Perceptual auxiliary secure communication method of mobile antenna auxiliary secure communication system

Abstract

The invention relates to a perception auxiliary safety communication method of a movable antenna auxiliary safety communication system, and belongs to the field of wireless communication. The method comprises the following steps: in an eavesdropper sensing stage, a base station adjusts the positions of a transmitting movable antenna and a receiving movable antenna, transmits L sensing beams and collects all echo signals to obtain an estimated value of a space arrival angle of an eavesdropper; in the secure communication stage, the range of the eavesdropper is obtained based on the sensing stage, a robust beam forming vector transmitted by a base station is designed, and the transmission security rate of a legal user and the eavesdropping rate of the eavesdropper are determined; establishing a two-stage joint optimization problem to maximize the transmission security rate of the legal user under the worst condition and meet the joint optimization problem of perception constraint; and solving the established joint optimization problem to realize safe communication of the legal users. According to the invention, the joint optimization of the position of the movable antenna and the safe beamforming is realized, and the safety and robustness of the perception auxiliary communication system are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of wireless communication, in particular to a sensing-assisted secure communication method of a movable antenna-assisted secure communication system. BACKGROUND

[0002] With the development of mobile communication technology, the demand for data transmission has increased dramatically, and data security problems have become increasingly prominent. Traditional network layer security mechanisms that rely on encryption have high computational complexity and key management difficulties, while physical layer security technology has received widespread attention due to its ability to utilize channel noise and randomness to achieve information confidentiality in wireless media. Secure beamforming is one of the key technologies, but existing methods are limited by fixed antenna positions and are difficult to deal with the problem of high channel correlation when an eavesdropper is close to a legitimate user, affecting the security performance. Movable antenna technology can dynamically adjust the antenna position, improve the legitimate channel and weaken the eavesdropping channel, thereby improving the security performance, and does not require additional hardware or algorithm overhead. Compared with fixed array systems, it has significant advantages in beamforming, spatial multiplexing, etc. However, in practical applications, it is difficult to obtain the channel state information of passive eavesdroppers, which is a key problem faced by physical layer security. Integrated sensing and communication (ISAC) is a research hotspot in 6G, which estimates the position of the eavesdropper through sensing function, providing a new direction to solve this problem. In the future, it is urgent to promote the cooperative integration of communication and sensing to enhance the overall security of the system. SUMMARY

[0003] The present application provides a sensing-assisted secure communication method of a movable antenna-assisted secure communication system, which can solve the problem of channel uncertainty and weak secure communication ability caused by fixed antenna layout and insufficient sensing accuracy.

[0004] The application provides a sensing-assisted secure communication method of a mobile antenna-assisted secure communication system, wherein the mobile antenna-assisted secure communication system comprises a full-duplex millimeter wave base station capable of sensing and communication, a legal user and an eavesdropper, the base station is equipped with N transmitting mobile antennas and M receiving mobile antennas, the legal user and the eavesdropper are equipped with a single fixed-position antenna, each transmission frame of the base station is divided into two stages, i.e. a sensing eavesdropper stage and a secure communication stage, the sensing-assisted secure communication method comprises the following steps: in the sensing eavesdropper stage, the base station adjusts the positions of the transmitting mobile antennas and the receiving mobile antennas, transmits L sensing beams and collects all echo signals to obtain an estimated value of the spatial direction of arrival of the eavesdropper; in the secure communication stage, based on the range of the spatial direction of arrival of the eavesdropper obtained in the sensing stage, a robust beamforming vector of the base station transmission is designed, and the transmission security rate of the legal user and the eavesdropping rate of the eavesdropper are determined; a two-stage joint optimization problem is established to maximize the transmission security rate of the legal user in the worst case while meeting the joint optimization problem of the sensing constraint; the joint optimization problem established above is solved to realize the secure communication of the legal user.

[0005] Optionally, in the sensing eavesdropper stage, the base station adjusts the positions of the transmitting mobile antennas and the receiving mobile antennas, transmits L sensing beams and collects all echo signals to obtain an estimated value of the spatial direction of arrival of the eavesdropper; comprising:

[0006] The sensing channel and the communication channel are respectively modeled, for the modeling of the sensing channel, the Cartesian coordinate system of the transmitting area of the mobile antenna and the receiving area of the mobile antenna is set, the base station is equipped with N transmitting mobile antennas and M receiving mobile antennas, the coordinates of the nth transmitting mobile antenna is t n , the coordinates of the mth receiving mobile antenna is r m , the spatial angle of departure u s and the spatial angle of arrival v s are obtained according to the physical elevation angle θ s and the azimuth angle between the base station and the eavesdropper, the angle of arrival in the vector form is χ s =[u s ,v s ] T , the transmitting field response function and the receiving field response function are established through the angle of arrival in the vector form χ s , and finally the channel matrix H is obtained, wherein, is the position set of the N transmitting mobile antennas, is the position set of the M receiving mobile antennas;

[0007] For modeling of the communication channel, a channel vector for the legitimate user communication is defined and a channel vector for the eavesdropper communication χ c is the angle of arrival of the legitimate user, χ e is the angle of arrival of the eavesdropper, the channel vector is obtained and the field response vector where i ∈ {c, e}, c is the legitimate user and e is the eavesdropper.

[0008] Optionally, the base station performs beam scanning using a discrete Fourier transform codebook of L beams to receive the echo signal where y s (l) is the echo signal received in the lth beam stage;

[0009] After receiving the echo signal Y s , the eavesdropper spatial angle of arrival estimate is estimated by a maximum likelihood method After angle estimation, the base station transmits a directional beam to obtain the echo time delay calculation base station and the distance d be of the eavesdropper.

[0010] Optionally, in the secure communication stage, based on the range of the eavesdropper obtained in the sensing stage, a robust beamforming vector transmitted by the base station is designed to determine the transmission security rate of the legitimate user and the eavesdropping rate of the eavesdropper; including:

[0011] In the secure communication stage, based on the range of the eavesdropper spatial angle of arrival true value obtained in the sensing stage A robust beamforming vector ω transmitted by the base station is designed, and the position of the mobile transmitting movable antenna is moved to realize the secure communication of the legitimate user, to determine the transmission rate R c of the legitimate user and the eavesdropping rate R e of the eavesdropper.

[0012] Optionally, a two-stage joint optimization problem is established to maximize the transmission security rate of the legitimate user in the worst case while satisfying the joint optimization problem of the sensing constraint; including:

[0013] The two-stage optimization problem is divided into a movable antenna movement problem in the eavesdropper sensing stage and a joint transmitting movable antenna movement and robust beamforming optimization problem in the secure communication stage;

[0014] The probability density function of the estimation error is set as a preset condition, which is subject to a Gaussian distribution with zero mean and Cramer-Rao lower bound variance, to obtain a first Cramer-Rao lower bound of the estimated spatial angle of arrival and a second Cramer-Rao lower bound

[0015] The first Cramer-Rao lower bound is set and the second Krammer lower bound the maximum threshold value η and the range of the eavesdropper spatial angle of arrival true value is a preset condition.

