Mobile antenna assisted covert communication method and system in communication and inductance integrated network

Abstract

The invention discloses a covert communication method and system assisted by a movable antenna in a communication-inductance integrated network, and the system comprises an ISAC base station which is provided with Nt movable transmitting antennas and Nr fixed receiving antenna arrays; k communication nodes, each of which is configured with a single antenna and is used for receiving a communication signal sent by the ISAC base station; the point-like sensing nodes are used for receiving the sensing signals sent by the ISAC base station; the eavesdropping node is provided with a single antenna and is used for trying to detect a signal sent by the ISAC base station; according to the invention, the movable antenna array is deployed in the covert communication system, so that the space coverage limitation of a traditional fixed antenna system can be broken through, and the wide-area coverage and deep penetration capabilities of communication services can be improved. The mobile antenna array network significantly enhances the transmission efficiency and link robustness of covert communication through multi-dimensional degree-of-freedom cooperative regulation and control such as precoding vector optimization, three-dimensional space position dynamic configuration and the like.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of communication network, and in particular to a hidden communication method and system assisted by a movable antenna in an integrated sensing and communication network. BACKGROUND

[0002] Integrated sensing and communication (ISAC) network is one of the important directions of future wireless communication network development, which can provide wireless communication and environmental parameter sensing services at the same time, and has attracted widespread attention from academia and industry. In order to improve the security transmission performance of the integrated sensing and communication network, related research introduces hidden communication into the ISAC network framework, designs and develops a series of novel hidden communication algorithms for ISAC network, which provides theoretical support for improving the performance of hidden communication in ISAC network. On the other hand, with the widespread initiative of global energy saving and emission reduction, the ISAC network also needs to further improve the energy efficiency of the hidden communication system to improve the transmission efficiency per unit energy.

[0003] With the rapid evolution of wireless communication technology, it has become an industry consensus to build the next generation communication system with wide-area seamless coverage, ultra-dense connectivity and ultra-high speed. However, the traditional fixed antenna system is limited by static beamforming and rigid spatial topology, and encounters bottlenecks in tracking time-varying channel state, multi-user interference cancellation and other core dimensions, and its channel capacity has reached the theoretical boundary of Shannon limit. SUMMARY

[0004] The purpose of the present application is to provide a hidden communication method and system assisted by a movable antenna in an integrated sensing and communication network, which can break through the spatial coverage limitation of the traditional fixed antenna system by deploying a movable antenna array in the hidden communication system, and realize the dual improvement of communication service in wide-area coverage and deep penetration capability. The movable antenna array network cooperatively regulates through multi-dimensional degrees of freedom such as precoding vector optimization and three-dimensional space position dynamic configuration, significantly enhances the transmission performance and link robustness of hidden communication.

[0005] To achieve this purpose, the present application adopts the following technical solutions: A hidden communication system assisted by a movable antenna in an integrated sensing and communication network is provided, characterized in that it comprises: An ISAC base station configured with Nt movable transmitting antennas and Nr fixed receiving antenna arrays; K communication nodes, each configured with a single antenna for receiving communication signals transmitted by the ISAC base station; A point-like sensing node for receiving sensing signals transmitted by the ISAC base station; The eavesdropping node is configured with a single antenna to attempt to detect signals transmitted by the ISAC base station; The ISAC base station is capable of transmitting signals in two operating modes: a mode that transmits only sensing signals for target parameter estimation, and a mode that transmits both sensing signals and covert communication signals simultaneously. The ISAC base station is configured to maximize the weighted sum of total communication rate and perceived mutual information by optimizing the transmit beamforming vector and the position of the movable antenna, while satisfying concealment constraints, transmit power constraints, and minimum distance constraints of the movable antenna.

[0006] As a preferred embodiment of a covert communication system assisted by a movable antenna in a sensor-integrated network, the signal transmitted by the ISAC base station is represented as follows: in, This indicates the perception-only transmission hypothesis. Corresponding to the ISAC hypothesis, and These represent the data symbol and dedicated sensing signal of the k-th user, respectively. and This represents the corresponding beamforming vector.

