A method and system for ultra-large scale movable antenna assisted hybrid beamforming near field secure communication

Abstract

The application relates to the technical field of wireless communication, and proposes a kind of ultra-large-scale movable antenna assisted hybrid beamforming near-field secure communication optimization method and system, constructs pure sight distance spherical wave near-field communication model including two-dimensional movable antenna array, hybrid beamformer, legal user and eavesdropper, with long-term average secret rate maximization as target, antenna position and analog precoding are divided into slow time scale variable, digital precoding is divided into fast time scale variable;Fast time scale adopts weighted least mean square error-minimization minimization deep unfolding network to solve digital precoding, slow time scale adopts projection gradient ascent deep unfolding network to jointly optimize analog precoding and antenna position, and through power, constant module, boundary and anti-collision projection to meet constraint.The application expands the traditional fast-slow time scale iterative optimization process into model-driven network of preset fixed layer number, realizes security requirement, and reduces online calculation complexity and processing delay.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and more specifically, to a secure communication method and system for line-of-sight spherical wave near-field environments, employing a base station-side movable antenna array and radio frequency chain-constrained hybrid beamforming. Background Technology

[0002] With the development of millimeter waves, terahertz waves, and ultra-large-scale arrays, the effective aperture of base stations continues to increase, and more and more terminals are located in the near-field region of the array. Traditional far-field plane wave models only retain the angular dimension, making it difficult to accurately describe the propagation distance from different array elements to the terminal; near-field spherical wave models have both angular and range domain resolution capabilities, enabling the formation of different energy focusing points at the same angle but different distances.

[0003] Physical layer security is typically achieved by widening the achievable rate difference between legitimate and eavesdropping links. When legitimate users and eavesdroppers are at similar angles or adjacent in distance, or when the eavesdropper is closer to the base station than the legitimate user, fixed arrays lack sufficient spatial degrees of freedom, and near-field focusing cannot inherently guarantee secure transmission. Movable antennas can adjust the position of array elements within a limited area, altering path loss, propagation phase, and channel correlation by reconstructing array geometry, thus providing additional degrees of freedom for forming a spatial structure that "focuses on legitimate users and suppresses eavesdroppers."

[0004] Existing joint optimization methods typically employ iterative algorithms such as alternating optimization, weighted minimum mean square error, principal minimization, manifold optimization, or projected gradient, and repeatedly solve the problem after each channel change. Since antenna mechanical movement, analog phase shifter updates, and digital baseband processing have different physical update rates, iterating all variables at the same frequency leads to frequent mechanical reconfigurations, high channel state information overhead, and unpredictable online latency. Therefore, it is necessary to construct a dual-timescale method that matches the hardware update rate, preserves the physically interpretable structure, and has fixed online complexity. Summary of the Invention

[0005] The purpose of this invention is to overcome at least one of the defects of the prior art and provide a hybrid beamforming near-field secure communication method and system assisted by a large-scale movable antenna, so as to improve the security rate in difficult near-field scenarios where the user and the eavesdropper are close in angle or adjacent in distance, and reduce the online complexity and latency of traditional joint iterative optimization.

[0006] To achieve the above-mentioned technical effects, the technical solution of the present invention is as follows: A hybrid beamforming near-field secure communication method assisted by a large-scale movable antenna includes the following steps: S10: Construct a near-field secure communication model, which includes a base station equipped with a large-scale two-dimensional movable antenna array and a radio frequency chain-constrained hybrid beamformer, a legitimate user, and an eavesdropper, and adopts a precise line-of-sight spherical wave channel; S20: Establish a dual-timescale joint optimization model with the objective of maximizing the long-term average security rate. The movable antenna position and analog precoding are set as slow-timescale variables, while digital precoding is set as a fast-timescale variable. Constraints are set for transmit power, analog precoding constant modulus, antenna movement area, and minimum antenna spacing. A slow-timescale block includes... A fast timescale time slot This is a preset integer greater than 1. Let the duration of the fast timescale slot be... The duration of the slow timescale block is Then the two satisfy The fast timescale corresponds to the update period of instantaneous channel state information. The digital precoding matrix is ​​updated according to the current instantaneous channel state information in each fast timescale slot. The slow timescale corresponds to the update period of long-term statistical channel state or statistical information formed by multiple instantaneous channel samples. The movable antenna position and the analog precoding matrix are updated between slow timescale blocks and remain unchanged within each slow timescale block. S30: Within each fast timescale slot, a weighted minimum mean square error-master minimization deep expansion network oriented towards the security rate is constructed based on the current instantaneous line-of-sight channel state information. The weighted minimum mean square error term for the legitimate link and the master minimization proxy term for the eavesdropping link are constructed. The digital precoding matrix is ​​obtained through candidate digital precoding solution, inter-layer damping and power feasibility. S40: At the beginning of each slow timescale block, a projection gradient ascent depth expansion network is constructed based on long-term statistical channel state information or statistical information formed by multiple instantaneous channel samples. The network updates the analog precoding and the position of the movable antenna, and performs constant modulus projection, position boundary projection and collision avoidance correction respectively. S50: Learnable parameters are obtained through phased training using fast and slow time-scale networks. After phased training is completed, joint fine-tuning is performed using a small learning rate to output the movable antenna position, analog precoding matrix, and digital precoding matrix.

[0007] Preferably, the Rayleigh distance is calculated based on the effective aperture of the base station array and the carrier wavelength to determine whether legitimate users and eavesdroppers are located in the near-field region of the array. The base station configuration... movable antenna RF chain and transmission Data stream, each movable antenna in a fixed position of Move within the plane, the first The two-dimensional position vector of a movable antenna is represented as: , Its three-dimensional physical coordinates are determined by fixed planar coordinates. and 2D optimized position It is jointly determined that any two movable antennas satisfy a preset minimum spacing constraint.

[0008] Preferably, the near-field channel uses only the line-of-sight spherical wave component and does not superimpose additional non-line-of-sight multipath terms; if scattering, obstruction, position error, or phase error are considered, they are input as independent extended states into the depth unfolding network.

[0009] Preferably, the near-field communication model adopts a line-of-sight spherical wave propagation model. Root movable antenna and receiver No. The propagation distance between the antennas is expressed as: , in, , , , Indicates a legitimate user. Indicates eavesdropper, Indicates the receiving end The number of receiving antennas, Indicates the receiving end The The three-dimensional coordinates of the root receiving antenna. This indicates embedding two-dimensional positions. The coordinate mapping matrix of a three-dimensional plane. The corresponding pure line-of-sight channel coefficients are expressed as follows: in, Power gain at reference distance This is the path loss index. The carrier wavelength is denoted by . Since the position of the movable antenna directly affects the propagation distance and phase response, optimizing the array geometry can further enhance the channel difference between legitimate users and eavesdroppers.

[0010] Preferably, the fast timescale network combines the weighted minimum mean square error equivalence relation of the legitimate user rate with the eavesdropping link master-minimized proxy term constructed based on the current expanded layer reference point, and expands the iterative update process into a network with a preset fixed number of layers; the learnable parameters of each expanded layer include damping coefficient, eavesdropping penalty coefficient and regularization parameter.

[0011] Preferably, the slow timescale network calculates the statistical security rate gradient based on a small batch of long-term channel samples; the analog precoding uses constant modulus projection, and the movable antenna position uses boundary projection and a fixed number of collision avoidance corrections.

