteristics of RF components such as power amplifiers, mixers, and analog-to-digital converters in transceivers. In real systems, HWIs lead to signal distortion, generate additional noise, and introduce phase shift errors, severely degrading beamforming accuracy and the beam control effect of RIS, resulting in a significant performance drop in practical deployments of designs based on ideal assumptions. Second, existing ISAC security research focuses primarily on optimizing the active transmit beam at the base station, failing to fully leverage the "environmental reconstruction" capability provided by RIS to fundamentally compensate for channel defects (such as strong obstruction) to achieve global optimization of communication, sensing, and security performance. Therefore, how to accurately model the real-world hardware impairments at the transceiver end and jointly design the active beamforming of the base station (including communication beams and artificial noise) and the passive reflection phase shift of RIS to maximize the physical layer security rate of the system while strictly ensuring multi-user communication quality and radar sensing performance has become a critical and highly challenging problem that urgently needs to be solved. Based on the aforementioned problems, a RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission system and optimization method are proposed. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission system and optimization method, which overcomes the deficiencies of existing technologies. By systematically modeling transceiver hardware impairments, jointly optimizing base station active beamforming and artificial noise, and RIS passive reflection phase shift, it effectively solves the problems in existing ISAC security research, such as performance overestimation due to ignoring hardware impairments, insufficient utilization of RIS environment reconfiguration capabilities, and difficulty in maximizing physical layer security rates while ensuring communication and sensing performance.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission system includes:

[0008] A dual-function radar communication base station equipped with Nt transmitting antennas;

[0009] A reconfigurable smart surface with M reflective units;

[0010] K legitimate single-antenna communication users; and a listening target located in a specific spatial direction;

[0011] The system works in collaboration with the base station and the reconfigurable smart surface to establish a downlink multi-user communication link serving the K legitimate communication users, and simultaneously uses the signal emitted by the base station to perform radar sensing of the direction of the eavesdropping target.

[0012] Based on the establishment of hardware impairment models including the transmitter, receiver, and target, the system maximizes the sum of the confidentiality rates of all legitimate users by jointly optimizing the active beamforming vector, artificial noise covariance matrix, and passive reflection phase shift matrix of the reconfigurable smart surface at the base station.

[0013] Preferably, the base station transmits signals. The mathematical expression for the superposition of communication signals, artificial noise, and noise caused by hardware defects at the transmitting end is:

[0014] ,

[0015] in, This represents the expected notification signal to be sent to the Kth legitimate user, and satisfies... Furthermore, the signals from different users are independent of each other;

[0016] and They represent and Precoding vector at the base station,

[0017] The AN generated by the dual-function base station satisfies These are complex Gaussian variables that are randomly generated to combat eavesdropping;

[0018] The independent Gaussian transmission distortion noise, i.e., hardware impairment noise, is statistically modeled as follows: ,in, The channel matrix from the base station to the reconfigurable smart surface describes the electromagnetic wave propagation characteristics.

[0019] A coefficient characterizing the degree of damage to the transmitting hardware;

[0020] ( X ) is a diagonal matrix.

[0021] Preferably, the received signal of the kth legitimate user consists of three parts: the transmitted signal after channel fading, the additive white Gaussian noise at the receiver, and the hardware impairment noise at the receiver, expressed as follows:

[0022] ,

[0023] in, For legitimate users Equivalent channel;

[0024] This represents additive white Gaussian noise. For noise variance;

[0025] The reflection coefficient matrix of a reconfigurable smart surface is expressed as follows: ,

[0026] Indicates the first Phase shift of each element;

[0027] , , These represent the distance from the base station to the user. Reconfigurable smart surfaces for users The channel vector from the base station to the reconfigurable smart surface;

[0028] also , , ,in Channel gain per unit distance; This represents the corresponding path loss index; , , Indicates distance; , , Represents the Rayleigh fading vector;

[0029] The distortion noise caused by hardware damage at the user receiver is modeled as follows: Indicates user Independent zero-mean Gaussian distortion noise at point, where , indicating user The ratio of the power of the distorted noise to the power of the undistorted received signal.

[0030] Preferably, the signal-to-interference-plus-noise ratio of the echo signal at the eavesdropping target is... The expression used to measure radar sensing performance is:

[0031]

[0032] in, Let be the array steering vector of the base station in the target direction θ, and its nth element is . λ is the carrier wavelength, and d is the antenna spacing; Let x be the covariance matrix of the transmitted signal;

[0033] Let be the beamforming vector transmitted by the base station to the k-th user;

[0034] This is the signal sent to the k-th user;

[0035] The vector of artificial noise transmitted by the base station;

[0036] The damage coefficient of the transmitting end hardware;

[0037] The hardware damage coefficient at the radar target; This represents the noise power of the radar receiving channel.

[0038] Preferably, when the eavesdropping target intends to eavesdrop on the information of the kth legitimate user, its received signal-to-interference-plus-noise ratio (SINR) is... for:

[0039] ,

[0040] in, Indicates the equivalent channel from the BS to the eavesdropping user and , Channel gain per unit distance; For distance, This is the path loss index. This is the Rayleigh fading vector;

[0041] Represents the beam vectors of other users.

[0042] This represents the hardware impairment coefficient of the eavesdropper's receiver.

[0043] This represents the additive white Gaussian noise power of the eavesdropper's receiving channel.

