Near-field xl-mimo covert communication beam training method, apparatus, and system

Abstract

This invention discloses a method, apparatus, and system for training beams in near-field XL-MIMO covert communication. The method includes modeling the joint optimization problem of beam training and power allocation as a non-convex optimization problem under covert constraints, with the objective of maximizing the effective reachable rate. This non-convex optimization problem is then decomposed into optimization problems for the beam training phase and data transmission phase. For the beam training phase optimization problem, a suitable simulated beamforming vector is calculated using a beam selection algorithm with covert probability, with the objective of maximizing the effective reachable rate. For the data transmission phase optimization problem, the optimal base station transmission power is calculated using the suitable simulated beamforming vector, with the objective of maximizing the base station transmission power, thus completing the near-field XL-MIMO covert communication beam training. This invention effectively compresses the training space dimension, reduces training overhead, and improves link directivity gain and covertness.

Description

Technical Field

[0001] This invention belongs to the field of XL-MIMO beam training, specifically relating to a near-field XL-MIMO covert communication beam training method, device, and system, and particularly to a near-field XL-MIMO covert communication beam training method, device, and system based on a multi-armed slot machine algorithm. Background Technology

[0002] In pursuit of higher spectral efficiency and network capacity, sixth-generation mobile communication systems are driving the evolution of multi-antenna technology towards "ultra-large scale." As the number of antennas deployed at base stations surges and array apertures significantly enlarge, their radiation field will break through the traditional far-field plane wave assumption and enter the near-field region characterized by spherical wave propagation. Research shows that in millimeter-wave and even terahertz bands, user equipment is likely located in the near-field Fresnel zone, hundreds of meters from the base station. This fundamental change in channel characteristics poses a severe challenge to traditional signal processing schemes based on angular domain sparsity and far-field steering vectors. Near-field channel models exhibit angle-distance coupling effects, requiring communication systems to possess the ability to perform precise beam focusing in two-dimensional or even three-dimensional space. Therefore, research on near-field channel characteristics and transmission technologies has become a core frontier in the XL-MIMO field.

[0003] Beamforming is crucial for establishing reliable communication links. In near-field scenarios, far-field codebooks based on Discrete Fourier Transform (DFT) suffer a sharp performance degradation due to their inability to match spherical wavefronts. To address this, researchers have designed near-field codebooks based on spherical wavefront models to achieve precise focusing at specific spatial locations. However, these codebooks have extremely high dimensionality, resulting in significant training overhead. To reduce this overhead, a series of near-field beamforming training schemes have been proposed. Existing schemes primarily follow the hierarchical search approach. For example, a two-stage hierarchical beamforming training scheme has been proposed, first performing a coarse angular domain search using the array's central subarray, followed by a refined joint angular and range search in the polar domain, reducing the overhead to the logarithmic level of the number of antennas. A fast near-field beamforming training scheme has also been proposed, further optimizing the training process by introducing compressed sensing theory for the range dimension. Furthermore, existing technologies have proposed introducing data-driven methods into near-field beamforming training, designing a two-stage learning strategy based on hierarchical codebooks. Finally, existing technologies have proposed starting with codebook design, proposing a spatial-chirp-based codebook scheme to improve training efficiency. Although these methods effectively reduce the training overhead per coherence time, none of them consider the correlation of the channel at different coherence times, nor do they take into account the security and privacy issues that the beam training process itself may cause.

[0004] Covert communication, also known as low-probability-of-detection communication, aims not to protect the content of the communication, but rather to conceal the existence of the communication activity, thereby providing a higher level of security. Existing technologies have established the theoretical foundation for covert communication in additive white Gaussian noise channels, proposing the well-known "square root rule." Subsequent research has focused on how to utilize the inherent uncertainties in the wireless environment to improve covert performance, mainly forming technical routes based on noise uncertainty, channel uncertainty, and cooperative interference. With in-depth research, the application scenarios of covert communication have expanded from the traditional microwave band to the millimeter-wave band. For the first time in existing technologies, beam training and data transmission have been fully considered in a millimeter-wave communication system, with joint optimization of transmit power to meet covert constraints. This work marks the beginning of the integration of covert communication research with actual communication processes. However, this research and subsequent work are all based on far-field channel models. In the new paradigm of near-field XL-MIMO, the extreme spatial resolution brings new opportunities to covert communication (such as more precise energy focusing). However, at the same time, the high-dimensional beam training space also creates new and more acute contradictions with the stringent constraints of covert communication on training signals (such as power and time). How to design an efficient beam training scheme in this new scenario is an unexplored problem.

[0005] To address the conflict between beam training and stealth requirements in near-field XL-MIMO systems, a low-overhead, high-precision beam training mechanism is urgently needed. Existing far-field solutions are unsuitable because they neglect near-field spherical wave effects, leading to inaccurate energy focusing. A better approach would be to leverage the sparsity of the near-field channel, utilize prior structural information to compress the training space dimension, and employ intelligent reflectors to assist in dynamic environment perception and beam pre-alignment. This would improve link directivity gain with a limited number of training iterations, balancing stealth and communication efficiency. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a near-field XL-MIMO covert communication beam training method, apparatus, and system, which can effectively compress the training space dimension, reduce training overhead, and improve link directivity gain and covertness.

[0007] To achieve the above-mentioned technical objectives and effects, the present invention is implemented through the following technical solution:

[0008] In a first aspect, the present invention provides a near-field XL-MIMO covert communication beam training method, comprising:

[0009] With the goal of maximizing the effective reachability rate, the joint optimization problem of beam training and power allocation is modeled as a non-convex optimization problem under the implicit constraint;

[0010] The non-convex optimization problem is decomposed into an optimization problem in the beam training phase and an optimization problem in the data transmission phase;

[0011] To address the optimization problem in the beam training phase, with the goal of maximizing the effective reachability rate, a suitable simulated beamforming vector is calculated by combining a beam selection algorithm with concealment probability.

[0012] To address the optimization issues in the data transmission phase, and in conjunction with the appropriate simulated beamforming vector, the optimal base station transmission power is calculated with the goal of maximizing base station transmission power, thus completing the near-field XL-MIMO covert communication beam training.

[0013] Secondly, the present invention provides a near-field XL-MIMO covert communication beam training device, comprising:

[0014] The modeling unit is used to model the joint optimization problem of beam training and power allocation as a non-convex optimization problem under hidden constraints with the goal of maximizing the effective reachability rate.