[0012] Preferably, the dual-timescale joint optimization model aims to maximize the long-term average security rate. Let the position vector of the movable antenna be... The simulated precoding matrix is The digital precoding matrix is The equivalent precoding matrix is Then the instantaneous security rate optimization problem can be expressed as: , in, Indicates instantaneous security rate, , For the rate achievable by legitimate users, To achieve the achievable rate for eavesdroppers. By optimizing the position of movable antennas, analog precoding, and digital precoding, the channel gain of legitimate users is enhanced, while the effective reception capability of eavesdroppers is reduced.

[0013] Preferably, the fast timescale digital precoding optimization employs a weighted minimum mean square error-mastery minimization depth expansion network. For legitimate user links, a receiver matrix is ​​introduced. and weight matrix The rate maximization problem is transformed into an equivalent weighted minimum mean square error optimization problem: in, This represents the error matrix for legitimate users.

[0014] For the eavesdropper link, a principal-minimized proxy matrix is ​​computed at the current unfolded layer reference point, and the eavesdropping link penalty term formed by the proxy matrix is ​​embedded into the digital precoding update subproblem. Each unfolded layer is configured with independently learnable damping coefficients, eavesdropping penalty coefficients, and regularization parameters. The eavesdropping link auxiliary inverse covariance matrix is ​​as follows: , No. The eavesdropping link master-minimized proxy matrix calculated by each unfolded layer at the current reference point is: in, For eavesdroppers, the equivalent baseband channel This is the baseband transmission covariance of the previous layer.

[0015] Preferably, given the updated legitimate user linear reception matrix, error weight matrix, and eavesdropping link master-minimize proxy matrix, a digital precoding update subproblem is constructed by combining regularization terms. A digital precoding candidate solution is obtained by solving a system of low-dimensional linear equations, and inter-layer damping is used to combine the digital precoding candidate solution with the output of the previous unfolded layer. Subsequently, transmit power feasibility is performed on the combined digital precoding matrix to obtain the digital precoding output of the current unfolded layer.

[0016] Preferably, the transmit power feasibility is achieved using at least one of a precise power projection method and a low-complexity radial scaling method. When using the precise power projection method, non-negative Lagrange multipliers are determined through a one-dimensional search, ensuring that the projected digital precoding matrix satisfies the total transmit power constraint in the actual antenna domain. When using the low-complexity radial scaling method, the candidate matrix is ​​scaled proportionally based on the actual transmit power corresponding to the candidate digital precoding matrix.

[0017] Preferably, the slow-timescale projection gradient ascent depth unrolling network includes a simulated precoding update branch and a movable antenna position update branch. The simulated precoding update branch updates the simulated precoding matrix based on the gradient of the long-term average security rate with respect to the simulated precoding matrix, and performs a fully connected phase shifter constant-mode projection on the update result; the movable antenna position update branch updates the movable antenna position vector based on the effective gradient of the long-term average security rate with respect to the movable antenna position, and sequentially performs box boundary projection and a fixed number of pairwise collision avoidance corrections.

[0018] Furthermore, in the In each slow-time-scale unfolding layer, the simulated precoding matrix and the movable antenna position vector are updated according to the direction of the statistical security rate gradient: in, This represents the index of the unfolded layer in a slow-timescale network. , Indicates the first The simulated precoding matrix of each unfolded layer No. The movable antenna position vector of the layer, This represents analog precoded constant modulus projection. This represents a position feasibility operator consisting of box-shaped boundary projection and a fixed number of paired anti-collision corrections. and Let represent the gradients of the security rate with respect to the analog precoding matrix and the antenna position, respectively. and These are the learnable update step sizes.

[0019] Through the aforementioned joint optimization structure using fast and slow time scales, the slow-time-scale network is responsible for long-term array geometry and analog beam adjustment, while the fast-time-scale network is responsible for instantaneous digital beam adaptive updates. This allows the system to simultaneously meet the varying requirements of mechanical movement speed, phase shifter update speed, and baseband processing speed. Compared to traditional alternating optimization methods, this invention reduces the complexity of online solutions by using a fixed-layer depth expansion while maintaining the physical interpretability of the optimization process.

[0020] Preferably, a slow timescale block comprises multiple fast time slots. The movable antenna position and the analog precoding matrix are updated at the beginning of the slow timescale block and remain unchanged within the block; the digital precoding matrix is ​​updated based on the instantaneous channel state information of each fast time slot. The slow timescale network uses the digital precoding response output by the fast timescale network as its inner layer response to optimize the long-term average security rate.

[0021] Preferably, in S20, based on the update cycles of different optimization variables in the system, the long-term average security rate maximization optimization model is decomposed into two sub-models for solution, including a first sub-model and a second sub-model. The first sub-model solves the fast-timescale digital precoding optimization problem, and the second sub-model solves the slow-timescale analog precoding and movable antenna position joint optimization problem. The first sub-model solves the digital precoding matrix optimization problem given the movable antenna position and the analog precoding matrix. Specifically, based on the instantaneous channel state information of the current time slot, a weighted minimum mean square error-mastery minimization depth expansion network is used to optimize the digital precoding. A fixed-layer network is used to achieve fast iterative solution while satisfying the base station transmit power constraint. The second sub-model jointly optimizes the analog precoding matrix and the movable antenna position vector under long-term statistical channel state information. Specifically, a projection gradient ascending depth expansion network is used to update the analog precoding matrix and the movable antenna position according to the long-term average security rate gradient. Constant modulus projection, position boundary projection, and collision avoidance correction are used to ensure that the optimization results satisfy both RF hardware constraints and antenna mechanical movement constraints.

[0022] Preferably, a nested optimization structure is used to solve the two sub-models. The first sub-model serves as the inner optimization process, updating the digital precoding matrix based on the current user and eavesdropper channel states within each fast timescale slot. The second sub-model serves as the outer optimization process, updating the analog precoding matrix and the movable antenna position vector based on long-term statistical states within the slow timescale period. This dual-timescale sub-model decomposition transforms the original high-dimensional non-convex joint optimization problem into two low-complexity optimization processes with clear physical meaning. This allows digital precoding to adapt to rapid channel changes, while simultaneously enabling the analog beam and antenna array structure to adapt to long-term spatial environment changes.

[0023] Preferably, the fast-timescale network and the slow-timescale network employ phased unsupervised training. The fast-timescale network uses the negative value of the average smoothed security rate corresponding to a small batch of instantaneous channel samples as the training loss. Under the condition of fixing or partially fixing the parameters of the fast-timescale network, the slow-timescale network uses the negative value of the average security rate calculated using a differentiable smoothed positive part function corresponding to long-term state samples and an antenna collision penalty term as the training loss. A position change penalty term and a network parameter regularization term can be further added according to training stability and mechanical movement requirements. After completing the phased training, a relatively small learning rate is used to jointly fine-tune the fast-timescale network and the slow-timescale network.