[0044] Preferably, the system's security rate is the sum of the security rates of all legitimate users, where the achievable security rate of the kth legitimate user is... Defined as the non-negative part of the difference between the user's reachable rate and the eavesdropper's eavesdropping rate:

[0045]

[0046] in, The signal-to-interference-plus-noise ratio (SINNR) of the kth legitimate user is expressed as:

[0047] in, This is the channel vector from the base station to the kth legitimate user; V1 is the beamforming vector sent by the base station to the kth legitimate user; V2 is the artificial noise covariance matrix. and These are the interference covariances caused by hardware damage at the transmitter and receiver at user k, respectively, and their forms are similar to the definition in the eavesdropping link. The additive white Gaussian noise power at user k;

[0048] The signal-to-interference-plus-noise ratio (SIR) of the eavesdropper on the k-th legitimate user; the total system security rate is... .

[0049] A RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission optimization method, used to implement a wireless transmission system, includes the following steps:

[0050] Step S1: Active Beamforming Optimization: Fix the reflection phase shift matrix Θ of the reconfigurable smart surface, and jointly optimize the set of communication beamforming vectors at the base station. Artificial noise covariance matrix V is used to maximize the overall security rate of the system.

[0051] Step S1.1: Introduce a set of auxiliary variables , will maximize The original objective function is equivalently transformed into a new objective function with a convex form, and a set of constraints related to the auxiliary variables are constructed.

[0052] Step S1.2: For the non-convex logarithmic inequality constraints on user reachability and eavesdropping rate generated in step S1.1, use the first-order Taylor expansion to obtain its global lower or upper bound at a given initial point or the solution of the previous iteration, and then transform the non-convex constraints into convex linear constraints.

[0053] Step S1.3: Set a minimum communication rate constraint for each legitimate user. The reconstructed expression is a nonlinear inequality concerning the signal covariance and the equivalent channel, and its non-convex part is approximated using a first-order Taylor expansion.

[0054] Step S1.4: Constrain the minimum signal-to-interference-plus-noise ratio of the radar echo. Reorganized into a matrix { The linear matrix inequalities or second-order cone constraints of} and V, which are given The following is about the matrix { } and V are convex;

[0055] Step S1.5: Employ a semi-positive definite relaxation algorithm, ignoring the beamforming matrix. The rank-one constraint of the artificial noise matrix V relaxes the optimization problem formed in steps S1.1 to S1.4 into a convex semidefinite programming problem, which is then solved using an interior-point solver.

[0056] Step S1.6: If the solution obtained or If the rank is greater than 1, then the Gaussian randomization method is used to extract a series of rank-1 beamforming vector candidate sets that satisfy the power constraint from the solution, and the one that makes the objective function optimal is selected as the approximate solution of the current subproblem.

[0057] Step S2: Passive phase shift optimization: Fix the optimal or suboptimal active beamforming matrix obtained in step S1. and Optimize the reflection phase shift matrix Θ of the reconfigurable smart surface or equivalently optimize its phase shift vector. ;

[0058] Step S2.1: Define auxiliary matrix variables and satisfy The unit modulus constraint is transformed into a convex constraint, but a rank-one constraint rank(Φ)=1 is introduced;

[0059] Step S2.2: Set the total system security rate It is re-expressed as a fraction in terms of Φ or the equivalent channel; the fractional objective function and the associated non-convex constraints are made convex by introducing additional auxiliary variables and utilizing the first-order Taylor expansion in the continuous convex approximation.

[0060] Step S2.3: Using semidefinite relaxation, temporarily ignoring the constraint rank(Φ)=1, the passive phase shift optimization subproblem is transformed into a convex semidefinite programming problem and solved;

[0061] Step S2.4: Apply the solution obtained... Perform eigenvalue decomposition. If the rank is not 1, use Gaussian randomization to generate multiple phase shift vector candidates that satisfy the unit modulus constraint, and select the one that optimizes the objective function as the solution to the current subproblem.

[0062] Step S3: Alternating Iteration: Using the solutions from steps S1 and S2 as inputs for each other's next iteration, repeat steps S1 and S2 until the total system security rate is reached. If the increment is less than the preset convergence accuracy threshold ϵ or reaches the maximum number of iterations Imax, the final output is a suboptimal solution of the jointly optimized active beamforming vector, artificial noise covariance matrix and reconfigurable smart surface phase shift matrix.

[0063] This invention provides a RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission system and optimization method. It has the following beneficial effects:

[0064] This invention systematically models hardware impairments at the transmitter, user, and eavesdropping ends in a RIS-assisted ISAC secure communication model and proposes a corresponding joint robust optimization algorithm. Simulation results show that, under the same non-ideal hardware conditions, the system security rate achieved by the proposed solution is significantly better than all comparative benchmark solutions. For example, in typical scenarios, its security rate is about 85% higher than the "no RIS" solution and also significantly higher than the "random RIS phase" solution. The proposed solution can effectively overcome the adverse effects of hardware impairments and achieve a substantial enhancement in security performance.

[0065] The algorithm proposed in this invention has extremely high tolerance to hardware impairment. Simulation analysis shows that although the system security rate decreases when the hardware impairment coefficient increases from 0.05 to 0.4, the performance degradation trend of the proposed scheme is much slower than that of the scheme that ignores the hardware impairment assumption. Even at higher impairment levels, the proposed scheme can still maintain a performance advantage over other schemes. It can effectively compensate for signal distortion and suppress impairment noise.