[0015] A splitting unit is used to split the non-convex optimization problem into an optimization problem in the beam training stage and an optimization problem in the data transmission stage;

[0016] The simulated beamforming vector calculation unit is used to address the optimization problem in the beam training phase, aiming to maximize the effective reachability rate. It combines a beam selection algorithm with concealment probability to calculate a suitable simulated beamforming vector.

[0017] The optimal base station transmission power calculation unit is used to address the optimization problem in the data transmission stage. By combining a suitable simulated beamforming vector, it calculates the optimal base station transmission power with the goal of maximizing the base station transmission power, and completes the training of the near-field XL-MIMO covert communication beam.

[0018] Thirdly, the present invention provides a near-field XL-MIMO covert communication beam training system, including a storage medium and a processor;

[0019] The storage medium is used to store instructions;

[0020] The processor is configured to operate according to the instructions to perform the method according to any one of the first aspects.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0022] This invention proposes a near-field XL-MIMO covert communication beam training method, device, and system, which can effectively compress the training space dimension, reduce training overhead, and improve link directivity gain and covertness.

[0023] Furthermore, this invention reduces training dimensionality and overhead through a two-stage hierarchical search strategy involving the far-field (angular domain) and near-field (polar domain). In the angular domain, a beam selection algorithm with concealment probability is used to achieve coarse angle alignment. In the polar domain, based on the angular domain results, a beam selection algorithm with concealment probability is used for joint angle and distance search. Through a power allocation mechanism, a closed-form expression for the maximum base station transmission power is derived to guide power allocation during the data transmission stage, and the base station transmission power is optimized to meet concealment requirements during the data transmission stage. Based on the near-field codebook and matching the near-field channel characteristics, precise beam focusing in two-dimensional space is achieved, which can effectively compress the training space dimension, reduce training overhead, and improve link directivity gain and concealment. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly described below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort, wherein:

[0025] Figure 1 This is a schematic diagram illustrating a scenario in which the near-field XL-MIMO covert communication beam training method of one embodiment of the present invention is used;

[0026] Figure 2 This is a flowchart illustrating a near-field XL-MIMO covert communication beam training method according to an embodiment of the present invention.

[0027] Figure 3 This is a schematic diagram illustrating the average reachability of each relevant block according to an embodiment of the present invention;

[0028] Figure 4 This is a schematic diagram comparing the performance of the method of the present invention with other beam training algorithms under different signal-to-noise ratios, according to one embodiment of the present invention.

[0029] Figure 5 This diagram illustrates a comparison of the concealment performance of the method of the present invention with other beam training algorithms under different signal-to-noise ratios, representing one embodiment of the present invention. Detailed Implementation

[0030] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0031] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. If the combination of technical solutions is contradictory or impossible to implement, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

[0032] Example 1

[0033] This invention provides a near-field XL-MIMO covert communication beam training method, such as... Figure 2 As shown, it includes:

[0034] With the goal of maximizing the effective reachability rate, the joint optimization problem of beam training and power allocation is modeled as a non-convex optimization problem under the implicit constraint;

[0035] The non-convex optimization problem is decomposed into an optimization problem in the beam training phase and an optimization problem in the data transmission phase;

[0036] To address the optimization problem in the beam training phase, with the goal of maximizing the effective reachability rate, a suitable simulated beamforming vector is calculated by combining a beam selection algorithm with concealment probability.

[0037] To address the optimization issues in the data transmission phase, and in conjunction with the appropriate simulated beamforming vector, the optimal base station transmission power is calculated with the goal of maximizing base station transmission power, thus completing the near-field XL-MIMO covert communication beam training.

[0038] In one specific embodiment of the present invention, the objective function and constraint conditions of the non-convex optimization problem under the hidden constraints are as follows:

[0039] ,

[0040] in:

[0041] ,

[0042] In the formula, The effective achievable rate for XL-MIMO systems; For the first The base station transmission power corresponding to each coherent block; For the first The simulated beamforming vectors corresponding to each coherent block; For eavesdroppers and The relative entropy between the received signal distributions under the two assumptions, as the first... The concealment constraints that need to be satisfied in each coherent block data transmission stage; For the sake of concealment, it is a constant; and These represent the data transmission stages. A coherent block of eavesdroppers and Likelihood functions of the receiver function under two assumptions Indicates the null hypothesis, Indicates alternative assumptions; This represents the maximum base station transmission power. This is a near-field codebook based on a spherical wave model; This represents the total number of coherent blocks; The number of symbols that can be transmitted in a coherent block; The number of symbols used in the training phase of each coherent block beam; For the first The channel vectors of the users corresponding to each coherent block , The channel covariance matrix of the user. The noise variance for the user.

[0043] In one specific embodiment of the present invention, the objective function and constraints of the optimization problem in the beam training phase are as follows:

[0044] .

[0045] In one specific embodiment of the present invention, the method for calculating the suitable analog beamforming vector includes:

[0046] First, an angular domain scan is performed. In the angular domain scan, each far-field codeword in the far-field codebook is used as an arm of a multi-armed slot machine, with the square of the modulus of the user's received signal as the reward.

[0047] During initialization, a code is randomly selected from the far-field codebook. The first training is performed on a far-field codeword, and the initial parameters, number of training iterations, average reward, and concealment probability of the trained far-field codeword are recorded; the training refers to sending the far-field codeword to the user through the base station so that the user receives the signal;

[0048] During the iteration process, a beam selection algorithm with concealment probability is used to select the beam with the highest CP-UCB value. A far-field codeword, for the selected Beam training is performed on each far-field codeword, updating the parameters, training times, average reward, and concealment probability of the corresponding far-field codeword, extracting the angle parameters from the far-field codeword to form a candidate angle set, and completing the coarse scanning of the angular domain.

[0049] Secondly, polar-domain scanning is performed. In polar-domain scanning, candidate near-field codewords are selected from the near-field codebook based on the angle parameters in the candidate angle set, thus obtaining the corresponding candidate polar-domain codeword angle set. Used for polar scanning, for any given angle parameter The formula for calculating the corresponding distance parameter is:

[0050] ,

[0051] in, For the first The first near-field codeword corresponds to the first The corresponding angle parameter is the first One distance parameter, For the first The first near-field codeword corresponds to the first An angle parameter, ; It is a threshold distance used to limit the coherence of near-field steering vector columns. , For the number of antennas, For wavelength, List the coherence control parameters; Indicates the first The number of distance parameters corresponding to each angle parameter;

[0052] Each near-field codeword is composed of an angle-distance pair. By definition, the expression for the near-field codebook is obtained as follows:

[0053]

[0054] In the formula, For near-field codebook, This is the near-field steering vector;

[0055] Near field codebook Each near-field codeword in the code is considered an arm of a multi-armed slot machine, and the reward is set to the square of the user's received signal modulus.