[0024] This invention also proposes a hybrid beamforming near-field secure communication system assisted by a very large-scale movable antenna, for implementing the above-mentioned near-field secure communication method. The system includes: A near-field communication model construction module is used to construct a near-field secure communication model assisted by a large-scale movable antenna. The model includes a base station configured with a large-scale two-dimensional movable antenna array and a hybrid beamforming structure, a legitimate user, and an eavesdropper, and constructs a line-of-sight spherical wave near-field channel based on the position of the movable antenna. The dual-timescale modeling module is used to set the movable antenna position and analog precoding as slow-timescale variables, and digital precoding as fast-timescale variables, to establish a long-term average security rate maximization optimization model. The optimization model solving module is used to decompose the optimization model into a first sub-model and a second sub-model; wherein, the first sub-model is used to optimize the digital precoding matrix based on the weighted minimum mean square error-mastery minimization depth unfolding network, and the second sub-model is used to jointly optimize the analog precoding matrix and the movable antenna position vector based on the projection gradient ascending depth unfolding network. The slow time-scale optimization module is used to perform constant modulus projection gradient ascent depth expansion of analog precoding and projection gradient ascent depth expansion of movable antenna position under the condition of given long-term statistical channel information or sampled channel information, and to jointly optimize and update the analog precoding matrix and movable antenna position vector. The constraint projection module is used to constrain variables during the optimization process, including analog precoding constant modulus projection, digital precoding transmit power feasibility, antenna position boundary projection, and collision avoidance correction. The training output module is used to perform phased training on the fast-timescale network and the slow-timescale network using an unsupervised loss function. After the phased training is completed, it performs joint fine-tuning with a small learning rate to obtain the learnable parameters of each unfolded layer and outputs the optimized movable antenna position, analog precoding matrix, and digital precoding matrix.

[0025] Compared with the prior art, the present invention has the following beneficial effects: By employing a collaborative design of movable antenna position reconstruction, analog phase control, and digital baseband interference suppression, the effective channel difference between legitimate users and eavesdroppers is amplified when they are at the same angle or close range, improving security distinguishability in challenging near-field scenarios. The weighted minimum mean square error—maintenance and projection gradient update are expanded into a network with a fixed number of layers. Through solving low-dimensional linear equations, inter-layer damping, and power feasibility, high-complexity direct optimization of large-dimensional transmission variables is avoided, making the online complexity and inference delay fixed and predictable. Each expanded layer corresponds to the update of the receiver matrix, the update of the error weight matrix, the construction of the surrogate term for the eavesdropping link maintenance minimization, the solution of digital precoding candidate solutions, and the processing of inter-layer damping or constraint feasibility. Each learnable parameter has a clear optimization meaning, maintaining the interpretability of the model-driven method. Slow variables are updated only when the long-term statistical state changes, while fast variables are updated according to the current line-of-sight channel, reducing antenna mechanical movement and analog phase shifter reconfiguration frequency, and matching the physical update speed of different hardware. Attached Figure Description

[0026] Figure 1 This is a flowchart illustrating the hybrid beamforming near-field secure communication method assisted by a large-scale movable antenna proposed in this embodiment of the invention. Figure 2 This diagram illustrates the ultra-large-scale mobile antenna-assisted near-field secure MIMO system proposed in this embodiment of the invention. Figure 3 This diagram illustrates the dual-timescale nested deep unfolding architecture composed of a fast-timescale network and a slow-timescale network proposed in this embodiment of the invention. Figure 4 This diagram illustrates the functional modules of the near-field secure communication system proposed in this embodiment of the invention. Figure 5 This diagram illustrates the relationship between the average security rate of different communication schemes proposed in this invention and the base station transmit power. Figure 6 This graph illustrates the relationship between the average security rate of different communication schemes proposed in this invention and the distance between the base station and the eavesdropper. Figure 7 This diagram illustrates the Pareto relationship between the average security rate and total running time of different communication schemes proposed in this invention. Detailed Implementation

[0027] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of protection of this invention. To better illustrate this embodiment, some dimensions, scales, or connection relationships in the drawings may be omitted, enlarged, or reduced.

[0028] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0029] Example 1 This embodiment provides a hybrid beamforming near-field secure communication method assisted by a very large-scale movable antenna. See [link to previous document]. Figure 1 This includes the following steps: S10: Construct a near-field secure communication model; the near-field secure communication model includes a base station equipped with a large-scale two-dimensional movable antenna array and a radio frequency chain-constrained hybrid beamformer, a legitimate user, and an eavesdropper, and uses precise line-of-sight spherical waves to describe the near-field channels from the base station to the legitimate user and the eavesdropper respectively; S20: Construct a long-term average security rate maximization optimization model; set the movable antenna position and analog precoding matrix as slow-time-scale variables, and the digital precoding matrix as fast-time-scale variables, and set constraints on transmit power, analog precoding constant modulus, antenna movement area, and minimum antenna spacing. A slow-time-scale block includes... A fast timescale time slot This is a preset integer greater than 1. Let the duration of the fast timescale slot be... The duration of the slow timescale block is Then the two satisfy The fast timescale corresponds to the update period of instantaneous channel state information. The digital precoding matrix is ​​updated according to the current instantaneous channel state information in each fast timescale slot. The slow timescale corresponds to the update period of long-term statistical channel state or statistical information formed by multiple instantaneous channel samples. The movable antenna position and the analog precoding matrix are updated between slow timescale blocks and remain unchanged within each slow timescale block. S30: Within each fast timescale slot, a weighted minimum mean square error-master minimization deep expansion network oriented towards the security rate is constructed based on the current instantaneous line-of-sight channel state information. The weighted minimum mean square error term for the legitimate link and the master minimization proxy term for the eavesdropping link are constructed. The digital precoding matrix is ​​obtained through candidate digital precoding solution, inter-layer damping and power feasibility. S40: At the beginning of each slow timescale block, a projection gradient ascent depth expansion network is constructed based on long-term statistical channel state information or statistical information formed by multiple instantaneous channel samples. The network updates the analog precoding and the position of the movable antenna, and performs constant modulus projection, position boundary projection and collision avoidance correction respectively. S50: Learnable parameters are obtained through phased training using fast and slow time-scale networks. After phased training, joint fine-tuning is performed using a small learning rate to output the optimized movable antenna position, analog precoding matrix, and digital precoding matrix.

[0030] In this embodiment, firstly, the array geometric degrees of freedom and near-field range domain focusing capability of the ultra-large-scale movable antenna are used to construct differentiated channels for legitimate users and eavesdroppers; secondly, the fast and slow variables are divided according to different speeds of mechanical movement, RF phase shifter updates, and digital baseband processing; then, a fixed-layer depth unfolding network is used to solve for digital precoding and analog precoding and antenna position; finally, through constrained projection and phased training (fast first, slow later), a joint optimization result that satisfies hardware and mechanical constraints is obtained.

[0031] Example 2 This embodiment further illustrates the near-field secure communication method described in Embodiment 1. For example... Figure 2 As shown, a large-scale two-dimensional movable antenna array and a radio frequency chain-constrained hybrid beamformer are set on the base station side, with legitimate users and eavesdroppers located in the near-field area of ​​the base station; the movable antenna reconstructs the line-of-sight spherical wave channel by changing the array element coordinates, analog precoding is used to adjust the radio frequency phase, and digital precoding is used to perform baseband beam control and interference suppression.

[0032] Based on the aforementioned near-field secure communication model, the long-term average security rate maximization optimization model is decomposed into a first sub-model and a second sub-model. The first sub-model solves for fast-timescale digital precoding given the movable antenna position and the analog precoding matrix. The second sub-model jointly solves for the slow-timescale analog precoding matrix and the movable antenna position under long-term statistical channel conditions. During the solution process, the first sub-model is embedded as an inner response into the second sub-model, allowing the update of the slow-timescale variables to consider the fast adaptive results of the digital precoding.

[0033] First, determine whether the transceiver is in the near field of the array based on the array aperture and carrier wavelength. Let the effective aperture of the base station array be... The carrier wavelength is Rayleigh distance is commonly used. Used to determine whether the transmitter or receiver is in the near field or far field:

[0034] When the transmission and reception distance is For sizes of the same or smaller, a spherical wave model should be used.