[0066] Through joint optimization, the spatial degrees of freedom provided by the RIS reflection unit and the base station antenna array can be efficiently utilized. Simulation verification shows that as the number of RIS units M increases from 20 to 60, the system security rate increases by more than 35%. When the number of base station transmit antennas Nt increases from 4 to 12, the security rate increases by 66%, which is far greater than the passive comparison scheme. It can convert additional hardware resources into security performance gains almost linearly, providing effective performance assurance for the future integrated application of large-scale RIS and large-scale MIMO.

[0067] Using the minimum signal-to-interference-plus-noise ratio (SINR) of radar sensing as one of the core constraints ensures basic sensing performance. Simulation results show that when the sensing requirements become stronger (the echo SINR threshold Γradar increases), the proposed solution can dynamically adjust resource allocation through the algorithm, meeting more stringent sensing requirements while only causing a decrease in the security rate of about 28.1%, and is always superior to other solutions.

[0068] The algorithm proposed in this invention, based on alternating optimization (AO), continuous convex approximation (SCA), and semidefinite relaxation (SDR), has a clear structure and reliable convergence. Simulation results show that the algorithm can quickly converge to a stable solution within a few iterations, with controllable computational complexity, meeting the real-time or near-real-time beam reconstruction requirements of practical systems, and making the entire joint design framework engineering feasible. Attached Figure Description

[0069] Figure 1This is a system model diagram of the present invention;

[0070] Figure 2 This is a flowchart of the optimization algorithm proposed in this invention;

[0071] Figure 3 This invention compares the total safe rate under different transmission powers.

[0072] Figure 4 This invention compares the total security rate under different SINR thresholds.

[0073] Figure 5 This relates the total safe speed of the invention to the number of RIS components;

[0074] Figure 6 This relates the total security rate of the invention to the number of base station transmitting antennas;

[0075] Figure 7 This relates the overall security rate of the invention to the hardware damage coefficient. Detailed Implementation

[0076] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, 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.

[0077] RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission system includes:

[0078] A dual-function radar communication base station equipped with Nt transmitting antennas;

[0079] A reconfigurable smart surface with M reflective units;

[0080] K are legitimate single-antenna communication users; and one eavesdropping target is located in a specific spatial direction; Nt is the number of base station transmitting antennas; M is the number of reflective elements of the reconfigurable smart surface. K is the number of legitimate communication users.

[0081] The system works in collaboration with the base station and the reconfigurable smart surface to establish a downlink multi-user communication link serving the K legitimate communication users, and simultaneously uses the signal emitted by the base station to perform radar sensing of the direction of the eavesdropping target.

[0082] Based on the establishment of hardware impairment models including the transmitter, receiver, and target, the system maximizes the sum of the confidentiality rates of all legitimate users by jointly optimizing the active beamforming vector, artificial noise covariance matrix, and passive reflection phase shift matrix of the reconfigurable smart surface at the base station.

[0083] The optimization process must satisfy the following constraints:

[0084] The total transmit power of the base station does not exceed the preset maximum power budget Pmax; Pmax is the maximum transmit power budget of the base station.

[0085] The achievable communication rate for each legitimate user shall not be lower than the minimum rate threshold Rmin,k of its quality of service requirements; Rmin,k is the minimum communication rate requirement for the kth legitimate user.

[0086] When the base station performs radar sensing on the eavesdropping target in a preset direction θ, the signal-to-interference-plus-noise ratio (SIR) of the received echo is not lower than the minimum threshold Γradar required to ensure reliable detection; θ: the direction angle of the radar-sensed target. Γradar is the minimum echo SIR threshold required for radar sensing;

[0087] Each reflective unit of the reconfigurable smart surface has a reflectivity coefficient with a unity modulus, meaning its amplitude is always 1 and only its phase is adjustable.

[0088] The base station transmits signals The mathematical expression for the superposition of communication signals, artificial noise, and noise caused by hardware defects at the transmitting end is:

[0089] ,

[0090] in, This represents the expected notification signal to be sent to the Kth legitimate user, and satisfies... Furthermore, the signals from different users are independent of each other;

[0091] and They represent and Precoding vector at the base station,

[0092] The AN generated by the dual-function base station satisfies These are complex Gaussian variables that are randomly generated to combat eavesdropping;

[0093] The independent Gaussian transmission distortion noise, i.e., hardware impairment noise, is statistically modeled as follows: ,in, The channel matrix from the base station to the reconfigurable smart surface (RIS) describes the electromagnetic wave propagation characteristics;

[0094] A coefficient characterizing the degree of damage to the transmitting hardware;

[0095] ( X ) is a diagonal matrix.

[0096] The received signal of the kth legitimate user consists of three parts: the transmitted signal after channel fading, the additive white Gaussian noise at the receiver, and the hardware impairment noise at the receiver, which is expressed as:

[0097] ,

[0098] in, For legitimate users Equivalent channel;

[0099] This represents additive white Gaussian noise. For noise variance;

[0100] The reflection coefficient matrix of a reconfigurable smart surface is expressed as follows: ,

[0101] Indicates the first Phase shift of each element;

[0102] , , These represent the distance from the base station to the user. Reconfigurable smart surfaces for users The channel vector from the base station to the reconfigurable smart surface;

[0103] also , , ,in Channel gain per unit distance; This represents the corresponding path loss index; , , Indicates distance; , , Represents the Rayleigh fading vector;

[0104] The distortion noise caused by hardware damage at the user receiver is modeled as follows: Indicates user Independent zero-mean Gaussian distortion noise at point, where , indicating user The ratio of the power of the distorted noise to the power of the undistorted received signal.

