Beamforming method for ris-aided noma-isac system against eavesdropping

Abstract

The application discloses a beamforming method of an RIS-aided NOMA-ISAC system against internal and external eavesdropping, which optimizes the transmitting beam of the base station and the phase shift matrix of the RIS intelligently, ensures that the radar sensing requirement is met under the condition of limited energy resources, effectively resists potential internal and external eavesdropping attacks, and thus significantly improves the safe communication performance of the system legal users. Specifically, the method ingeniously uses the radar signal of the base station, performs the radar target sensing task while interfering potential eavesdroppers with the radar signal as artificial noise, and realizes the dual functions of target sensing and safe communication. However, since the optimization problem of minimizing the system legal signal power has non-convex constraints, it is difficult to solve directly, therefore the original problem is decomposed into three sub-problems, and then the semi-positive relaxation technology is used to convert the sub-problems into convex optimization problems, and finally the CVX toolbox is used for alternating optimization solution, which effectively reduces the complexity of the problem and improves the calculation efficiency.

Description

Technical Field

[0001] The present invention relates to a beamforming technology, and in particular to a beamforming method for a NOMA-ISAC (Non-Orthogonal Multiple Access; Integrated Sensing and Communication) system assisted by a RIS (Reconfigurable Intelligent Surface) for preventing internal and external eavesdropping. The beamforming method is applicable to scenarios where internal and external eavesdroppers exist. The method aims to minimize the communication signal power of legitimate users, taking into account the unknown channel state information (CSI) of external eavesdroppers. Under the constraints of ensuring the communication rate of legitimate users, the internal eavesdropping rate, radar perception performance, and NOMA decoding order, the beamforming vector corresponding to the communication signal of the legitimate user, the covariance matrix of the radar signal transmitted by the base station, the phase shift matrix of the RIS, and the scale factor of the ideal beam pattern of the base station are jointly optimized to achieve secure communication and radar perception functions of the system. Background Art

[0002] Sixth-generation (6G) networks are expected to revolutionize emerging applications such as smart connected vehicles, smart cities, intelligent manufacturing, and environmental monitoring. These applications place extremely high demands on the wireless connectivity and perception capabilities of 6G networks, particularly in terms of accuracy and reliability. Within the broader 6G vision, perception is widely considered to play a more crucial role than ever before. Against this backdrop, ISAC (Integrated Sensing and Communication) technology has garnered significant attention from academia, industry, and standardization bodies, and has been identified as a key enabling technology for 6G networks. ISAC technology enables the synergy between perception and communication functions by sharing software and hardware resources or information, effectively improving the system's spectrum efficiency, hardware efficiency, and information processing efficiency. This enables ISAC technology to facilitate high-throughput, ultra-reliable, and low-latency wireless communications, as well as ultra-precise, high-resolution, and flexible wireless perception.

[0003] While ISAC technology can enhance communication and perception capabilities by improving spectrum efficiency, hardware efficiency, and information processing efficiency, it is unlikely to address future network congestion as global demand for intelligent connectivity and large-scale data transmission continues to rise. NOMA technology, another revolutionary technology, significantly improves spectrum utilization and provides higher system capacity by allowing multiple users to communicate simultaneously on the same spectrum resource. Combining NOMA with ISAC technology can effectively address communication and perception issues in future congested networks. Furthermore, ISAC systems may encounter problems such as link obstruction and coverage blind spots in practical applications. RIS technology, which reconstructs the electromagnetic propagation environment and establishes virtual line-of-sight paths, offers a new approach to addressing these issues. RIS actively controls the wireless environment through programmable means, transforming the traditional design approach of passively adapting to the wireless environment to a new model of intelligently shaping the environment. This new model is driving the comprehensive development of 6G communication and perception capabilities.

[0004] The RIS-assisted NOMA-ISAC system significantly improves wireless communication and sensing capabilities, but security issues are becoming increasingly prominent in the context of the development of smart interconnection and smart cities. Threats such as information eavesdropping and interference attacks can seriously impact system reliability and data privacy, especially in the NOMA environment with shared spectrum resources, where information security is particularly vulnerable. To address these challenges, physical layer security (PLS) methods have emerged, leveraging the physical properties of signals to enhance transmission security. By carefully modulating the signal and designing interference, the system can effectively reduce the ability of an eavesdropper to receive information. Although some inventions have studied the security performance of the RIS-assisted NOMA-ISAC system, they only consider the single scenario of a purely external eavesdropper. However, in reality, some eavesdroppers may impersonate legitimate users to avoid exposing their own identity information. This potential internal eavesdropping also poses a significant threat to system security. To address this challenge, the present invention considers the security issues of the RIS-assisted NOMA-ISAC system in the presence of both internal and external eavesdroppers, thereby improving the system's security performance and enhancing protection against malicious attacks. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a beamforming method for a RIS-assisted NOMA-ISAC system that is resistant to internal and external eavesdropping. In the presence of both internal and external eavesdroppers, the method jointly optimizes the beamforming vector corresponding to the communication signal transmitted by the base station, the covariance matrix of the radar signal transmitted by the base station, the phase shift matrix of the RIS, and the scale factor of the ideal beam pattern of the base station, so as to ensure the system's secure communication and radar perception requirements under limited energy resources.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: a beamforming method of a RIS-assisted NOMA-ISAC system that is resistant to internal and external eavesdropping, characterized by comprising the following steps:

[0007] Step 1: Construct a RIS-assisted NOMA-ISAC system model. The model includes a base station with both radar and communication functions, a RIS for reflecting the base station's transmitted signals, radar targets that the base station perceives, legitimate users communicating with the base station, external eavesdroppers attempting to eavesdrop on legitimate users' communication signals, and legitimate users acting as potential internal eavesdroppers attempting to eavesdrop on other legitimate users' communication signals. A RIS controller is set between the RIS and the base station to jointly control the base station's beamforming and the RIS's phase shift.

[0008] Step 2: For legitimate users, the secure communication performance is measured by calculating the signal-to-interference-plus-noise ratio (SINR) of the legitimate user's decoded communication signals and those of other legitimate users. Furthermore, the communication rate of the legitimate user decoding its own communication signals and the internal eavesdropping rate of the legitimate user decoding the communication signals of other legitimate users are calculated. For external eavesdroppers, the secure communication performance is measured by calculating the SINR of the legitimate user's decoded communication signals and the external eavesdropping rate of the legitimate user's decoded communication signals. Radar perception performance is measured by calculating the mean square error between the base station's ideal beam pattern and the designed beam pattern.