[0035] Base station equipped Root movable antenna, RF chain and transmit There are multiple data streams, with legitimate users and eavesdroppers each configuring their own receiving antennas. Each movable antenna moves only within a fixed plane, its two-dimensional position being an optimization variable, and its three-dimensional physical coordinates being determined by both fixed coordinate components and its two-dimensional position.

[0036] Legitimate users and eavesdroppers are recorded as follows: and The number of receiving antennas are respectively and . No. The two-dimensional optimization variables for the root MA are: in, This represents the two-dimensional position vector of the m-th movable antenna within a fixed moving plane. and These represent its coordinates along the y-axis and z-axis, respectively. T represents transpose, and m is the index of the movable antenna.

[0037] Its three-dimensional physical coordinates for:

[0038] The global position vector formed by sequentially stacking the two-dimensional positions of all movable antennas is: Its dimension is .

[0039] receiver The The coordinates of the root antenna are: in, , and These represent the position components of the receiving antenna in the three coordinate axes.

[0040] The mechanically feasible region of a movable antenna is defined as follows: in, This represents the minimum permissible physical distance between any two antennas. Indicates difference from Another antenna index. For the first rectangular moving area of ​​the root antenna . in, , , and These represent the lower and upper bounds of the movement of the m-th movable antenna in the y-axis and z-axis directions, respectively.

[0041] The precise propagation distance from the m-th movable antenna to the receiver q of the n-th antenna is:

[0042] This embodiment uses only a pure line-of-sight spherical wave channel, corresponding to the pure line-of-sight complex channel coefficients between the transmitting and receiving antennas. and the receiver q-channel matrix consisting of all pure line-of-sight channel coefficients. They are respectively: in, Indicates reference distance Power gain at that point Indicated to the receiving end The path loss index of the link. Represents the imaginary unit. Represents the complex field.

[0043] Let the transmitted symbol Satisfying unit covariance: in, express The transmitted symbol vector consists of several data streams. Indicates statistical expectation. express An identity matrix; this formula indicates that the data streams are independent of each other and the average power has been normalized.

[0044] The dimensionality relationship between the analog precoding matrix and the digital precoding matrix is ​​as follows: Analog precoding will RF chain mapped to The root transmitting antenna, digital precoding will Data streams mapped to One radio frequency chain.

[0045] Equivalent hybrid precoding matrix for: Base station sends signals for: Received signal vector at receiver q for: in, , This represents an additive complex Gaussian noise vector. This represents the noise power on a single receiving antenna. This represents a zero-mean circularly symmetric complex Gaussian distribution.

[0046] achievable rate of receiver q for: Where det(·) represents the determinant, express 3D identity matrix, superscript This indicates the conjugate transpose.

[0047] When the number of data streams is less than the number of receiving antennas, the achievable rate formula is equivalent. The dimension is expressed in the following form: This form reduces the dimensionality of determinant calculations.

[0048] Instantaneous security rate for: .in, and These represent the reachable speeds of legitimate users and eavesdroppers, respectively. This indicates positive part operation, used to ensure that the security rate is not less than zero.

[0049] The differentiable smooth approximation of the positive part function is: , where κ is the smoothing coefficient; the larger κ is, the closer the function is to the true positive part function.

[0050] During the testing and performance reporting phases, the difference between the legitimate user rate and the eavesdropper rate is calculated using the true positive part function, instead of the smooth approximation used during the training phase.

[0051] After obtaining the channel matrix of legitimate users and the channel matrix of eavesdroppers, a joint optimization model with two time scales is further constructed.

[0052] To illustrate the coupling relationship between the optimization variables, given the instantaneous channel state, the joint optimization problem corresponding to a single fast time slot can be expressed as the instantaneous security rate maximization problem. The movable antenna position, analog precoding matrix and digital precoding matrix are jointly optimized, and the transmit power constraint, constant modulus constraint, antenna movement area constraint and minimum antenna spacing constraint are satisfied.

[0053] To illustrate the coupling relationship between the optimization variables, given the instantaneous channel state, the joint optimization problem corresponding to a single fast time slot is expressed as an instantaneous security rate maximization problem, with respect to the position of the movable antenna. Analog precoding matrix and digital precoding matrix Perform joint optimization while satisfying transmit power constraints, constant mode constraints, antenna movement area constraints, and minimum antenna spacing constraints:

[0054] And limit the total transmit power after hybrid precoding: This represents the Frobenius norm.

[0055] Each analog phase shifter coefficient has a fixed amplitude. :

[0056] Movable antenna position vector Belongs to the mechanically feasible domain This simultaneously satisfies the moving boundary and minimum antenna spacing constraints:

[0057] This embodiment adopts a fully connected hybrid beamforming architecture. Each RF chain is connected to each movable antenna through a corresponding analog phase shifter. Each element of the analog precoding matrix has the same amplitude, and its phase is the variable to be optimized.

[0058] Suppose a slow timescale block contains There are 1 fast time slot, and the fast time slot index is 1. ,in Using random states This represents the user's location, the eavesdropper's location, path loss, propagation phase, or channel estimation state. Slow variables consist of the movable antenna position and analog precoding, while fast variables consist of digital precoding. Channel of receiver q under a fast time slot for: Set of variables with slow time scales for: . No. Fast timescale variables of a fast time slot for: The slow-timescale problem and its fast-timescale inner-layer problem are as follows:

[0059] in, Represents the long-term random state Take the expected value. This represents the digital precoding response output by the first sub-model, given the slow-timescale variables and the current state, used to approximate the optimal response of the fast-timescale digital precoding optimization problem. in, This represents the set of digital precoding solutions that maximize the security rate. For the fast timescale response in the set.

[0060] Emit power constraints for fast timescale inner-layer problems:

[0061] To solve for the movable antenna position and the precoding matrix, the security rate gradient and the derivative of the line-of-sight spherical wave channel with respect to the antenna position are further calculated.

[0062] The covariance matrix of the received signal at receiver q It is composed of the sum of the noise covariance and the useful signal covariance.

[0063] Using the Wirtinger derivative, The Wirtinger gradient with respect to the conjugate variables of the equivalent precoding matrix V is: in, express The inverse matrix, Used to convert the natural logarithmic derivative into a rate derivative with base 2.

[0064] exist Within a differentiable region, the security rate is related to the equivalent precoding matrix. gradient of conjugate variables for: Depend on have to

[0065] Let the projection of the receiving antenna on the yz plane be... The gradient of the distance with respect to the two-dimensional position is: The gradient direction points from the projection position of the receiving antenna to the current position of the transmitting antenna.

[0066] The position gradient of the pure line-of-sight channel coefficients is The real part in parentheses reflects the change in path loss, while the imaginary part reflects the change in propagation phase.

[0067] make Let the transmitted signal covariance matrix be denoted as , then for any position component The rate derivative is: All location gradients are stacked as .

