Covert communication method based on movable antenna auxiliary relay

Abstract

The invention provides a covert communication method based on a movable antenna auxiliary relay, in a covert communication scene, confidential information from a transmitter to a receiver is forwarded through a relay node, the relay is provided with Mr movable antennas, and the physical position is allowed to be dynamically adjusted; the transmission model comprises: a first stage: a transmitter sends a signal to a relay node through a beam forming matrix, and the relay node receives, amplifies and forwards the signal through a movable antenna; in the second stage, the relay node forwards the signal to the receiver by transmitting a beam forming vector; the position of the movable antenna, a transmitter beam forming matrix and a relay transmitting beam forming vector are jointly optimized to meet the following constraints: the joint detection error probability of a listener on two-stage signals is constrained by statistical difference; the position of the movable antenna is limited in a preset area omega r, the minimum spacing dmin is equal to lambda / 2, and lambda is the wavelength of a carrier wave; and the hidden throughput is maximized through the optimization.

Description

Technical Field

[0001] The present invention belongs to the technical fields such as wireless communication technology, and specifically relates to a covert communication method based on a movable antenna-assisted relay. Background Art

[0002] In recent years, the wireless communication system has an increasing demand for concealment and transmission efficiency. Especially in security-sensitive scenarios such as military communication and financial data transmission, how to achieve efficient information transmission without being detected by eavesdroppers has become a key research direction. Traditional covert communication technologies mainly rely on the following two types of solutions:

[0003] Covert transmission under a fixed antenna architecture:

[0004] A fixed array antenna or an omnidirectional antenna is adopted, and means such as power control, artificial noise injection, and coding modulation are used to reduce the detection probability of eavesdroppers. However, the physical position and beam direction of the fixed antenna cannot dynamically adapt to channel changes, resulting in the following limitations:

[0005] Channel rigidity: In a multipath time-varying channel, it is difficult for a fixed antenna to actively utilize the multipath diversity gain, and the signal-to-noise ratio of the legitimate link is limited by static beamforming;

[0006] Concealment-throughput contradiction: To meet the concealment requirements, it is usually necessary to significantly reduce the transmission power or sacrifice the spectral efficiency, resulting in a significant decrease in the transmission rate.

[0007] Technical attempts for dynamic channel optimization:

[0008] Some studies attempt to adjust the channel characteristics through dynamic platforms such as intelligent reflecting surfaces (IRS) or unmanned aerial vehicle relays. However, they rely on external device reflection or mobile trajectory planning and have the following problems:

[0009] High hardware complexity: The IRS needs to deploy a large number of passive components and relies on precise phase control, making the engineering implementation difficult;

[0010] Lack of real-time performance: The optimization of the movement trajectory of the unmanned aerial vehicle relay requires global channel information and it is difficult to cope with a rapidly time-varying environment;

[0011] Limited multipath utilization: Existing solutions do not fully exploit the spatial degrees of freedom of the multipath channel, and eavesdroppers can still crack the concealment through a multi-antenna receiver.

[0012] In addition, existing covert communication technologies mostly adopt a single-dimensional optimization strategy (such as only optimizing the transmission power or beamforming), lacking the joint design of physical layer hardware control and transmission protocols, resulting in the following common bottlenecks:

[0013] Non - convex optimization problem: The strong coupling of variables such as antenna position, beamforming, and power allocation makes global optimization difficult to achieve, and often relies on sub - optimal heuristic algorithms;

[0014] Insufficient concealment guarantee: Listeners can improve the detection probability by jointly detecting multi - stage signals or using the correlation of channel state information (CSI), while existing solutions lack targeted suppression mechanisms for this.