[0009] Step 3: Under the constraints of the communication rate of the legitimate user decoding its own communication signal, the internal eavesdropping rate of the legitimate user decoding the communication signals of other legitimate users, and the mean square error between the ideal beam pattern of the base station and the designed beam pattern, the beamforming vector corresponding to the legitimate user's communication signal, the covariance matrix of the radar signal transmitted by the base station, the phase shift matrix of the RIS, and the scale factor of the base station's ideal beam pattern are jointly optimized to minimize the legitimate user's communication signal power, thus constructing an optimization problem.

[0010] Step 4: Decompose the optimization problem into three sub-problems. The first sub-problem is sub-problem 1, which is to optimize the scale factor of the base station's ideal beam pattern. The second sub-problem is sub-problem 2, which is to optimize the beamforming vector corresponding to the legitimate user's communication signal and the covariance matrix of the radar signal transmitted by the base station, given the scale factor of the base station's ideal beam pattern and the phase shift matrix of the RIS. The third sub-problem is sub-problem 3, which is to optimize the phase shift matrix of the RIS, given the beamforming vector corresponding to the legitimate user's communication signal and the covariance matrix of the radar signal transmitted by the base station.

[0011] Step 5: Calculate the first-order partial derivative of the constraint condition in subproblem 1 with respect to the scale factor variable and set it to zero, thereby obtaining the optimal solution for the scale factor of the ideal beam pattern of the base station.

[0012] Step 6: Use the alternating optimization algorithm to iteratively solve the convex problem transformed from subproblem 2 and the convex problem transformed from subproblem 3 to gradually approach the optimal solution of the optimization problem.

[0013] In step 1, the number of base stations is 1, and the transmitting end of the base station is equipped with a uniform linear array with half-wavelength spacing and N elements; the number of RIS is 1, and the RIS is equipped with a uniform planar array with half-wavelength spacing and M elements; the number of radar targets is L, and each is equipped with a single antenna; the number of legitimate users is I, and each is equipped with a single antenna; the number of external eavesdroppers is K, and each is equipped with a single antenna.

[0014] In step 2, the communication signal x of the j'th legal user is decoded by the i-th legal user. j' Signal-to-interference-noise ratio Expressed as Decode the communication signal x of the j'th legal user by the i-th legal user j' Achievable rate Expressed as When i=j' is the communication rate, when i≠j' is the internal eavesdropping rate, and the kth external eavesdropper decodes the communication signal x of the j'th legitimate user j' Signal-to-interference-noise ratio Expressed as The kth external eavesdropper decodes the communication signal x of the j'th legitimate user j' External eavesdropping rate Expressed as Among them, the decoding order of the communication signal of the legal user is the first legal user, the second legal user, ..., the Ith legal user, and there is an inequality Established, i, j'=1,2,…,I, “|·|” is the modulo operator, (·) H represents the Hermitian conjugate transpose operation, represents the channel coefficient from the base station to the i-th legal user, The dimension is N×1, represents the channel coefficient from RIS to the i-th legal user, The dimension is M×1, represents the channel coefficient from the base station to the RIS, The dimension is M×N, Θ represents the phase shift matrix of RIS, diag(·) represents the reconstruction of a vector into a diagonal matrix or the reconstruction of a diagonal matrix into a vector, e is a natural constant, j is an imaginary unit, ν mrepresents the phase shift of the mth element of RIS and is in the range [0,2π), m=1,2,…,M, And there is Established, And there is holds, β represents the imperfect SIC factor and is in the range [0,1), S r Indicates the radar signal transmitted by the base station The covariance matrix, S r The dimension is N×N, The receiving noise z of the legitimate user is U The covariance matrix of , k=1,2,…,K, represents the channel coefficient from the base station to the kth external eavesdropper, The dimension is N×1, represents the channel coefficient from RIS to the kth external eavesdropper, The dimension is M×1, w i Represents the communication signal x of the i-th legal user i The corresponding beamforming vector, w i The dimension is N×1, represents the receiving noise z of the external eavesdropper E The covariance matrix of .

[0015]

[0016] Where β0 represents the path loss at a reference distance of 1 meter, represents the distance from the base station to the i-th legal user, represents the distance from the base station to the kth external eavesdropper, d B,R Indicates the distance from the base station to the RIS, represents the distance from RIS to the i-th legal user, represents the distance from RIS to the kth external eavesdropper, represents the path loss index of the link from the base station to the i-th legal user, represents the path loss index of the link from the base station to the kth external eavesdropper, α B,R represents the path loss index of the link from the base station to the RIS, represents the path loss index of the link from RIS to the i-th legal user, represents the path loss exponent of the link from RIS to the kth external eavesdropper, κ B,R represents the Ricean factor of the link from the base station to the RIS, represents the Ricean factor of the link from RIS to the i-th legal user, the RIS-to-kth external eavesdropper link, and are both complex Gaussian distributed with mean 0 and covariance matrix I N corresponds to the NLOS part of corresponds to the NLOS part of I N denotes the N x N identity matrix, and are both element-wise independent and identically complex Gaussian distributed, corresponds to the NLOS part of corresponds to the NLOS part of corresponds to the NLOS part of corresponds to the LOS part of and corresponds to the LOS part of and corresponds to the LOS part of and denotes the base station-to-RIS azimuth of arrival, b denotes the base station-to-RIS elevation of arrival, b denotes the base station-to-RIS azimuth of departure, denotes the RIS-to-ith legitimate user azimuth of departure, i denotes the RIS-to-ith legitimate user elevation of departure, denotes the RIS-to-kth external eavesdropper azimuth of departure, k denotes the RIS-to-kth external eavesdropper elevation of departure, P (·, ·) denotes the RIS’s transmit steering vector, L (·) denotes the base station’s transmit steering vector, are both obtained by is the Kronecker product operation,

[0017] M x and M z correspond to the number of elements of the RIS along the x-axis and z-axis directions, respectively, and the equation M x x M z = M holds, and the superscript “T” denotes the transpose operation.​​​​​​

[0018] In step 2, the mean square error between the ideal beam pattern of the base station and the designed beam pattern is calculated as Expressed as Where η represents the scale factor of the ideal beam pattern, R s represents the covariance matrix of the base station's transmitted signal s, It means to find the mathematical expectation. S' represents the total number of discrete angles taken at intervals of 0.1° within the radar operating range of the base station [-90°, 90°), θ s' represents the s'th discrete angle at 0.1° intervals within the radar operating range of the base station [-90°, 90°), θ s' Substitute the definition expression of the ideal beam pattern of the base station into Get θ is the angle variable, θ l represents the angle of the lth radar target relative to the base station, Δ θ represents the beam width of the radar target area of ​​interest, θ s' Substitute into the definition expression of the base station's designed beam pattern Get a L (θ)=[1,e jπsin(θ) ,...,e jπ(N-1)sin(θ) ] T ,

[0019] In step 3, the optimization problem is described as:

[0020] Then replace the constraint C2 in the optimization problem with Among them, “||·||” is the binary norm operator, ε i represents the minimum achievable rate requirement of the i-th legal user, ε e represents the maximum internal eavesdropping rate of a legitimate user, satisfying ε i >ε e ,∈ represents the maximum beam pattern matching error, Tr(·) represents the trace of the matrix, p max Indicates the maximum transmit power of the base station.