[0068] Specifically, the long-term average security rate maximization optimization model is solved using a nested deep expansion approach with fast and slow time scales, and the digital precoding matrix output by the first sub-model is used as the inner layer response of the second sub-model when optimizing the slow time scale variables. Let the fixed number of expansion layers in the slow time scale network be... Specifically, it includes the following steps: S401: Initialize the slow timescale unfolding layer index Simulate the precoding matrix and the movable antenna position vector, and extract a small batch of channel state samples from the long-term state distribution; S402: Given the current analog precoding matrix and the movable antenna position vector, call the first sub-model for each channel state sample to obtain the corresponding digital precoding matrix and calculate the mini-batch average security rate. S403: Based on the gradient of the small-batch average security rate with respect to the simulated precoding matrix, perform projection gradient ascent update on the simulated precoding matrix and execute constant modulus projection to obtain the updated simulated precoding matrix. S404: Based on the updated analog precoding matrix and the current movable antenna position, call the first sub-model to obtain the corresponding digital precoding response, and calculate the gradient of the mini-batch average security rate with respect to the movable antenna position; S405: Update the position vector of the movable antenna according to the position gradient, and sequentially perform position boundary projection and a fixed number of pairwise anti-collision corrections; S406: Calculate the updated long-term average security rate and check the analog precoding constant modulus constraint, antenna movement area constraint, and minimum antenna spacing constraint. S407: Determine if the current expanded layer index has reached the fixed number of expanded layers. If it is not achieved, then... Repeat steps S402 to S407; if the condition is met, proceed to step S408. S408: Output the analog precoding matrix and movable antenna position vector used in the current slow time scale block, and call the first sub-model in each fast time scale slot within the slow time scale block to output the corresponding digital precoding matrix.

[0069] In the inner-layer optimization, the process of solving the first sub-model is as follows:

[0070] Given the movable antenna location and analog precoding, define the equivalent baseband channel for legitimate users and eavesdroppers. The digital precoding is updated using the instantaneous pure line-of-sight channel state information of the current time slot.

[0071] In an equivalent baseband channel, the receiver q consists of a digitally precoded signal and additive noise:

[0072] Introducing the legitimate user linear reception matrix U and error matrix The weighted minimum mean square error equivalent formula for the legal user rate, as well as the optimal receiver and weights, are:

[0073] The equivalence between the legal user rate and the weighted minimum mean square error objective: Where W represents the positive definite weight matrix, Used to characterize weight gain This represents the weighted mean square error.

[0074] use and These represent the optimal linear receiver matrix and the optimal weight matrix under the current digital precoding, respectively. This indicates the use of the optimal receiver matrix. The error matrix corresponding to the time.

[0075] For the eavesdropper link, define the baseband transmit covariance. : ,

[0076] Since the eavesdropper's achievable rate is a concave function with respect to the baseband transmission covariance matrix, in the k-th unfolded layer, with As the current reference point, construct a first-order affine global upper bound on the achievable rate of the eavesdropper: in, The matrix represents the first-order tangent plane coefficients of the eavesdropping rate at the reference point; the right-hand side is the global first-order upper bound of the eavesdropping rate. This first-order affine upper bound is equal to the value of the original eavesdropper's reachable rate function at the current reference point, thus forming the first... The mainization of each expanded layer—minimizing surrogate terms.

[0077] The eavesdropping link mastering-minimizing proxy matrix is:

[0078] in, This represents the equivalent baseband channel matrix of the eavesdropper. This indicates the noise power at the receiver of the eavesdropper. express 3D identity matrix This is used to characterize the local sensitivity of the eavesdropper's reachable rate to changes in the baseband transmit covariance. Substituting the first-order upper bound, the eavesdropping link proxy term related to the current digital precoding matrix to be updated can be expressed as:

[0079] To preserve the physical meaning of the lower bound of the secrecy rate formed by the upper bound of the eavesdropping rate, a completely free learnable matrix is ​​not used as a direct substitute. The k-th unfolded layer is set with a learnable eavesdropping penalty coefficient. Interlayer damping coefficient and regularization parameters The parameterization method used is as follows: , , .in, , , , and The first Unconstrained learnable scalars in each expanded layer; Used to adjust the weight of the eavesdropping link proxy penalty term. Used to improve the numerical stability of the digital precoding update subproblem. Used to control the combination ratio between the current candidate solution and the output of the previous expansion layer.

[0080] Given a receiver matrix Error weight matrix and the mastering of the eavesdropping link—minimizing the proxy matrix Under the given conditions, the weighted minimum mean square error—maintaining the surrogate objective—is used in the k-th layer to update the digital precoding. for: The first term represents the weighted mean square error of the legitimate user link, the second term represents the information leakage penalty term formed by the eavesdropping link master-minimize proxy matrix, and the third term represents the regularization term.

[0081] Expanding further, we define: ,

[0082] Candidate solutions to the digital precoding update subproblem are obtained by solving the following system of low-dimensional linear equations: Then interlayer damping is implemented:

[0083] in, Indicates the first The coefficient matrix of the unfolded layer digital precoding update subproblem contains a legal link weighted mean square error term, an eavesdropping link proxy penalty term, and a regularization term; This represents the signal-driven matrix expected by legitimate users; Indicates the first Each unfolded layer obtains digital precoding candidate solutions by solving linear equations. This represents the digital precoding candidate matrix after interlayer damping and before transmitting power feasibility is performed.

[0084] Digital precoding after transmit power feasibility for: in, Indicates that in a given analog precoding matrix Projection of the feasible domain of the transmit power at that time.

[0085] The precise power projection of digital precoding is: in, This represents the power metric matrix induced by the analog precoding matrix, used to convert digital precoding power into actual antenna domain transmit power.

[0086] The optimal solution to the optimization problem is: , in, in, This represents the candidate matrix of digital precoding to be projected. Let represent the variable to be solved in the power projection problem; the projection seeks the variable in the matrix that satisfies the actual transmit power constraint. The closest solution.

[0087] When candidate matrix When the transmit power constraint is already satisfied, the optimal projection result is: This means that there is no need to change the current digital precoding.

[0088] When the candidate matrix violates the power constraint Denotes non-negative Lagrange multipliers. express A dimensional identity matrix; by choosing ν, the projection result lies on the power constraint boundary. in, Determined through a one-dimensional search. To further reduce complexity, radial scaling can be used to achieve low-complexity power feasibility:

[0089] After a fixed number of layers, the fast time-scale digital precoding output is obtained: in, This represents a fast timescale depth unrolling mapping with a fixed number of layers. Represents all its learnable parameters, output This is an approximate optimal solution for digital precoding.

[0090] In the outer layer optimization, the process of solving the second sub-model is as follows:

[0091] For the analog precoding branch, in each slow-timescale unfolded layer, a mini-batch of samples is drawn from the long-term state distribution, and the fast-timescale network is invoked to obtain the digital precode corresponding to each sample. The statistical confidentiality rate gradient, unconstrained update, and constant modulus projection are: in, Indicates the first in a small batch A long-term state sample, , This represents the digital precoded response of the sample obtained by calling a fast timescale network under the current slow variable.

[0092] No. The average simulated precoding gradient of a slow timescale unfolded layer for: in, Indicates the number of samples in a mini-batch. Indicates the first The secrecy rate is calculated for each sample using a smoothed positive part function.

[0093] Analog precoding candidate matrix before constant modulus projection for: in, Indicates the learnable step size, satisfying , This indicates element-wise multiplication.

[0094] No. The radio frequency chain is connected to the first Analog precoding coefficients of a movable antenna for: Where ∠(·) represents the complex phase; this formula projects each element onto an amplitude of The set of constant moduli.

[0095] If adopted A bit-quantization phase shifter maps a phase to a set of discrete phases that can be used. :

[0096] The output of the simulated precoding branch after passing through a fixed number of layers is: in, This represents the simulated precoded projective gradient ascent unrolling mapping. This represents the learnable parameters of the branch.

[0097] For the movable antenna location branch, the statistical location gradient, optional soft anti-collision term, and location-unconstrained update are as follows: in, Indicates the first A small-batch average position gradient of the slowly unfolded layer is used to guide the update of the movable antenna position in the direction of improving the security rate.