[0015] The above - mentioned technical defects indicate that traditional solutions are difficult to achieve the collaborative optimization of concealment - throughput - real - time performance in complex wireless environments. There is an urgent need for a new type of covert communication technology that deeply integrates the dynamic control of physical - layer hardware and the design of communication protocols. Summary of the Invention

[0016] Aiming at the defects and deficiencies of the existing technology, the present invention provides a covert communication method and system based on a movable antenna - assisted relay. Its core innovative design points include:

[0017] Dynamic antenna position optimization mechanism: Real - time adjust the physical position of the movable antenna of the relay node through mechanical drive or electronic control, actively adapt to the time - varying characteristics of the channel, enhance the signal - to - noise ratio of the legitimate link, and at the same time make the signals received by listeners in a deep - fading state, significantly reducing the detection probability;

[0018] Hierarchical joint optimization framework: Decouple the antenna position and beamforming parameters. The outer layer uses the projected gradient descent method to optimize the antenna position, and the inner layer uses the semi - definite relaxation method (SDR) and the block coordinate descent method to solve the non - convex beamforming problem to maximize the covert throughput;

[0019] Deep utilization of multipath diversity gain: Dynamically match the antenna position based on the characteristics of the multipath channel, and use the superimposed fading effect brought by the increase in the number of paths to further suppress the detection ability of listeners;

[0020] Two - stage KL - divergence joint constraint: By jointly restricting the sum of the KL - divergences of two - stage signals, ensure that the detection error probability of listeners in the worst - case scenario is higher than the threshold, breaking through the limitations of traditional single - stage concealment constraints;

[0021] Hardware - protocol co - design: Adopt a two - dimensional planar movable antenna architecture (motor drive + slide - rail control), combined with the amplify - and - forward (AF) mode, to achieve low - complexity and high - flexibility hardware support for covert communication.

[0022] Compared with traditional fixed - antenna schemes, the present invention can increase the covert throughput by several times under the same concealment coefficient, especially with more significant performance advantages in multipath scenarios, providing a theoretical support and an engineering implementation path for high - security wireless communication.

[0023] The technical solutions specifically adopted by the present invention to solve its technical problems are:

[0024] A Covert Communication Method Based on Movable Antenna-Assisted Relay

[0025] In the covert communication scenario, the confidential information from the transmitter to the receiver is forwarded by a relay node, and the relay is equipped with M r movable antennas, and the physical positions are allowed to be dynamically adjusted;

[0026] The transmission model includes:

[0027] The first stage: The transmitter sends a signal to the relay node through a beamforming matrix, and the relay node receives, amplifies and forwards it through the movable antennas;

[0028] The second stage: The relay node forwards the signal to the receiver through a transmit beamforming vector;

[0029] Jointly optimize the positions of the movable antennas, the transmitter beamforming matrix and the relay transmit beamforming vector to meet the following constraints:

[0030] The joint detection error probability of the eavesdropper for the two-stage signals is constrained by the statistical difference;

[0031] The positions of the movable antennas are restricted in a preset region Ω r , and the minimum spacing d min = λ / 2, where λ is the carrier wavelength;

[0032] Maximize the covert throughput through the above optimization.

[0033] Furthermore, the statistical difference constraint is jointly restricted by the KL divergence of the two-stage signals, specifically satisfying:

[0034]

[0035] where, respectively represent the probability distributions of the signals received by the eavesdropper when there is communication and no communication in the first stage;

[0036] respectively represent the probability distributions of the signals received by the eavesdropper when there is communication and no communication in the second stage;

[0037] is the Kullback-Leibler divergence, which is used to quantify the statistical difference between the two probability distributions;

[0038] ∈ is the covert coefficient, and its value is determined through the optimization process to ensure that the detection error probability of the eavesdropper is higher than a preset threshold.

[0039] Furthermore, the field response matrix of the movable antenna is calculated from the path difference and the carrier wavelength, specifically:

[0040] The field response vector of the m-th antenna satisfies:

[0041]

[0042] where i is the imaginary unit, is the path difference of the m-th antenna with respect to the L k -th path; (x m , y m ) is the coordinate of the m-th movable antenna.

[0043] Furthermore, the joint optimization is implemented by a hierarchical optimization algorithm:

[0044] Outer layer optimization: Fix the beamforming parameters and optimize the antenna positions using the projected gradient descent method;

[0045] Inner layer optimization: Fix the antenna positions and transform the beamforming optimization problem into a convex problem for solution;

[0046] The joint optimization ensures convergence to the global optimal solution by alternately iterating the antenna positions and the beamforming parameters.