[0007] As a preferred option for a covert communication system assisted by a movable antenna in a sensor-integrated network, each communication node adopts a multipath channel model, and the path response vector of the k-th communication node is modeled as follows: Where L represents the number of channel paths, It is the first Complex channel coefficients of each path, It is the fading coefficient at the reference distance. This represents the distance between the base station and the k-th user. It is the path loss index.

[0008] As a preferred embodiment of a covert communication system assisted by a movable antenna in a sensor-integrated network, the covertness constraint is as follows: in, This represents the transmission direction vector of the eavesdropping node. , , Q is the acceptable threshold for the probability of detecting eavesdropping nodes, and Q is the number of samples.

[0009] As a preferred embodiment of a covert communication system assisted by a movable antenna in a sensor-integrated network, the transmit power constraint is as follows: wherein, is the total transmit power budget.

[0010] The minimum distance constraint for the movable antennas is: wherein, denotes the position vector of the n-th movable antenna, is the minimum distance threshold.

[0011] The application further provides a movable antenna assisted covert communication method in a CNI network, comprising the following steps: S1: initializing a beamforming vector and a movable antenna position ; S2: fixing the movable antenna position , solving a beamforming optimization sub-problem to obtain a new beamforming vector ; S3: fixing the beamforming vector , solving a movable antenna position optimization sub-problem to obtain a new movable antenna position ; S4: calculating an updated weighted sum rate ; S5: repeating the above steps until a maximum iteration number or a convergence condition is reached, and outputting an optimization result, wherein the convergence condition is that a relative change amount of the weighted sum rate in two adjacent iterations is less than a set threshold.

[0012] As a preferred solution of the movable antenna assisted covert communication method in the CNI network, the step of solving the beamforming optimization sub-problem comprises: adopting a semi-definite relaxation algorithm to degrade the optimization problem into a semi-positive definite constraint problem; using a difference convex programming technique to convert the non-convex objective function into a lower bound of a concave function; solving the converted convex optimization problem by a convex optimization tool to obtain an optimized beamforming matrix; performing eigenvalue decomposition on the optimized beamforming matrix to reconstruct the beamforming vector.

[0013] As a preferred solution of the movable antenna assisted covert communication method in the CNI network, when the rank of the optimized sensing signal beamforming matrix is greater than 1, a Gaussian randomization technique is adopted to construct a rank-1 approximate solution.

[0014] As a preferred solution of the movable antenna assisted covert communication method in the integrated communication and sensing network, the step of solving the movable antenna position optimization sub-problem comprises: First-order Taylor expansion is performed on the core correlation function to define a tight lower bound and an upper limit; The proxy function is used to convert the non-convex objective function into the lower bound of the concave function; The covert constraint and the minimum distance constraint are converted into the form of a convex function; The converted convex optimization problem is solved by a convex optimization tool to obtain the optimized movable antenna position.

[0015] As a preferred solution of the movable antenna assisted covert communication method in the integrated communication and sensing network, the weighted sum rate is a linear combination of the total communication rate and the sensing mutual information, that is: Wherein, is a weight coefficient, is the total communication rate, is the sensing mutual information; The total communication rate is expressed as: Wherein, is the signal-to-noise ratio of the kth communication node; The sensing mutual information is expressed as: Wherein, is the number of receiving antennas, is the sensing signal attenuation coefficient, is the sensing signal noise variance, is the emission direction vector of the sensing target, is the total emission covariance matrix of all signals.

[0016] The beneficial effects of the present application: the movable antenna assisted covert communication method and system in the integrated communication and sensing network proposed by the present application can break through the spatial coverage limitation of the traditional fixed antenna system by deploying a movable antenna array in the covert communication system, and realize the dual improvement of the communication service in the wide area coverage and the deep penetration ability. The movable antenna array network cooperates and regulates through multi-dimensional degrees of freedom such as precoding vector optimization and three-dimensional space position dynamic configuration, and significantly enhances the transmission efficiency and link robustness of the covert communication. BRIEF DESCRIPTION OF DRAWINGS

[0017] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required to be used in the embodiments of the present application will be briefly introduced as follows. Obviously, the drawings described below are only some of the embodiments of the present application, and for those skilled in the art, other drawings can also be obtained from these drawings without creative labor.