[0021] In step 5, the constraint condition Taking the first-order partial derivative with respect to the variable η and setting it to zero, we obtain: Then solve this equation to get the optimal solution η * ,

[0022] The specific process of step 6 is as follows:

[0023] Step 6.1: Let q represent the number of iterations, and the initial value of q is 0; define definition

[0024] Step 6.2: Initialize w i 、S r and Let w i 、S r and The initial value of and Then there is Calculate the initial power consumption J (0) ,

[0025] Step 6.3: Let q = q + 1, where “=” is the assignment symbol;

[0026] Step 6.4: In the qth iteration, given η * and Use the CVX toolbox to solve the convex problem transformed from subproblem 2 and S r Their respective solutions are recorded as and Among them, when q=1 for When q>1 Indicates the result obtained during the q-1th iteration The solution;

[0027] Step 6.5: In the qth iteration, given and Use the CVX toolbox to solve the convex problem transformed from subproblem 3 The solution is denoted as

[0028] Step 6.6: If The rank of is one, then the eigenvalue decomposition is used to obtain w in the qth iteration process i Solution Otherwise, use Gaussian randomization method to get w i Approximate solution of Likewise, if The rank of is one, then the eigenvalue decomposition is used to obtain the qth iteration process Solution Otherwise, the Gaussian randomization method is used to obtain Approximate solution of

[0029] Step 6.7: During the qth iteration, calculate the power consumption J during the qth iteration (q) ,

[0030] Step 6.8: If the iteration tolerance abs(J (q) -J (q-1) ) is less than the set threshold Or the number of iterations reaches the set maximum number Q, the iteration stops and the output and Otherwise, execute the process from step 6.3 to step 6.7 again, where abs(·) is the absolute value function, and when q=1, J (q-1) For J (0) , q>1 when J (q-1) It represents the power consumption during the q-1th iteration process.

[0031] In step 6.4, the semi-positive definite relaxation technique is used to transform subproblem 2 into a convex problem. The specific process is as follows:

[0032] Step 6.4.1: Define intermediate variables Combined with get and Then ignore the rank-one condition And η * Substituting this into subproblem 2, we get: Among them, rank(·) means finding the rank of the matrix,

[0033] Step 6.4.2: Transform the constraint C1 in Equation 1 into C1', C1': Transform the constraint C2 in Equation 1 into C2', C2': Then rewrite Equation 1 as: Equation 2 is the convex problem transformed from sub-problem 2.

[0034] In step 6.5, the semi-positive definite relaxation technique is used to transform subproblem 3 into a convex problem. The specific process is as follows:

[0035] Step 6.5.1: Define intermediate variables Combined with Ignore the rank-one condition Rewrite subproblem 3 as: in, rank(·) means finding the rank of the matrix, find means finding a feasible solution, 1 (M+1)×1 Represents a vector of all 1s with a dimension of (M+1)×1;

[0036] Step 6.5.2: Transform the constraint C1 in Equation 3 into C1”, C1”: , transform the constraint C2 in Equation 3 into C2”, C2”: Then rewrite Equation 3 as:

[0037]

[0038] Step 6.5.3: By introducing non-negative auxiliary variables {μ i ,ψ i,j' ,λ i,j'},i,j'=1,2,…,I, Equation 4 is treated as a convex problem with an explicit objective function, which is described as:

[0039]

[0040] stC1: C2:

[0041] C3:

[0042] C4:

[0043] C5:

[0044] C6: S r ≥0

[0045] Compared with the prior art, the advantages of the present invention are:

[0046] 1) The method of the present invention introduces RIS into the secure NOMA-ISAC system, and by jointly optimizing the phase shift of RIS and the transmit beam of the base station, the security performance and perception capability of the system are greatly improved. Specifically, by linking with RIS, the base station can achieve more precise beamforming to meet the communication needs of multiple users, especially in high user density and multi-path propagation environments. This efficient use of resources not only reduces signal interference, but also improves the data transmission rate, thereby achieving a higher user experience. In addition, the system's intelligent adjustment capability enables it to adapt to different network environments and usage scenarios, enhancing the system's adaptability and flexibility. This optimized balance between security, perception, and resource utilization makes the method of the present invention have important application prospects in modern wireless communications.

[0047] 2) The method of the present invention takes into account the common reality of the coexistence of internal and external eavesdroppers within the system. By dynamically adjusting the phase shift of the RIS, the system can redirect signal propagation, thereby enhancing the signal strength received by legitimate users while suppressing the signal strength received by other legitimate users. Furthermore, considering the real-world scenario where an external eavesdropper is an illegal node in the system and its CSI cannot be obtained by the base station, the method of the present invention reuses radar signals as AN signals, effectively countering attacks from external eavesdroppers, significantly reducing system complexity and improving resource utilization. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a flowchart of the overall implementation of the method of the present invention;

[0049] Figure 2 A simple diagram of the RIS-assisted secure NOMA-ISAC system model;

[0050] Figure 3 A comparison curve of changes in the secure communication rate of legitimate users when the maximum transmission power of the base station changes between the method of the present invention and the non-RIS method used for comparison;

[0051] Figure 4 The figure is a comparison curve of the changes in the secure communication rate of legitimate users between the method of the present invention and the non-RIS method used for comparison when the number of external eavesdroppers changes. DETAILED DESCRIPTION

[0052] The present invention will be described in further detail below with reference to the accompanying drawings and embodiments.

[0053] The present invention proposes a beamforming method for a RIS-assisted NOMA-ISAC system that is resistant to internal and external eavesdropping. In the system, legitimate users conducting legitimate communications with base stations will not only be eavesdropped by external eavesdroppers who are illegal nodes of the system, but also by other legitimate users who are internal eavesdroppers. The radar target is illuminated by the communication and perception signals transmitted by the base station. The legitimate users (internal eavesdroppers) and external eavesdroppers not only receive the communication and perception signals transmitted from the base station, but also receive the signals reflected from the RIS. Radar perception and secure communication requirements are achieved without consuming additional power and under the premise that the total power of the system is limited. Since the CSI of the external eavesdropper who is an illegal node of the system is unknown, the radar signal transmitted by the base station is considered to be an artificial noise (AN) signal and the AN signal power is maximized to interfere with the external eavesdropper. The goal of the method of the present invention is to minimize the power of the legitimate signal of the system while satisfying the constraints of basic secure communication, radar perception performance and NOMA decoding order. Since the optimization variables in the established optimization problem are coupled with each other and there are non-convex constraints, the optimization problem is difficult to solve directly. First, the original problem is decomposed into three sub-problems, and then the semi-definite relaxation technique is used to transform the sub-problems into convex problems. Finally, the optimal solution of the original problem is gradually approached by alternately optimizing the sub-problems.