[0047] Furthermore, the outer layer optimization uses the projected gradient descent method, and the inner layer optimization uses the semidefinite relaxation method and the block coordinate descent method.

[0048] Furthermore, the improvement effect of the covert throughput is positively correlated with the number of relay - listener paths. The more the number of paths, the more significant the multipath superposition fading of the listener's signal.

[0049] Furthermore, the position adjustment of the movable antenna is realized by a motor drive and a slide rail mechanism, and the movement accuracy is controlled by the channel state feedback;

[0050] The position adjustment period of the movable antenna matches the channel coherence time to achieve dynamic optimization.

[0051] Furthermore, the covert throughput is determined by the transmission rate R b and the transmission success rate 1 - δ, specifically:

[0052] η = NR b (1 - δ)

[0053] where N is the code length and δ is the transmission outage probability.

[0054] Furthermore, the relay adopts the signal amplification and forwarding mode, and the transmitter is equipped with M a antennas, the receiver is equipped with a single antenna, and the listener is equipped with M w antennas.

[0055] And, a covert communication system based on a movable antenna-assisted relay, comprising:

[0056] Transmitter: Equipped with M a antennas, for generating and transmitting confidential information;

[0057] Relay node: Equipped with M r movable antennas, dynamically adjusting the antenna positions through a motor and a slide rail mechanism, and performing signal amplification and forwarding;

[0058] Receiver: Equipped with a single antenna, for receiving the signals relayed by the relay;

[0059] Listener detection suppression module: Jointly optimizing the antenna positions and beamforming parameters according to the KL divergence constraint to ensure the undetectability of covert communication.

[0060] And, an electronic device, comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the program, the steps of the above-mentioned method are implemented.

[0061] A non-transitory computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above-mentioned method are implemented.

[0062] Compared with the prior art, the present invention and its preferred solutions at least include the following beneficial effects:

[0063] Synergistic improvement of concealment and throughput: By dynamically adjusting the physical positions of the relay movable antennas to actively adapt to the channel characteristics, not only the signal quality of the legitimate link is enhanced, but also the signals received by the listener fall into deep fading, significantly reducing its detection ability, breaking through the contradiction between security and transmission efficiency in traditional covert communication;

[0064] Efficient solution to complex optimization problems: Adopting a hierarchical optimization framework to decompose the non-convex coupling problem into an alternating iterative process of antenna position optimization and beamforming parameter optimization, greatly reducing the computational complexity and ensuring the convergence and real-time performance of the algorithm;

[0065] Deep utilization of multipath resources: By dynamically matching the antenna positions with the multipath channels, fully utilizing the path diversity gain, strengthening the superimposed fading effect of the listener signals, and further enhancing the concealment guarantee ability;

[0066] Enhanced detection robustness: Based on the two-stage KL divergence joint constraint, strictly restricting the statistical detection difference of the communication signals by the listener, and still ensuring the non-identifiability of covert communication even in the face of the worst detection scenario (joint analysis of two-stage signals);

[0067] Hardware Architecture Flexibility and Reliability: The two-dimensional planar movable antenna design combined with the motor drive mechanism takes into account the flexibility of small-range position adjustment and the feasibility of engineering implementation, providing a stable hardware foundation for dynamic channel optimization. Brief Description of the Drawings

[0068] The present invention will be further described in detail below in conjunction with the drawings and specific embodiments:

[0069] Figure 1 It is a schematic diagram of the system structure of the embodiment of the present invention.

[0070] Figure 2 It is a network structure diagram of the optimization algorithm adopted in the embodiment of the present invention.