[0016] Optionally, for the movable antenna movement problem of the sensing stage, by proposing the Krammer lower bound minimization problem P1 and its constraints, the sensing stage obtains better sensing performance:

[0017]

[0018] wherein C1 is the movement range constraint of the transmitting and receiving movable antennas, C2 is the minimum distance between two adjacent transmitting movable antennas, C3 is the minimum distance between two adjacent receiving movable antennas, and C4 is the maximum threshold constraint of the Krammer lower bound;

[0019] For the joint transmitting movable antenna movement and robust beamforming optimization problem of the secure communication stage, the influence of antenna movement, sensing result and secure beamforming is jointly considered, and the two-stage joint optimization problem P2 about ω is obtained:

[0020]

[0021] s.t.C1:||ω|| 2 ≤P t ,

[0022]

[0023] wherein [X] + = max(X, 0), C1 is the maximum communication transmission power constraint of the base station, C2 is the movement range constraint of the transmitting movable antenna, C3 is the minimum distance between two adjacent transmitting movable antennas, C4 is the value range of the real spatial angle of arrival, and C5 is the value range of the eavesdropper spatial angle of arrival estimated value;

[0024] The objective function of the optimization problem P2 represents that, in the worst case, for all eavesdropper spatial angle of arrival estimated values Optimize the antenna position to maximize the secure rate, and for each eavesdropper spatial angle of arrival estimated value design a robust secure beamforming ω to avoid information leakage in the estimated eavesdropper spatial angle of arrival true value range.

[0025] Optionally, the joint optimization problem established above is solved to realize the secure communication of the legitimate user. Including:

[0026] ​For the problem of moving a movable antenna during the eavesdropper's perception phase, according to the Cauchy-Schwarz inequality, we obtain the constraints C2 and C3 of the transformed optimization problem P1:

[0027]

[0028] Among them, t a p =[x a p ,y a ] T ,r b p =[x b p ,y b ] T , t a p Let r be the position of the transmitting antenna in the p-th iteration. b p Let a be the position of the receiving antenna in the p-th iteration. b, All of these represent the serial numbers of the movable antennas;

[0029] The constraint C4 of optimization problem P1 is transformed using the continuous convex approximation method, resulting in the first transformed constraint C4 of optimization problem P1:

[0030]

[0031] Where β is a constant, the constraint C4 of the optimization problem P1 in the first transformation is transformed into a standard quadratic form, resulting in the standard quadratic form of the constraint C4 of the optimization problem P1:

[0032]

[0033] in, For vector x t variance For vector x r variance Let y be a vector t variance Let y be a vector r variance For x t ,y t covariance, For x r ,y r covariance, and All are positive semi-definite matrices;

[0034] Set the x-coordinate set for transmitting the movable antenna. t The set of ordinates y for transmitting movable antennas t The set of x-coordinates for receiving movable antennas r and the set of y coordinates for receiving movable antennas r The set of x-coordinates of a fixed receiving movable antenna r The set of ordinates y for receiving movable antennas r The set of y coordinates for transmitting movable antennas t After several iterations, the transformation is performed to obtain the set of x-coordinates of the transmitting movable antenna. t Minimize the maximum threshold of the Cramérault lower bound (P3):

[0035]

[0036] The set of x-coordinates for a fixed receiving movable antenna r The set of ordinates y for receiving movable antennas r and the set of x-coordinates of the transmitting movable antenna. t After several iterations, the transformation is performed to obtain the set of ordinates y for transmitting the movable antenna. t Minimize the maximum threshold of the lower bound of Cramérault (P4):

[0037]

[0038]

[0039] The set of x-coordinates of a fixed transmitting movable antenna t The set of ordinates y for transmitting movable antennas t and the set of y coordinates for receiving movable antennas r After several iterations, a transformation is performed to obtain the set of x-coordinates of the receiving movable antenna. r Minimize the maximum threshold of the Cramérault lower bound (P5):

[0040]

[0041] The set of x-coordinates of a fixed transmitting movable antenna t The set of ordinates y for transmitting movable antennas t and the set of x-coordinates of the receiving movable antenna. r After several iterations, a transformation is performed to obtain the set of ordinates y for receiving movable antennas. r Minimize the maximum threshold of the Cramérault lower bound (P6):

[0042]

[0043]

[0044] solving the movable antenna moving problem of the eavesdropper sensing phase by the movable antenna assisted sensing algorithm, initializing the loop ordinal number, the horizontal coordinate of the transmitting movable antenna, the vertical coordinate of the transmitting movable antenna, the horizontal coordinate of the receiving movable antenna and the vertical coordinate of the receiving movable antenna, setting a first precision threshold ε1;

[0045] a first phase loop, fixing the horizontal coordinate of the receiving movable antenna, the vertical coordinate of the receiving movable antenna and the vertical coordinate of the transmitting movable antenna, and optimizing the horizontal coordinate of the transmitting movable antenna;

[0046] a second phase loop, fixing the horizontal coordinate of the receiving movable antenna, the vertical coordinate of the receiving movable antenna and the horizontal coordinate of the transmitting movable antenna, and optimizing the vertical coordinate of the transmitting movable antenna;

[0047] a third phase loop, fixing the horizontal coordinate of the transmitting movable antenna, the vertical coordinate of the transmitting movable antenna and the vertical coordinate of the receiving movable antenna, and optimizing the horizontal coordinate of the receiving movable antenna;

[0048] a fourth phase loop, fixing the horizontal coordinate of the transmitting movable antenna, the vertical coordinate of the transmitting movable antenna and the horizontal coordinate of the receiving movable antenna, and optimizing the vertical coordinate of the receiving movable antenna;

[0049] each phase loop until the absolute value of the Cramér-Rao lower bound threshold of two adjacent times is less than the first precision threshold ε1, obtaining the optimal value of the horizontal coordinate of the transmitting movable antenna, the optimal value of the vertical coordinate of the transmitting movable antenna, the optimal value of the horizontal coordinate of the receiving movable antenna and the optimal value of the vertical coordinate of the receiving movable antenna.

[0050] Optionally, the joint movable antenna moving and robust beamforming optimization problem of the secure communication phase is a joint optimization problem, the objective function of the joint optimization problem is complex and contains non-convex constraints, and the joint optimization problem is decomposed into a robust beamforming problem of the secure communication phase and a transmitting movable antenna moving problem of the secure communication phase.

[0051] Optionally, the solving process of the robust beamforming problem of the secure communication phase comprises:

[0052] the range of the true value of the eavesdropper spatial angle of arrival a first weight μ is selected according to a heuristic method k for the preset condition, the robust beamforming vector maximization problem P10 is obtained:

[0053] s.t.C1:||ω|| 2 = 1, wherein, a channel matrix for a user, a channel matrix for an eavesdropper, a noise variance at the user is the same as a noise variance at the eavesdropper;

[0054] By the Cauchy-Schwarz inequality and under the condition that its equality holds, the optimal value of the first weight μ k

[0055] The variable of the robust beamforming vector maximization problem P10 includes a maximum generalized eigenvector eig(A,B) and a maximum generalized eigenvalue λ max (A,B);

[0056] The robust beamforming problem in the secure communication stage is solved by the robust beamforming design algorithm, a second precision threshold ε2 is set, a loop number m=0 is initialized, and a second weight μ k 0 is initialized.

