Method for implementing secure communication by star-ris assisted movable antenna

Abstract

The application provides a method for realizing safe communication by STAR-RIS assisted movable antenna, and relates to the technical field of wireless communication. The method maximizes the safety and rate of the system by jointly optimizing the base station beam forming, the movable antenna position and the STAR-RIS coefficient matrix. Specifically, the method comprises the following steps: constructing a downlink MIMO system and establishing a joint optimization problem; using an alternating optimization framework to decompose the joint optimization problem into three sub-problems; using a particle swarm optimization algorithm, a weighted least mean square error method combined with a Majorization-Minimization algorithm to solve each sub-problem; and alternately performing relevant steps until the system safety and rate converge, to obtain the solution of the joint optimization problem. The application uses the above method, significantly improves the system safety communication performance, realizes full space coverage and accurate beam control, and has strong algorithm convergence and high solution efficiency, and is suitable for a downlink system with multiple users and multiple eavesdropping nodes.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, and in particular to a method for implementing secure communication by STAR-RIS assisted movable antenna. BACKGROUND

[0002] With the large-scale commercialization of the fifth generation mobile communication system (5G) and the continuous advancement of the research and development of the sixth generation mobile communication system (6G), wireless communication faces higher requirements in terms of transmission rate, connection density and reliability. In order to improve system capacity, the communication frequency band is gradually expanding to high frequency bands such as millimeter waves and terahertz. However, high frequency electromagnetic waves have poor penetration ability and are easily blocked by obstacles, resulting in limited coverage and unstable links, which seriously affect communication quality and user experience.

[0003] To improve the wireless propagation environment, reconfigurable intelligent surface (RIS) technology has emerged. RIS is composed of a large number of low-cost passive elements, and can reconfigure the channel response by intelligently controlling the phase, amplitude and other parameters of electromagnetic waves, thereby enhancing signal strength, expanding coverage and suppressing interference. However, traditional RIS can only reflect incident signals and cannot simultaneously transmit, and its control ability is limited to half space, which has obvious limitations in achieving global coverage and multi-user service.

[0004] To solve the above problems, simultaneously transmitting and reflecting RIS (STAR-RIS) is proposed. STAR-RIS can dynamically allocate the reflection and transmission energy of incident signals, realize continuous control of the full-space communication environment, and significantly improve the system degree of freedom and deployment flexibility. On the other hand, movable antenna (MA) technology can actively adapt to the channel space variation characteristics by mechanically adjusting the physical position of the antenna in the two-dimensional plane, further exploiting the spatial dimension gain and improving the system capacity and link reliability.

[0005] Although STAR-RIS and MA technologies have shown great potential, existing research has not fully explored the synergistic gain of the two in secure communication scenarios. Especially in a multi-user, multi-eavesdropping node downlink system, how to jointly optimize the base station beamforming, STAR-RIS coefficients and MA position configuration to systematically improve the secure communication rate is still an open and significant application value research problem. SUMMARY

[0006] The application aims to provide a method for implementing secure communication by STAR-RIS assisted movable antennas, which maximizes the security and rate of the system by jointly optimizing the base station beamforming, MA position and STAR-RIS coefficient matrix, and solves the problems of insufficient security and poor channel adaptability of the existing wireless communication system in a complex environment.

[0007] To achieve the above-mentioned purpose, the application provides a method for implementing secure communication by STAR-RIS assisted movable antennas, which comprises the following steps:

[0008] Step S1, constructing a downlink MIMO system, establishing a joint optimization problem containing base station beamforming vectors, all movable antenna positions and STAR-RIS coefficient matrixes, and taking maximizing the security and rate of the system as the target;

[0009] Step S2, decomposing the joint optimization problem into three sub-problems by using an alternating optimization framework, including a movable antenna position optimization sub-problem, a base station beamforming vector optimization sub-problem and a STAR-RIS coefficient matrix optimization sub-problem;

[0010] Step S3, solving the movable antenna position optimization sub-problem by using a particle swarm optimization algorithm;

[0011] Step S4, for the base station beamforming vector optimization sub-problem and the STAR-RIS coefficient matrix optimization sub-problem, reconstructing the problem by using a weighted least mean square error method, and applying a Majorization-Minimization algorithm to process the non-convex constraint, converting the sub-problems into second-order cone programming or quadratic programming problems and then solving them by using a convex optimization solver;

[0012] Step S5, alternately executing step S3 and step S4, updating the beamforming vectors, STAR-RIS coefficient matrixes, movable antenna positions and corresponding auxiliary variables, until the security and rate of the system converge, and obtaining the solution of the joint optimization problem.