[0098] Soft anti-collision penalty function for: in, This indicates that only positive violations are retained; when any antenna spacing is less than At that time, a positive penalty is generated for the corresponding antenna pair.

[0099] Effective position gradient after adding anti-collision correction for: in, Indicates the first Collision penalty weights for layers.

[0100] Candidate position vector before position projection for: in, For a positive learnable step size, Indicates the first The layer is a learnable scalar without sign constraints; the softplus function is used to guarantee the step size for position updates. Greater than zero.

[0101] After considering the constraints of the rectangular moving boundary and the minimum antenna spacing, the feasible region is a non-convex set, and it is usually difficult to obtain a concise closed-form solution by accurately projecting onto this feasible region. To keep the number of network layers fixed and reduce the computational complexity of each layer, this embodiment adopts a location feasibility method that combines box-shaped boundary projection with a fixed number of pairwise collision avoidance corrections: in, The location approximation feasibility operator consists of box-shaped boundary projection and a fixed number of pairwise anti-collision corrections; the operator is used to guarantee location boundary constraints and reduce or eliminate the degree of violation of minimum antenna spacing constraints. This represents the candidate feasible position vector during the projection process.

[0102] In this approach, box-shaped boundary projection ensures that the positions of each movable antenna are within a preset moving area. Paired anti-collision correction further reduces the degree of minimum spacing violation based on the box-shaped projection results, ensuring that the updated position vectors satisfy the region boundary constraints and, as far as possible, the minimum spacing constraints. Since the minimum spacing constraints introduce non-convexity, this embodiment adopts a fixed-depth, low-complexity approximate feasible implementation instead of solving a high-complexity non-convex projection subproblem in each unfolded layer.

[0103] To maintain the ascent structure of the projection gradient and avoid solving a quadratic programming problem at each layer, a fixed number of pairwise collision corrections can be performed after box projection. For any distance The antenna pair, making in, Indicates the first Root and First The relative displacement vector between the antennas Indicates the current spacing. Represents the pairwise separation correction coefficient. To prevent tiny positive numbers with a denominator of zero.

[0104] To increase the distance between the two antennas that are too close, move them symmetrically in opposite directions while keeping the center position of the antenna pair as unchanged as possible.

[0105] After completing pairwise collision avoidance correction, box-shaped boundary projection is performed again on the movable antenna positions. By pre-setting and fixing the number of collision avoidance correction rounds, the network deployment depth can be kept constant, and the online processing latency can be made predictable. Since a fixed number of corrections may not guarantee strict satisfaction of the minimum antenna spacing constraint for all samples, the antenna position boundary constraints and minimum antenna spacing constraints are checked sample by sample during the simulation phase to verify the feasibility of the output results.

[0106] The output of the movable antenna position branch is: in, This represents the ascent and unfolding mapping of the projection gradient at the position of the movable antenna. Represents the long-term state sample set. This represents the learnable parameters of the branch. This indicates the antenna position output after fixing the number of layers.

[0107] After constructing the first and second sub-models, learnable parameters are obtained through phased unsupervised training using fast and slow time-scale networks. Joint fine-tuning is then performed using a relatively small learning rate after the phased training is complete. The specific process is as follows:

[0108] Fast-timescale networks and slow-timescale networks are represented as follows: in, This indicates the current status input of the fast time slot. according to , and Output digital precoding ; The meaning is the same as before. This represents a slow-timescale network mapping. This represents all learnable parameters for the analog precoding branch and the position branch.

[0109] The fast-timescale network and the slow-timescale network employ a staged unsupervised training approach, with corresponding training losses set for each. The unsupervised training loss for the fast-timescale network is:

[0110] Under the condition of fixing or partially fixing the parameters of the fast timescale network, the unsupervised training loss of the slow timescale network focuses on maximizing the average security rate, and can be further supplemented with collision risk penalty terms, position change penalty terms, and parameter regularization terms according to the needs of constraint satisfaction and training stability, in the following form: in, This indicates the overall loss in unsupervised training. Represents all network parameters. , and These represent the weights of the collision risk penalty, position change penalty, and parameter regularization term, respectively. This indicates the antenna position used in the previous slow timescale block. The first term in the slow timescale network formula is used to maximize the average smooth security rate of the mini-batch, while the remaining terms are optional auxiliary regularization terms used to reduce the risk of antenna collisions, suppress excessive position changes, and improve training stability.

[0111] During training, the movable antenna position and simulated precoding are fixed first, and a fast-timescale weighted minimum mean square error-mastery minimization unfolded network is trained. Then, the trained fast network is embedded, and simulated precoding projection gradient ascending layers and position projection gradient ascending layers are trained separately. Based on this, a small learning rate is used to jointly fine-tune the fast-timescale and slow-timescale networks, and the positions, distances, angles, and signal-to-noise ratios of the user and eavesdropper are randomized in the training set. The testing phase uses real-world security rate, real-world constant modulus constraints, and minimum spacing feasibility for evaluation.

[0112] To reduce computational complexity, the fast timescale employs a weighted minimum mean square error-mastery minimization deep unfolded network oriented towards security rate to solve digital precoding. In each unfolded layer, the linear receiver matrix and error weight matrix of the legitimate user are updated. A digital precoding update subproblem is constructed by combining the eavesdropping penalty term and regularization term formed by the mastery minimization proxy matrix constructed based on the current unfolded layer reference point. Candidate solutions for digital precoding are obtained by solving a system of low-dimensional linear equations, and then the current layer output is obtained through inter-layer damping and power feasibility optimization. Power feasibility optimization employs radial scaling or determines the Lagrange multipliers through a one-dimensional search. Both the fast and slow timescale networks use a preset fixed number of layers. Each layer of the fast timescale network has independently learnable damping coefficients, eavesdropping penalty coefficients, and regularization parameters. The analog precoding update branch and antenna position update branch of the slow timescale network each have independently learnable step sizes, and gradient pruning can be used to improve training stability.

[0113] In one alternative implementation, the system's parameter configuration, operating mode, and performance evaluation are as follows.

[0114] The near-field secure communication system employs a dual-timescale optimization approach. A slow-timescale block comprises multiple fast-timescale coherent time slots; in evaluating algorithm complexity and online processing latency, a slow-timescale block preferably includes 100 fast-timescale time slots. The movable antenna position and the analog precoding matrix are used as slow-timescale variables, updated at the beginning of each slow-timescale block and remaining unchanged within the block. The digital precoding matrix is ​​used as a fast-timescale variable, updated based on the instantaneous channel state information within each fast-timescale time slot.

[0115] The long-term average security rate maximization optimization model is decomposed into a first sub-model and a second sub-model. The first sub-model is used to solve for the fast-timescale digital precoding matrix, while the second sub-model is used to jointly solve for the slow-timescale analog precoding matrix and the movable antenna position vector. The specific solution processes for the first and second sub-models are detailed above and will not be repeated here.

[0116] In contrast, traditional dual-timescale alternating optimization methods and single-timescale alternating optimization methods are employed. The traditional dual-timescale alternating optimization method uses a projected gradient ascent method to optimize the analog precoding matrix and movable antenna position in the slow timescale, and uses a weighted minimum mean square error-mastery minimization iterative method oriented towards security rate to optimize the digital precoding matrix in the fast timescale. The single-timescale alternating optimization method re-jointly optimizes the movable antenna position, analog precoding matrix, and digital precoding matrix in each fast timescale time slot.