[0071] Figure 3 It is a schematic diagram of the change of the covert throughput with the covert coefficient in the embodiment of the present invention. Specific Embodiments

[0072] To make the features and advantages of the present invention more obvious and understandable, specific embodiments are given below for detailed description as follows:

[0073] It should be noted that the following detailed description is illustrative and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0074] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0075] The covert communication scenario assumed in the embodiment of the present invention is as follows: The transmitter sends confidential information to the receiver, but the link between the two is not directly reachable and needs to be relayed through a relay. The relay is equipped with a movable antenna to enhance data transmission, and the eavesdropper tries to determine whether the transmitter sends confidential information based on the received signal; the transmitter is equipped with M a transmitting antennas; the receiver is equipped with a single receiving antenna; the eavesdropper is equipped with M w receiving antennas; the relay is equipped with M r movable antennas;

[0076] Therefore, the embodiment of the present invention provides a covert communication method based on the optimization of the position of the movable antenna, and the construction process of its scheme includes the following steps:

[0077] Step S1: Construct a corresponding communication model according to the wireless covert transmission scenario of the application, and describe its received signal expression and channel expression;

[0078] Step S2: Construct a detection model for the received signal of the eavesdropper according to the wireless communication scenario, and analyze the detection error probability expression and the covert constraint expression;

[0079] Step S3: Maximize the covert throughput by optimizing the position of the movable antenna at the relay, the beamforming matrix at the transmitter, and the transmit beamforming vector at the relay.

[0080] As a preferred solution of this embodiment, in step S1, the confidential information is transmitted from the transmitter to the receiver in two stages.

[0081] In the first stage, the transmitter sends the confidential information to the relay. In the second stage, the relay forwards the information received from the transmitter to the receiver. The relay adopts the signal amplification and forwarding mode and is equipped with M r movable antennas. The position of the movable antennas at the relay on the antenna board is characterized by establishing a Cartesian coordinate system, denoted as where the position of the m-th movable antenna is expressed as r m =[x m ,y m T .

[0082] Assume that the number of paths between the relay and the transmitter, the receiver, and the eavesdropper are L ar , L rb and L rw respectively. Denote the above number of paths as L k (k ∈ {ar, rb, rw}). For the j-th (1 ≤ j ≤ L k ) path, its elevation angle and azimuth angle are denoted as and Taking the origin of the coordinate system as the reference point, the path difference of the j-th path of the m-th antenna with respect to the reference point can be expressed as Therefore, the field response vector of the m-th movable antenna is expressed as

[0083]

[0084] where i represents the imaginary unit and λ represents the wavelength of the carrier. Therefore, the field response matrix of the movable antenna is expressed as

[0085]

[0086] For the channel H ar between the transmitter and the relay, it can be expressed as

[0087] ​

[0088] Among them, represents the effective path response matrix of the transmitter's transmission area. Similarly, the channel h between the relay and the receiver rb is expressed as

[0089]

[0090] Among them, represents the effective path response matrix of the receiver's receiving area. Therefore, in the first-stage transmission, the received signal at the relay Relay can be expressed as

[0091]

[0092] Among them, the noise is Gaussian white noise, following a complex Gaussian distribution with a mean of 0 and a variance of . Denote P a as the transmission power of the transmitter, and w ar as the transmission beamforming matrix at the transmitter end. After the relay receives the signal from the transmitting end, it forwards the signal in the AF mode. Therefore, the signal at the receiver can be expressed as

[0093]

[0094] Among them, the noise is Gaussian white noise, following a complex Gaussian distribution with a mean of 0 and a variance of . Denote P r as the transmission power of the relay, and W rb as the transmission beamforming vector of the relay. The signal-to-noise ratio of the received signal at the receiver can be expressed as

[0095]

[0096] For a given transmission outage probability δ, in the case of the code length N, the achievable covert transmission rate at the receiver is expressed as

[0097]

[0098] Among them, Q -1 (δ) represents the inverse function of. Therefore, the effective throughput of the transmission is expressed as

[0099] η = NR b (1 - δ)

[0100] As a preferred solution of this embodiment, in step S2, considering the worst detection situation, the eavesdropper is in a continuous monitoring state and can detect the signals in both stages.