[0057] A preset condition that a spatial departure angle is uniformly distributed in the interval [-1, 1] is set, and the initial value of the maximum generalized eigenvector and the initial value of the maximum generalized eigenvalue are obtained by solving the robust beamforming vector maximization problem P10.

[0058] In the mth loop, m=m+1 is set, and the second weight μ k is updated according to the first weight μ k m in the mth loop until the objective function γ m in the mth loop and the objective function γ m-1 in the (m-1)th loop satisfy the condition |γ m -γ m-1 |≤ε2, the loop is ended, and the optimal value of the robust beamforming vector is obtained.

[0059] Optionally, the solving process of the optimization problem of the transmitting movable antenna position in the secure communication stage includes:

[0060] The optimization problem P2 is rewritten to obtain the optimization problem P11:

[0061]

[0062] The longitudinal coordinate of the transmitting movable antenna is fixed to obtain the optimization problem P12:

[0063]

[0064] The horizontal coordinate maximization problem P13 of the transmitting movable antenna is solved by the feasible direction method:

[0065] ​

[0066] in, For x t p In R(x) t ,y t The gradient of ) y t ] T Let d[n] be the position of the transmitting antenna. A constant vector of linear constraints. It is a sparse matrix;

[0067] The step size τ is obtained by exhaustive search within the interval [0,1], and finally the updated x-coordinate of the transmit movable antenna is obtained;

[0068] By fixing the x-coordinate of the movable transmitting antenna, we obtain the problem of maximizing the y-coordinate of the movable transmitting antenna, P14:

[0069]

[0070] To solve the problem of maximizing the ordinate of the transmitting movable antenna (P14), the gradient of the objective function is calculated using the same method as that used for maximizing the abscissa of the transmitting movable antenna (P13). The step size τ is then obtained through exhaustive search within the interval [0,1], and finally, the updated ordinate of the transmitting movable antenna is obtained.

[0071] The problem of transmitting movable antenna movement during the secure communication phase is solved using a movable antenna-assisted secure communication algorithm. The number of noise samples is set to I, and the loop sequence numbers i = 0, p = 0, q = 0 are initialized. The accuracy threshold ε3 and the initial x-coordinate of the transmitting movable antenna are also set. t 0 and the initial value of the ordinate y of the transmitting movable antenna. t 0 ;

[0072] In the i-th loop, let i = i + 1, and use the maximum likelihood estimation method to obtain the noisy estimated angle of arrival. For each estimation result, the corresponding robust beamforming vector ω is obtained through a robust beamforming design algorithm until i = I, and the minimum safe rate and the corresponding noisy estimated angle of arrival are output.

[0073] In the p-th loop, estimate the angle of arrival with noise based on the minimum safe rate. and the initial value of the ordinate y of the transmitting movable antenna. t 0 Calculate the first gradient Solve the maximum problem P13 of the longitudinal coordinate of the transmitting movable antenna, calculate the step size τ, update x t p+1 , let p = p + 1, until the increment of R(x t ,y p ) is less than ε3, and the horizontal coordinate x t of the transmitting movable antenna is obtained. t ;

[0074] In the qth cycle, according to the minimum safety rate corresponding to the noisy estimated angle of arrival and the initial value x t of the horizontal coordinate of the transmitting movable antenna, the second gradient is calculated. Solve the optimization problem P14, calculate the step size τ, update y t q +1 , let q = q + 1, until the increment of R(x t ,y t q ) is less than ε3, and the longitudinal coordinate y t of the transmitting movable antenna is obtained.

[0075] Iteratively update the horizontal coordinate x t of the transmitting movable antenna and the longitudinal coordinate y t of the transmitting movable antenna until the increment of the worst-case safety rate R(x t ,y t ) is less than ε3.

[0076] The present application considers a model in which a base station simultaneously deploys a transmitting movable antenna array and a receiving movable antenna array. Compared with a model in which a transmitting movable antenna array and a receiving movable antenna array are deployed as the same array, the transmitting and receiving arrays can be independently optimized and configured according to actual needs, thereby reducing interference and improving signal quality. In the perception stage and the communication stage, the movable antennas are moved according to corresponding index requirements, which can greatly improve the performance of perception and communication, and has research and application value. Robust beamforming is designed based on the estimation range, which is more close to the actual complex safety scenario. When estimating the spatial angle of arrival, the Monte Carlo method is used for multiple estimations, and the worst-case safety rate is optimized, further improving the robustness of the proposed scheme. BRIEF DESCRIPTION OF DRAWINGS

[0077] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the description of the embodiments of the present application will be briefly introduced. Obviously, the drawings in the following description are only some embodiments of the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0078] Figure 1 Method flowchart provided for the present application;

[0079] Figure 2 System model diagram provided for the present application;

[0080] Figure 3 Process flowchart of the movable antenna assisted sensing algorithm provided for the present application;

[0081] Figure 4 Process flowchart of the robust beamforming design algorithm provided for the present application;

[0082] Figure 5 Process flowchart of the movable antenna assisted secure communication algorithm provided for the present application;

[0083] Figure 6 Cramer-Rao lower bound with sensing power change diagram provided for the present application;

[0084] Figure 7 Secure rate with maximum communication transmit power change diagram provided for the present application;

[0085] Figure 8 Secure rate of robust scheme and non-robust scheme with different eavesdropper positions change diagram provided for the present application. DETAILED DESCRIPTION

[0086] The technical solutions in the embodiments of the present application will be described clearly and completely below with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0087] Figure 1 Method flowchart provided for the present application. As shown in Figure 1 the method comprises: modeling a channel, obtaining eavesdropper information by adjusting an antenna position and receiving a preset signal in a first stage, and transmitting a preset vector and adjusting the antenna position based on the eavesdropper information in a second stage; using a worst-case secure rate as an objective function, obtaining a first problem and a second problem based on maximizing the worst-case secure rate objective; converting the first problem and the second problem into optimization problems to obtain solving steps of the first problem and the second problem; and maximizing the worst-case secure rate by a first algorithm, a second algorithm and a third algorithm.

[0088] Figure 2System model diagram provided for the present application. Consider a mobile antenna assisted ISAC system, including a full-duplex millimeter wave base station capable of sensing and communication, a legitimate user and a sensing target (passive eavesdropper). Assume that the base station is equipped with N transmit mobile antennas and M receive mobile antennas, while the legitimate user and the eavesdropper are equipped with a single fixed-position antenna. The legitimate user and the eavesdropper are located on the same side, which usually results in higher channel correlation between them compared to being located on different sides. Therefore, the physical elevation angle and the directional angle range of the area where the legitimate user and the eavesdropper can be deployed are both [0, π].

[0089] Since the channel gain of the line-of-sight link dominates the channel gain of the non-line-of-sight link in millimeter wave systems, the present application considers a line-of-sight link channel model. Assume that the channel state information of the legitimate user is available, while the channel state information of the eavesdropper is unknown at the base station. As shown in Figure 2 To estimate the channel state information of the eavesdropper to enable secure communication, the present application proposes a sensing-assisted secure communication method for a mobile antenna assisted secure communication system, which divides each transmission frame into two stages, i.e., a sensing eavesdropper stage and a secure communication stage. Assume that the length of a coherent transmission frame and the duration of each sensing beam are (T + 2τ a + τ d , and τ, respectively, τ d is the fixed time to estimate the distance between the base station and the eavesdropper, and τ a is the fixed time for each antenna movement.