[0018] Figure 1 is a system block diagram of the mobile antenna assisted covert communication system in the integrated sensing and communication network according to an embodiment of the present application; Figure 2 is a schematic diagram of the direction angle of the mobile antenna array; Figure 3 is an iterative optimization flowchart; Figure 4 is a comparison diagram of the weighted sum rate performance and the benchmark scheme Figure 5 is a flowchart of the mobile antenna assisted covert communication method in the integrated sensing and communication network according to an embodiment of the present application; DETAILED DESCRIPTION The embodiments of the present disclosure will be described in detail below with reference to the drawings.

[0019] The embodiments of the present disclosure will be described in detail below with reference to the drawings.

[0020] Referring to Figure 1 , the system block diagram of the mobile antenna assisted covert communication system in the ISAC network is shown. The system block diagram we consider includes an ISAC base station, a communication node , a point sensing node and 1 warden node. The communication node and the warden node are both configured as a single antenna, and the ISAC base station transmitting antenna is A movable antenna, the receiving antennas are Nr fixed antenna arrays. ISAC base station has two working modes: one is to continuously transmit sensing signals for target parameter estimation (such as position / speed), and the other is to embed covert signals therein. Therefore, the signals transmitted by the ISAC base station according to the two assumptions can be expressed as: In the above formula, represents only the perception transmission assumption, and corresponds to the ISAC assumption, allowing simultaneous transmission of perception and communication signals. and respectively represent the data symbol and the dedicated sensing signal of the kth user, and represent the corresponding beamforming vectors.

[0021] On the other hand, each communication user adopts a multipath channel model. Given that the size of MA is much smaller than the signal propagation distance, we assume that all MA experience the same channel parameters, including elevation angle, azimuth angle, and amplitude of each channel path, for each communication user. Therefore, the path response vector of the kth user can be modeled as: where L represents the number of channel paths, is the complex channel coefficient of the th path, is the fading coefficient at the reference distance. represents the distance between the base station and the kth user, is the path loss exponent.

[0022] Assuming that for each communication user k , the elevation angle and the direction angle of the corresponding l th multipath are and , respectively, and the position vector of the nth antenna element is , then the corresponding transmission path difference can be expressed as: Based on the geometric channel model, a uniform hemispherical distribution model is used to represent the directional path component. The elevation angle and the azimuth angle follow statistically independent distributions, defined as follows: The field response vector between the kth user and the nth MA is: where represents the wavelength of the carrier frequency. Therefore, the field response matrix between the base station and the kth user is: The channel vector of the kth user is denoted as , which is determined by the field response matrix and the path response vector of the wireless channel, i.e., can be expressed as: Therefore, the received signal of the kth user is: where represents the additive white Gaussian noise received by the nth receiving point, and its mean is zero and its variance is . Assuming that the ISAC base station can obtain the ideal CSI vector of the communication node, and the sensing signal is cancelled from the received signal by interference cancellation technology, the signal-to-noise ratio SNR of the communication user is: where and represent the transmit covariance matrix of the kth user and the sensing target, respectively. Therefore, the achievable data rate of the kth user can be determined as: The total communication rate of all communication users is: Let and represent the elevation angle and the azimuth angle between the transmitting MA and the sensing target, respectively, and the transmitting direction vector of the sensing target is: The receiving direction vector is: The signal model of the ISAC receiving radar target can be expressed as follows: where , is the wavelength, is the scattering cross section of the radar surface, is the transmitting direction vector, is the receiving direction vector, is the transmitting signal, is the receiving noise. The above formula obtains the sensing signal-to-noise ratio SIRN: where the total power of all signals is , and the mutual information of the sensing link is: ​In the ISAC network, let and denote the elevation and azimuth angles between the transmitting MA and the guardian, respectively, then the transmit steering vector of the guardian is where denotes the propagation delay between the th MA and the guardian. Therefore, according to the covert communication constraint, the received signal of the eavesdropping node under the two assumptions can be expressed as: The guardian detects the communication signal from the base station by evaluating whether the average received power of Q sampling observations exceeds a pre-defined detection threshold τ. This binary hypothesis test can be expressed as: where is the number of samples, is the threshold set by the listener.