[0101] For the channel H between the relay and the eavesdropper rw Denoted as

[0102]

[0103] where is the effective path response matrix representing the receiving area of the eavesdropper. Therefore, the received signal at the eavesdropper in the first phase is expressed as

[0104]

[0105] The received signal at the eavesdropper in the second phase is expressed as

[0106]

[0107] where the noise is Gaussian white noise, following a complex Gaussian distribution with a mean of 0 and a variance of Denoted as Event represents that the eavesdropper judges that there is no communication between the transmitter and the receiver, and event the eavesdropper judges that there is communication between the transmitter and the receiver. Define and as the probability distributions of the received signals in the first phase under and , and as the probability distributions of the received signals in the second phase under and . Therefore, when the code length is N, the KL divergences of the two phases can be obtained as

[0108]

[0109] and

[0110]

[0111] where Considering a worst-case scenario where Willie jointly detects the signals in these two phases, the secrecy constraint can be expressed as

[0112]

[0113] where ∈ is the secrecy coefficient.

[0114] As a preferred solution of this embodiment, in step S3, the formula for maximizing the secrecy throughput is expressed as

[0115]

[0116] Among them, Ω r represents the antenna board area at the relay, that is, the area where the movable antenna can move. d min = λ / 2 represents the minimum spacing between the movable antennas to avoid the electromagnetic coupling effect between the antennas. By optimizing the positions of the movable antennas and beamforming, the throughput under covert conditions is maximized.

[0117] Furthermore, considering that the above optimization problem is highly non-convex and coupled and difficult to solve directly. Therefore, the present invention provides a hierarchical optimization solution algorithm. The outer-layer optimization fixes the beamforming matrix and aims to maximize the covert throughput, and uses the projected gradient descent method to optimize the positions of the antennas at the relay; the inner-layer optimization fixes the positions of the antennas and uses the semidefinite relaxation method and the block coordinate descent method to transform the non-convex problem into a convex sub-problem, and aims to maximize the signal-to-noise ratio at the relay and the receiver respectively, and uses convex optimization for solution. Specifically as follows:

[0118] When fixing the beamforming matrix in the outer-layer optimization, set the step size of the gradient change to υ, update along the negative gradient direction of the covert throughput with respect to the antenna positions at the relay, and at the same time project the position update result into the feasible region. The update rule for the (k + 1)-th round can be expressed as

[0119]

[0120] Among them, is the gradient of the covert throughput with respect to the antenna positions, υ is the step size of the gradient change, and Proj{} represents the projection operation to satisfy the spacing constraint and boundary constraint of each antenna at the relay.

[0121] When fixing the antenna positions in the inner-layer optimization, alternately optimize the receive beamforming w ar and the transmit beamforming W rb . When optimizing w ar , let The optimization problem can be expressed as

[0122]

[0123] W ar > 0

[0124] rank(W ar ) = 1

[0125] Among them, rank(W ar ) = 1 means that the rank of the matrix is 1. By ignoring the rank-1 constraint, the problem becomes a convex optimization problem, which is solved using the existing CVX toolbox. If the obtained matrix W ar has a rank of 1, w ar can be obtained through eigenvalue decomposition. If the obtained matrix War The rank is not 1, and a high-quality rank-1 solution is recovered by using a Gaussian randomization process. The same method is used to optimize the transmit beamforming W at the relay. rb .

[0126] Based on the above design, in this embodiment, a two-dimensional planar movable antenna is considered at the relay in the device design. Its physical architecture is as follows: The relay core central processing unit (CPU) is connected to the movable antenna through a flexible cable, and a stepper motor and a mechanical slide rail are equipped at the same time. After the CPU receives the corresponding control signal, it uses the moving motor to assist in executing the corresponding moving steps, and the antenna can be repositioned to a specific target position to achieve small-range antenna movement.

[0127] In the embodiment of the present invention, the position of the movable antenna at the relay, the transmit beamforming vector at the transmitter, and the beamforming matrix for relay forwarding are jointly optimized to maximize the covert throughput. This technology effectively ensures the security and reliability of the communication system.

[0128] As Figure 1 shown, this example provides a covert communication method based on the optimization of the movable antenna position. Among them, the transmitter sends confidential information to the receiver, but the link between the two is not directly reachable and needs to be relayed through a relay. The relay is equipped with a movable antenna to enhance data transmission, and the eavesdropper tries to determine whether the transmitter sends confidential information based on the received signal; the transmitter is equipped with M a transmit antennas; the receiver is equipped with a single receive antenna; the eavesdropper is equipped with M w receive antennas; the relay is equipped with M r movable antennas;

[0129] The transmission of confidential information is divided into two stages. The first stage is that the transmitter sends confidential information to the relay, and the second stage is that the relay forwards the information received from the transmitter to the receiver. The relay adopts the signal amplification and forwarding mode and is equipped with M r movable antennas. By establishing a Cartesian coordinate system to characterize the position of the movable antenna at the relay on the antenna board, it is denoted as where the position of the m-th movable antenna is expressed as r m = [x m , y m T .