[0105] The signal-to-interference-plus-noise ratio of the echo signal at the eavesdropping target The expression used to measure radar sensing performance is:

[0106] ,

[0107] in, Let be the array steering vector of the base station in the target direction θ, and its nth element is . λ is the carrier wavelength, and d is the antenna spacing; Let x be the covariance matrix of the transmitted signal; ,

[0108] Let be the beamforming vector transmitted by the base station to the k-th user;

[0109] This is the signal sent to the k-th user;

[0110] The vector of artificial noise transmitted by the base station;

[0111] The damage coefficient of the transmitting end hardware;

[0112] This represents the hardware damage coefficient at the radar target (i.e., the eavesdropping end); This represents the noise power of the radar receiving channel.

[0113] When the eavesdropping target intends to eavesdrop on the information of the kth legitimate user, its received signal-to-interference-plus-noise ratio (SINR) for:

[0114] ,

[0115] in, Indicates the equivalent channel from the BS to the eavesdropping user and , Channel gain per unit distance; For distance, This is the path loss index. This is the Rayleigh fading vector;

[0116] Represents the beam vectors (interference terms) of other users.

[0117] This represents the hardware impairment coefficient of the eavesdropper's receiver.

[0118] This represents the additive white Gaussian noise power of the eavesdropper's receiving channel; if a beam vector exists to interfere with the eavesdropper... ,but The item exists; otherwise, the item is 0.

[0119] The system's security rate is the sum of the security rates of all legitimate users, where the achievable security rate for the kth legitimate user is... Defined as the non-negative part of the difference between the user's reachable rate and the eavesdropper's eavesdropping rate:

[0120]

[0121] in, The signal-to-interference-plus-noise ratio (SINNR) of the kth legitimate user is expressed as: ,

[0122] in, This is the channel vector from the base station to the kth legitimate user; V1 is the beamforming vector sent by the base station to the kth legitimate user; V2 is the artificial noise covariance matrix. and These are the interference covariances caused by hardware damage at the transmitter and receiver at user k, respectively, and their forms are similar to the definition in the eavesdropping link. The additive white Gaussian noise power at user k;

[0123] The signal-to-interference-plus-noise ratio (SIR) of the eavesdropper on the k-th legitimate user; the total system security rate is... .

[0124] A RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission optimization method is proposed for implementing a wireless transmission system. It employs an alternating optimization framework, iteratively solving two sub-problems—active beamforming and passive phase shifting—to address variable coupling and non-convexity. The method includes the following steps:

[0125] Step S1: Active Beamforming Optimization: Fix the reflection phase shift matrix Θ of the reconfigurable smart surface, and jointly optimize the set of communication beamforming vectors at the base station. Artificial noise covariance matrix V is used to maximize the overall security rate of the system.

[0126] Step S1.1: Introduce a set of auxiliary variables , will maximize The original objective function is equivalently transformed into a new objective function with a convex form, and a set of constraints related to the auxiliary variables are constructed.

[0127] Step S1.2: For the non-convex logarithmic inequality constraints on user reachability and eavesdropping rate generated in step S1.1, use the first-order Taylor expansion to obtain its global lower or upper bound at a given initial point or the solution of the previous iteration, and then transform the non-convex constraints into convex linear constraints.

[0128] Step S1.3: Set a minimum communication rate constraint for each legitimate user. The reconstructed expression is a nonlinear inequality concerning the signal covariance and the equivalent channel, and its non-convex part is approximated using a first-order Taylor expansion.

[0129] Step S1.4: Constrain the minimum signal-to-interference-plus-noise ratio of the radar echo. Reorganized into a matrix { The linear matrix inequalities or second-order cone constraints of} and V, which are given The following is about the matrix { } and V are convex;

[0130] Step S1.5: Employ a semi-positive definite relaxation algorithm, ignoring the beamforming matrix. The rank-one constraint of the artificial noise matrix V relaxes the optimization problem formed in steps S1.1 to S1.4 into a convex semidefinite programming problem, which is then solved using an interior-point solver.

[0131] Step S1.6: If the solution obtained or If the rank is greater than 1, then the Gaussian randomization method is used to extract a series of rank-1 beamforming vector candidate sets that satisfy the power constraint from the solution, and the one that makes the objective function optimal is selected as the approximate solution of the current subproblem.

[0132] Step S2: Passive phase shift optimization: Fix the optimal or suboptimal active beamforming matrix obtained in step S1. and Optimize the reflection phase shift matrix Θ of the reconfigurable smart surface or equivalently optimize its phase shift vector. ;

[0133] Step S2.1: Define auxiliary matrix variables and satisfy The unit modulus constraint is transformed into a convex constraint, but a rank-one constraint rank(Φ)=1 is introduced;

[0134] Step S2.2: Set the total system security rate It is re-expressed as a fraction in terms of Φ or the equivalent channel; the fractional objective function and the associated non-convex constraints are made convex by introducing additional auxiliary variables and utilizing the first-order Taylor expansion in the continuous convex approximation.