[0054] The present invention provides a beamforming method for a RIS-assisted NOMA-ISAC system that is resistant to internal and external eavesdropping. The overall implementation flow chart is as follows: Figure 1 As shown, it includes the following steps:

[0055] Step 1: Build a RIS-assisted NOMA-ISAC system model, such as Figure 2 As shown in the figure, the model consists of a base station with both radar and communication functions, a RIS (Remotely Identifier) ​​for reflecting the base station's transmitted signals, radar targets that the base station perceives, legitimate users communicating with the base station, and external eavesdroppers attempting to eavesdrop on legitimate users' communications. Legitimate users also act as potential internal eavesdroppers, attempting to eavesdrop on other legitimate users' communications. A RIS controller is located between the RIS and the base station, jointly controlling the base station's beamforming and the RIS's phase shift. In this system model, legitimate users can act as potential internal eavesdroppers, eavesdropping on communications between other legitimate users. They can also become targets of external eavesdroppers attempting to eavesdrop on legitimate users' communications. The base station utilizes the auxiliary functions of the RIS to effectively and securely communicate with legitimate users and detect radar targets.

[0056] Specifically, there is one base station, and the base station's transmitter is equipped with a uniform linear array (ULA) with half-wavelength spacing and N elements, that is, there are N antennas; there is one RIS, and the RIS is equipped with a uniform planar array (URA) with half-wavelength spacing and M elements, that is, there are M reflective elements; there are L radar targets, each equipped with a single antenna; there are I legal users, each equipped with a single antenna, and the i-th legal user is denoted as U i , i=1,2,…,I; the number of external eavesdroppers is K and each is equipped with a single antenna, and the kth external eavesdropper is denoted as E k , k=1,2,…,K; Since the base station's transmission signal reaches the legitimate user and the external eavesdropper through the direct link and the RIS reflection link, the received signal of the i-th legitimate user is Expressed as The received signal of the kth external eavesdropper Expressed as represents the receiving noise of the i-th legal user, In this embodiment, N=8, M=30, L=3, I=2, and K=5.

[0057] Step 2: For legitimate users, the secure communication performance is measured by calculating the signal-to-interference-plus-noise ratio (SINR) of the legitimate user decoding its own communication signal and that of other legitimate users, and then calculating the communication rate of the legitimate user decoding its own communication signal, as well as the internal eavesdropping rate of the legitimate user decoding the communication signal of other legitimate users. For external eavesdroppers, the secure communication performance is measured by calculating the SINR of the communication signal decoded by the external eavesdropper, and then calculating the external eavesdropping rate of the communication signal decoded by the external eavesdropper. The radar perception performance is measured by calculating the mean square error between the ideal beam pattern of the base station and the designed beam pattern.

[0058] Specifically, the communication signal x of the j'th legal user is decoded by the i-th legal user j' Signal-to-interference-noise ratio Expressed as Decode the communication signal x of the j'th legal user by the i-th legal user j' Achievable rate Expressed as When i=j' is the communication rate, when i≠j' is the internal eavesdropping rate, and the kth external eavesdropper decodes the communication signal x of the j'th legitimate user j' Signal-to-interference-noise ratio denotes The kth external eavesdropper decodes the communication signal x j' of the j'th legitimate user denotes where for the legitimate users, they can decode their own communication signals by using Successive Interference Cancellation (SIC) technique, in order to reduce the impact of interference, the radar signals are decoded first, then the communication signals are decoded according to their communication service quality, without loss of generality, assuming the decoding order of the communication signals of the legitimate users is the 1st legitimate user, the 2nd legitimate user, …, the Ith legitimate user, then the inequality holds, for the external eavesdroppers, they have less prior knowledge of the legitimate transmissions, thus it is difficult for them to use SIC technique to cancel the interference, i,j' = 1,2, …, I, “|·|” is the modulo operator, (·) H denotes the Hermitian conjugate transpose operation, is defined as denotes the channel coefficient from the base station to the ith legitimate user, has a dimension of N x 1, denotes the channel coefficient from the RIS to the ith legitimate user, has a dimension of M x 1, denotes the channel coefficient from the base station to the RIS, has a dimension of M x N, Θ denotes the phase shift matrix of the RIS, diag(·) denotes reconstructing a vector into a diagonal matrix or reconstructing a diagonal matrix into a vector, e is a natural constant, e = 2.71…, j is the imaginary unit, v m denotes the phase shift of the mth element of the RIS, and is in the range of [0, 2π), m = 1,2, …, M, w j' denotes the communication signal x j' of the j'th legitimate user, corresponds to the beamforming vector, and has holds, w j” denotes the communication signal x j” of the j'th legitimate user, corresponds to the beamforming vector, and has holds, β denotes the imperfect SIC factor and is in the range of [0, 1), in this specific embodiment, β = 0.1, S r denotes the radar signal transmitted by the base station, has a mean of 0, The dimension is N×1, S r The dimension is N×N, The receiving noise z of the legitimate user is U The covariance matrix, z U The mean of is 0, that is In this specific embodiment, k=1,2,…,K, represents the channel coefficient from the base station to the kth external eavesdropper, The dimension is N×1, represents the channel coefficient from RIS to the kth external eavesdropper, The dimension is M×1, w i Represents the communication signal x of the i-th legal user i The corresponding beamforming vector, w i The dimension is N×1, represents the receiving noise z of the external eavesdropper E The covariance matrix, z E The mean of is 0, that is In this specific embodiment,

[0059] Consider a quasi-static flat fading channel, which remains constant within a channel coherence block but varies between blocks. RIS is commonly used to provide a one-hop line-of-sight link from a base station to a legitimate user when a direct line-of-sight link between the base station and the legitimate user does not exist. Without loss of generality, assume that the links from the base station to the legitimate user and the external eavesdropper are modeled as Rayleigh channels, and the links through the RIS are modeled as Ricean channels. Their channel coefficients can be expressed as:

[0060] Where β0 represents the path loss at a reference distance of 1 meter, and here β0 = -30dB. represents the distance from the base station to the i-th legal user, represents the distance from the base station to the kth external eavesdropper, d B,R Indicates the distance from the base station to the RIS, represents the distance from RIS to the i-th legal user, represents the distance from RIS to the kth external eavesdropper, represents the path loss index of the link from the base station to the i-th legal user, represents the path loss index of the link from the base station to the kth external eavesdropper, α B,R represents the path loss index of the link from the base station to the RIS, represents the path loss index of the link from RIS to the i-th legal user, represents the path loss index of the link from RIS to the kth external eavesdropper, where κ B,R represents the Ricean factor of the link from the base station to the RIS, represents the Ricean factor of the link from RIS to the i-th legal user, represents the Ricean factor of the link from RIS to the kth external eavesdropper, where and All of them have a mean of 0 and a covariance matrix of I N The standard complex Gaussian distribution of correspond The non-line-of-sight portion of correspond The non-line-of-sight portion, I N represents the identity matrix of dimension N×N, that is and are all element-independent and obey the same standard complex Gaussian distribution, correspond The non-line-of-sight portion of correspond The non-line-of-sight portion of correspond The non-line-of-sight portion of correspond The sight distance part, and there is correspond The sight distance part, and there is correspond The sight distance part, and there is represents the arrival azimuth from the base station to the RIS, φ b represents the arrival elevation angle from the base station to the RIS, θ b represents the departure azimuth from the base station to the RIS, represents the departure azimuth from RIS to the i-th legal user, φ i represents the departure pitch angle from RIS to the i-th legal user, represents the departure azimuth from RIS to the kth external eavesdropper, φ k represents the departure pitch angle from RIS to the kth external eavesdropper, a P (·,·) represents the transmission steering vector of RIS, a L (·) represents the transmission steering vector of the base station, All passed get, is the Kronecker product operation,

[0061] M x and M z Correspondingly represents the number of elements in the RIS along the x-axis and z-axis directions, and there is an equation M x ×M z =M is ​​established, here we take M x =6,M z =5, the superscript “T” indicates the transpose operation.

[0062] Specifically, the mean square error between the ideal beam pattern of the base station and the designed beam pattern is calculated Expressed as Where η represents the scale factor of the ideal beam pattern, R s represents the covariance matrix of the base station's transmitted signal s, It means to find the mathematical expectation. S' represents the total number of discrete angles taken at intervals of 0.1° within the radar operating range of the base station [-90°, 90°). In this specific embodiment, S'=1801, θ s' represents the s'th discrete angle at 0.1° intervals within the radar operating range of the base station [-90°, 90°), θ s' Substitute the definition expression of the ideal beam pattern of the base station into Get θ is the angle variable, θ l represents the angle of the lth radar target relative to the base station. In this specific embodiment, θ1 = -40°, θ2 = 0°, θ3 = 40°, and Δ θ Indicates the beam width of the radar target area of ​​interest. In this specific embodiment, Δ θ =20°,θ s' Substitute into the definition expression of the base station's designed beam pattern Get a L (θ)=[1,e j πsin(θ) ,...,e jπ(N-1)sin(θ) ] T ,

[0063] The beam pattern matching error (BME), the mean square error between the base station's ideal beam pattern and the designed beam pattern (i.e., the transmitted beam pattern), is used as a key performance indicator for evaluating radar perception. It characterizes the degree of match between the ideal and designed beam patterns, ensuring that signal power is concentrated in the main lobe, thereby suppressing echo interference from undesired directions and achieving better radar perception performance. At the same time, the beam pattern matching error allows for flexible selection of the beam pattern main lobe width, which can effectively account for the uncertainty of radar target angles.

[0064] Step 3: Since the communication between the base station, RIS and the legitimate user is cooperative, it is reasonable to assume that the CSI between them is known. In contrast, considering that the ISAC system and the external eavesdropper are uncooperative, the CSI from the base station and RIS to the external eavesdropper is often not accurately obtained. To solve this problem, the present invention considers the radar signal emitted by the base station. It does not contain communication information, so it can be used as an artificial noise (AN) signal to interfere with external eavesdroppers. Since the total transmission power of the base station is the power of the communication signals of all legitimate users and the radar signal The sum of the powers of all legitimate users is the sum of their powers. Therefore, the smaller the power of all legitimate users' communication signals, the greater the AN signal power. Therefore, under the constraints of the communication rate at which legitimate users decode their own communication signals, the internal eavesdropping rate at which legitimate users decode other legitimate users' communication signals, and the mean square error between the base station's ideal and designed beam patterns, the present invention jointly optimizes the beamforming vectors corresponding to the legitimate users' communication signals, the covariance matrix of the radar signal transmitted by the base station, the phase shift matrix of the RIS, and the scale factor of the base station's ideal beam pattern to minimize the legitimate users' communication signal power and construct an optimization problem.

[0065] Specifically, the optimization problem is described as:

[0066] Then replace the constraint C2 in the optimization problem with Among them, min is the minimum function, st means "subject to...", "||·||" is the two-norm operator symbol, ε i represents the minimum achievable rate requirement of the i-th legal user, ε e Indicates the maximum internal eavesdropping rate of legitimate users. In order to achieve secure communication, ε must be satisfied. i >ε e ,∈ represents the maximum beam pattern matching error, Tr(·) represents the trace of the matrix, p max Indicates the maximum transmission power of the base station. In this specific embodiment, ε1 = 4 bps / Hz, ε2 = 5 bps / Hz, and ε e =0.1bps / Hz,∈=0.01,pmax =15dBm, constraint C1 ensures the minimum communication rate requirement of the legitimate user, constraint C2 ensures the maximum internal eavesdropping rate requirement of the legitimate user, constraint C3 ensures that the mean square error between the ideal beam pattern and the designed beam pattern does not exceed ∈, that is, the radar perception performance is guaranteed, and constraint C4 ensures that the total transmission power of the base station does not exceed p max , constraint C5 ensures the NOMA decoding order requirement, and constraint C6 ensures the covariance matrix S of the radar signal r is semi-positive definite. Under the constraints C1 and C2, all channels are considered to meet the requirements of communication rate and internal eavesdropping rate. To facilitate the solution, we only focus on some channels and revisit the case of i≠j'. Considering that the imperfect SIC factor β is usually small, in order to effectively protect the information of the j'th legitimate user from the attack of the internal eavesdropper, we focus on destroying (increasing) the i≠j' It is reformulated as It is not difficult to see that there are holds, and constraint C2 is now replaced by

[0067] Step 4: Decompose the optimization problem into three sub-problems. The first sub-problem is sub-problem 1, which is to optimize the scale factor of the ideal beam pattern of the base station. The second sub-problem is sub-problem 2, which is to optimize the beamforming vector corresponding to the communication signal of the legitimate user and the covariance matrix of the radar signal transmitted by the base station given the scale factor of the ideal beam pattern of the base station and the phase shift matrix of the RIS. The third sub-problem is sub-problem 3, which is to optimize the phase shift matrix of the RIS given the beamforming vector corresponding to the communication signal of the legitimate user and the covariance matrix of the radar signal transmitted by the base station.

[0068] Step 5: Calculate the first-order partial derivative of the constraint in subproblem 1 with respect to the scale factor variable and set it to zero, and then solve for the optimal solution of the scale factor of the ideal beam pattern of the base station.