[0013] Preferably, in step S1, the downlink MIMO system comprises a base station equipped with multiple movable antennas, a STAR-RIS and two legitimate users and two eavesdropping users distributed in the reflection area and the transmission area of the STAR-RIS.

[0014] Preferably, the channel from the base station to the STAR-RIS adopts a field response model, and the channel from the STAR-RIS to the user end is modeled as Rayleigh fading.

[0015] Preferably, in step S1, the joint optimization problem is as follows:

[0016]

[0017] wherein, Φk coefficient matrix representing the reflection or transmission elements of STAR-RIS, w k k beamforming vector of legitimate user U n k,s k max min s ε μ m,k m,k m,r m,t

[0018]

[0019]

[0020]

[0021]

[0022]

[0023] ​​​​​​​​​​​​​​​​​​​The particle position is continuously optimized by iterative updating until the termination condition is met, and finally the optimal particle position configuration corresponding to the optimal particle in the population is output as the solution to the sub-problem.

[0024] Preferably, the correction process uses a correction function [gamma(r)] u As follows:

[0025]

[0026] Wherein, [r] u The u-th component of the vector r, A represents the edge length of the movable antenna feasible movement region.

[0027] Preferably, the fitness function is as follows:

[0028]

[0029] Wherein, The fitness value of particle b in the i-th iteration, R k,s The security rate of the legitimate user U k , and eta represents the adaptive penalty factor, The position of the movable antenna pair in the particle position vector that violates the constraint C15.

[0030] Preferably, in step S4, the weighted least square error method is used for problem reconstruction, which means that the auxiliary variable is introduced to convert the security and rate maximization problem into a weighted least square error minimization problem.

[0031] Preferably, in step S4, the Majorization-Minimization algorithm is applied to process the non-convex constraint, which specifically includes first-order Taylor expansion linearization of the power constraint quadratic term in the base station beamforming vector optimization sub-problem, and linearization of the unit modulus constraint in the STAR-RIS coefficient matrix optimization sub-problem.

[0032] Preferably, in step S5, the judgment condition for system performance convergence is that the relative change of system and security rate is less than a preset threshold or the maximum iteration number is reached.

[0033] Therefore, the STAR-RIS assisted movable antenna for secure communication method has the following beneficial technical effects:

[0034] (1)Significantly improve the system security communication performance: By jointly optimizing the base station active beamforming, STAR-RIS reflection / transmission coefficients and the spatial position of the movable antenna, the channel characteristics can be dynamically and accurately matched, which enhances the signal reception strength of the legitimate user while effectively suppressing the signal reception quality of the eavesdropping user, thereby significantly improving the system security and rate. Simulation results show that, under the same transmit power and antenna configuration, the present scheme can achieve higher security rate compared with the traditional fixed antenna scheme (STAR-RIS-FPA) and the random phase shift scheme (STAR-RIS-MA-Ran).

[0035] (2) Achieve full spatial coverage and precise beam control: By utilizing the STAR-RIS's simultaneous transmission and reflection characteristics, the traditional RIS half-space coverage limitation is broken, and the legitimate users in different positions of the reflection and transmission areas can be served simultaneously. Combined with the movable antenna technology, the spatial degree of freedom is further introduced at the transmitting end, realizing intelligent control of the communication environment in the whole domain with high freedom, greatly enhancing the adaptability and reliability of the system in complex environments.