[0135] Step S2.3: Using semidefinite relaxation, temporarily ignoring the constraint rank(Φ)=1, the passive phase shift optimization subproblem is transformed into a convex semidefinite programming problem and solved;

[0136] Step S2.4: Apply the solution obtained... Perform eigenvalue decomposition. If the rank is not 1, use Gaussian randomization to generate multiple phase shift vector candidates that satisfy the unit modulus constraint, and select the one that optimizes the objective function as the solution to the current subproblem.

[0137] Step S3: Alternating Iteration: Using the solutions from steps S1 and S2 as inputs for each other's next iteration, repeat steps S1 and S2 until the total system security rate is reached. If the increment is less than the preset convergence accuracy threshold ϵ or reaches the maximum number of iterations Imax, the final output is a suboptimal solution of the jointly optimized active beamforming vector, artificial noise covariance matrix and reconfigurable smart surface phase shift matrix.

[0138] In step S1.1, the equivalent transformation of the objective function specifically includes:

[0139] Define auxiliary variables and Then maximize Equivalent to minimizing This is further equivalent to being under constraint and Minimize By introducing exponential variables and continuous convex approximation, the objective function is ultimately processed into a convex function with respect to the new variables.

[0140] In steps S1.2 and S1.3, the application of the first-order Taylor expansion is specifically as follows: for forms of The constraints, where A and B are functions of the optimization variables, are equivalent to: When A or B is a non-convex function of the variable, for example... In optimization If Φ is a nonconvex function, then we can use the first-order Taylor expansion. At the previous iteration point We construct its lower bound at a certain point, thereby obtaining convex linear matrix inequality constraints.

[0141] The method, through the joint design of active beamforming, artificial noise, and passive phase shift, enables the system to adaptively cope with performance degradation caused by hardware impairments and maintain robust security and sensing performance under different system parameters, as specifically demonstrated below:

[0142] Under the same maximum transmit power of the base station, the achievable security rate obtained by the proposed method is significantly higher than the benchmark scheme with no reconfigurable smart surface assistance, no artificial noise, random phase configuration of reconfigurable smart surfaces, or neglect of hardware impairment.

[0143] When the radar sensing requires an echo signal-to-interference-plus-noise ratio threshold When improving, the proposed method can dynamically adjust the power distribution of beamforming and artificial noise, so as to ensure the sensing performance while making the decrease in security rate less than that of other comparative schemes.

[0144] As the number of reconfigurable smart surface reflective units M or the number of base station transmit antennas Nt increases, the proposed method achieves a greater improvement in security rate than the benchmark scheme, demonstrating its ability to effectively utilize spatial degrees of freedom to enhance security performance.

[0145] Hardware impairment coefficient at the transceiver end Under increased non-ideal conditions, the performance degradation of the proposed method is relatively more gradual, demonstrating its strong robustness to hardware damage and its practical engineering value.

[0146] Implementation, for example Figure 1 As shown, a RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission system is presented. Considering the interdependencies among the variables involved, the AO algorithm is a suitable choice for managing variable coupling. Furthermore, to address non-convex constraints, equivalent transformations can be used to redefine the variables. Specifically, the original problem is first redefined, and then decomposed into two subproblems within the AO framework. By reconstructing the objective function and non-convex constraints, the subproblems are optimized using first-order Taylor expansion and SDR methods, and then solved separately using SCA. A suboptimal solution to the original problem is obtained using an alternating iterative strategy.

[0147] Step 1: First, Equivalent , Furthermore, in order to overcome quadratic forms, we define... This represents all transmitted beams, including user beams and artificial noise. . Describes the equivalent channel, where Similarly This represents the equivalent channel of the eavesdropping user; therefore, the objective function can be reformulated as:

[0148] (14)

[0149] To perform convex optimization of the objective function, introducing an exponential auxiliary variable yields the following formula related to the objective function:

[0150] (15)

[0151] (16)

[0152] (17)

[0153] (18)

[0154] Therefore, according to formulas (15)-(18), a new objective function expression can be obtained:

[0155] (19)

[0156] It is clear that the objective function is convex at this point, so regarding The constraints can be expressed as:

[0157] ,

[0158] Clearly, inequalities (20)-(23) are equal at the optimum, which can be verified by the monotonicity of the objective function. However, after the transformation, due to Since (21) and (22) appear on the right side of the non-convex constraint, they remain non-convex. To resolve the aforementioned non-convexity, a first-order Taylor approximation is used. Specifically, (21) and (22) appear on the right side of the non-convex constraint. In the next iteration, it can be written as:

[0159] (twenty four)

[0160] (25)

[0161] in This represents the value from the previous iteration and is used for linearization.

[0162] For non-convex constraints (11), define Then we can get:

[0163] (26)

[0164] Next, we deal with the non-convex constraint (12). First, we can make the original inequality equivalent to:

[0165] (27)

[0166] Then transform it into:

[0167] (28)

[0168] At this time, this is about The function has nonlinear constraints, but the right side is a convex function with respect to the trace, while the left side is linear, and can be solved iteratively within the SCA framework.