[0090] In the sensing stage, the base station first moves the positions of the transmit mobile antennas and the receive mobile antennas, then transmits L sensing beams and collects all the echo signals to estimate the direction of the eavesdropper.

[0091] In the secure communication stage, the base station transmits confidential information to the legitimate user by moving the position of the transmit mobile antennas and designing secure beamforming, avoiding leakage to the eavesdropper within the estimated range of the eavesdropper.

[0092] First, model the sensing channel. In the transmit region and the receive region of the mobile antennas, respectively, establish a Cartesian coordinate system, the base station is equipped with N transmit mobile antennas and M receive mobile antennas, the coordinates of the nth transmit mobile antenna are written as and the coordinates of the mth receive mobile antenna are written as The position set of the N transmit mobile antennas is The position set of the M receive mobile antennas is

[0093] The physical elevation and azimuth of the line-of-sight link between the base station and the eavesdropper are denoted as θ s and The angle of departure (AoD) and angle of arrival (AoA) are defined as and v s = cos θ s ∈ [-1, 1]. Let χ s = [u s , v s ] T ∈ [-1, 1] x [-1, 1], then The propagation distance difference between the nth transmit antenna and the mth receive antenna and their corresponding coordinate origins is calculated. Then the transmit and receive field response vectors and channel matrix of the channel between the base station and the eavesdropper are:

[0094]

[0095]

[0096] wherein, represents a complex channel coefficient, d be represents the distance from the base station to the eavesdropper, λ represents the wavelength, and ε represents the radar cross section of the target.

[0097] Secondly, the communication channel is modeled. Let c be the legitimate user and e be the eavesdropper) represent the channel vector of the communication, wherein is given by the following formula:

[0098] is the field response vector from the base station to the legitimate user or the eavesdropper, is the channel response of the base station to the legitimate user, is the channel response of the base station to the eavesdropper. Wherein, is the signal propagation distance difference, is the phase difference.

[0099] In the sensing phase, since the channel of the legitimate user is known, it can be directly used. The eavesdropper channel information will be estimated by the sensing method. A discrete Fourier transform codebook of L beams is used for beam scanning. In the lth beam stage, the expression of the received echo signal is:

[0100]

[0101] wherein, p s represents the transmit power of the base station, represents the scanning signal transmitted by the base station, z s(l) represents the noise at the base station receiving end, whose variance is After L beam sweeping, the echo signal received by the base station can be represented as:

[0102]

[0103] where, is the set of sweeping signals transmitted by the base station, Z s = [z s (1), z s (2),..., z s (L)] is the set of noise at the base station end, is the variance. In order to ensure uniform sensing performance, X s generates an omnidirectional beam in the angle domain, uniformly scans the target in all possible directions, and generally requires X s is a row orthogonal matrix, and the corresponding covariance matrix is:

[0104]

[0105] The above formula holds if and only if L≥N. At this time, After receiving the echo signal, the maximum likelihood estimation method is used to estimate the spatial arrival angle χ s = [u s , v s ] T , and the obtained estimation value is The Cramer-Rao lower bound (CRLB) of the estimation is derived. After completing the angle estimation, the base station transmits a directional beam to obtain the echo time delay calculation d be .

[0106] In the secure communication phase, based on the spatial arrival angle χ s = [u s , v s ] T obtained in the sensing phase, the base station transmits a robust beamforming vector is designed and the position of the movable antenna is moved to realize the secure communication of the legitimate user.

[0107] The transmission rate of the legitimate user is:

[0108]

[0109] The eavesdropping rate of the eavesdropper is:

[0110]

[0111] To evaluate the accuracy of the angle estimation, mean square error (MSE) can be used, but the expression of MSE is difficult to obtain, so CRLB is used instead. Assuming that the probability density function (PDF) of the estimation error obeys a Gaussian distribution with zero mean and CRLB variance, the distance estimation error problem is not considered in this application. The CRLB of the estimated spatial arrival angle can be expressed as:

[0112]

[0113] To ensure the sensing performance, it is assumed that The maximum threshold of is η. The real spatial arrival angle of the eavesdropper is located in The probability that the real spatial arrival angle of the eavesdropper is located in the range of is 0.9973. In order to reduce the computational complexity and improve robustness, let var(a) is the variance of vector a, and cov(a, b) represents the covariance of vectors a and b.

[0114] For the movable antenna movement problem in the sensing phase, in order to make the antenna movement in the sensing phase obtain better sensing performance, the following minimization problem is proposed:

[0115]

[0116] C1 represents the movement range constraint of the transmitting and receiving movable antennas. In this application, it is considered that is a convex two-dimensional region. C2 represents the minimum distance between two adjacent transmitting movable antennas, which is non-convex. C3 represents the minimum distance between two adjacent receiving movable antennas, which is non-convex. C4 represents the maximum threshold constraint of CRLB. The optimization problem is non-convex, and can be efficiently solved by alternating optimization: fixing other variables, optimizing one variable, and repeating the process.

[0117] For the joint optimization problem in the communication phase, in order to jointly consider the influence of antenna movement, sensing result and secure beamforming, the two-stage joint optimization problem about ω is proposed to maximize the worst-case secure rate while satisfying the CRLB threshold constraint. The optimization problem P2 can be written as:

[0118]

[0119] s.t.C1:||ω|| 2 ≤P t ,

[0120]

[0121] where [X] += max(X, 0). The objective function of optimization problem P2 represents the worst-case scenario for all potential estimates Optimizing antenna positions to maximize the safe rate, and for each sensing result Designing a robust safe beamforming ω to avoid information leakage for all potential estimates within the range. C1 is the maximum communication transmission power constraint of the base station. C2 is the moving range constraint of the transmitting movable antenna. C3 is the minimum distance between two adjacent transmitting movable antennas, which is non-convex. C4 is the range of the true spatial angle of arrival. C5 is the range of the estimated .

[0122] Since the objective function of problem P2 is complex and contains non-convex constraints, it is a difficult problem to solve directly. To solve this problem, it is decomposed into two sub-problems and solved by reverse induction.

[0123] The following is the movable antenna movement problem in the sensing phase. According to the Cauchy-Schwarz inequality, the non-convex constraints C2, C3 of optimization problem P1 can be written as:

[0124]

[0125] where t a p = [x a p , y a ] T , r b p = [x b p , y b ] T , t a p and r b p represent the positions of the transmitting antenna and the receiving antenna in the pth iteration, respectively. Therefore, the constraints C2, C3 can be relaxed into linear form, represented as:

[0126]

[0127] where a, b, represent the serial numbers of the movable antennas.