[0036] (3) Strong convergence and high efficiency: For the high-dimensional, non-convex, and multi-variable coupled complex optimization problem constructed, an efficient iterative algorithm based on the alternating optimization (AO) framework is designed. The algorithm decomposes the original problem into three sub-problems, and uses particle swarm optimization (PSO), weighted minimum mean square error (WMMSE), and Majorization-Minimization (MM) algorithm to solve them respectively, effectively handling non-convex constraints and variable coupling. Simulation results show that the algorithm has good convergence, and usually converges to a stable state after a few iterations, ensuring the realizability of the scheme in practical systems. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 Model of a simultaneous transmission and reflection reconfigurable intelligent surface assisted downlink movable antenna security communication system

[0038] Figure 2 Simulation setup for a simultaneous transmission and reflection reconfigurable intelligent surface assisted downlink movable antenna communication system

[0039] Figure 3 Curve of system security and rate versus iteration number

[0040] Figure 4 Curve of system security and rate versus base station transmit power

[0041] Figure 5 Curve of system security and rate versus base station antenna number DETAILED DESCRIPTION

[0042] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0043] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning as understood by one of ordinary skill in the art to which this invention pertains.

[0044] Example 1

[0045] I. Construction of system model and optimization problem.

[0046] like Figure 1 As shown, the system consists of one base station, one STAR-RIS, and two legitimate users (U... r and U t ) and two eavesdropping users (Eve r and Eve t The system consists of several components. The channel model uses a field response-based approach, ignoring direct links; communication is conducted via STAR-RIS. All legitimate users and eavesdropping users are equipped with a fixed receiving antenna. The base station has N movable antennas, and STAR-RIS comprises M elements. Each movable antenna (MA) is connected to the RF link via a flexible cable, enabling communication within a local two-dimensional area at the base station. The upward movement of the nth movable antenna aims to improve the channel for legitimate users. The position of the nth movable antenna is represented by rectangular coordinates as follows: Where, x n The x-axis coordinate of the nth movable antenna is represented by the y-axis coordinate. n Let represent the y-coordinate of the nth movable antenna, and T represent the transpose of the vector. Represents a set, This represents a square region of size A×A. The set of STAR-RIS cells is defined as:

[0047] Assume all channels experience quasi-static flat fading, and that the CSI (Channel State Information) of all relevant channels is fully known to both the BS (Base Station) and STAR-RIS. Furthermore, direct links are ignored due to the presence of obstacles. Therefore, the BS requires the assistance of STAR-RIS to transmit signals to the user; the transmitted signal can be represented as:

[0048] x = w r s r +w t s t (1);

[0049] where x denotes the transmitted signal, s r and s t denote the signals sent to users U r and U t , respectively, and s k denotes the signal sent to users U r and U t , and satisfies denotes the expectation operator, k denotes the set symbol, denotes the set of user indices, t and r both denote user identities, and denote the corresponding beamforming vectors of s r and s t , respectively.

[0050] The received signals at the legitimate user and the eavesdropping user are denoted as:

[0051]

[0052] where y k,u denotes the received signal at the legitimate user, y k,e denotes the received signal at the eavesdropping user, denotes the channel response between the STAR-RIS and the legitimate user U k , denotes the channel response between the STAR-RIS and the eavesdropping user Eve k , denotes the channel response between the base station and the STAR-RIS, denotes the coefficient matrix of the reflecting or transmitting elements of the STAR-RIS, and has e denotes the natural constant, j denotes the imaginary unit, a m,k and ξ m,k denote the amplitude and phase shift coefficient of the m-th reflecting or transmitting element on the STAR-RIS, n k,u and n k,e denote the circularly symmetric complex Gaussian noise at the legitimate user and the eavesdropping user, respectively, and have and denote the circularly symmetric complex Gaussian distribution, denotes the variance of n k,u , denotes the variance of n k,e .