[0169] After the above operations, the optimization problem can be reformulated as P2:

[0170] (29)

[0171] (30)

[0172] (31)

[0173] (32)

[0174] Due to the non-convexity constraint of rank-1, this constraint can be temporarily relaxed using SDR, making P2 a convex problem that can be solved using existing tools such as CVX. Alternatively, if the result does not satisfy the rank-1 condition, Gaussian randomization and rank-1 approximation methods can be used.

[0175] Step Two: Due to Since the RIS is already fixed, it will not change the total transmit power and will not affect the optimization objective. Therefore, after obtaining active beamforming, it can be re-formulated as optimization problem P3:

[0176] (33)

[0177] (34)

[0178] Define user Receive beam The equivalent channel is ,also ,in , Same settings and In subproblem 2, the solution to subproblem 1 is used to fix the variables, thereby achieving the desired result. The optimization process is illustrated in the flowchart below. Figure 2 As shown.

[0179] To simplify formula writing, legitimate users... The equivalent channel is .because The expression does not contain Therefore, Therefore, the objective function can be rewritten as:

[0180] (35)

[0181] in User The diagonal HWI matrix receives interference from hardware impairment leakage. Similarly, auxiliary variables are introduced. Through a first-order Taylor expansion, it can be reformulated as P4:

[0182] (36)

[0183] (37)

[0184] (38)

[0185] (39)

[0186] (40)

[0187] Since the rank-1 constraint may be difficult to guarantee, SDR is used to relax this constraint. Then, an SCA-based method is used to solve P4, and the CVX method is used. At the same time, Gaussian randomization and rank-1 approximation methods are used to obtain the actual value.

[0188] Finally, using the solution to problem P2, problems P3 and P4 are solved through alternating optimization. That is, after fixing the result of active beamforming P2, the passive reflection coefficient of RIS is further optimized, and the two are iterated alternately to finally obtain the optimal solution of joint beamforming.

[0189] This study uses MATLAB software to verify the performance of an iterative algorithm for a RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission system, specifically in small-scale fading channels. Modeled as:

[0190] (41)

[0191] in, It is a deterministic line-of-sight (LoS) channel component, while This represents the scattering component. Furthermore, That is the corresponding Rician factor.

[0192] Other required parameter settings are as follows: Number of base station antennas The number of RIS reflection units is 8. =20, Number of valid users =3, maximum transmit power of the base station =30 dBm, AWGN noise at the legal user location = -80 dBm, AWGN noise of the target eavesdropper = -70 dBm, hardware impairment factor Radar echo SINR threshold =10dBm.

[0193] like Figure 2 As shown, a flowchart of the proposed optimization algorithm is presented. This flowchart illustrates that the entire algorithm is based on a block coordinate descent (BCD) structure of SCA + SDR, with the two parts alternately optimizing to gradually approach a feasible solution. Figure 3 As can be seen from this, in the RIS-assisted ISAC system, under different baseline schemes, the achievable security rate varies with the maximum transmit power of the base station. The proposed algorithm considers both artificial noise (AN) and hardware impairment (HI). As shown in the figure, the proposed scheme achieves the highest security rate across the entire transmit power range, demonstrating the effectiveness of jointly optimizing transmit beamforming and RIS phase design even with actual hardware impairment. In the high transmit power region, the "no hardware impairment" scheme slightly outperforms the proposed scheme, indicating that hardware impairment has a negative impact. However, even under non-ideal hardware conditions, the proposed design remains highly robust. Removing artificial noise significantly reduces performance, validating its crucial role in enhancing physical layer security. Furthermore, in the "random phase" scheme, the RIS components are not optimized, resulting in significantly worse performance than the optimized RIS, further highlighting the importance of a well-designed RIS phase. The worst performance occurs in the "no RIS" scheme, demonstrating the critical role of RIS in enhancing secure communication and radar sensing capabilities.

[0194] like Figure 4 As shown, different radar echo SINR thresholds are illustrated. Below, the security rate performance of various schemes is analyzed. Specifically, when... At -10 dB, the proposed algorithm can achieve a security rate of approximately 12.8 bit / s / Hz, while... At 10dB, the signal drops to approximately 9.2 bit / s / Hz, a decrease of about 28.1%. In comparison, at At 10 dB, the "RIS-free" and "random phase" schemes can only achieve 6.9 and 8.1 bit / s / Hz, respectively, highlighting the importance of RIS optimization. This is because the proposed algorithm can... The method dynamically transfers some power from interference (artificial noise) to the sensing task during addition, while the optimized RIS phase can compensate for the resulting beamforming distortion. Furthermore, the "AN-free" scheme exhibits a performance degradation of approximately 1.5 bit / s / Hz compared to the proposed method, further demonstrating the crucial role of artificial noise in secure communication. The "HI-free" scheme performs well in low-frequency applications. In some cases, it is similar to the optimal solution, but in high-level cases... The slightly better performance compared to the proposed solution in the scenario indicates that ignoring hardware impairments would lead to an overestimation of system performance. Therefore, the proposed joint design can provide robust and reliable secure communication performance under various radar sensing requirements.