[0128] Since the constraint C4 of optimization problem P1 is non-convex, it can be converted into a convex constraint condition using the continuous convex approximation method. The constraint C4 can be re-expressed as:

[0129]

[0130] where, is a constant. Rewrite the re-expressed constraint C4 as a standard quadratic form, first write var(x t ), var(x r ), var(y t ), var(y r ), cov(x t , y t ), cov(x r , y r ) as:

[0131]

[0132] where, B1, B2 are both positive semi-definite matrices. Thus the re-expressed constraint C4 is equivalent to:

[0133]

[0134] Let the horizontal coordinate set of the transmitting movable antenna be and the vertical coordinate set be Let the horizontal coordinate set of the receiving movable antenna be and the vertical coordinate set be

[0135] (1) Fix x r , y t , y r , optimize x t .

[0136] Given the x t obtained in the pth iteration, Since x T t B1x t is convex about x N , perform a first-order Taylor expansion at x p to obtain the global lower bound:

[0137] x t T B1x t ≥(x t p ) T B1x t p +2(x t p ) T B1(x t -x t p )=2(x t p ) TB1x t -(x t p ) T B1x t p

[0138] When x r ,y t ,y r is given, (x t T B1y t ) 2 = x t T B1y t y t T B1x t is a convex quadratic function about x t , 2x t T B1y t x r T B2y r is a linear function about x t . Therefore, in the pth iteration of the continuous optimization, the constraint C4 of the optimization problem P1 is relaxed to a convex quadratic constraint for x t , i.e.:

[0139]

[0140] Therefore in the pth iteration, the optimization problem for x t can be relaxed as:

[0141]

[0142]

[0143] Since P3 is a convex optimization problem, it can be solved efficiently using existing optimization toolboxes such as fmincon.

[0144] (2) Fix x t , x r , y r , optimize y t .

[0145] The optimization step is the same as (1), and the optimization problem P1 can be represented as:

[0146]

[0147] (3) Fix x t , y t , y r , optimize xr .

[0148] The optimization step is the same as (1), and the optimization problem P1 can be expressed as:

[0149]

[0150] (4) Fix x t ,y t ,x r , optimize y r .

[0151] The optimization step is the same as (1), and the optimization problem P1 can be expressed as:

[0152]

[0153] The following is to solve the robust beamforming problem in the joint optimization problem. Given the perception result, it is solved by using reverse induction method, first fix the position of the transmitting movable antenna In the range of robust beamforming ω. By setting ω = 0, it can be ensured that the objective function of P2 is non-negative, and the optimization problem P2 can be re-expressed as:

[0154]

[0155] s.t.C1:||ω|| 2 ≤P t ,

[0156]

[0157] Considering that log2(·) is a monotonically increasing function, the optimization problem P7 can be written as:

[0158]

[0159] s.t.C1:||ω|| 2 ≤P t ,

[0160]

[0161] wherein, is the channel matrix of the user, is the channel matrix of the eavesdropper, is the noise variance at the user, which is the same as the noise variance at the eavesdropper.

[0162] A convex hull is constructed to approximate the range of the angle of arrival: μ k is the weighting coefficient, For the k-th sample element, K is the number of samples. Then, the following equations are equivalent:

[0163]

[0164] To obtain the beamforming weight vector, let The optimization problem P8 can be written as:

[0165]

[0166] s.t. C1: ||ω||2 2 = 1, P≤P t ,

[0167]

[0168] The robust beamforming weight vector can be obtained analytically by a heuristic method: first, select K discrete samples, obtain Then, given P and {μ k}, since is a Hermitian matrix, is both a Hermitian matrix and a positive definite matrix, then the form of the generalized Rayleigh quotient is:

[0169]

[0170] s.t. C1: ||ω||2 2 = 1,

[0171] By calculation, we have is the maximum generalized eigenvector, denotes the maximum generalized eigenvalue, eig(A, B) is the generalized eigenvector corresponding to the maximum generalized eigenvalue of the matrix pair (A, B), λ max (A, B) is the maximum generalized eigenvalue.

[0172] Because in the objective function of the optimization problem P9, the numerator is the legitimate user communication related term, and the denominator is the eavesdropper communication related term, in general, the enhancement of the legitimate user communication signal to the objective function will be greater than the suppression of the eavesdropping communication signal to the objective function. The objective function is a monotonically increasing function of P, P * = P t .

[0173] The value of μ k is to minimize the objective function of the optimization problem P9, and by using the Cauchy-Schwarz inequality, we have:

[0174]

[0175] iff The equation holds iff We have

[0176]

[0177] The following is to solve the problem of moving the transmitting movable antenna in the joint optimization problem. Now we will discuss the optimization problem of the transmitting movable antenna position in the communication phase, by considering all possible spatial angles of arrival and the corresponding robust beamforming vector ω * of each sensing result, to maximize the worst-case secure rate. The optimization problem P2 can be rewritten as

[0178]

[0179] Due to the randomness of caused by additive white Gaussian noise, it is difficult to obtain a closed-form expression of the objective function of the optimization problem P11. Therefore, the present application uses the method of Monte Carlo simulation to obtain multiple sensing results, and for the worst-case secure rate among them, the movable antenna position is moved to maximize it.

[0180] (1) Fix y t , optimize x t .

[0181] Since the optimization problem P11 is a non-convex problem, a continuous convex approximation method can be used to convert it into a convex optimization problem. Similar to the relaxation method of optimization problem P3, optimization problem P11 can be rewritten as

[0182]

[0183] Transforming the constraint C2 of the optimization problem P12 into a standard linear constraint about x t :

[0184]

[0185] where is the constant vector of the linear constraint, and the non-zero elements of the sparse matrix can be defined as

[0186]

[0187] where represents the element index of the vector or the row index of the matrix. Since the optimization problem P12 is a convex optimization problem, it can be effectively solved by the feasible direction method. In the pth iteration, the following ascending direction finding subproblem is solved first:

[0188]

[0189] where, is x t p At R(x t ,y t ), the gradient of, is the position of the transmit antenna corresponding to d[n]. The nth element of can be written as:

[0190]

[0191] where, is a vector with the nth entry equal to 1 and other entries equal to 0. Assuming the antenna moving region is rectangular, the constraint C1 is linear, and the objective function and the constraint C2 are also linear, the optimization problem P13 is a linear programming problem. This kind of problem can be solved efficiently by means of existing optimization algorithms or toolboxes, for example, the linprog function of MATLAB software.

[0192] Next, the step size is determined by solving the following one-dimensional search problem:

[0193]

[0194] can be obtained by exhaustive search in the interval [0, 1] Finally, x t p+1 is updated as:

[0195] x t p+1 = x t p + τ(d - x t p )

[0196] (2) Fix x t , optimize y t .

[0197] The optimization problem P11 can be rewritten as:

[0198]

[0199] The solution steps of the optimization problem P14 are the same as those of the optimization problem P12.

[0200] The first algorithm, the second algorithm and the third algorithm correspond to the movable antenna assisted sensing algorithm, the robust beamforming design algorithm and the movable antenna assisted secure communication algorithm of the present application, respectively.

[0201] The application optimizes the position of the transmitting and receiving movable antennas (movable antenna assisted sensing algorithm) in the sensing phase to minimize the CRLB of the estimated spatial angle of arrival, and optimizes the beamforming vector (robust beamforming design algorithm) and the position of the transmitting movable antenna (movable antenna assisted safe communication algorithm) in the communication phase to maximize the worst-case safe rate. The specific algorithm steps of the three algorithms are written below respectively.