[0056] During the iteration process, a beam selection algorithm with concealment probability is employed, specifically including: selecting the beam with the highest current CP-UCB value. For each selected near-field codeword, after training, a training pilot signal is sent to obtain the corresponding real reward sample value. It also updates the parameters of the corresponding near-field codeword, including: the number of near-field codeword selections, the average reward, and the concealment probability.

[0057] In one specific embodiment of the present invention, the formula for calculating the concealment probability corresponding to the far-field codeword is:

[0058] ,

[0059] in:

[0060] ,

[0061] ,

[0062] ,

[0063] In the formula, Typing for far field The corresponding concealment probability; and These are all intermediate parameters; Indicates the first Coherent block far-field codewords Whether or not to be selected, ; To select far-field codewords for the eavesdropper during the beam training phase The received signal; Typing for far field The number of times it was selected; The channel covariance matrix of the eavesdropper; The noise variance of the eavesdropper;

[0064] The formula for calculating the concealment probability corresponding to a near-field codeword is:

[0065] ,

[0066] in:

[0067] ,

[0068] ,

[0069] In the formula, This represents the concealment probability corresponding to the near-field codeword. For intermediate parameters, Indicates the first Near-field codewords of coherent blocks Whether or not it was selected; , To select near-field codewords for the eavesdropper during the beam training phase The received signal; For near-field typing The number of times it was selected.

[0070] In one specific embodiment of the present invention, the first A far-field code The formula for calculating the CP-UCB value is:

[0071] ,

[0072] in:

[0073] ,

[0074] ,

[0075] In the formula, For the first Coherent block far-field codewords The corresponding CP-UCB value, For the first Coherent block far-field codewords Historical average reward For the first Coherent block far-field codewords The corresponding concealment probability. Typing for far field The number of times it was selected; The average beam gain of the far-field codeword. ; For intermediate parameters; It is a constant; For the user's noise variance;

[0076] No. Near-field code The formula for calculating the CP-UCB value is:

[0077] ,

[0078] in:

[0079] ,

[0080] ,

[0081] In the formula, For the first Near-field codewords of coherent blocks The corresponding CP-UCB value, For the first Near-field codewords of coherent blocks The corresponding concealment probability. For the first Near-field codewords of coherent blocks Historical average reward For near-field typing The number of times selected, The average beam gain of the near-field codeword. ; For intermediate parameters; It is a constant.

[0082] In one specific embodiment of the present invention, the objective function and constraints of the optimization problem in the data transmission stage are as follows:

[0083] .

[0084] In one specific embodiment of the present invention, the method for calculating the optimal base station transmission power includes:

[0085] eavesdropper Assuming only noise is received, the eavesdropper's received signal during the data transmission phase... The expression for the likelihood function is:

[0086] ;

[0087] in, for exist Assuming the following... The likelihood function corresponding to each coherent block yes The The first coherent block The corresponding eavesdropper's received signal; The noise variance of the eavesdropper;

[0088] eavesdropper Assuming that noise and leakage signals are received simultaneously, the eavesdropper's received signal during the data transmission phase... The mathematical expression for the likelihood function is:

[0089] ,

[0090] in:

[0091] ,

[0092] In the formula, for exist Assuming the following... The likelihood function corresponding to each coherent block For intermediate parameters, The noise variance of the eavesdropper. For the first The channel vector of the eavesdropper corresponding to each coherent block;

[0093] Will and Substitute the first The relative entropy of each coherent block data transmission stage And through Taylor expansion, the formula for calculating the optimal base station transmission power is obtained as follows:

[0094] ,

[0095] in:

[0096] ,

[0097] In the formula, For intermediate parameters, It indicates a desire for the expected value.

[0098] The method in the embodiments of the present invention will be described in detail below with reference to a specific implementation method.

[0099] This embodiment provides a near-field XL-MIMO covert communication beam training method, specifically a near-field beam training and power allocation method for an XL-MIMO downlink covert communication system where legitimate users and eavesdroppers reuse scattering clusters under multiple scattering clusters. This method is applicable to Alice base station configurations. Uniform linear array of antennas and finite radio frequency chain This scenario involves serving a single-antenna legitimate user, Bob, while simultaneously having a single-antenna eavesdropper, Willie. See details in the original text. Figure 1 The legitimate user Bob is located in the near-field region (distance less than Rayleigh distance). The channel adopts a spherical wave model, and the channel vector consists of multiple scattering clusters. Each cluster contains several paths, and each path contains angle, distance, and phase information. The near-field XL-MIMO covert communication beam training method specifically includes the following steps:

[0100] Step 1: Establish a channel model

[0101] The near-field channels from base station Alice to user Bob and to eavesdropper Willie can be modeled as follows:

[0102] ,

[0103] ,

[0104] in, It is the first Channel vectors of each coherent block user It is the number of scattering clusters. It is the first [connection / relationship] between the user and the target location. The scattering cluster of the first The distance of the path, For the number of antennas, Indicates the first The scattering cluster of the first Complex gain of the path, It is the identity matrix. and These are the relationships between the base station and the user, and between the base station and the eavesdropper. The number of paths in each scattering cluster. Uniformly distributed in [0,1], For the first The scattering cluster of the first Phase shift of the path, λ is the wavelength. It is the near-field channel steering vector, which is defined as:

[0105]

[0106] In the formula, and Indicates the first The scattering cluster of the first The angle and distance of the path, The base station's number root antenna to the first The distance between the scattering clusters ; , is the antenna spacing.

[0107] Using the Carhenen-Lowell notation, the first The channel vector of user Bob in each coherent block Specifically, it is expressed as follows: Its channel covariance matrix Specifically, it is expressed as follows: In the formula, For the first The contribution of each scattering cluster and satisfying , Let von Mises' distribution function be used. The number of scattering clusters from the base station to the user. and The base station's number root and first root antenna to the first A specific location within a scattering cluster (by angle) (Determined) distance, This is a small-scale fading. Similarly, the first... The channel vector of the eavesdropper Willie in each coherent block Specifically, it is expressed as follows: .