[0023] To ensure that the detection probability of the guardian remains below an acceptable threshold ξ, the joint design of the transmit beamforming and MA locations must satisfy the following constraint: where is the rate of change of the average received signal power under the two assumptions, which is a monotonically increasing function defined as: Define the total transmit power budget of the ISAC signal as: To avoid MA overlap and excessive electromagnetic interference, we add a minimum distance constraint to any two MAs: Assume that the ISAC base station has perfect channel state information for all network nodes. By optimizing the transmit beamforming vector and the MA location matrix, the proposed framework maximizes the weighted sum rate of the total achievable communication rate RC and the perceptual mutual information RS, i.e., the weighted total information rate function: By dynamically adjusting the position vector of each element in the movable antenna system, the transmission channel of wireless communication can be precisely controlled. In the ISAC network, the optimization problem corresponding to the covert communication system assisted by movable antennas can be expressed as: 1 Objective function transformation Optimization problem , which is difficult to solve directly, we adopt an alternating optimization framework to find a suboptimal solution to the above optimization problem. First, fix the position vector to seek the optimal solution of the beamforming vector. Using a rank-penalization algorithm, we degrade the optimization problem to a semidefinite constrained problem. We introduce the following objective function: Since it is still nonconvex due to the coupling variables in its objective and constraints, we utilize the SDR algorithm to transform it into an equivalent optimization problem. First, rewrite the concealment constraint as the following equation: The transmit power constraint can be rewritten as: Therefore, the problem can be equivalently transformed as: Again, The rank-one constraint of the concealment constraint in the problem is still a nonconvex constraint. To simplify the problem, we relax the rank-one constraint and only keep the semidefinite cone constraint. Therefore, the relaxed problem is formulated as: By solving the problem (P2.2), we can construct a rank-one solution to solve the problem (P2.1) as follows: , we can construct a rank-one solution to solve the problem (P2.1) as follows: Therefore, the optimal beamforming vector solution can be obtained by the eigenvalue decomposition of the matrix , resulting in , where and denote the principal eigenvalue and its corresponding eigenvector of the matrix , respectively. For the matrix​ then the same decomposition can directly lead to a rank-1 solution, provided that satisfies the rank-1 condition. When the rank of

[0024] Since all the constraints of problem (P2.2) satisfy convexity or matroid property, the focus is on the reformulation of the objective function. The objective function is a linear combination of and , and their mathematical properties need to be characterized separately. First, the function is concave with respect to , which ensures the tractability of its maximization. In contrast, is neither concave nor convex with respect to , and thus needs to be further reformulated. We can rewrite the sum of the communication user communication rates as the difference of concave functions as follows: Clearly, are concave functions with respect to and respectively. By performing a first-order Taylor expansion around a feasible local solution , we obtain the following upper bound on : where and . Clearly, the upper bound is an affine function with respect to each matrix variable and , and the lower bound on the objective function of problem (P2.2) can be obtained as follows: Since the first and third terms in the above expression are concave functions, and the second term is an affine function with respect to and , it follows that is also a concave function. Therefore, given a feasible point, problem (P2.2) can be converted to where is the solution at the th iteration, and it is easy to see that The problem is a convex optimization problem, which can be solved numerically by using classical convex optimization tools, such as CVX, etc.