[0053] The channel model based on field response is adopted to model the channel response G from the base station to the STAR-RIS, i.e., the channel response G is characterized by the superposition of the coefficients of multiple channel paths between the base station and the STAR-RIS. In addition, since the propagation distance of the signal is much larger than the size of the moving area , the far-field channel condition between the base station and the STAR-RIS is guaranteed. Therefore, the AODs and the amplitude of the complex path coefficients of the multiple channel paths remain unchanged with the movement of the MA. This means that only the phase of the multiple channel paths will be affected by the change of the MA position in the transmission area. At this time, the channel response G from the base station to the STAR-RIS is represented as:

[0054]

[0055] where, represents the transmit field response vector at the base station, L represents the number of transmission paths between the base station and the STAR-RIS, represents the transmission FRV between the nth MA and the STAR-RIS, and has λ represents the wavelength, ρ n,l = [sinθ n,l cosφ n,l , cosθ n,l ] T represents the signal transmission phase difference of the lth transmission path, θ n,l and φ n,l represent the elevation angle and the azimuth angle of the lth path, respectively, v l represents the complex response of the lth path, represents the receive field response vector at the STAR-RIS.

[0056] According to the Shannon formula, the received information rates at the legitimate user and the eavesdropping user can be represented as:

[0057]

[0058] where, R k,u represents the received information rate of the legitimate user, R k,ei represents the received information rate of the eavesdropping user, and k'≠k, i, k' represent the user index. Therefore, the security rate R k of the legitimate user U k,s is:

[0059]

[0060] To obtain the maximum system security and rate, the following optimization problem is constructed:

[0061]

[0062] where Pmaxdenotes the maximum transmit power at the base station, dmin denotes the minimum distance between each pair of MAs to avoid coupling effects between the transmit area antennas, t denotes the straight coordinates of the e-th movable antenna, e denotes the index of the movable antenna, t denotes the straight coordinates of the m-th movable antenna, m denotes the index of the movable antenna, a denotes the amplitude of the m-th reflecting unit on the STAR-RIS, a denotes the amplitude of the m-th transmitting unit on the STAR-RIS. C11 denotes the power constraint of the base station, C12 denotes the amplitude constraint of the STAR-RIS, C13 denotes the phase shift constraint of the STAR-RIS, C14 denotes the position constraint of the MAs, and C15 denotes the distance constraint of each pair of MAs. max min ε μ m,r m,t

[0063] II. Particle swarm optimization for MA positions at the base station.

[0064] Given the base station beamforming w k and the coefficient matrix of the STAR-RIS Φ k , the particle swarm optimization algorithm is used to solve the MA position optimization subproblem at the base station. Therefore, the original optimization problem (P1) can be simplified as follows:

[0065]

[0066] Since the objective function and the constraint C22 are non-convex, in order to effectively solve the problem, the particle swarm optimization algorithm is introduced. First, the positions of B particles are randomly initialized as and the velocities of B particles are randomly initialized as where denotes the initial straight coordinates of the B-th particle, denotes the initial velocity of the B-th particle, and the position of each particle represents a feasible implementation of the MA position vector at the base station, i.e.: to ensure that the initial position of each MA is located within the feasible moving area, so that the constraint C22 is satisfied, denotes a uniform distribution, and A denotes the side length of the feasible moving area of the movable antenna.

[0067] Then, each particle updates its position according to the individual experience (known local optimal position, i.e. r b,pbest ) and the group experience (known global optimal position, i.e. r gbest ). Therefore, for each iteration, the velocity and position of the particle are updated as:

[0068] ​​​​​​

[0069] wherein, represents the Cartesian coordinates of the bth particle at the ith iteration, represents the velocity of the bth particle at the ith iteration, represents the velocity of the bth particle at the (i+1)th iteration, represents the Cartesian coordinates of the bth particle at the (i+1)th iteration, 1≤b≤B, i represents the number of iterations, c1 and c2 represent the individual learning factor and the global learning factor, respectively, and represents the step length of each particle moving towards the best position, represents a random parameter, whose purpose is to enhance the randomness of the parameters to escape from the local optimal solution, and ω represents the inertia weight, which is used to maintain the inertia of the particle motion. In particular, in order to balance the speed and accuracy of the particle swarm search, the inertia weight is continuously reduced during the iteration process, as follows:

[0070]

[0071] wherein, ω min and ω max represent the minimum and maximum values of ω, respectively, and I represents the maximum number of iterations.

[0072] In addition, due to the constraint C21, if a particle moves outside the boundary of the feasible region, its position needs to be corrected, i.e. the position components are projected onto the corresponding maximum or minimum position, and the correction function [γ(r)] u The specific form is as follows:

[0073]

[0074] wherein, 1≤u≤2N, [r] u represents the u-th component of the vector r.