[0108] Step 2: Modeling the Joint Optimization Problem

[0109] Assuming statistical channel state information (S-CSI) is in Within each coherent block, the beam training and power allocation are modeled as a joint optimization problem, with the optimization objective being to maximize the system's effective achievable rate. This joint optimization problem can be expressed as:

[0110] ,

[0111] in, ;

[0112] In the formula, The effective achievable rate for XL-MIMO systems; For the first The base station transmission power corresponding to each coherent block; For the first The simulated beamforming vectors corresponding to each coherent block; For eavesdroppers and The relative entropy between the received signal distributions under the two assumptions, as the first... The concealment constraints that need to be satisfied in each coherent block data transmission stage; For the sake of concealment, it is a constant; and These represent the data transmission stages. A coherent block of eavesdroppers and Likelihood functions of the receiver function under two assumptions Indicates the null hypothesis, Indicates alternative assumptions; This represents the maximum base station transmission power. This is a near-field codebook based on a spherical wave model; This represents the total number of coherent blocks; The number of symbols that can be transmitted in a coherent block; The number of symbols used in each coherent block beam training phase (i.e., the overhead of each coherent block beam training phase). For the first The channel vectors of the users corresponding to each coherent block , The channel covariance matrix of the user. The noise variance for the user.

[0113] Step 3: Constructing the Two-Stage Optimization Problem

[0114] A phased iterative optimization algorithm is employed to discuss the power constraints and concealment constraints of the beam training phase (BA phase) and the data transmission phase (DT phase) separately. Since the original problem is a multi-objective, multi-constraint joint optimization problem, it is difficult to solve directly. Therefore, this embodiment of the invention proposes to decompose the joint optimization problem into two sub-problems: the beam training phase and the concealment-constrained data transmission phase, and to perform iterative optimization on each sub-problem separately.

[0115] During the beam training phase, the optimization objective is to select the simulated beamforming vector. Although the beam training phase is not subject to the same strict implicit inequalities as the data transmission phase (i.e., ... However, to minimize the risk of being detected by eavesdroppers during training, this embodiment of the invention embeds the concealment metric (i.e., concealment probability) as a weighted term into the design of the Covertness Probability Upper Confidence Bound (CP-UCB) algorithm. Specifically, the optimization problem in the beam training phase is formulated as follows:

[0116] ,

[0117] During the data transmission phase, communication is based on the simulated beamforming vectors obtained during the beam training phase. The optimization objective at this stage is to maximize the base station's transmission power while satisfying the concealment constraints of the data transmission phase. This improves the system's effective achievable rate, so the optimization problem in the data transmission phase can be described as:

[0118] ,

[0119] in, For eavesdroppers and The relative entropy between the received signal distributions under the two assumptions, as the first... The concealment constraints that need to be satisfied in each coherent block data transmission stage; For the sake of concealment, it is a constant. and These represent the data transmission stages. A coherent block of eavesdroppers and Likelihood functions of the receiver function under two assumptions Indicates the null hypothesis, This indicates an alternative hypothesis.

[0120] Through the above two-stage decomposition, the original complex non-convex problem is transformed into two well-structured and separately solvable subproblems: the BA stage obtains the simulated beamforming vector (i.e., the high-quality beam) through covert awareness-based intelligent search, and the DT stage solves for maximizing the base station transmission power in the beam direction while satisfying strict covert constraints. (i.e., optimal power).

[0121] Step 4: Representation of concealment probability during beam training

[0122] According to the Neyman-Pearson criterion, the optimal rule to minimize the detection error of the eavesdropper Willie is the likelihood ratio test, which is expressed as follows:

[0123] ,

[0124] in, and Corresponding to the hypothesis and Assuming The likelihood function, Indicates the first Each coherent block selects a codeword Willie's received signal at that time and These correspond to the hypotheses respectively. and The binary judgment.

[0125] Furthermore, the expression for the likelihood ratio test can be restated to an equivalent form as:

[0126]

[0127] in, This indicates Willie's optimal detection threshold. . Depends on the code , , .

[0128] Assuming in and Under these conditions, the received signal of the eavesdropper Willie follows a complex Gaussian distribution, with its modulus squared... The cumulative density functions (CDFs) are as follows:

[0129] ,

[0130] ,

[0131] In the formula, Represents the cumulative density function;

[0132] Therefore, based on the optimal detection threshold Give the probability of error detection and the probability of missed detection The calculation formula is as follows:

[0133] .

[0134] According to the formula for the total detection error probability, the concealment probability is defined as the sum of the false detection probability and the false negative probability of the eavesdropper Willie, i.e. This value directly reflects the overall risk of Willie detecting communication behavior under specific beam illumination.

[0135] To adapt to the two-stage hierarchical structure of beam training, it is necessary to calculate the calculations for the first stage separately. The first coherent block The far-field codeword and the first The concealment probabilities corresponding to each near-field codeword are respectively and Both calculations rely on the channel covariance matrix of the eavesdropper Willie. However, in a real system, the instantaneous channel of the eavesdropper Willie and the precise channel covariance matrix are crucial. This information cannot be obtained by the base station Alice. Therefore, this invention proposes an approximation method based on historical observations: using far-field codewords... For example, using the eavesdropper Willie's received signals and corresponding far-field codewords during the previous coherent block beam training phase. Number of times selected ,available The estimated value ,in, Indicates the first Each coherent block selects far-field codewords. The signal received by the eavesdropper Willie For the first Each coherent block selects far-field codewords. An indicator function indicating whether it has been selected. Therefore, the first... The first coherent block The concealment probability of a far-field codeword The calculation formula is as follows: Similarly, the first The first coherent block Near-field code Near-field concealment probability The calculation formula is: ,in: , In the formula, This represents the concealment probability corresponding to the near-field codeword. For intermediate parameters, Indicates the first Near-field codewords of coherent blocks Whether or not to be selected, To select near-field codewords for the eavesdropper during the beam training phase The received signal; For near-field typing The number of times it was selected.

[0136] Step 5: Optimization Scheme for Beam Training Phase

[0137] The beam training phase (BA phase) optimization aims to optimize the selection of simulated beamforming vectors and maximize the effective reachability of the system while satisfying the concealment constraint.