[0025] Then, the MA location matrix t is further optimized with the beamforming vector fixed. Thus, the subproblem of matrix t optimization can be expressed as: When , the following surrogate function can be obtained by first-order Taylor expansion of the cosine function and applying the remainder theorem: and Obviously, the surrogate function about is a concave function, while is a convex function. Moreover, when , both surrogate functions reach tightness.

[0026] Let denote the core correlation function, then the achievable rate of the th user can be rewritten as: By successively applying the path response vector model of the th user, the transmission wave phase difference, the field response vector between the th user and the th MA, the field response matrix between the base station and the th user, and the channel vector of the th user, the closed-form expression of is derived as follows: where and In addition, the gradient of is given by: By using the surrogate function obtained when , the tight lower bound and upper bound of can be derived as follows: and are denoted as Here, denotes the position solution in the th iteration, and it can be observed that is a concave function with respect to and is a convex function with respect to , therefore, given a feasible local solution , by performing a first-order Taylor expansion on and using surrogate function definitions for a tight lower bound and upper limit of , a tight lower bound of can be obtained as It can be concluded that is a concave function with respect to .

[0027] Similarly, by analyzing the mutual information of the sensing link using the same method, given a feasible local solution , by applying Cauchy-Schwarz inequality to the Hermitian quadratic form of , we can obtain In the above equation, since the second term is a constant, we only need to analyze the first term, based on the method of deriving the closed-form expression of , we can restate the first term as where and , by continuing the lower bound surrogate function operation on the above equation, we can obtain the lower bound of as where and It can be observed that is a concave function with respect to . By substituting the lower bound of and into , we can obtain the lower bound of as Therefore, it can be concluded that is also a concave function.​

[0028] By substituting the lower bound of and the lower bound of into the constraints of problem , we can obtain a tight lower bound of the objective function of problem : We can obtain that is a concave function about .

[0029] 2Joint design constraint analysis of transmit beamforming and MA location Let denote the relevant kernel function of joint design constraint of transmit beamforming and MA location, we can rewrite as: where . By using the algorithm of lower bound surrogate function operation, we can construct the upper and lower bounds of as: and where, and Therefore, the joint design constraint of transmit beamforming and MA location can be rewritten as the following convex function form: In addition, the minimum distance constraint can be equivalently transformed into a quadratic form expression: After applying the Cauchy-Schwarz inequality, the left side of the above equation obtains a lower bound: Using the first-order Taylor expansion, it is transformed into the following affine constraint: In summary, given a feasible point, the optimization subproblem can be restated as follows: 3 Algorithm analysis Algorithm 1: Iterative optimization algorithm for problem (P2) based on SDA Input: initial feasible solution for problem (P2.3) 1. Initialize iteration number: , compute initial weighted sum rate .

[0030] 2. Set maximum iteration number and convergence threshold

[0031] .

[0032] 3. Repeat. 4. Given the previous solution , solve problem (P2.3) via convex optimization solver to obtain new solution

[0033] . 5. Compute updated sum rate

[0034] . 6. Increment iteration number:

[0035] . 7. Until or

[0036] . 8. Reconstruct beamforming vector for problem (P2) via Theorem II and eigenvalue decomposition

[0037] . 9. If

[0038] . 10. Construct

[0039] using Gaussian randomization method .

[0040] 11. Check end condition. 12. Output: final beamforming vector

[0041] . Algorithm 2: Iterative optimization algorithm for problem (P3) based on surrogate model Input: initial feasible solution for problem (P3.1) .

[0042] 1. Initialize iteration number: , compute initial weighted sum rate .

[0043] 2. Set maximum iteration number and convergence threshold .

[0044] 3. Repeat.

[0045] 4. Based on the current solution , solve problem (P3.1) by the convex optimization solver to obtain a new solution .

[0046] 5. Compute the updated sum rate .

[0047] 6. Increment the iteration count: .

[0048] 7. Termination condition: or .

[0049] 8. Output: Final position matrix .