[0130] Assume that the number of paths between the relay and the transmitter, the receiver, and the eavesdropper are L ar , L rb and L rw , respectively. Denote the above number of paths as L k (k ∈ {ar, rb, rw}). For the j-th (1 ≤ j ≤ Lk ) paths, and their elevation angles and azimuth angles are denoted as and Taking the origin of the coordinate system as the reference point, the path difference of the j-th path of the m-th antenna with respect to the reference point can be expressed as Therefore, the field response vector of the m-th movable antenna is expressed as

[0131]

[0132] where, i represents the imaginary unit, and λ represents the wavelength of the carrier. Therefore, the field response matrix of the movable antenna is expressed as

[0133]

[0134] For the channel H between the transmitter and the relay ar , it can be expressed as

[0135]

[0136] where, represents the effective path response matrix of the transmitter's transmission area. Similarly, the channel h between the relay and the receiver rb is expressed as

[0137]

[0138] where, represents the effective path response matrix of the receiver's receiving area. Therefore, in the first-stage transmission, the received signal at the relay Relay can be expressed as

[0139]

[0140] where, the noise is Gaussian white noise, following a complex Gaussian distribution with a mean of 0 and a variance of , denoted as P a represents the transmission power of the transmitter, and w ar represents the transmission beamforming matrix at the transmitter end. After the relay receives the signal from the transmitter end and forwards the signal in the AF mode, therefore, the signal at the receiver can be expressed as

[0141]

[0142] where, the noise is Gaussian white noise, following a complex Gaussian distribution with a mean of 0 and a variance of , denoted as P r represents the transmission power of the relay, and W rb is the transmission beamforming vector of the relay. The signal-to-noise ratio of the received signal at the receiver can be expressed as

[0143]

[0144] For a given transmission outage probability δ, the achievable covert transmission rate at the receiver is expressed as a function of the code length N as

[0145]

[0146] where Q -1 (δ) represents the inverse function of . Therefore, the effective throughput of the transmission is expressed as

[0147]

[0148] Considering the worst-case detection scenario, the eavesdropper is in a continuous monitoring state and can detect the two-phase signal. For the channel H between the relay and the eavesdropper rw is expressed as

[0149]

[0150] where is the effective path response matrix representing the eavesdropper's reception area. Therefore, the received signal at the eavesdropper in the first phase is expressed as

[0151]

[0152] The received signal at the eavesdropper in the second phase is expressed as

[0153]

[0154] where the noise is complex Gaussian white noise with a mean of 0 and a variance of . Denote the event as the event that the eavesdropper judges that there is no communication between the transmitter and the receiver, and the event as the event that the eavesdropper judges that there is communication between the transmitter and the receiver. Define and as the probability distributions of the received signals in the first phase under and , and and as the probability distributions of the received signals in the second phase under and . Therefore, when the code length is N, the KL divergences for the two phases can be obtained as

[0155]

[0156] and

[0157]

[0158] Among them, Considering a worst-case scenario where Willie jointly detects the two-stage signal, the secrecy constraint can be expressed as

[0159]

[0160] where ∈ is the secrecy coefficient. Therefore, the formula for maximizing the secrecy throughput is expressed as

[0161]

[0162] where Ω r represents the antenna panel area at the relay, that is, the area where the movable antenna can move. d min = λ / 2 represents the minimum spacing between the movable antennas to avoid the electromagnetic coupling effect between the antennas. By optimizing the positions of the movable antennas and beamforming, the throughput maximization under the secrecy condition is achieved.