[0138] For beam training, a two-layer scanning strategy is employed, specifically including: coarse scanning in the angular domain and fine scanning in the polar domain. Both rely on the CP-UCB algorithm to achieve intelligent codeword selection. The formula for calculating the CP-UCB value is:

[0139]

[0140]

[0141]

[0142] in, For the first Coherent block far-field codewords The corresponding CP-UCB value, For the first Coherent block far-field codewords The corresponding concealment probability. For the first Coherent block far-field codewords Historical average reward Typing for far field The number of times it was selected.

[0143] Similarly, the formula for calculating the near-field CP-UCB value is:

[0144] ,

[0145] ,

[0146] ,

[0147] in, For the first Near-field codewords of coherent blocks The corresponding near-field CP-UCB value, For the first Near-field codewords of coherent blocks The corresponding near-field concealment probability. For the first Near-field codewords of coherent blocks Historical average reward For near-field typing The number of times it was selected.

[0148] Far field codebook Each far-field codeword (i.e., angle codeword) in the code is considered as one "arm" of a multi-armed slot machine. During initialization, a random selection is made. For each far-field codeword, initial training is performed, recording the number of training iterations, average reward, and concealment probability. Untrained far-field codewords are not initialized initially. During iteration, for each far-field codeword... Calculate its CP-UCB value Send pilot signals to obtain actual rewards And update the concealment probability according to the formula in step four. Update the training count of the selected far-field codewords. And extract their angle parameters to form a candidate angle set. .

[0149] In the design of the near-field codebook, each near-field codeword is determined by both angle and distance parameters. To adapt to the characteristics of the near-field channel, multiple distance sampling points are associated with each angular direction. For any given angle... The corresponding distance parameter can be determined by the following formula:

[0150]

[0151] Among them, the The first near-field codeword corresponds to the first The corresponding angle parameter is the first One distance parameter, For the first The first near-field codeword corresponds to the first An angle parameter, ; It is a threshold distance used to limit the coherence of near-field steering vector columns. , For the number of antennas, For wavelength, List the coherence control parameters; Indicates the first The number of distance parameters corresponding to each angle parameter;

[0152] Each near-field codeword is considered as an "arm" of a multi-armed slot machine, and the reward is set as the square of the magnitude of the received signal by user Bob. The CP-UCB algorithm is used in the iteration: [The remaining text appears to be incomplete and requires further context.] Step, select the current front with the highest near-field CP-UCB value. A set of near-field codewords is formed, which constitutes a set of near-field candidate codewords. After training the selected near-field codewords, training pilot signals are sent to obtain the corresponding real sample values. And update the parameters of the selected near-field codeword, the parameters including: the number of times the near-field codeword was selected (the corresponding update formula is...). ), average reward (the corresponding update formula is) (and update the near-field concealment probability according to the formula in step four) .

[0153] After the beam training phase, the system selects from the near-field candidate codeword set. Select CP-UCB value The largest near-field codeword is used as the analog beamforming vector. This is used for data transmission during the data transmission phase. The two-layer scanning mechanism in this embodiment of the invention utilizes CP-UCB balanced exploration and utilization to compress the search space while ensuring the accuracy and stealth of beam training, providing a reliable beam for the data transmission phase.

[0154] Step Six: Optimization Scheme for Data Transmission Stage

[0155] After completing the beam training phase and obtaining the simulated beamforming vectors... Afterward, the system enters the data transmission phase (which can be simply referred to as the DT phase). The core objective of this phase is to transmit information in the determined beam direction and optimize the transmit power. The goal is to maximize the effective reachability of the system while strictly satisfying the concealment constraints. The optimization in the DT phase is based on the beam focusing gain and concealment resource allocation provided in the BA phase, and its complete scheme is as follows.

[0156] First, based on the simulated beamforming vector output from the BA stage. The received signal model for the DT (Digital Transmission) stage was thus established. Subsequently, resource optimization in the DT stage was modeled as an optimization problem with transmission power as the variable. The objective function of this optimization problem is to maximize the base station transmission power. Because the effective achievable rate of the system is limited when the beam direction is fixed during the DT phase. yes The function is a monotonically increasing function. The optimization problem requires satisfying two constraints simultaneously: first, the transmit power in the DT stage must not exceed its hardware limit. Secondly, it must satisfy the concealment constraint against the eavesdropper Willie during the DT phase. This concealment constraint is determined by the parameters. Control. Therefore, the optimization problem in the DT stage can be formally expressed as:

[0157] ,

[0158] in, This indicates that during the entire symbol transmission time in the DT phase, the eavesdropper Willie received the signal under the null hypothesis (…). (no transmission) and alternative assumptions ( The relative entropy between probability distributions under transmission conditions.

[0159] To solve the above optimization problem, the concealment constraint term needs to be processed in depth. Considering that Willie's observations during the DT phase contain multiple consecutive data symbols, his received signal vector is... Assuming the data contains only noise and that all data symbols are independent and identically distributed; Under the given assumptions, the signal includes the superposition of beamformed signal and noise. By modeling the probability distribution of the received signal under both assumptions and using Pinsker's inequality to transform the detection error probability constraint into a relative entropy constraint, we can obtain... Regarding base station transmission power The expression for channel gain.

[0160] However, this expression is usually complex, non-convex, and difficult to solve directly. Therefore, this invention employs an efficient approximate derivation method. First, the Taylor expansion is used to refine the relative entropy expression... Perform a second-order expansion at that point, simplifying it to about The quadratic form:

[0161] ,

[0162] Next, the relative entropy form of the concealment constraint is parametrically replaced using the following formula:

[0163] ,

[0164] ,

[0165] It can be converted to:

[0166] ,

[0167] Then in Performing a second-order Taylor expansion at that point, we obtain:

[0168] ,

[0169] Ultimately, we can obtain:

[0170] ,

[0171] The optimal transmit power in the DT phase can be obtained. Closed expression:

[0172]

[0173] This closed-form solution has a clear physical meaning: the maximum safe power in the DT stage is determined by two bottlenecks. One is the upper limit of the system's hardware power. The second factor is the "covertness power limit," which is determined by factors such as concealment requirements, noise levels, transmission duration, and the degree of signal leakage in the direction of the eavesdropper. When beam alignment performance is excellent, i.e., the focusing gain for the legitimate user Bob is high while the leakage gain for the eavesdropper Willie is low, the covertness power limit will increase. This allows the system to use higher transmission power while meeting concealment requirements, thereby significantly improving the effective reachable rate.