[0069] Further limitation: since the optimization scale factor η only exists in constraint C3, and the constraint condition is a convex quadratic function, the constraint condition Taking the first-order partial derivative with respect to the variable η and setting it to zero, we obtain: Then solve this equation to get the optimal solution of η * ,

[0070] Step 6: Use the alternating optimization algorithm to iteratively solve the convex problem transformed from subproblem 2 and the convex problem transformed from subproblem 3 to gradually approach the optimal solution of the optimization problem.

[0071] Further defining, the specific process of step 6 is:

[0072] Step 6.1: Let q represent the number of iterations, and the initial value of q is 0; define definition

[0073] Step 6.2: Initialize w i 、S r and Let w i 、S r and The initial value of and Then there is Calculate the initial power consumption J (0) ,

[0074] Step 6.3: Let q=q+1, where “=” is the assignment symbol.

[0075] Step 6.4: In the qth iteration, given η * and Use the CVX toolbox to solve the convex problem transformed from subproblem 2 and S r Their respective solutions are recorded as and Among them, when q=1 for When q>1 Indicates the result obtained during the q-1th iteration The solution.

[0076] In this specific embodiment, in step 6.4, since subproblem 2 is non-convex, the semidefinite relaxation (SDR) technique is used to transform subproblem 2 into a convex problem. The specific process is as follows:

[0077] Step 6.4.1: Define intermediate variables Combined with get and Then ignore the rank-one condition And η * Substituting this into subproblem 2, we get: Among them, rank(·) means finding the rank of the matrix,

[0078] Step 6.4.2: Since the constraints C1 and C2 in Equation 1 are still non-convex, the constraint C1 in Equation 1 can be transformed into C1', C1': Transform the constraint C2 in Equation 1 into C2', C2': Then rewrite Equation 1 as: Equation 2 is the convex problem transformed from subproblem 2. Since the objective function and constraints of Equation 2 are both convex, it is a convex problem and can be solved using the CVX toolbox.

[0079] Step 6.5: In the qth iteration, given and Use the CVX toolbox to solve the convex problem transformed from subproblem 3 The solution is denoted as

[0080] In this specific embodiment, in step 6.5, since subproblem 3 is non-convex, the semidefinite relaxation (SDR) technique is used to transform subproblem 3 into a convex problem. The specific process is as follows:

[0081] Step 6.5.1: Define intermediate variables Combined with Ignore the rank-one condition Rewrite subproblem 3 as: in, rank(·) means finding the rank of the matrix, find means finding a feasible solution, 1 (M+1)×1 Represents a vector of all 1s with dimension (M+1)×1.

[0082] Step 6.5.2: Since constraints C1 and C2 in Equation 3 are still non-convex, constraint C1 in Equation 3 can be transformed into C1”, C1”: , transform the constraint C2 in Equation 3 into C2”, C2”: Then rewrite Equation 3 as:

[0083] Step 6.5.3: Since Equation 4 is a feasible solution problem without an objective function, in order to obtain a better converged solution, a non-negative auxiliary variable {μ i ,ψ i,j' ,λ i,j'},i,j'=1,2,…,I, Equation 4 is treated as a convex problem with an explicit objective function, which is described as:

[0084] stC1: C2:

[0085] C3:

[0086] C4:

[0087] C5:

[0088] C6: S r ≥0

[0089] , this problem is still a convex problem and can be solved using the CVX toolbox. max is the maximum value function.

[0090] Step 6.6: If The rank of is one, then the eigenvalue decomposition is used to obtain w in the qth iteration process i Solution Otherwise, use Gaussian randomization method to get w i Approximate solution of Likewise, if The rank of is one, then the eigenvalue decomposition is used to obtain the qth iteration process Solution Otherwise, the Gaussian randomization method is used to obtain Approximate solution of

[0091] Step 6.7: During the qth iteration, calculate the power consumption J during the qth iteration (q) ,

[0092]

[0093] Step 6.8: If the iteration tolerance abs(J (q) -J (q-1) ) is less than the set threshold Or the number of iterations reaches the set maximum number Q, the iteration stops and the output and Otherwise, execute the process from step 6.3 to step 6.7 again, where abs(·) is the absolute value function, and when q=1, J (q-1) For J (0) , q>1 when J (q-1) Indicates the power consumption during the q-1th iteration process. In this specific embodiment, Q=30.

[0094] The feasibility and effectiveness of the method of the present invention are further illustrated by the following simulation.

[0095] The three-dimensional coordinates of the base station are (5, 0, 10) meters, the three-dimensional coordinates of the first legal user are (8, 40, 0) meters, the three-dimensional coordinates of the second legal user are (3, 60, 0) meters, the three-dimensional coordinates of the RIS are (0, 50, 6) meters, and the external eavesdroppers are randomly distributed within a range with a radius of 20 meters centered at (4, 40, 0) meters.

[0096] Figure 3 The comparative curves of the changes in the secure communication rate of legitimate users between the method of the present invention and the non-RIS method used for comparison when the maximum transmission power of the base station changes are shown. Figure 3 In the RIS-free approach, RIS is not deployed in the system under consideration, so the legitimate users (internal eavesdroppers) and external eavesdroppers in the system only receive the communication and perception signals transmitted from the base station. Figure 3 In the example, the j'th legal user U j' Secure communication rate The calculation formula is in, Max is the maximum value function. Figure 3 It can be seen that as the maximum transmission power of the base station p max As p increases, the secure communication rate of legitimate users increases and approaches the communication rate threshold of legitimate users. This phenomenon can be attributed to the following: max When the AN signal power increases, the power of the AN signal used to interfere with external eavesdroppers is also enhanced, which increases the system's ability to resist external eavesdroppers. At the same time, the system's internal eavesdropping rate is strictly guaranteed to be below a very small threshold in the established optimization problem, resulting in an upward trend in the secure communication rate of legitimate users. When the AN signal power is large enough, the system is minimally affected by internal and external eavesdropping, resulting in the secure communication rate of legitimate users approaching the communication rate threshold. In contrast, the RIS-free method lacks the gain brought to the system by RIS, and its performance in p is better than that in p. max The secure communication rate when the RIS is smaller is significantly lower than that of the method of the present invention. This is because, without RIS, the power used by legitimate users for communication increases, which indirectly reduces the AN signal power used to counter external eavesdropping. This demonstrates that the method of the present invention demonstrates significant advantages and effectiveness in improving the overall security of the communication system, effectively ensuring the confidentiality and integrity of data transmission.