[0075] Further, the fitness of each particle needs to be evaluated. The objective function is taken as part of the particle fitness evaluation function, and to ensure the constraint C22, an adaptive penalty factor η is introduced in the fitness function, and the specific form is as follows:

[0076]

[0077] wherein, represents the fitness value of the particle b at the ith iteration, represents a set, and each element in it represents the position of the movable antenna pair that violates the constraint C22 in the particle position vector r, which can be defined as:

[0078]

[0079] Moreover, η denotes a large positive penalty parameter which ensures the inequality equation This holds for all MA position vectors. At the same time, it also ensures that each particle moves to a position which guarantees the minimum MA distance, since if each particle does not move to a position which guarantees the minimum MA distance, its fitness function value will decrease to less than zero, and only at the position of the minimum distance, the fitness function value will be maximum and greater than zero. This means that during the iteration, will be close to zero, i.e. the constraint C22 is eventually satisfied.

[0080] Finally, by evaluating the fitness of each particle, their local and global best positions are improved until convergence, resulting in the best particle position, i.e. the optimal position of the movable antenna, which is also the suboptimal solution of the non-convex optimization problem (P2).

[0081] III. Optimization problem reformulation and optimization of auxiliary variables

[0082] The objective function is converted into a form which is easy to handle later. Here, we first introduce a lemma.

[0083] Lemma: For a D x D matrix function:

[0084]

[0085] where E(.) denotes a matrix function defined with respect to matrices U and V, U and V denote the matrix variables to be optimized, I denotes the identity matrix, and N denotes an arbitrary positive definite matrix, the following equality holds:

[0086]

[0087] where W denotes an auxiliary optimization variable, and Tr denotes the trace symbol.

[0088] Based on the above lemma, the original optimization problem (P1) can be transformed into the following form:

[0089]

[0090] Finally, a slack variable t is introduced to the objective function k , which has the following specific form:

[0091]

[0092] Given the base station end MA position, the base station beamforming vector and the coefficient vector at STAR-RIS, the auxiliary variables {β k,u ,β k,ei} and

[0093] According to the lemma, the auxiliary variable β k,u , β k,ei and the auxiliary variable have the following optimal values:

[0094] IV. Base station beamforming vector design

[0095] Firstly, the reconstructed optimization problem (P4) is simplified as follows:

[0096]

[0097] Then, the functions f k,u and f k,ei are expanded, and then the MM method is used to linearize the quadratic term of w in C51, and finally, the new optimization problem is obtained:

[0098]

[0099] where,

[0100] The optimization problem (P6) is a standard second-order cone programming problem, which is solved directly by the CVX solver.

[0101] V. STAR-RIS coefficient matrix optimization

[0102] For a given MA position t n , the auxiliary variable and the base station beamforming w k , and the functions f k,u and f k,ei are rearranged into the explicit function of the optimization variable Φ k , and the optimization problem (P4) can be simplified as follows:

[0103]

[0104] where, * represents complex conjugate, ξ m,k represents the phase shift coefficient of the mth reflection or transmission unit on the STAR-RIS,

[0105] Due to the constraint C91, the optimization problem (P9) is non-convex. In order to deal with this optimization problem, the MM method is used to linearize the constraint C91, which is written as follows:

[0106]

[0107] where, is an optimization variable The optimal solution in the last iteration. So far, the original non-convex optimization problem has been transformed into a convex optimization problem, which can be solved using CVX.

[0108] The application will be further described below through simulation tests.

[0109] To verify the effectiveness and superiority of the method proposed in the application, in the following simulation tests, the method of the application is compared with the following two benchmark schemes:

[0110] Benchmark scheme one (STAR-RIS-FPA): fixed antenna scheme.

[0111] This scheme discards the movable antenna (MA) technology of the application. The base station in the system is equipped with the same number of antennas, but the positions of these antennas at the base station are fixed (Fixed Position Antenna, FPA) and do not change, usually assumed to be uniformly distributed in the mobile area. At the same time, this scheme only jointly optimizes the beamforming vector of the base station and the coefficient matrix of the STAR-RIS, and the antenna position is not an optimization variable. This scheme is used to prove the performance gain brought by introducing the movable antenna and optimizing its position.