[0174] This invention discloses a near-field XL-MIMO covert communication beam training method, which, compared with traditional beam training methods, can significantly reduce training overhead while maintaining comparable beamforming performance.

[0175] The near-field XL-MIMO covert communication beam training method in this embodiment mainly revolves around XL-MIMO communication system initialization, channel information acquisition, two-stage optimization execution, and data transmission.

[0176] First, the XL-MIMO communication system is deployed and its parameters are initialized. The XL-MIMO communication system includes a base station, a single-antenna legitimate user Bob, and a single-antenna eavesdropper Willie. The base station is configured with... A uniform linear array composed of antennas and A finite radio frequency chain is used. Legitimate user Bob is located in the near-field region, meaning his distance from the base station is less than the Rayleigh distance. The system employs a near-field spherical wave channel model based on multiple scattering clusters, where the channel vector is composed of multiple scattering clusters, each containing several paths, and each path containing angle, distance, and phase information. The base station pre-constructs the user's channel covariance matrix based on the aforementioned near-field spherical wave channel model. and the channel covariance matrix of the eavesdropper Among them, the contribution of each scattering cluster Normalized, the angular distribution is characterized by the von Mises function. Using the Carhennan-Louis expansion, the user's channel vector can be expressed as... The channel vector of the eavesdropper can be represented as Meanwhile, the XL-MIMO communication system uses a pre-defined far-field codebook for beam training. and near-field codebook Set a threshold for concealment requirements. and maximum base station transmit power .

[0177] Entering the beam training phase, the XL-MIMO communication system will perform the proposed two-stage optimization based on the concealment probability-based UCB algorithm. In the beam training phase (i.e., the BA phase), the primary task is to perform beam selection in conjunction with the concealment probability. Specifically:

[0178] During the beam training phase, the XL-MIMO communication system implements the proposed two-layer scanning strategy.

[0179] The first layer is a coarse scan of the angular domain, specifically including: scanning the far-field codebook. Each far-field codeword (i.e., angle codeword) is considered an "arm". During initialization, arms are randomly selected. The first training iteration uses 10 far-field codewords, recording the number of training iterations and the average reward (the reward is the square of the magnitude of the received signal by user Bob) for each far-field codeword. After initialization, in each subsequent coherent block, 100 training iterations are performed for each far-field codeword. Calculate its CP-UCB value:

[0180]

[0181] XL-MIMO communication systems select the front with the highest CP-UCB value. Training pilots are sent to each of the selected far-field codewords to update the parameters of each codeword, and the angle parameters corresponding to these codewords are extracted to form a candidate angle set. .

[0182] The second layer is polar-domain fine scanning, specifically including: based on the candidate angle set The selected candidate angles are in the near-field codebook. Further search for the optimal "angle-distance" pair. Near-field codebook Each near-field codeword in the array is also considered an "arm," and its CP-UCB value is calculated in the same way. After initialization, the top-ranked codeword with the highest CP-UCB value is selected in each iteration. The algorithm trains on a set of near-field codewords and updates its parameters. After multiple iterations, the algorithm converges to a stable set of high-gain codewords. and select from them The largest near-field codeword is used as the analog beamforming vector. The beam training phase has been completed.

[0183] The data transmission phase then begins. At this point, the XL-MIMO communication system utilizes the simulated beamforming vectors obtained during the beam training phase. Signal transmission is then performed. The optimization objective of the data transmission phase simplifies to maximizing the transmission power while satisfying the concealment constraint of this phase. By analyzing the statistical distribution of the signal received by the eavesdropper Willie throughout the entire data transmission process, and again utilizing the relative entropy constraint, the optimal base station transmission power for the data transmission phase is derived. (i.e., optimal power) closed-form solution, maximizing base station transmission power. The calculation formula is:

[0184]

[0185] Finally, in the simulated beamforming vector and optimal base station transmission power Once confirmed, the base station sends data to the legitimate user Bob. The received signal for the legitimate user Bob is... ,in, To send symbols, It is Gaussian noise.

[0186] The XL-MIMO communication system dynamically maintains a high-performance covert communication link in a time-varying near-field environment by continuously repeating the above-mentioned channel estimation, two-stage optimization, and data transmission process.

[0187] Figure 3 The performance of the near-field XL-MIMO covert communication beam training method (CP-UCB scheme) in the proposed embodiments of the present invention is shown at various coherence times. From Figure 3 As can be observed, during the initial coherence time of approximately 40 seconds, the algorithm is in an exploratory phase, making extensive attempts at various angles and distances, resulting in a low and fluctuating average reachability. As time progresses, the algorithm gradually converges to a high-quality beam, and the average reachability steadily increases. After the coherence time reaches approximately 100 seconds, the curve flattens out, and the average reachability stabilizes at around 5.5 bits / s / Hz, indicating that the algorithm has completed convergence and can continuously select near-optimal beams. This convergence characteristic conforms to the theoretical expectation of UCB-type algorithms, namely, that the accumulated regret increases logarithmically while the regret per unit time slot gradually decreases. Simulation results verify that the algorithm proposed in this invention can effectively learn statistical channel information with limited training overhead and stably select high-performance beams.

[0188] like Figure 4 As shown, the near-field XL-MIMO covert communication beam training method (CP-UCB scheme) in this embodiment of the invention is compared with other training schemes in the prior art. From Figure 4As can be seen, the CP-UCB scheme proposed in this invention performs only as well as the Non-Covert scheme (training scheme without shielding probability), exhibiting excellent overall performance. Although the Non-Covert scheme achieves the highest achievable rate, it is not feasible in practical covert communication scenarios because it completely ignores the concealment constraint, and can only be used as a performance upper limit reference. The Fast two-stage scheme and the Hier scheme, due to their use of fixed transmit power and the lack of deep coupling between their beam training process and the concealment criterion, result in a significantly lower steady-state rate than the CP-UCB scheme in this invention.