[0097] Figure 4 The comparison curves of the secure communication rate of legitimate users between the method of the present invention and the non-RIS method used for comparison are shown as the number of external eavesdroppers changes. Figure 4As can be seen from the figure, the secure communication rate of legitimate users using the non-RIS method decreases as the number of external eavesdroppers increases. However, the secure communication rate of legitimate users using the proposed method remains almost constant and significantly higher than that of the comparison method. This is because as the number of external eavesdroppers increases, external eavesdropping poses a greater threat to the system's secure communications. The introduction of RIS effectively enhances the system's ability to resist eavesdropping. Specifically, the proposed method, by comprehensively considering radar target perception and communication security, not only meets perception requirements when allocating base station power, but also actively utilizes radar signals as artificial noise to suppress eavesdropping. Furthermore, the introduction of RIS further exploits the system's secure communication and perception capabilities. This strategy significantly increases the secure communication rate of legitimate users, demonstrating the effectiveness of the proposed method in ensuring system communication security.

Claims

1. A beamforming method for a RIS-assisted NOMA-ISAC system that is resistant to internal and external eavesdropping, characterized in that The following steps are involved: Step 1: Construct a RIS-assisted NOMA-ISAC system model. The model includes a base station with both radar and communication functions, a RIS for reflecting the base station's transmitted signals, radar targets that the base station perceives, legitimate users communicating with the base station, external eavesdroppers attempting to eavesdrop on legitimate users' communication signals, and legitimate users acting as potential internal eavesdroppers attempting to eavesdrop on other legitimate users' communication signals. A RIS controller is set between the RIS and the base station to jointly control the base station's beamforming and the RIS's phase shift. Step 2: For legitimate users, the secure communication performance is measured by calculating the signal-to-interference-plus-noise ratio (SINR) of the legitimate user's decoded communication signals and those of other legitimate users. Furthermore, the communication rate of the legitimate user decoding its own communication signals and the internal eavesdropping rate of the legitimate user decoding the communication signals of other legitimate users are calculated. For external eavesdroppers, the secure communication performance is measured by calculating the SINR of the legitimate user's decoded communication signals and the external eavesdropping rate of the legitimate user's decoded communication signals. Radar perception performance is measured by calculating the mean square error between the base station's ideal beam pattern and the designed beam pattern. Step 3: Under the constraints of the communication rate of the legitimate user decoding its own communication signal, the internal eavesdropping rate of the legitimate user decoding the communication signals of other legitimate users, and the mean square error between the ideal beam pattern of the base station and the designed beam pattern, the beamforming vector corresponding to the legitimate user's communication signal, the covariance matrix of the radar signal transmitted by the base station, the phase shift matrix of the RIS, and the scale factor of the base station's ideal beam pattern are jointly optimized to minimize the legitimate user's communication signal power, thus constructing an optimization problem. Step 4: Decompose the optimization problem into three sub-problems. The first sub-problem is sub-problem 1, which is to optimize the scale factor of the base station's ideal beam pattern. The second sub-problem is sub-problem 2, which is to optimize the beamforming vector corresponding to the legitimate user's communication signal and the covariance matrix of the radar signal transmitted by the base station, given the scale factor of the base station's ideal beam pattern and the phase shift matrix of the RIS. The third sub-problem is sub-problem 3, which is to optimize the phase shift matrix of the RIS, given the beamforming vector corresponding to the legitimate user's communication signal and the covariance matrix of the radar signal transmitted by the base station. Step 5: Calculate the first-order partial derivative of the constraint condition in subproblem 1 with respect to the scale factor variable and set it to zero, thereby obtaining the optimal solution for the scale factor of the ideal beam pattern of the base station. Step 6: Use the alternating optimization algorithm to iteratively solve the convex problem transformed from subproblem 2 and the convex problem transformed from subproblem 3 to gradually approach the optimal solution of the optimization problem.

2. The beamforming method of the RIS-assisted NOMA-ISAC system for preventing internal and external eavesdropping according to claim 1 is characterized in that In step 1, the number of base stations is 1, the transmitting end of the base station is equipped with a uniform linear array with half-wavelength spacing, and the number of elements is N; the number of RIS is 1, the RIS is equipped with a uniform planar array with half-wavelength spacing, and the number of elements is M; The number of radar targets is L and each is equipped with a single antenna; the number of legitimate users is I and each is equipped with a single antenna; the number of external eavesdroppers is K and each is equipped with a single antenna.

3. The beamforming method of the RIS-assisted NOMA-ISAC system for preventing internal and external eavesdropping according to claim 2 is characterized in that In step 2, the communication signal x of the j'th legal user is decoded by the i-th legal user. j' Signal-to-interference-noise ratio Expressed as Decode the communication signal x of the j'th legal user by the i-th legal user j' Achievable rate Expressed as When i=j' is the communication rate, when i≠j' is the internal eavesdropping rate, and the kth external eavesdropper decodes the communication signal x of the j'th legitimate user j' Signal-to-interference-noise ratio Expressed as The kth external eavesdropper decodes the communication signal x of the j'th legitimate user j' External eavesdropping rate Expressed as Among them, the decoding order of the communication signal of the legal user is the first legal user, the second legal user, ..., the Ith legal user, and there is an inequality Established, i, j'=1,2,…,I, "|·|" is the modulo operator, (·) H represents the Hermitian conjugate transpose operation, represents the channel coefficient from the base station to the i-th legal user, The dimension is N×1, represents the channel coefficient from RIS to the i-th legal user, The dimension is M×1, represents the channel coefficient from the base station to the RIS, The dimension is M×N, Θ represents the phase shift matrix of RIS, diag(·) represents the reconstruction of a vector into a diagonal matrix or the reconstruction of a diagonal matrix into a vector, e is a natural constant, j is an imaginary unit, ν m represents the phase shift of the mth element of RIS and is in the range [0,2π), m=1,2,…,M, And there is Established, And there is holds, β represents the imperfect SIC factor and is in the range [0,1), S r Indicates the radar signal transmitted by the base station The covariance matrix, S r The dimension is N×N, The receiving noise z of the legitimate user is U The covariance matrix of , k=1,2,…,K, represents the channel coefficient from the base station to the kth external eavesdropper, The dimension is N×1, represents the channel coefficient from RIS to the kth external eavesdropper, The dimension is M×1, w i Represents the communication signal x of the i-th legal user i The corresponding beamforming vector, w i The dimension is N×1, represents the receiving noise z of the external eavesdropper E The covariance matrix of .