[0117] like Figure 5 As shown, Figure 5 The horizontal axis represents the base station transmit power, and the vertical axis represents the average security rate. As transmit power increases, the average security rate of the traditional dual-timescale alternating optimization method, the single-timescale alternating optimization method, and the proposed dual-timescale deep unfolding method all generally increase. The proposed dual-timescale deep unfolding method outperforms the traditional dual-timescale alternating optimization method overall, and the performance improvement is limited when the number of fast-timescale unfolding layers increases from 5 to 50, indicating that good security performance can be achieved with fewer unfolding layers.

[0118] like Figure 6 As shown, Figure 6 The horizontal axis represents the distance between the base station and the eavesdropper, and the vertical axis represents the average security rate. As the eavesdropper approaches the location of the legitimate user, the channel correlation between the two increases, and the average security rate decreases significantly. When the eavesdropper moves away from the location of the legitimate user, the difference between the two in the distance or angle domains increases, and the average security rate recovers accordingly. The near-field method can utilize both angle and distance domain information simultaneously, and in the scenario shown, it outperforms the comparative method under the far-field channel model.

[0119] like Figure 7 As shown, Figure 7 The horizontal axis represents the total running time, and the vertical axis represents the average security rate. Compared with the 50-layer deep unfolding scheme, the proposed 5-layer fast timescale deep unfolding method can achieve a higher security rate with a shorter running time, demonstrating a good trade-off between performance and complexity. The traditional dual-timescale alternating optimization method has lower performance, while the strictly single-timescale alternating optimization method, although achieving a higher security rate, has a significantly increased running time.

[0120] Example 3 This embodiment provides a hybrid beamforming near-field secure communication system assisted by an ultra-large-scale movable antenna, used to implement the methods described in Embodiments 1 and 2. See [link to documentation]. Figure 4 The system includes: The near-field channel modeling module is used to receive the two-dimensional position of the movable antenna, the three-dimensional position of the legitimate user and the eavesdropper, the carrier wavelength and path loss parameters, calculate the accurate propagation distance from each transmitting antenna to each receiving antenna, and construct the legitimate user channel matrix and the eavesdropper channel matrix. The dual-timescale modeling module is used to determine the movable antenna position and the analog precoding matrix as slow-timescale variables, and the digital precoding matrix as fast-timescale variables, and to establish a long-term average security rate maximization model based on transmit power, constant modulus, position boundary and minimum antenna spacing constraints. The fast timescale optimization module is used to solve the first sub-model. It performs weighted minimum mean square error-maintenance minimization depth expansion based on the instantaneous channel state of the current fast time slot, and sequentially performs updates of the legitimate user reception matrix and error weight matrix, construction of the eavesdropping link maintenance minimization proxy term, solution of digital precoding candidate solution, inter-layer damping, and transmit power feasibility. The slow time-scale optimization module is used to solve the second sub-model. It performs simulated precoding constant modulus projection gradient ascent expansion and movable antenna position projection gradient ascent expansion based on long-term channel state samples. The constraint projection module is used to perform transmit power projection feasibility for digital precoding, constant modulus projection for analog precoding, boundary projection for movable antenna positions, and anti-collision correction a fixed number of times for antenna pairs with an antenna spacing smaller than a preset minimum spacing. The training and output module is used to train the first and second sub-models in stages using an unsupervised loss function, and to perform joint fine-tuning with a small learning rate after the staged training is completed, so as to obtain the learnable parameters of each unfolded layer, and output the optimized movable antenna position, analog precoding matrix and digital precoding matrix. The fast timescale optimization module corresponds to the first sub-model, and the slow timescale optimization module corresponds to the second sub-model. The output of the first sub-model can be used as the inner-layer response when the second sub-model calculates the long-term average security rate and its gradient. The movable antenna position and simulated precoding matrix output by the second sub-model are used as the input of the first sub-model in subsequent fast time slots, thus forming a fast and slow timescale co-optimization relationship. When the system is working, the near-field channel modeling module first forms the legitimate user channel and the eavesdropper channel corresponding to the current state; the dual-timescale modeling module selects the variables to be updated according to the update cycle; the slow-timescale optimization module outputs the movable antenna position and the analog precoding matrix at the beginning of the block, and the fast-timescale optimization module outputs the digital precoding matrix in each time slot within the block; the constraint projection module performs feasibility processing on each output, and the training and output module saves the network parameters and sends the corresponding control quantities to the base station radio frequency terminal, baseband terminal and antenna driving mechanism. The system modules in this embodiment correspond to the method steps in Embodiment 1 and Embodiment 2. Channel models, optimization variables, deep expansion layers, constraint projections, and training processes not detailed in this embodiment can all be executed with reference to the foregoing embodiments.

[0121] The above embodiments are only used to clearly illustrate the present invention and are not intended to limit the implementation of the present invention. Modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A near-field safety optimization method for hybrid beamforming assisted by a large-scale movable antenna, characterized in that, Includes the following steps: S10: Construct a near-field secure communication model; The near-field secure communication model includes a base station equipped with a large-scale two-dimensional movable antenna array and a radio frequency chain-limited hybrid beamformer, a legitimate user, and an eavesdropper, and uses precise line-of-sight spherical waves to describe the near-field channels from the base station to the legitimate user and the eavesdropper, respectively. S20: Establish a joint optimization model; with the objective of maximizing the long-term average security rate, set the movable antenna position and analog precoding as slow-time-scale variables, and digital precoding as fast-time-scale variables, and set transmit power constraints, analog precoding constant modulus constraints, antenna movement area constraints, and minimum antenna spacing constraints. A slow-time-scale block includes... A fast timescale slot This is a preset integer greater than 1. Let the duration of the fast timescale slot be... The duration of the slow timescale block is Then the two satisfy The fast timescale corresponds to the update period of instantaneous channel state information. The digital precoding matrix is ​​updated according to the current instantaneous channel state information in each fast timescale slot. The slow timescale corresponds to the update period of long-term statistical channel state or statistical information formed by multiple instantaneous channel samples. The movable antenna position and the analog precoding matrix are updated between slow timescale blocks and remain unchanged within each slow timescale block. S30: Within each fast timescale slot, a weighted minimum mean square error-dominant minimization deep unfolded network oriented towards the security rate is constructed based on the current instantaneous line-of-sight channel state information. The legitimate user linear reception matrix and error weight matrix are updated in each unfolded layer. A surrogate term for the eavesdropping link is constructed based on the current unfolded layer reference point. The digital precoding candidate matrix is ​​solved by combining the surrogate term and the regularization term. The digital precoding matrix is ​​obtained through inter-layer damping and power feasibility. S40: At the beginning of each slow timescale block, a projection gradient ascent depth expansion network is constructed based on long-term statistical channel state information or statistical information formed by multiple instantaneous channel samples to update the analog precoding and movable antenna positions, and constant modulus projection, position boundary projection and collision avoidance correction are performed respectively; the analog precoding and movable antenna positions remain unchanged within the current slow timescale block; S50: A phased training method is adopted. First, the fast time-scale network is trained, and then the slow time-scale network is trained under the condition of fixing or partially fixing the parameters of the fast time-scale network. The fast and slow time-scale networks are jointly fine-tuned with a small learning rate to obtain the learnable parameters of each unfolded layer and output the movable antenna position, analog precoding matrix and digital precoding matrix.