[0202] The steps of the movable antenna assisted sensing algorithm are as follows:

[0203] (1) Set the number of transmitting movable antennas N, the number of receiving movable antennas M, the moving area of the transmitting movable antennas The distance D between the two antennas, the moving area of the receiving antennas Set J different starting positions

[0204] (2) Let the loop serial number j=0, p=0, q=0, a=0, b=0, and the accuracy threshold ε1=10 -3 , initialize the threshold value of CRLB η=0.005,

[0205] (3) Repeat the following steps: p=p+1, given y t 0 ,x r 0 ,y r 0 Solve the optimization problem P3 until the absolute value of the increment of η in the pth loop is less than ε1, end the loop, and output x t s =x t p ;

[0206] (4) Repeat the following steps: q=q+1, given x t s ,x r 0 ,y r 0 Solve the optimization problem P4 until the absolute value of the increment of η in the qth loop is less than ε1, end the loop, and output y t s =y t q ;

[0207] (5) Repeat the following steps: a=a+1, given x t s ,y t s ,y r0 , solve optimization problem P5 until the absolute value of the increment of η in the a-th iteration is less than ε1, end the loop, and output x r s = x r a ;

[0208] (6) Repeat the following steps: b = b + 1, given x t s , y t s , x r s , solve optimization problem P6 until the absolute value of the increment of η in the b-th iteration is less than ε1, end the loop, and output y r s = y r b ;

[0209] (7) If j ≠ J, let j = j + 1, and repeat steps (2)-(6); if j = J, select x t s , y t s , x r s , y r s as the position selection of the transmitting movable antenna and the receiving movable antenna in the sensing phase, as shown in the specific flowchart of Figure 3 .

[0210] The following are the steps of the robust beamforming design algorithm:

[0211] (1) Set the channel vector from the base station to the user the transmit power P t of the transmitting movable antenna

[0212] (2) Let the loop number m = 0, and the precision threshold ε2 = 10 -3 , initialize P = P t ,

[0213] (3) Assume that u s and v s both obey uniform distribution in [-1, 1], and further establish

[0214] (4) Obtain and γ 0 by solving optimization problem P10;

[0215] (5) Repeat this step: m = m + 1, according to the formula Update μ k m ,calculate and γ m Until the objective function γ in the m-th iteration. m With the objective function γ of the (m-1)th cycle m-1 Satisfy condition | γ m -γ m-1 The loop ends when |≤ε2;

[0216] (6) Order The detailed flowchart is as follows: Figure 4 As shown.

[0217] The following are the steps of the movable antenna-assisted secure communication algorithm:

[0218] (1) Set the number of movable transmitting antennas N, and the moving area of ​​the movable transmitting antennas. The distance D between the two antennas, the number of noise samples I, and the channel vector from the base station to the user. Transmit power P during communication phase t ;

[0219] (2) Let the cycle number i = 0, p = 0, q = 0, and the precision threshold ε3 = 10. -3 Initialize x t 0 =x t s y t 0 =y t s The location of the movable antenna transmitted during the sensing phase is used as the initial value for the location of the movable antenna transmitted during the communication phase.

[0220] (3) If i ≠ I, let i = i + 1, and use the maximum likelihood estimation method to obtain the noisy estimate AoA. For each estimation result, the corresponding robust beamforming vector ω is obtained through a robust beamforming design algorithm, and this step is repeated; if i = I, the minimum safe rate and the corresponding...

[0221] (4) Repeat the following steps: based on the minimum safe rate and y t 0 Calculate the gradient Solve the optimization problem P13 to obtain d, calculate the step size τ, and update x. t p+1 Let p = p + 1, until R(x) t p ,yt ) is less than ε3, and get x t ;

[0222] (5) Repeat the following steps: according to the minimum safety rate corresponding to and x t 0 , calculate the gradient Solve the optimization problem P14 to get d, calculate the step size τ, update y t q+1 , let q = q + 1, until R(x t ,y t q ) is less than ε3, and get y t ;

[0223] (6) Repeat steps (4)-(5) until the worst-case safety rate R(x t ,y t ) increases by less than ε3, and the specific flow chart is shown in Figure 5 .

[0224] In the sensing phase, the application estimates the spatial angle of arrival of the eavesdropper by moving the position of the movable antenna to emit a scanning beam. Figure 6 The sensing scheme proposed in the application is compared with the lower bound of the Cramér-Rao bound threshold η, the CRLB index of the uniform planar array with a distance of , the maximum aperture uniform planar array, the random antenna position scheme, and the antenna selection scheme (here ), it can be clearly seen that as the sensing power increases, the CRLB of the scheme proposed in the application is significantly better than other benchmark schemes and very close to the lower bound of the threshold η, which reflects that the spatial degree of freedom realized by the movement of the movable antenna significantly improves the sensing performance, and it is necessary to move the antenna in the sensing phase.

[0225] In the communication phase, the application moves the position of the movable antenna and designs a robust beamforming based on the estimated range. In Figure 7 , “no antenna movement” represents a scheme that does not move the antenna in the communication phase, “antenna movement” represents a scheme that moves the antenna in the communication phase, and “30m”, “50m”, “70m”, “90m” represent the distance between the legitimate user and the base station. Figure 7 It is shown that as the communication transmit power increases, the worst-case safety rate also increases, and the closer the legitimate user is to the base station, the greater the worst-case safety rate. In addition, the performance of the scheme without antenna movement in the communication phase is significantly lower than that of the scheme with antenna movement, and it can be seen that the spatial diversity gain realized by the movement of the antenna significantly improves the communication performance, and it is also very necessary to move the antenna in the communication phase.

[0226] The blue part represents the robust beamforming scheme proposed in the present application, and the red part represents the scheme of designing beamforming for the estimated spatial angle of arrival. It can be seen that the robust scheme can keep the security rate at a high level regardless of the change of the position of the eavesdropper, while the non-robust scheme is susceptible to noise due to the estimation of the angle of arrival, and the security rate achieved has certain randomness and cannot be maintained at a stable high performance, which reflects that the beamforming design of the present application has strong robustness. Figure 8

[0227] In several embodiments provided in the present application, it should be understood that the disclosed method and device can be implemented in other ways. For example, the above-described device embodiment is only schematic, for example, the division of the unit is only a logical function division, and actual implementation can have another division manner, for example, a plurality of units or components can be combined or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the units shown or discussed can be indirect coupling or communication connection through some interface, device or unit, and can be electrical, mechanical or other forms.