4. The beamforming method of the RIS-assisted NOMA-ISAC system for preventing internal and external eavesdropping according to claim 3 is characterized in that Where β0 represents the path loss at a reference distance of 1 meter, represents the distance from the base station to the i-th legal user, represents the distance from the base station to the kth external eavesdropper, d B,R Indicates the distance from the base station to the RIS, represents the distance from RIS to the i-th legal user, represents the distance from RIS to the kth external eavesdropper, represents the path loss index of the link from the base station to the i-th legal user, represents the path loss index of the link from the base station to the kth external eavesdropper, α B,R represents the path loss index of the link from the base station to the RIS, represents the path loss index of the link from RIS to the i-th legal user, represents the path loss exponent of the link from RIS to the kth external eavesdropper, κ B,R represents the Ricean factor of the link from the base station to the RIS, represents the Ricean factor of the link from RIS to the i-th legal user, represents the Ricean factor of the link from RIS to the kth external eavesdropper, and All of them have a mean of 0 and a covariance matrix of I N The standard complex Gaussian distribution of correspond The non-line-of-sight portion of correspond The non-line-of-sight portion, I N represents the identity matrix of dimension N×N, and are all element-independent and obey the same standard complex Gaussian distribution, correspond The non-line-of-sight portion of correspond The non-line-of-sight portion of correspond The non-line-of-sight portion of correspond The sight distance part, and there is correspond The sight distance part, and there is correspond The sight distance part, and there is represents the arrival azimuth from the base station to the RIS, φ b represents the arrival elevation angle from the base station to the RIS, θ b represents the departure azimuth from the base station to the RIS, represents the departure azimuth from RIS to the i-th legal user, φ i represents the departure pitch angle from RIS to the i-th legal user, represents the departure azimuth from RIS to the kth external eavesdropper, φ k represents the departure pitch angle from RIS to the kth external eavesdropper, a P (·,·) represents the transmission steering vector of RIS, a L (·) represents the transmission steering vector of the base station, All passed get, is the Kronecker product operation, M x and M z Correspondingly represents the number of elements in the RIS along the x-axis and z-axis directions, and there is an equation M x ×M z =M holds true, and the superscript "T" indicates a transpose operation.

5. The beamforming method of the RIS-assisted NOMA-ISAC system for preventing internal and external eavesdropping according to claim 3 or 4 is characterized in that In step 2, the mean square error between the ideal beam pattern of the base station and the designed beam pattern is calculated as Expressed as Where η represents the scale factor of the ideal beam pattern, R s represents the covariance matrix of the base station's transmitted signal s, It means to find the mathematical expectation. S' represents the total number of discrete angles taken at intervals of 0.1° within the radar operating range of the base station [-90°, 90°), θ s' represents the s'th discrete angle at 0.1° intervals within the radar operating range of the base station [-90°, 90°), θ s' Substitute the definition expression of the ideal beam pattern of the base station into Get θ is the angle variable, Indicates the The angle of the radar target relative to the base station, Δ θ represents the beam width of the radar target area of ​​interest, θ s' Substitute into the definition expression of the base station's designed beam pattern Get a L (θ)=[1,e jπsin(θ) ,...,e jπ(N-1)sin(θ) ] T , 6. The beamforming method of the RIS-assisted NOMA-ISAC system for preventing internal and external eavesdropping according to claim 5 is characterized in that In step 3, the optimization problem is described as: Then replace the constraint C2 in the optimization problem with Among them, "||·||" is the binary norm operator, ε i represents the minimum achievable rate requirement of the i-th legal user, ε e represents the maximum internal eavesdropping rate of a legitimate user, satisfying ε i >ε e ,∈ represents the maximum beam pattern matching error, Tr(·) represents the trace of the matrix, p max Indicates the maximum transmit power of the base station.

7. The beamforming method of the RIS-assisted NOMA-ISAC system for preventing internal and external eavesdropping according to claim 6 is characterized in that In step 5, the constraint condition Taking the first-order partial derivative with respect to the variable η and setting it to zero, we obtain: Then solve this equation to get the optimal solution η * , 8. The beamforming method of the RIS-assisted NOMA-ISAC system for preventing internal and external eavesdropping according to claim 7 is characterized in that The specific process of step 6 is as follows: Step 6.1: Let q represent the number of iterations, and the initial value of q is 0; define definition Step 6.2: Initialize w i 、S r and Let w i 、S r and The initial value of and Then there is Calculate the initial power consumption J (0) , Step 6.3: Let q = q + 1, where "=" is the assignment symbol; Step 6.4: In the qth iteration, given η * and Use the CVX toolbox to solve the convex problem transformed from subproblem 2 and S r Their respective solutions are recorded as and Among them, when q=1 for When q>1 Indicates the result obtained during the q-1th iteration The solution; Step 6.5: In the qth iteration, given and Use the CVX toolbox to solve the convex problem transformed from subproblem 3 The solution is denoted as Step 6.6: If The rank of is one, then the eigenvalue decomposition is used to obtain w in the qth iteration process i Solution Otherwise, use Gaussian randomization method to get w i Approximate solution of Likewise, if The rank of is one, then the eigenvalue decomposition is used to obtain the qth iteration process Solution Otherwise, the Gaussian randomization method is used to obtain Approximate solution of Step 6.7: During the qth iteration, calculate the power consumption J during the qth iteration (q) , Step 6.8: If the iteration tolerance abs(J (q) -J (q-1) ) is less than the set threshold Or the number of iterations reaches the set maximum number Q, the iteration stops and the output and Otherwise, execute the process from step 6.3 to step 6.7 again, where abs(·) is the absolute value function, and when q=1, J (q-1) For J (0) , q>1 when J (q-1) It represents the power consumption during the q-1th iteration process.

9. The beamforming method of the RIS-assisted NOMA-ISAC system for preventing internal and external eavesdropping according to claim 8 is characterized in that In step 6.4, the semi-positive definite relaxation technique is used to transform subproblem 2 into a convex problem. The specific process is as follows: Step 6.4.1: Define intermediate variables Combined with get and Then ignore the rank-one condition And η * Substituting this into subproblem 2, we get: Among them, rank(·) means finding the rank of the matrix, Step 6.4.2: Transform the constraint C1 in Equation 1 into C1', C1': Transform the constraint C2 in Equation 1 into C2', C2': Then rewrite Equation 1 as: Equation 2 is the convex problem transformed from sub-problem 2.

10. The beamforming method of the RIS-assisted NOMA-ISAC system for preventing internal and external eavesdropping according to claim 8, characterized in that In step 6.5, the semi-positive definite relaxation technique is used to transform subproblem 3 into a convex problem. The specific process is as follows: Step 6.5.1: Define intermediate variables Combined with Ignore the rank-one condition Rewrite subproblem 3 as: in, rank(·) means finding the rank of the matrix, find means finding a feasible solution, 1 (M+1)×1 Represents a vector of all 1s with a dimension of (M+1)×1; Step 6.5.2: Transform the constraint C1 in Equation 3 into C1”, C1”: Transform the constraint C2 in Equation 3 into C2”, C2”: Then rewrite Equation 3 as: Step 6.5.3: By introducing non-negative auxiliary variables {μ i ,ψ i,j' ,λ i,j' },i,j'=1,2,…,I, Equation 4 is treated as a convex problem with an explicit objective function, which is described as: s.t.C1: C2: C3: C4: C5: C6: 。

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