[0195] like Figure 5 As shown, the security rate varies with the number of RIS components under different schemes. The situation of change. It can be observed that, with... With the increase of , the security rate of all schemes continues to improve. This is because a larger RIS surface can provide finer phase control, thereby enhancing the legitimate channel gain while suppressing eavesdropping links. In particular, when When the number of bits increased from 20 to 60, the confidentiality rate of the proposed algorithm improved from approximately 12.2 bit / s / Hz to 16.6 bit / s / Hz, an improvement of over 35%. The "RIS-free" scheme performed the worst, indicating that RIS plays a fundamental role in improving system performance. The "random phase" scheme performed slightly better, but its performance was still limited due to the lack of phase optimization. Furthermore, the curves for "no hardware impairment" and "no artificial noise" showed performance degradation, validating the effectiveness of the proposed joint design in real-world ISAC scenarios.

[0196] like Figure 6 As shown, the security rate varies with the number of transmitting antennas. The changes. With With increasing size, the security rate of all schemes steadily improves because larger antenna arrays allow for higher beamforming gain and more accurate spatial focusing capabilities. Increasing the security rate from 4 to 12 improves the proposed algorithm's security rate from 8.6 bit / s / Hz to 14.3 bit / s / Hz, a 66% increase. The limited performance improvements of the "RIS-free" and "random phase" schemes indicate their inability to effectively utilize RIS-assisted beamforming capabilities. Notably, in the "AN-free" scheme, when... At that time, the security rate stabilized at about 9.4 bit / s / Hz, which shows that if artificial noise is not introduced, increasing the number of transmitting antennas would actually benefit the eavesdropper.

[0197] like Figure 7 As shown, the system exhibits different algorithm schemes and varying hardware impairment coefficients at the transceiver end (denoted as ). Security rate performance under changing conditions. With... As the density increases, the security rate of all schemes decreases. This is because hardware impairments introduce signal distortion and amplify noise, thereby reducing channel quality and deteriorating physical layer security performance. When the value is increased from 0.05 to 0.4, the security rate of the proposed scheme decreases from 13.8 bit / s / Hz to 6.8 bit / s / Hz, a decrease of approximately 50%. Compared with the "no hardware impairment" scheme, the proposed method consistently maintains superior performance, verifying the importance of modeling and compensating for hardware impairments. Furthermore, the curve of the "no artificial noise" scheme shows a more significant decrease, indicating that ignoring artificial noise significantly weakens the system's ability to suppress eavesdropping, because as... As the noise level increases, the intensity of interference cannot increase synchronously, leading to a decrease in security; "random phase" and "RIS-free" solutions are almost entirely unresilient to hardware damage. As the pressure increases, the security rate decreases rapidly. This highlights the crucial role of RIS phase calibration in mitigating beamforming errors caused by hardware impairments. The proposed algorithm maintains a security performance advantage of over 85%. In summary, these results validate the strong robustness and security performance of the proposed algorithm even under non-ideal hardware conditions.

[0198] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission system, characterized in that, include: A dual-function radar communication base station equipped with Nt transmitting antennas; A reconfigurable smart surface with M reflective units; K single-antenna legitimate communication users; And a listening target located in a specific spatial direction; The system works in collaboration with the base station and the reconfigurable smart surface to establish a downlink multi-user communication link serving the K legitimate communication users, and simultaneously uses the signal emitted by the base station to perform radar sensing of the direction of the eavesdropping target. Based on the establishment of hardware impairment models including the transmitter, receiver, and target, the system maximizes the sum of the confidentiality rates of all legitimate users by jointly optimizing the active beamforming vector, artificial noise covariance matrix, and passive reflection phase shift matrix of the reconfigurable smart surface at the base station.

2. The wireless transmission system according to claim 1, characterized in that, The base station transmits signals The mathematical expression for the superposition of communication signals, artificial noise, and noise caused by hardware defects at the transmitting end is: ， in, This represents the expected notification signal to be sent to the Kth legitimate user, and satisfies... Furthermore, the signals from different users are independent of each other; and They represent and Precoding vector at the base station, The AN generated by the dual-function base station satisfies These are complex Gaussian variables that are randomly generated to combat eavesdropping; The independent Gaussian transmission distortion noise, i.e., hardware impairment noise, is statistically modeled as follows: ,in, The channel matrix from the base station to the reconfigurable smart surface describes the electromagnetic wave propagation characteristics. A coefficient characterizing the degree of damage to the transmitting hardware; ( X ) is a diagonal matrix.

3. The wireless transmission system according to claim 2, characterized in that, The received signal of the kth legitimate user consists of three parts: the transmitted signal after channel fading, the additive white Gaussian noise at the receiver, and the hardware impairment noise at the receiver, which is expressed as: , in, For legitimate users Equivalent channel; This represents additive white Gaussian noise. For noise variance; The reflection coefficient matrix of a reconfigurable smart surface is expressed as follows: , Indicates the first Phase shift of each element; , , These represent the distance from the base station to the user. Reconfigurable smart surfaces for users The channel vector from the base station to the reconfigurable smart surface; also , , ,in Channel gain per unit distance; This represents the corresponding path loss index; , , Indicates distance; , , Represents the Rayleigh fading vector; The distortion noise caused by hardware damage at the user receiver is modeled as follows: Indicates user Independent zero-mean Gaussian distortion noise at point, where , indicating user The ratio of the power of the distorted noise to the power of the undistorted received signal.