[0112] Benchmark scheme two (STAR-RIS-MA-Ran): random phase shift scheme.

[0113] This scheme uses the movable antenna (MA) technology of the application and also uses the particle swarm optimization algorithm to optimize the antenna position. However, this scheme discards the optimization of the STAR-RIS coefficient matrix. The reflection and transmission coefficients (including amplitude and phase shift) of the STAR-RIS are randomly generated and satisfy the unit modulus constraint, and remain unchanged during the optimization process. This scheme is used to prove the necessity and synergistic gain of jointly optimizing the STAR-RIS parameters based on the MA technology.

[0114] The simulation tests verify the effectiveness of the proposed STAR-RIS assisted MA scheme. As Figure 2 , in the simulation system model, the base station equipped with 4 movable antennas (N = 4) and the STAR-RIS with 8 units (M = 8) jointly serve two single antenna legitimate users (labeled as U r and U t , respectively). Among them, the base station and the STAR-RIS are located at the polar coordinates (30, 0, π / 2) and (0, 0, 0), respectively, and U r and U t are randomly distributed on a semicircle with the STAR-RIS as the center and a radius of 5m. In addition, there is also a eavesdropping user Eve in the reflection and transmission regions of the STAR-RIS.r and Eve t The STAR-RIS is located 10 m away from the base station. The MAs at the base station are restricted to move within a square area of size A x A, where A = 5λ and λ denotes the signal wavelength. The channel from the base station to the STAR-RIS is modeled as the field response model in (1), and the channels from the STAR-RIS to the two legitimate users and two eavesdroppers are modeled as Rayleigh channels. The number of transmit paths L = 5 from the base station to the STAR-RIS, and the elevation angle θ n,l and azimuth angle φ n,l are uniformly distributed, i.e., have The maximum transmit power at the base station is P max = 35 dBm, the additive complex Gaussian noise at the receiver is σ = -60 dBm, the path loss at 1 m is -15 dB, and the path loss exponent for the communication channels from the base station to the STAR-RIS and from the STAR-RIS to the legitimate users and eavesdroppers is defined as 2.8.

[0115] Figure 3 The convergence behavior of the proposed iterative algorithm is plotted for different numbers of movable antennas N. It can be observed from Figure 3 that (1) the security and rate of the system can converge to a stable value after a few iterations. For example, when N = 4, the proposed algorithm converges to a stable value in about 5 iterations. This verifies that the proposed algorithm has good convergence performance in the STAR-RIS-aided MA scheme. (2) A higher security and rate can be achieved when N is larger. This is because increasing the number of movable antennas N can make the base station more accurately direct the signal energy to the target user through beamforming, which can better adapt to the transmission channel of the user and improve the security performance of the system. (3) The larger N is, the more iterations are needed to converge to a stable value, because the dimension and computational complexity of the optimization problem increase with N.

[0116] Figure 4 The impact of the proposed method and the benchmark scheme on the system security and rate is plotted for different base station transmit powers, and two different cases of transmit channel path numbers L = 2 and L = 5 are considered. It can be observed from Figure 4From this, we can see that: (1) When the base station transmit power increases, the system security and speed of both the proposed method and the benchmark scheme increase, indicating that increasing transmission energy can effectively resist eavesdropping by eavesdropping users, thereby improving the system security performance. (2) When the number of transmission channel paths increases, the system security and speed of both the proposed method and the benchmark scheme increase. This is because as the number of channel paths increases, the dimension of the field response matrix of the transmitter increases, providing more degrees of freedom for improving system security and speed. (3) When the base station transmit power is the same, the proposed method can achieve higher system security and speed compared to the benchmark scheme. This is because, compared with the STAR-RIS-FPA scheme, the proposed method can reasonably change the position of the transmit antenna according to the channel state information, thereby better adapting to the user channel and obtaining greater system security and speed; compared with the STAR-RIS-MA-Ran scheme, the proposed method further optimizes the phase shift matrix of STAR-RIS, making the channel difference between legitimate users and eavesdropping users larger, thereby improving the system security performance. (4) As the base station transmit power increases, the difference in system security and rate between the two benchmark schemes decreases, but the difference between the proposed method and the two benchmark schemes increases. This is because when the base station transmit power is low, the user's signal-to-interference-plus-noise ratio is low, and the movable antenna can better improve the channel quality, resulting in a greater improvement in system security and rate. However, as the base station transmit power increases, the received signal strength increases, and the channel difference caused by optimizing the STAR-RIS phase shift is more conducive to improving system security and rate.