[0163] Figure 2 A hierarchical optimization algorithm provided in an embodiment of the present invention is shown. The outer-layer optimization fixes the beamforming matrix, aims to maximize the secrecy throughput, and uses the projected gradient descent method to optimize the positions of the antennas at the relay; the inner-layer optimization fixes the positions of the antennas, uses the semidefinite relaxation method and the block coordinate descent method to transform the non-convex problem into a convex sub-problem, aims to maximize the signal-to-noise ratio at the relay and the receiver respectively, and uses convex optimization for solution. Specifically as follows:

[0164] When fixing the beamforming matrix in the outer-layer optimization, set the step size of the gradient change to υ, update along the negative gradient direction of the secrecy throughput with respect to the antenna positions at the relay, and at the same time project the position update result into the feasible region. The update rule for the (k + 1)-th round can be expressed as

[0165]

[0166] where is the gradient of the secrecy throughput with respect to the antenna positions, υ is the step size of the gradient change, and Proj{} represents the projection operation to satisfy the spacing constraint and boundary constraint of each antenna at the relay.

[0167] When fixing the antenna positions in the inner-layer optimization, alternately optimize the receive beamforming w ar and the transmit beamforming W rb . When optimizing w ar , let The optimization problem can be expressed as

[0168]

[0169] W ar > 0

[0170] rank(W ar ) = 1

[0171] where rank(W ar ) = 1 indicates that the rank of the matrix is 1. By ignoring the rank-1 constraint, the problem becomes a convex optimization problem, which can be solved using the existing CVX toolkit. If the obtained matrix W ar has a rank of 1, w can be obtained through eigenvalue decomposition ar . If the obtained matrix W ar does not have a rank of 1, a Gaussian randomization process is adopted to recover a high-quality rank-1 solution. The transmit beamforming W at the relay is optimized using the same method rb .

[0172] Figure 3 shows the results of the covert throughput varying with the covert coefficient under different schemes and numbers of paths. It can be observed that in the initial stage, due to the low covert coefficient, that is, the strong covert constraint, the throughput is low or even zero at this time. As the covert constraint is relaxed, the covert throughput also increases. When the number of paths is the same, it can be observed that the covert throughput obtained by the movable antenna scheme is much larger than that of the fixed antenna scheme, verifying the effectiveness of the proposed scheme of the present invention. When the number of paths increases, the multipath superposition effect is more obvious, and the deep fading state at the eavesdropper is strengthened. Therefore, the achievable covert throughput is larger when the number of paths is larger

[0173] Based on the same inventive concept, the present invention also provides a computer device, which includes: one or more processors, and a memory for storing one or more computer programs; the program includes program instructions, and the processor is used to execute the program instructions stored in the memory. The processor may be a central processing unit (CPU), or may also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing core and control core of the terminal, and is used to implement one or more instructions, specifically used to load and execute one or more instructions in the computer storage medium to implement the above method

[0174] It should be further noted that, based on the same inventive concept, the present invention also provides a computer storage medium, on which a computer program is stored, and when the computer program is run by a processor, it executes the above-mentioned method. The storage medium can adopt any combination of one or more computer-readable media. The computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electrical, magnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples (non-exhaustive list) of the computer-readable storage medium include: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present invention, the computer-readable storage medium can be any tangible medium that contains or stores a program, and this program can be used by or in combination with an instruction execution system, apparatus, or device.

[0175] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meanings understood by those with ordinary skills in the field to which the present invention belongs. The "first", "second", and similar terms used in the present invention do not denote any order, quantity, or importance, but are only used to distinguish different components. Words such as "including" or "comprising" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. Words such as "connected" or "coupled" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right", etc. are only used to represent relative position relationships, and when the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0176] As mentioned above, these are only the preferred embodiments of the present invention, and the present invention is not limited to other forms. Any person skilled in the relevant art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.

[0177] The present invention is not limited to the above-described optimal embodiments. Anyone can derive various other forms of covert communication methods based on movable antenna-assisted relay under the inspiration of the present invention. All equivalent changes and modifications made within the scope of the patent application of the present invention shall fall within the scope covered by the present invention.