[0228] The above is the preferred embodiment of the present application, and it should be pointed out that for ordinary skilled in the art, without departing from the principles described in the present application, a number of improvements and refinements can be made, and these improvements and refinements should be considered as the protection scope of the present application.​

Claims

1. A sensing-assisted secure communication method for a movable antenna-assisted secure communication system, wherein the movable antenna-assisted secure communication system includes a full-duplex millimeter-wave base station capable of sensing and communicating, a legitimate user, and an eavesdropper; the base station is equipped with N transmitting movable antennas and M receiving movable antennas; the legitimate user and the eavesdropper are equipped with a single fixed-position antenna; each transmission frame of the base station is divided into two stages: an eavesdropper sensing stage and a secure communication stage; characterized in that... The perception-assisted secure communication method includes the following steps: During the eavesdropper detection phase, the base station adjusts the positions of the transmitting and receiving movable antennas, transmits L sensing beams and collects all echo signals to obtain an estimate of the eavesdropper's angle of arrival. In the secure communication phase, based on the range of the eavesdropper obtained in the perception phase, a robust beamforming vector transmitted by the base station is designed to determine the transmission security rate of legitimate users and the eavesdropping rate of the eavesdropper. Establish a two-stage joint optimization problem to maximize the transmission security rate of legitimate users in the worst case, while satisfying perception constraints. Solve the joint optimization problem established above to achieve secure communication for legitimate users.

2. The method according to claim 1, characterized in that, During the eavesdropper detection phase, the base station adjusts the positions of the transmitting and receiving movable antennas, transmits L sensing beams and collects all echo signals to obtain an estimated value of the eavesdropper's spatial angle of arrival. include: The sensing channel and the communication channel are modeled separately. For the modeling of the sensing channel, the transmission area of ​​the movable antenna is set. and the receiving area of ​​the movable antenna Using a Cartesian coordinate system, the base station is equipped with N movable transmitting antennas and M movable receiving antennas. The coordinates of the nth movable transmitting antenna are t. n The coordinates of the m-th receiving movable antenna are r. m Based on the physical elevation angle θ of the line-of-sight link between the base station and the eavesdropper s and azimuth Obtain the spatial departure angle u s and spatial arrival angle v s The angle of arrival, expressed in vector form, is χ. s =[u s ,v s ] T The angle of arrival χ, expressed in vector form s Establish launch site response function With the received field response function Finally, the channel matrix is ​​obtained. in, Let N be the set of locations of the movable transmitting antennas. Let M be the set of locations of the movable receiving antennas; For modeling communication channels, channel vectors for legitimate user communication are defined respectively. and the channel vector of the eavesdropper's communication χ c χ is the angle of arrival for legitimate users. e Given the angle of arrival of the eavesdropper, the channel vector is obtained. sum field response vector Where i∈{c,e}, c is a legitimate user, and e is an eavesdropper.

3. The method according to claim 2, characterized in that, include: The base station uses a discrete Fourier transform codebook of L beams for beam scanning to receive echo signals. Where y s (l) represents the echo signal received in the l-th beam stage; Received echo signal Y s Then, the spatial arrival angle of the eavesdropper is estimated using the maximum likelihood method. After completing the angle estimation, the base station transmits a directional beam, obtains the echo delay, and calculates the distance d between the base station and the eavesdropper. be .

4. The method according to claim 3, characterized in that, In the secure communication phase, based on the range of the eavesdropper obtained in the sensing phase, a robust beamforming vector transmitted by the base station is designed to determine the transmission security rate for legitimate users and the eavesdropping rate for the eavesdropper; including: During the secure communication phase, the range of the true spatial arrival angle of the eavesdropper is obtained based on the perception phase. Design a robust beamforming vector ω for base station transmission, move the position of the movable transmitting antenna to achieve secure communication for legitimate users, and determine the transmission rate R for legitimate users. c And the eavesdropper's eavesdropping rate R e .

5. The method according to claim 4, characterized in that, A two-stage joint optimization problem is established to maximize the transmission security rate of legitimate users in the worst case, while simultaneously satisfying perception constraints; including: The two-stage optimization problem is divided into the movable antenna movement problem in the eavesdropper detection stage and the joint transmission movable antenna movement and robust beamforming optimization problem in the secure communication stage. By setting the probability density function of the estimation error to follow a Gaussian distribution with zero mean and a Cramer-Rao lower bound variance as a preset condition, the first Cramer-Rao lower bound of the estimated spatial angle of arrival is obtained. and the second carmelo lower realm Set the first Clamello lower boundary and the second carmelo lower realm The maximum threshold η and the range of the true value of the eavesdropper's spatial arrival angle These are preset conditions.

6. The method according to claim 5, characterized in that, include: For the problem of moving movable antennas during the sensing phase, a Cramer-Rao lower bound minimization problem P1 and its constraints are proposed to achieve better sensing performance during the sensing phase: Where C1 is the movement range constraint of the transmitting and receiving movable antennas, C2 is the minimum distance between two adjacent transmitting movable antennas, C3 is the minimum distance between two adjacent receiving movable antennas, and C4 is the maximum threshold constraint of the Cramero lower bound. For the joint optimization problem of movable antenna movement and robust beamforming during secure communication, the effects of antenna movement, sensing results, and secure beamforming are jointly considered to obtain the following... The two-stage joint optimization problem P2 of ω: s.t.C1:||ω|| 2 ≤P t , Among them, [X] + =max(X,0), C1 is the maximum communication transmission power constraint of the base station, C2 is the movement range constraint of the transmitting movable antenna, C3 is the minimum distance between two adjacent transmitting movable antennas, C4 is the range of the actual spatial angle of arrival, and C5 is the range of the estimated spatial angle of arrival of the eavesdropper. The objective function of the optimization problem P2 represents the worst-case estimate of the spatial angle of arrival for all eavesdroppers. Optimize antenna position To maximize the security rate, and for each eavesdropper's spatial angle of arrival estimate Design robust and secure beamforming ω to avoid estimating the true value of the eavesdropper's spatial angle of arrival. Information leakage within the scope.