[0050] Algorithm 3: Alternating optimization algorithm for problem (P1) Input: Initial feasible solution for problem (P1) 1. Initialize the iteration count: , compute the initial weighted sum rate .

[0051] 2. Set the maximum number of iterations and the convergence threshold .

[0052] 3. Repeat.

[0053] 4. Based on the current solution , solve problem (P2) by Algorithm I to obtain a new solution .

[0054] 5. Based on the current solution , solve problem (P3) by Algorithm I to obtain a new solution .

[0055] 6. Compute the updated sum rate .

[0056] 7. Increment the iteration count: .

[0057] 8. Termination condition: or .

[0058] 9. Output: Final optimization result .

[0059] For the three algorithms mentioned above, the computational complexity is analyzed. Because problem (P2.3) contains with two affine constraints. According to the standard complexity estimation method of convex optimization problems, the computational complexity of Algorithm 1 can be expressed as: where denotes the precision of the solution. Similarly, the computational complexity of Algorithm 2 is: In summary, the overall computational complexity of Algorithm 3 is: 4. Iterative optimization procedure 1. Initialization: Initialize the beam vector and the MA position according to the constraints, and set the iteration number .

[0060] 2. Solve the beam optimization subproblem using convex optimization tools under the given condition, and output the optimal beamforming matrix .

[0061] 3. Solve the position optimization subproblem using convex optimization tools under the given condition, and output the optimal antenna position .

[0062] 4. Update the iteration number .

[0063] 5. If or , output the result optimal beam vector , optimal antenna position , and maximum weighted system performance ; otherwise, go to step-2.

[0064] Figure 4 The proposed alternating optimization algorithm (Algorithm 3) is compared with three benchmark methods in terms of weighted sum rate performance under the default configuration. The benchmark methods include: fixed antenna array matched filter beamforming scheme, optimized beamforming fixed antenna array scheme based on Algorithm 1, and mobile antenna matched filter beamforming scheme based on Algorithm 2. The experimental results show that the proposed Algorithm 3 outperforms all benchmark methods significantly, verifying that jointly optimizing antenna position and beamforming vector can effectively exploit the spatial degrees of freedom of mobile antennas in covert ISAC networks. Specifically, at a transmit power of 36 dBm, the proposed algorithm can achieve a 57.9% improvement in weighted sum rate compared to the traditional fixed antenna matched filter scheme, while maintaining about 21% performance advantage over the mobile antenna matched filter scheme, fully demonstrating the necessity of joint optimization strategy.

[0065] In the description of the application, it is to be understood that the orientation or positional relationship indicated by the terms "intermediate", "length", "upper", "lower", "front", "back", "vertical", "horizontal", "inner", "outer", "radial", "circumferential" and the like is based on the orientation or positional relationship shown in the drawings, and is only for the convenience of describing the application and simplifying the description, and does not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the application.

[0066] In the present application, unless otherwise explicitly specified and limited, the first feature "on" the second feature can be direct contact of the first and second features, or indirect contact of the first and second features through an intermediate medium. The meaning of "a plurality of" is at least two, such as two, three, etc., unless otherwise explicitly specified and limited.

[0067] In the present application, unless otherwise explicitly specified and limited, the terms "mounting", "connecting", "connecting", "fixing" and the like should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or it can be integrated; it can be mechanically connected, or it can be electrically connected or in communication with each other; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the internal communication of two elements or the interaction relationship between two elements, unless otherwise explicitly limited. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0068] The above is only to illustrate the embodiments of the present application, and is not used to limit the present application. Any modification, equivalent replacement, improvement, etc. made by those skilled in the art within the spirit and principles of the present application without creative labor shall be included in the protection scope of the present application.