2. The near-field secure communication method according to claim 1, characterized in that, ... The effective aperture of the base station array is The carrier wavelength is The near-field region is determined using Rayleigh distance, wherein the Rayleigh distance satisfies: The base station includes Root movable antenna, RF chain and transmit Each data stream, the three-dimensional physical coordinates of each movable antenna are derived from the coordinates of a fixed plane. and 2D optimized position It is jointly determined that the positions of all movable antennas are constrained by a preset rectangular moving area and the minimum spacing between any two antennas.

3. The near-field secure communication method according to claim 2, characterized in that, No. A movable antenna to the receiver No. The propagation distance of the antenna is accurately calculated using three-dimensional Euclidean distance, and the line-of-sight spherical wave channel coefficient satisfies: in, , , , Indicates a legitimate user. Indicates eavesdropper, This indicates the number of receiving antennas at the receiver q. For the power gain at the reference distance, Indicates the distance from the base station to the receiving end. The path loss index of the link. The carrier wavelength is denoted by λ; both the legitimate user channel matrix and the eavesdropper channel matrix are composed of corresponding channel coefficients.

4. The near-field secure communication method according to claim 3, characterized in that, The simulated precoding matrix is The digital precoding matrix is The equivalent precoding matrix is ; Receiver achievable rate and instantaneous security rate They respectively satisfy: in, Represents the position vector of the movable antenna Given a specific channel matrix from the base station to the receiver q, This represents the noise power at the receiver q. Represents a 3D identity matrix, with superscript This indicates the conjugate transpose. Represents a determinant. This indicates positive part operation.

5. The near-field secure communication method according to claim 4, characterized in that, A slow timescale block contains multiple fast timescale slots. Slow timescale variables remain unchanged within the slow timescale block. Fast timescale digital precoding is updated based on the user location, eavesdropper location, path loss, propagation phase, or channel estimation state for each slot. The slow timescale objective is to maximize the long-term average security rate under the digital precoding response output by the fast timescale network.

6. The near-field secure communication method according to claim 5, characterized in that, In each unfolded layer, the fast timescale deep unfolded network updates the linear receiver matrix and error weight matrix of legitimate users based on the current digital precoding matrix, and constructs a surrogate term for minimizing the eavesdropping link based on the reference point of the current unfolded layer. The surrogate term and the regularization term are combined to construct a digital precoding update subproblem. The digital precoding candidate solution is obtained by solving the digital precoding update subproblem, and inter-layer damping update and transmit power feasibility are performed sequentially to obtain the digital precoding matrix of the current unfolded layer. The learnable parameters of each unfolded layer include damping coefficient, eavesdropping penalty coefficient, and regularization parameter.

7. The near-field secure communication method according to claim 6, characterized in that, The transmit power feasibility method includes an accurate power projection method and a low-complexity radial scaling method. When using the accurate power constraint solution method, the Lagrange multipliers are determined through a one-dimensional search; when using the low-complexity power feasibility method, radial scaling is performed on the damped updated digital precoding matrix. in, This represents the digital precoding candidate matrix obtained after the interlayer damping update. This represents the projected digital precoding matrix. , This indicates the maximum transmission power of the base station.

8. The near-field secure communication method according to claim 6, characterized in that, The slow-timescale projection gradient ascent depth unrolling network includes a simulated precoding update branch and a movable antenna position update branch. In the analog precoding update branch, the first Each unrolling layer updates the simulated precoding matrix output by the previous unrolling layer based on the gradient of the long-term average security rate with respect to the simulated precoding matrix, resulting in the simulated precoding candidate matrix before constant modulus projection: in, , This indicates a pre-defined fixed number of layers in a slow-timescale network. This represents the gradient of the long-term average security rate with respect to the analog precoding matrix. This represents the learnable step size of the simulated precoding update branch. This indicates element-wise multiplication. Subsequently, a fully connected phase shifter constant modulus projection is performed on the simulated precoding candidate matrix to obtain the simulated precoding matrix of the current unfolded layer. In the... In the unfolded layer, the first The radio frequency chain is connected to the first The analog precoding coefficients of the root movable antenna satisfy: in Represents the imaginary unit. Represents complex phase. In the movable antenna position update branch, the first Each unfolded layer updates the movable antenna position vector of the previous unfolded layer along the effective gradient direction of the long-term average security rate with respect to the antenna position, thus obtaining the candidate position vector before the position boundary projection: in, This represents the effective position gradient after considering the confidentiality rate gradient and collision penalty. This indicates the step size for position updates. After performing box boundary projection on the candidate position vector, if the first root movable antenna and the first If the distance between the movable antennas is less than the preset minimum spacing, then a pairwise separation correction is performed along the line connecting the two antennas: in, Represents the pairwise separation correction factor. Indicates by the first The root antenna points to the first The unit correction direction of the antenna.

9. The near-field secure communication method according to claim 8, characterized in that, The fast timescale network and the slow timescale network are trained in a phased unsupervised manner. First, the fast timescale network is trained based on a small batch of instantaneous channel samples, and the negative value of the average smoothed security rate corresponding to the network output is used as the fast timescale training loss. Subsequently, with the fast timescale network parameters fixed or partially fixed, the slow timescale network is trained based on long-term channel state samples. The slow timescale training loss includes at least the negative value of the average smooth security rate and an antenna collision penalty term.

10. A hybrid beamforming near-field secure communication system assisted by an ultra-large-scale movable antenna, used to implement the method according to any one of claims 1-9, characterized in that, include: The near-field channel modeling module is used to construct a line-of-sight spherical wave near-field channel model related to the position of the movable antenna array on the base station side, based on the two-dimensional position information of the movable antenna array on the base station side, the spatial position information of the legitimate user and the eavesdropper, the carrier wavelength, the path loss parameters, and the line-of-sight propagation relationship, so as to obtain the channel matrix of the legitimate user and the channel matrix of the eavesdropper. The dual-timescale modeling module is used to divide the system optimization variables into two timescales based on the differences between the mechanical movement rate of the movable antenna, the analog precoding update rate, and the digital precoding update rate. The movable antenna position and the analog precoding matrix are determined as slow-timescale variables, and the digital precoding matrix is ​​determined as fast-timescale variables. The module also establishes a long-term average security rate maximization target. The fast timescale optimization module is used to perform a weighted minimum mean square error-dominant minimization depth expansion oriented towards the security rate, based on the instantaneous channel state information of the current fast time slot, given the location of the movable antenna and the analog precoding matrix, update the legitimate user reception matrix and the error weight matrix, construct the eavesdropping link dominant minimization surrogate term, and obtain the digital precoding matrix through solving digital precoding candidate solutions, inter-layer damping and power feasibility. The slow time-scale optimization module is used to perform constant modulus projection gradient ascent depth expansion of analog precoding and projection gradient ascent depth expansion of movable antenna position under the condition of given long-term statistical channel information or sampled channel information, and to jointly optimize and update the analog precoding matrix and movable antenna position vector. The constraint projection module is used to perform projection correction on various constraints during the optimization process, including performing constant modulus projection on the analog precoding matrix, position boundary projection on the movable antenna positions, power constraint projection on the digital precoding, and collision prevention correction on the minimum spacing constraint between movable antennas, so as to ensure that the optimization results meet the feasibility requirements. The training and output module is used to train the fast timescale optimization module and the slow timescale optimization module in stages using an unsupervised loss function. After the staged training is completed, a small learning rate is used to jointly fine-tune all network layers, so that the update of the slow timescale variable can be combined with the response results of the fast timescale digital precoding for collaborative optimization. After training, the optimized movable antenna position vector, analog precoding matrix, and digital precoding matrix are output to achieve near-field secure communication transmission.

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