7. The method according to claim 6, characterized in that, Solve the joint optimization problem established above to achieve secure communication for legitimate users. This includes: For the problem of moving a movable antenna during the eavesdropper's perception phase, according to the Cauchy-Schwarz inequality, we obtain the constraints C2 and C3 of the transformed optimization problem P1: Among them, t a p =[x a p ,y a ] T ,r b p =[x b p ,y b ] T , t a p Let r be the position of the transmitting antenna in the p-th iteration. b p Let a be the position of the receiving antenna in the p-th iteration. b, All of these represent the serial numbers of the movable antennas; The constraint C4 of optimization problem P1 is transformed using the continuous convex approximation method, resulting in the first transformed constraint C4 of optimization problem P1: Where β is a constant, the constraint C4 of the optimization problem P1 in the first transformation is transformed into a standard quadratic form, resulting in the standard quadratic form of the constraint C4 of the optimization problem P1: in, For vector x t variance For vector x r variance Let y be a vector t variance Let y be a vector r variance For x t ,y t covariance, For x r ,y r covariance, and All are positive semi-definite matrices; Set the x-coordinate set for transmitting the movable antenna. t The set of ordinates y for transmitting movable antennas t The set of x-coordinates for receiving movable antennas r and the set of y coordinates for receiving movable antennas r The set of x-coordinates of a fixed receiving movable antenna r The set of ordinates y for receiving movable antennas r The set of y coordinates for transmitting movable antennas t After several iterations, the transformation is performed to obtain the set of x-coordinates of the transmitting movable antenna. t Minimize the maximum threshold of the Cramérault lower bound P3: The set of x-coordinates for a fixed receiving movable antenna r The set of ordinates y for receiving movable antennas r and the set of x-coordinates of the transmitting movable antenna. t After several iterations, the transformation is performed to obtain the set of ordinates y for transmitting the movable antenna. t Minimize the maximum threshold of the lower bound of Cramérault (P4): The set of x-coordinates of a fixed transmitting movable antenna t The set of ordinates y for transmitting movable antennas t and the set of y coordinates for receiving movable antennas r After several iterations, a transformation is performed to obtain the set of x-coordinates of the receiving movable antenna. r Minimize the maximum threshold of the Cramérault lower bound (P5): The set of x-coordinates of a fixed transmitting movable antenna t The set of ordinates y for transmitting movable antennas t and the set of x-coordinates of the receiving movable antenna. r After several iterations, a transformation is performed to obtain the set of ordinates y for receiving movable antennas. r Minimize the maximum threshold of the Cramérault lower bound (P6): The problem of moving the movable antenna during the eavesdropper's perception stage is solved by using a movable antenna-assisted sensing algorithm. The loop number, the x-coordinate of the transmitting movable antenna, the y-coordinate of the transmitting movable antenna, the x-coordinate of the receiving movable antenna, and the y-coordinate of the receiving movable antenna are initialized, and the first accuracy threshold ε1 is set. In the first stage of the loop, the horizontal coordinate of the receiving movable antenna, the vertical coordinate of the receiving movable antenna, and the vertical coordinate of the transmitting movable antenna are fixed, while the horizontal coordinate of the transmitting movable antenna is optimized. The second stage loop fixes the x-coordinate of the receiving movable antenna, the y-coordinate of the receiving movable antenna, and the x-coordinate of the transmitting movable antenna, while optimizing the y-coordinate of the transmitting movable antenna. The third stage of the cycle fixes the x-coordinate of the transmitting movable antenna, the y-coordinate of the transmitting movable antenna, and the y-coordinate of the receiving movable antenna, while optimizing the x-coordinate of the receiving movable antenna. The fourth stage of the cycle fixes the x-coordinate of the transmitting movable antenna, the y-coordinate of the transmitting movable antenna, and the x-coordinate of the receiving movable antenna, while optimizing the y-coordinate of the receiving movable antenna. Each stage is repeated until the absolute value of the lower bound threshold of two consecutive Cramer-Rao thresholds is less than the first accuracy threshold ε1, thus obtaining the optimal values ​​of the x-coordinate of the transmitting movable antenna, the optimal values ​​of the y-coordinate of the transmitting movable antenna, the optimal values ​​of the x-coordinate of the receiving movable antenna, and the optimal values ​​of the y-coordinate of the receiving movable antenna.

8. The method according to claim 7, characterized in that, The joint optimization problem of movable antenna movement and robust beamforming in the secure communication phase is a joint optimization problem. The objective function of the joint optimization problem is complex and contains non-convex constraints. The joint optimization problem is decomposed into a robust beamforming problem in the secure communication phase and a movable transmitting antenna movement problem in the secure communication phase.

9. The method according to claim 8, characterized in that, The solution process for the robust beamforming problem in the secure communication phase includes: The range of the true value of the spatial arrival angle of the eavesdropper Several discrete samples are selected based on a heuristic method, and a first weight μ is set. k Given the preset conditions, we obtain the robust beamforming vector maximization problem P10: s.t.C1:||ω|| 2 =1, in, For the user's channel matrix, For the eavesdropper's channel matrix, The noise variance at the user's location is the same as the noise variance at the eavesdropper's location; The first weight μ is obtained by applying the Cauchy-Schwarz inequality and ensuring that its equality holds. k optimal value The variables in the robust beamforming vector maximization problem P10 include the maximum generalized eigenvector eig(A,B) and the maximum generalized eigenvalue λ. max (A,B); The robust beamforming problem in the secure communication phase is solved using a robust beamforming design algorithm. A second accuracy threshold ε2 is set, and the loop number m = 0 and the second weight μ are initialized. k 0 ; The initial condition is that the spatial departure angle follows a uniform distribution in the interval [-1,1]. The initial values ​​of the maximum generalized eigenvector and the maximum generalized eigenvalue are obtained by solving the robust beamforming vector maximization problem P10. In the m-th loop, let m = m + 1, according to the first weight μ k Update the second weight μ in the m-th loop. k m Until the objective function γ in the m-th iteration. m With the objective function γ of the (m-1)th cycle m-1 Satisfy condition | γ m -γ m-1 The loop ends when |≤ε2, and the optimal value of the robust beamforming vector is obtained.

10. The method according to claim 9, characterized in that, The solution process for the optimization problem of the movable antenna position during the secure communication phase includes: Rewriting optimization problem P2, we get optimization problem P11: By fixing the ordinate of the movable transmitting antenna, we obtain the optimization problem P12: Solving the problem of maximizing the x-coordinate of a movable transmitting antenna using the feasible direction method (P13): in, For x t p In R(x) t ,y t The gradient of ) Let d[n] be the position of the transmitting antenna. A constant vector of linear constraints. It is a sparse matrix; The step size τ is obtained by exhaustive search within the interval [0,1], and finally the updated x-coordinate of the transmit movable antenna is obtained; By fixing the x-coordinate of the movable transmitting antenna, we obtain the problem of maximizing the y-coordinate of the movable transmitting antenna, P14: To solve the problem of maximizing the ordinate of the transmitting movable antenna (P14), the gradient of the objective function is calculated using the same method as that used for maximizing the abscissa of the transmitting movable antenna (P13). The step size τ is then obtained through exhaustive search within the interval [0,1], and finally, the updated ordinate of the transmitting movable antenna is obtained. The problem of transmitting movable antenna movement during the secure communication phase is solved using a movable antenna-assisted secure communication algorithm. The number of noise samples is set to I, and the loop sequence numbers i = 0, p = 0, q = 0 are initialized. The accuracy threshold ε3 and the initial x-coordinate of the transmitting movable antenna are also set. t 0 and the initial value of the ordinate y of the transmitting movable antenna. t 0 ; In the i-th loop, let i = i + 1, and use the maximum likelihood estimation method to obtain the noisy estimated angle of arrival. For each estimation result, the corresponding robust beamforming vector v is obtained through a robust beamforming design algorithm until i = I, and the minimum safe rate and the corresponding noisy estimated angle of arrival are output. In the p-th loop, estimate the angle of arrival with noise based on the minimum safe rate. and the initial value of the ordinate y of the transmitting movable antenna. t 0 Calculate the first gradient Solve the problem of maximizing the ordinate of the transmitting movable antenna on page 13, calculate the step size τ, and update... Let p = p + 1, until R(x) t p ,y t The increment of ) is less than ε3, thus obtaining the x-coordinate of the transmitting movable antenna. t ; In the q-th loop, estimate the angle of arrival with noise based on the minimum safe rate. and the initial value of the horizontal coordinate x of the transmitting movable antenna. t Calculate the second gradient Solve optimization problem P14, calculate step size τ, and update y. t q+1 Let q = q + 1, until R(x t ,y t q The increment of ) is less than ε3, thus obtaining the ordinate y of the transmitting movable antenna. t ; Iteratively update the x-coordinate of the transmitting movable antenna. t and the ordinate y of the transmitting movable antenna t Until the worst-case safe rate R(x) t ,y t The increment is less than ε3.

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