Claims

1. A movable antenna assisted covert communication system in a C4I integrated network, characterized in that, Comprising: an ISAC base station configured with Nt movable transmit antennas and Nr fixed receive antenna arrays; K communication nodes, each configured with a single antenna for receiving communication signals transmitted by the ISAC base station; a point-like sensing node for receiving sensing signals transmitted by the ISAC base station; an eavesdropping node configured with a single antenna for attempting to detect signals transmitted by the ISAC base station; the ISAC base station is capable of transmitting signals in two modes of operation: a mode of transmitting only sensing signals for target parameter estimation, and a mode of transmitting both sensing signals and covert communication signals; the ISAC base station is configured to maximize a weighted sum of communication total rate and sensing mutual information, subject to covertness constraints, transmit power constraints, and minimum distance constraints of movable antennas, by optimizing transmit beamforming vectors and positions of movable antennas.

2. The movable antenna assisted covert communication system in a SIGINT fusion network of claim 1, wherein, signals transmitted by the ISAC base station are represented as: wherein, denotes a sensing only transmission hypothesis, corresponds to an ISAC hypothesis, and denotes the data symbol and the dedicated sensing signal for the k-th user, respectively, and denotes the corresponding beamforming vector.

3. The movable antenna assisted covert communication system in a SIGINT fusion network of claim 1, wherein, each communication node adopts a multipath channel model, and the path response vector of the k-th communication node is modeled as: where L denotes the number of channel paths, is the first path complex channel coefficient, is the fading coefficient at the reference distance, denotes the distance between the base station and the kth user, is the path loss exponent.

4. The movable antenna assisted covert communication system in a SIGINT fusion network of claim 1, wherein, the covertness constraints are: wherein, denotes the transmit steering vector of the eavesdropping node, , , is an acceptable threshold for the detection probability of the eavesdropping node, Q is the number of samples.

5. The movable antenna assisted covert communication system in a SIGINT fusion network of claim 1, wherein, the transmit power constraints are: wherein, is the total transmit power budget. the minimum distance constraints of movable antennas are: wherein, represents the position vector of the n-th movable antenna, is a minimum distance threshold value.

6. A method for mobile antenna assisted covert communication in a C4I integrated network, characterized in that, comprising the following steps: Initializing a beamforming vector and a movable antenna position ; Fixing a movable antenna position solving the beamforming optimization sub-problem to obtain a new beamforming vector ; Fixed beamforming vectors solving the movable antenna position optimization sub-problem to obtain a new movable antenna position ; Computing the updated weighted sum rate ; repeating the above steps until a maximum number of iterations is reached or a convergence condition is met, outputting the optimization result, wherein the convergence condition is that the relative change in the weighted sum rate of the last two iterations is less than a set threshold.

7. The method of claim 6, wherein, the step of solving the beamforming optimization sub-problem comprises: using a semidefinite relaxation algorithm to degenerate the optimization problem into a semidefinite constraint problem; using a difference convex programming technique to convert the non-convex objective function into a lower bound of a concave function; solving the converted convex optimization problem by a convex optimization tool to obtain the optimized beamforming matrix; performing eigenvalue decomposition on the optimized beamforming matrix to reconstruct the beamforming vector.

8. The method of claim 6, wherein, when the rank of the optimized sensing signal beamforming matrix is greater than 1, a Gaussian randomization technique is used to construct an approximate solution with a rank of 1.

9. The method of claim 6, wherein, the step of solving the movable antenna position optimization sub-problem comprises: performing a first-order Taylor expansion on the core correlation function to define a tight lower bound and an upper limit; using a surrogate function to convert the non-convex objective function into a lower bound of a concave function; converting the covertness constraints and minimum distance constraints into convex function forms; solving the converted convex optimization problem by a convex optimization tool to obtain the optimized movable antenna positions.

10. The method of claim 6, wherein, the weighted sum rate is a linear combination of the communication total rate and the sensing mutual information, i.e.: wherein, is a weight coefficient, is a total communication rate, is a perceived mutual information; The communication total rate is represented as: wherein, Snrk is the signal-to-noise ratio for the kth communication node; The perceived mutual information is represented as: wherein, is the number of receive antennas, is the perceived signal attenuation coefficient, is the perceived signal noise variance, is the transmit direction vector of the perceived target, is the total transmit covariance matrix of all signals.

Images