[0117] Figure 5 The impact of the proposed method and the benchmark scheme on system security and speed under different numbers of base station antennas is plotted, and the base station transmit power P is considered. B =35dBm and P B = 30dBm in two different cases. From Figure 5 Observations show that: (1) When the number of base station antennas increases, the system security and speed of both the proposed method and the benchmark scheme increase. This is because increasing the number of base station antennas increases the spatial degree of freedom of the transmitter, enabling the base station to generate a more focused beam pointing towards the receiver, thereby reducing signal loss and interference during transmission, and thus improving system security and speed. (2) When the base station transmit power increases, the system security and speed of both the proposed method and the benchmark scheme also increase. This is related to... Figure 4 The results are consistent with those in the previous section. (3) When the number of base station antennas is the same, the proposed method can achieve higher system security and speed compared with the benchmark scheme. Furthermore, the system security and speed of the proposed method when the number of base station antennas N=2 is greater than that of the benchmark scheme when the number of base station antennas N=10. This shows that under the same system security and speed requirements, the proposed method can greatly reduce the number of transmit antennas at the base station, which also verifies the advantage of the proposed method over the benchmark scheme.

[0118] It is worth noting that the content not elaborated in the present application is all the prior art, which is well known to those skilled in the art.

[0119] Therefore, the application adopts the above-mentioned STAR-RIS assisted movable antenna to realize the method of safe communication, and by jointly optimizing the base station beam forming, the MA position and the STAR-RIS coefficient matrix, the safety and rate of the system are maximized, and the problems of insufficient safety and poor channel adaptability of the existing wireless communication system in complex environment are solved.

[0120] Finally, it should be noted that: the above examples are only used to illustrate the technical solutions of the present application, but not to limit them, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that: the technical solutions of the present application can still be modified or replaced by the equivalent, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present application.

Claims

1. A method for implementing secure communication with the assistance of a STAR-RIS movable antenna, characterized in that, The method comprises the following steps: Step S1, constructing a downlink MIMO system, establishing a joint optimization problem containing base station beamforming vectors, all movable antenna positions, and STAR-RIS coefficient matrices, and taking maximizing system security and rate as the goal; Step S2, decomposing the joint optimization problem into three sub-problems, including a movable antenna position optimization sub-problem, a base station beamforming vector optimization sub-problem, and a STAR-RIS coefficient matrix optimization sub-problem, by using an alternating optimization framework; Step S3, solving the movable antenna position optimization sub-problem by using a particle swarm optimization algorithm; Step S4, for the base station beamforming vector optimization sub-problem and the STAR-RIS coefficient matrix optimization sub-problem, reconstructing the problem by using a weighted least mean square error method, and processing the non-convex constraint in the problem by using a Majorization-Minimization algorithm, so that the sub-problems are converted into a second-order cone programming or a quadratic programming problem, and then the sub-problems are solved by using a convex optimization solver; Step S5, alternately performing Step S3 and Step S4, updating the beamforming vectors, the STAR-RIS coefficient matrices, the movable antenna positions, and corresponding auxiliary variables, until the system security and rate converge, and the solution of the joint optimization problem is obtained.

2. The method for STAR-RIS assisted movable antenna to realize secure communication according to claim 1, wherein, In Step S1, the downlink MIMO system comprises a base station equipped with multiple movable antennas, a STAR-RIS, and two legitimate users and two eavesdropping users distributed in the reflection region and the transmission region of the STAR-RIS.