Claims

1. A covert communication method based on a movable antenna-assisted relay, characterized in that: In the covert communication scenario, confidential information from the transmitter to the receiver is forwarded through a relay node, and the relay is equipped with M r movable antennas, and the physical location allows dynamic adjustment; The transmission model includes: The first stage: The transmitter sends a signal to the relay node through a beamforming matrix, and the relay node receives and amplifies and forwards it through a movable antenna; The second stage: The relay node forwards the signal to the receiver through a transmit beamforming vector; Jointly optimize the position of the movable antenna, the transmitter beamforming matrix, and the relay transmit beamforming vector to satisfy the following constraints: The joint detection error probability of the eavesdropper for the two-stage signals is constrained by statistical differences; The position of the movable antenna is restricted to a preset area Ω r , and the minimum spacing d min = λ / 2, where λ is the carrier wavelength; Maximize the covert throughput through the above optimization.

2. The covert communication method based on a movable antenna-assisted relay according to claim 1, characterized in that: The statistical difference constraint is jointly restricted by the KL divergence of the two-stage signals, specifically satisfying: Among them, respectively represent the probability distributions of the signals received by the listener when there is communication and no communication in the first stage; respectively represent the probability distributions of the signals received by the listener when there is communication and no communication in the second stage; is the KL divergence, which is used to quantify the statistical difference between two probability distributions; ∈ is a covert coefficient, and its value is determined through the optimization process to ensure that the detection error probability of the eavesdropper is higher than a preset threshold.

3. The covert communication method based on a movable antenna-assisted relay according to claim 1, characterized in that: The field response matrix of the movable antenna is calculated from the path difference and the carrier wavelength, specifically: The field response vector of the m-th antenna satisfies: where \(i\) is the imaginary unit, is the path difference of the \(m\)-th antenna for the \(L\)-th k path; \((x m , y m )\) is the coordinate of the \(m\)-th movable antenna.

4. The covert communication method based on a movable antenna-assisted relay according to claim 1, characterized in that: The joint optimization is achieved through a hierarchical optimization algorithm: Outer layer optimization: Fix the beamforming parameters and optimize the antenna position using the projected gradient descent method; Inner layer optimization: Fix the antenna position and transform the beamforming optimization problem into a convex problem for solution; The joint optimization ensures convergence to the global optimal solution by alternately iterating the antenna position and the beamforming parameters.

5. The covert communication method based on a movable antenna-assisted relay according to claim 4, wherein: The outer layer optimization uses the projected gradient descent method, and the inner layer optimization uses the semidefinite relaxation method and the block coordinate descent method.

6. The method for covert communication based on a movable antenna-assisted relay according to claim 1, wherein: The improvement effect of the covert throughput is positively correlated with the number of relay-eavesdropper paths. The more paths there are, the more significant the multipath superposition fading of the eavesdropper's signal is.

7. The covert communication method based on a movable antenna-assisted relay according to claim 1, characterized in that: The position adjustment of the movable antenna is realized through a motor drive and a slide rail mechanism, and the movement accuracy is controlled by channel state feedback; The position adjustment period of the movable antenna matches the channel coherence time to achieve dynamic optimization.

8. The covert communication method based on a movable antenna-assisted relay according to claim 1, characterized in that: The hidden throughput is determined by the transmission rate R b and the transmission success rate 1 - δ, specifically as follows: η = NR b (1 - δ) Where N is the code length and δ is the transmission outage probability.

9. The method for covert communication based on a movable antenna-assisted relay according to claim 1, characterized in that: The relay adopts a signal amplification and forwarding mode, and the transmitter is equipped with M a antennas, the receiver is equipped with a single antenna, and the eavesdropper is equipped with M w antennas.

10. A covert communication system based on a movable antenna-assisted relay, characterized in that, Including: Transmitter: Equipped with M a antennas for generating and transmitting confidential information; Relay node: Equipped with M r root movable antenna, dynamically adjusts the antenna position through the motor and slide rail mechanism, and performs signal amplification and forwarding; Receiver: Equipped with a single antenna to receive the signal relayed by the relay; Eavesdropper detection suppression module: Jointly optimize the antenna position and the beamforming parameters according to the KL divergence constraint to ensure the undetectability of the covert communication.

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