[0189] Figure 5 This paper presents the comparison between relative entropy and concealment thresholds for various schemes considering concealment at different Bob signal-to-noise ratios. Figure 5 It can be observed that the relative entropy generated by all schemes remains below the preset threshold, strictly satisfying the concealment constraint. The CP-UCB scheme proposed in this invention has the highest relative entropy value compared to other schemes. This indicates that, thanks to dynamic power allocation technology and beam training with concealment probability, this scheme avoids the overly conservative concealment effect caused by Fast and Hier schemes, which force zeroing when power is fixed and constraints are not met. In contrast, the Fast and Hier schemes have the lowest relative entropy values. Although they can guarantee good concealment, they also reflect that their conservative power strategy leads to serious performance loss.

[0190] The above embodiments demonstrate the complete process of the present invention, from system modeling and intelligent beam search to power closed-loop optimization. By deeply embedding concealment constraints into beam training and power allocation decisions, and utilizing the CP-UCB algorithm to efficiently explore the near-field high-dimensional beam space, the present invention effectively solves the problem of covert communication in near-field XL-MIMO systems in practice, significantly improving the effective reachability rate of the system while ensuring concealment. Simulation results show that, compared with existing modular and non-modular beam training schemes for covert communication, the proposed scheme exhibits significant advantages in training overhead, average reachability rate performance, and computational complexity.

[0191] Example 2

[0192] Based on the same inventive concept as Embodiment 1, this embodiment of the invention provides a near-field XL-MIMO covert communication beam training device, comprising:

[0193] The modeling unit is used to model the joint optimization problem of beam training and power allocation as a non-convex optimization problem under hidden constraints with the goal of maximizing the effective reachability rate.

[0194] A splitting unit is used to split the non-convex optimization problem into an optimization problem in the beam training stage and an optimization problem in the data transmission stage;

[0195] The simulated beamforming vector calculation unit is used to address the optimization problem in the beam training phase, aiming to maximize the effective reachability rate. It combines a beam selection algorithm with concealment probability to calculate a suitable simulated beamforming vector.

[0196] The optimal base station transmission power calculation unit is used to address the optimization problem in the data transmission stage. By combining a suitable simulated beamforming vector, it calculates the optimal base station transmission power with the goal of maximizing the base station transmission power, and completes the training of the near-field XL-MIMO covert communication beam.

[0197] Everything else is the same as in Example 1.

[0198] Example 3

[0199] This invention provides a near-field XL-MIMO covert communication beam training system, including a storage medium and a processor;

[0200] The storage medium is used to store instructions;

[0201] The processor is configured to operate according to the instructions to execute the method according to any one of Embodiment 1.

[0202] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0203] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0204] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0205] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0206] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

[0207] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A near-field XL-MIMO covert communication beam training method, characterized in that, include: With the goal of maximizing the effective reachability rate, the joint optimization problem of beam training and power allocation is modeled as a non-convex optimization problem under the implicit constraint; The non-convex optimization problem is decomposed into an optimization problem in the beam training phase and an optimization problem in the data transmission phase; To address the optimization problem in the beam training phase, with the goal of maximizing the effective reachability rate, a suitable simulated beamforming vector is calculated by combining a beam selection algorithm with concealment probability. To address the optimization issues in the data transmission phase, and in conjunction with the appropriate simulated beamforming vector, the optimal base station transmission power is calculated with the goal of maximizing the base station transmission power, thus completing the near-field XL-MIMO covert communication beam training. The suitable method for calculating the simulated beamforming vector includes: First, an angular domain scan is performed. In the angular domain scan, each far-field codeword in the far-field codebook is used as an arm of a multi-armed slot machine, with the square of the modulus of the user's received signal as the reward. During initialization, a code is randomly selected from the far-field codebook. The first training is performed on a far-field codeword, and the initial parameters, number of training iterations, average reward, and concealment probability of the trained far-field codeword are recorded; the training refers to sending the far-field codeword to the user through the base station so that the user receives the signal; During the iteration process, a beam selection algorithm with concealment probability is used to select the beam with the highest CP-UCB value. A far-field codeword, for the selected Beam training is performed on each far-field codeword, updating the parameters, training times, average reward, and concealment probability of the corresponding far-field codeword, extracting the angle parameters from the far-field codeword to form a candidate angle set, and completing the coarse scanning of the angular domain. Secondly, polar-domain scanning is performed. In polar-domain scanning, candidate near-field codewords are selected from the near-field codebook based on the angle parameters in the candidate angle set, thus obtaining the corresponding candidate polar-domain codeword angle set. Used for polar scanning, for any given angle parameter The formula for calculating the corresponding distance parameter is: ， in, For the first The first near-field codeword corresponds to the first The corresponding angle parameter is the first One distance parameter, For the first The first near-field codeword corresponds to the first An angle parameter, ; It is a threshold distance used to limit the coherence of near-field steering vector columns. , For the number of antennas, For wavelength, List the coherence control parameters; Indicates the first The number of distance parameters corresponding to each angle parameter; Each near-field codeword is composed of an angle-distance pair. By definition, the expression for the near-field codebook is obtained as follows: ， In the formula, This is the near-field steering vector; Near field codebook Each near-field codeword in the code is considered an arm of a multi-armed slot machine, and the reward is set to the square of the user's received signal modulus. During the iteration process, a beam selection algorithm with concealment probability is employed, specifically including: selecting the beam with the highest current CP-UCB value. For each selected near-field codeword, after training, a training pilot signal is sent to obtain the corresponding real reward sample value. It also updates the parameters of the corresponding near-field codeword, including: the number of near-field codeword selections, the average reward, and the concealment probability.

2. The near-field XL-MIMO covert communication beam training method according to claim 1, characterized in that: The objective function and constraints of the nonconvex optimization problem under the hidden constraints are as follows: ， in: ， In the formula, The effective achievable rate for XL-MIMO systems; For the first The base station transmission power corresponding to each coherent block; For the first The simulated beamforming vectors corresponding to each coherent block; For eavesdroppers and The relative entropy between the received signal distributions under the two assumptions, as the first... The concealment constraints that need to be satisfied in each coherent block data transmission stage; For the sake of concealment, it is a constant; and These represent the data transmission stages. A coherent block of eavesdroppers and Likelihood functions of the receiver function under two assumptions Indicates the null hypothesis, Indicates alternative assumptions; This represents the maximum base station transmission power. This is a near-field codebook based on a spherical wave model; This represents the total number of coherent blocks; The number of symbols that can be transmitted in a coherent block; The number of symbols used in the training phase of each coherent block beam; For the first The channel vectors of the users corresponding to each coherent block , The channel covariance matrix of the user. The noise variance for the user.