3. The method of claim 2, wherein, The channel from the base station to the STAR-RIS adopts a field response model, and the channel from the STAR-RIS to the user end is modeled as Rayleigh fading.

4. The method for STAR-RIS assisted movable antenna to realize secure communication according to claim 1, wherein, In Step S1, the joint optimization problem is as follows: P1: s.t.C11: C12: C13: C14: C15: where Φ k denotes the coefficient matrix of the reflecting or transmitting elements of STAR-RIS, w k denotes the beamforming vector of the legitimate user U k , t n denotes the Cartesian coordinates of the n-th movable antenna position, k denotes the set symbol, denotes the set of user indices, R k,s denotes the security rate of the legitimate user U k , P max denotes the maximum transmit power at the base station, d min denotes the minimum distance between each pair of MAs, denotes a square region of size A x A, t ε denotes the Cartesian coordinates of the e-th movable antenna, t μ denotes the Cartesian coordinates of the m-th movable antenna, a m,k and ξ m,k denote the amplitude and phase shift coefficient of the m-th reflecting or transmitting element on STAR-RIS, a m,r denotes the amplitude of the m-th reflecting element on STAR-RIS, a m,t denotes the amplitude of the m-th transmitting element on STAR-RIS, C11 denotes the power constraint of the base station, C12 denotes the amplitude constraint of STAR-RIS, C13 denotes the phase shift constraint of STAR-RIS, C14 denotes the position constraint of MAs, and C15 denotes the distance constraint of each pair of MAs.

5. The method of claim 4, wherein, In Step S3, the movable antenna position optimization sub-problem is solved by using a particle swarm optimization algorithm, comprising the following steps: initializing a population containing B particles, and the position vector of each particle represents a feasible configuration of the positions of all N movable antennas of the base station, and the initial position of each antenna is located in a preset moving region; updating the speed and position of each particle, and the updating process simultaneously considers the historical optimal position of the particle itself and the global historical optimal position of the population, wherein the inertia weight adopts a linearly decreasing strategy with the increase of the iteration number; if the antenna position exceeds the boundary of the moving region, the position is corrected, that is, the position component is projected onto the corresponding maximum or minimum position; designing an adaptive function, and the value of the function is determined by the system security rate under the current antenna position configuration and a penalty term that violates the minimum distance constraint, wherein the penalty term is positively correlated with the number of antenna pairs that violate the constraint and the violation degree; continuously optimizing the particle position by iteration updating until the termination condition is met, and finally outputting the movable antenna position configuration corresponding to the optimal particle in the population as the solution of the sub-problem.

6. The method of claim 5, wherein, The correction process uses a correction function [γ(r)] u As follows: where [r] u denotes the u-th component of the vector r, and A denotes the edge length of the movable antenna movable region.

7. The method of claim 5, wherein the STAR-RIS assisted movable antenna implements secure communication, and wherein the STAR-RIS assisted movable antenna implements secure communication, and wherein the STAR-RIS assisted movable antenna implements secure communication. The adaptive function is as follows: wherein represents the fitness value of the particle b in the i-th iteration, R k,s represents the security rate of the legitimate user U k , and η represents the adaptive penalty factor, represents the position of the movable antenna pair that violates the constraint C15 in the particle position vector.

8. The method for STAR-RIS assisted movable antenna to realize secure communication according to claim 1, wherein, In Step S4, reconstructing the problem by using a weighted least mean square error method means that an auxiliary variable is introduced to convert the security and rate maximization problem into a weighted mean square error minimization problem.

9. The method for STAR-RIS assisted movable antenna to realize secure communication according to claim 1, wherein, In step S4, the Majorization-Minimization algorithm is applied to handle the non-convex constraints, specifically including first-order Taylor expansion linearization of the quadratic term of the power constraint in the base station beamforming vector optimization subproblem, and linearization of the unit modulus constraint in the STAR-RIS coefficient matrix optimization subproblem.

10. The method for STAR-RIS assisted movable antenna to realize secure communication according to claim 1, wherein, In step S5, the judgment condition for system performance convergence is that the relative change of the system sum rate and the safety rate is less than a preset threshold or the maximum number of iterations is reached.

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