4. The wireless transmission system according to claim 1 or 2, characterized in that, The signal-to-interference-plus-noise ratio of the echo signal at the eavesdropping target The expression used to measure radar sensing performance is: ， in, Let be the array steering vector of the base station in the target direction θ, and its nth element is . λ is the carrier wavelength, and d is the antenna spacing; Let x be the covariance matrix of the transmitted signal; , Let be the beamforming vector transmitted by the base station to the k-th user; This is the signal sent to the k-th user; The vector of artificial noise transmitted by the base station; The damage coefficient of the transmitting end hardware; The hardware damage coefficient at the radar target; This represents the noise power of the radar receiving channel.

5. The wireless transmission system according to claim 4, characterized in that, When the eavesdropping target intends to eavesdrop on the information of the kth legitimate user, its received signal-to-interference-plus-noise ratio (SINR) for: ， in, Indicates the equivalent channel from the BS to the eavesdropping user and , Channel gain per unit distance; For distance, This is the path loss index. This is the Rayleigh fading vector; Represents the beam vectors of other users. This represents the hardware impairment coefficient of the eavesdropper's receiver. This represents the additive white Gaussian noise power of the eavesdropper's receiving channel.

6. The wireless transmission system according to claim 5, characterized in that, The system's security rate is the sum of the security rates of all legitimate users, where the achievable security rate for the kth legitimate user is... Defined as the non-negative part of the difference between the user's reachable rate and the eavesdropper's eavesdropping rate: ， in, The signal-to-interference-plus-noise ratio (SINNR) of the kth legitimate user is expressed as: , in, This is the channel vector from the base station to the kth legitimate user; V1 is the beamforming vector sent by the base station to the kth legitimate user; V2 is the artificial noise covariance matrix. and These are the interference covariances caused by hardware damage at the transmitter and receiver at user k, respectively, and their forms are similar to the definition in the eavesdropping link. The additive white Gaussian noise power at user k; The signal-to-interference-plus-noise ratio (SIR) of the eavesdropper on the k-th legitimate user; the total system security rate is... .

7. A RIS-assisted downlink MU-MISO multi-user ISAC wireless transmission optimization method for implementing the wireless transmission system according to any one of claims 1-6, comprising the following steps: Step S1: Active Beamforming Optimization: Fix the reflection phase shift matrix Θ of the reconfigurable smart surface, and jointly optimize the set of communication beamforming vectors at the base station. Artificial noise covariance matrix V is used to maximize the overall security rate of the system. Step S1.1: Introduce a set of auxiliary variables , will maximize The original objective function is equivalently transformed into a new objective function with a convex form, and a set of constraints related to the auxiliary variables are constructed. Step S1.2: For the non-convex logarithmic inequality constraints on user reachability and eavesdropping rate generated in step S1.1, use the first-order Taylor expansion to obtain its global lower or upper bound at a given initial point or the solution of the previous iteration, and then transform the non-convex constraints into convex linear constraints. Step S1.3: Set a minimum communication rate constraint for each legitimate user. The reconstructed expression is a nonlinear inequality concerning the signal covariance and the equivalent channel, and its non-convex part is approximated using a first-order Taylor expansion. Step S1.4: Constrain the minimum signal-to-interference-plus-noise ratio of the radar echo. Reorganized into a matrix { The linear matrix inequalities or second-order cone constraints of} and V, which are given The following is about the matrix { } and V are convex; Step S1.5: Employ a semi-positive definite relaxation algorithm, ignoring the beamforming matrix. The rank-one constraint of the artificial noise matrix V relaxes the optimization problem formed in steps S1.1 to S1.4 into a convex semidefinite programming problem, which is then solved using an interior-point solver. Step S1.6: If the solution obtained or If the rank is greater than 1, then the Gaussian randomization method is used to extract a series of rank-1 beamforming vector candidate sets that satisfy the power constraint from the solution, and the one that makes the objective function optimal is selected as the approximate solution of the current subproblem. Step S2: Passive phase shift optimization: Fix the optimal or suboptimal active beamforming matrix obtained in step S1. and Optimize the reflection phase shift matrix Θ of the reconfigurable smart surface or equivalently optimize its phase shift vector. ; Step S2.1: Define auxiliary matrix variables and satisfy The unit modulus constraint is transformed into a convex constraint, but a rank-one constraint rank(Φ)=1 is introduced; Step S2.2: Set the total system security rate It is re-expressed as a fraction in terms of Φ or the equivalent channel; the fractional objective function and the associated non-convex constraints are made convex by introducing additional auxiliary variables and utilizing the first-order Taylor expansion in the continuous convex approximation. Step S2.3: Using semidefinite relaxation, temporarily ignoring the constraint rank(Φ)=1, the passive phase shift optimization subproblem is transformed into a convex semidefinite programming problem and solved; Step S2.4: Apply the solution obtained... Perform eigenvalue decomposition. If the rank is not 1, use Gaussian randomization to generate multiple phase shift vector candidates that satisfy the unit modulus constraint, and select the one that optimizes the objective function as the solution to the current subproblem. Step S3: Alternating Iteration: Using the solutions from steps S1 and S2 as inputs for each other's next iteration, repeat steps S1 and S2 until the total system security rate is reached. If the increment is less than the preset convergence accuracy threshold ϵ or reaches the maximum number of iterations Imax, the final output is a suboptimal solution of the jointly optimized active beamforming vector, artificial noise covariance matrix and reconfigurable smart surface phase shift matrix.

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