3. The near-field XL-MIMO covert communication beam training method according to claim 2, characterized in that: The objective function and constraints of the optimization problem in the beam training phase are as follows: 。 4. The near-field XL-MIMO covert communication beam training method according to claim 1, characterized in that: The formula for calculating the concealment probability corresponding to a far-field codeword is: ， in: ， ， ， In the formula, Typing for far field The corresponding concealment probability; and These are all intermediate parameters; Indicates the first Coherent block far-field codewords Whether or not to be selected, ; To select far-field codewords for the eavesdropper during the beam training phase The received signal; Typing for far field The number of times it was selected; The channel covariance matrix of the eavesdropper; The noise variance of the eavesdropper; The formula for calculating the concealment probability corresponding to a near-field codeword is: ， in: ， ， In the formula, This represents the concealment probability corresponding to the near-field codeword. For intermediate parameters, Indicates the first Near-field codewords of coherent blocks Whether or not it was selected; , To select near-field codewords for the eavesdropper during the beam training phase The received signal; For near-field typing The number of times it was selected.

5. The near-field XL-MIMO covert communication beam training method according to claim 3, characterized in that: No. A far-field code The formula for calculating the CP-UCB value is: ， in: ， ， In the formula, For the first Coherent block far-field codewords The corresponding CP-UCB value, For the first Coherent block far-field codewords Historical average reward For the first Coherent block far-field codewords The corresponding concealment probability. Typing for far field The number of times it was selected; The average beam gain of the far-field codeword. ; For intermediate parameters; It is a constant; For the user's noise variance; No. Near-field code The formula for calculating the CP-UCB value is: ， in: ， ， In the formula, For the first Near-field codewords of coherent blocks The corresponding CP-UCB value, For the first Near-field codewords of coherent blocks The corresponding concealment probability. For the first Near-field codewords of coherent blocks Historical average reward For near-field typing The number of times it was selected The average beam gain of the near-field codeword. ; For intermediate parameters; It is a constant.

6. The near-field XL-MIMO covert communication beam training method according to claim 3, characterized in that: The objective function and constraints of the optimization problem in the data transmission phase are as follows: 。 7. The near-field XL-MIMO covert communication beam training method according to claim 6, characterized in that: The method for calculating the optimal base station transmission power includes: eavesdropper Assuming only noise is received, the eavesdropper's received signal during the data transmission phase... The expression for the likelihood function is: ； in, for exist Assuming the following... The likelihood function corresponding to each coherent block yes The The first coherent block The corresponding eavesdropper's received signal; The noise variance of the eavesdropper; eavesdropper Assuming that noise and leakage signals are received simultaneously, the eavesdropper's received signal during the data transmission phase... The mathematical expression for the likelihood function is: ， in: ， In the formula, for exist Assuming the following... The likelihood function corresponding to each coherent block For intermediate parameters, The noise variance of the eavesdropper. For the first The channel vector of the eavesdropper corresponding to each coherent block; Will and Substitute the first The relative entropy of each coherent block data transmission stage And through Taylor expansion, the formula for calculating the optimal base station transmission power is obtained as follows: ， in: ， In the formula, For intermediate parameters, It indicates a desire for the expected value.

8. A near-field XL-MIMO covert communication beam training device, characterized in that, include: The modeling unit is used to model the joint optimization problem of beam training and power allocation as a non-convex optimization problem under hidden constraints with the goal of maximizing the effective reachability rate. A splitting unit is used to split the non-convex optimization problem into an optimization problem in the beam training stage and an optimization problem in the data transmission stage; The simulated beamforming vector calculation unit is used to address the optimization problem in the beam training phase, aiming to maximize the effective reachability rate. It combines a beam selection algorithm with concealment probability to calculate a suitable simulated beamforming vector. The optimal base station transmission power calculation unit is used to calculate the optimal base station transmission power by combining appropriate simulated beamforming vectors to maximize the base station transmission power, thereby completing the near-field XL-MIMO covert communication beam training for optimization problems in the data transmission stage. The suitable method for calculating the simulated beamforming vector includes: First, an angular domain scan is performed. In the angular domain scan, each far-field codeword in the far-field codebook is used as an arm of a multi-armed slot machine, with the square of the modulus of the user's received signal as the reward. During initialization, a code is randomly selected from the far-field codebook. The first training is performed on a far-field codeword, and the initial parameters, number of training iterations, average reward, and concealment probability of the trained far-field codeword are recorded; the training refers to sending the far-field codeword to the user through the base station so that the user receives the signal; During the iteration process, a beam selection algorithm with concealment probability is used to select the beam with the highest CP-UCB value. A far-field codeword, for the selected Beam training is performed on each far-field codeword, updating the parameters, training times, average reward, and concealment probability of the corresponding far-field codeword, extracting the angle parameters from the far-field codeword to form a candidate angle set, and completing the coarse scanning of the angular domain. Secondly, polar-domain scanning is performed. In polar-domain scanning, candidate near-field codewords are selected from the near-field codebook based on the angle parameters in the candidate angle set, thus obtaining the corresponding candidate polar-domain codeword angle set. Used for polar scanning, for any given angle parameter The formula for calculating the corresponding distance parameter is: ， in, For the first The first near-field codeword corresponds to the first The corresponding angle parameter is the first One distance parameter, For the first The first near-field codeword corresponds to the first An angle parameter, ; It is a threshold distance used to limit the coherence of near-field steering vector columns. , For the number of antennas, For wavelength, List the coherence control parameters; Indicates the first The number of distance parameters corresponding to each angle parameter; Each near-field codeword is composed of an angle-distance pair. By definition, the expression for the near-field codebook is obtained as follows: ， In the formula, This is the near-field steering vector; Near field codebook Each near-field codeword in the code is considered an arm of a multi-armed slot machine, and the reward is set to the square of the user's received signal modulus. During the iteration process, a beam selection algorithm with concealment probability is employed, specifically including: selecting the beam with the highest current CP-UCB value. For each selected near-field codeword, after training, a training pilot signal is sent to obtain the corresponding real reward sample value. It also updates the parameters of the corresponding near-field codeword, including: the number of near-field codeword selections, the average reward, and the concealment probability.

9. A near-field XL-MIMO covert communication beam training system, characterized in that, Including storage media and processor; The storage medium is used to store instructions; The processor is configured to operate according to the instructions to perform the method according to any one of claims 1-7.

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