A method and system for covert communication of unmanned aerial vehicles supported by a mobile antenna

Abstract

The application provides a movable antenna supported unmanned aerial vehicle covert communication method and system, comprising the following steps: calculating the maximum communication rate of a legal user under the support of a movable antenna according to a movable antenna communication scene; calculating the minimum detection error rate under multi-illegal guard cooperative detection according to the movable antenna communication scene; establishing a joint optimization problem of time slot segmentation, beam forming, unmanned aerial vehicle trajectory and movable antenna position based on the maximum communication rate and the minimum detection error rate, wherein the optimization target is to maximize the minimum throughput of the legal user under the condition of meeting the covert communication constraint; and obtaining the optimized time slot segmentation, beam forming, unmanned aerial vehicle trajectory and movable antenna position parameters by using an iterative algorithm based on block coordinate descent and continuous convex approximation, and applying the parameters to the covert communication of the unmanned aerial vehicle. The method provided by the application can well meet the concealment requirement of unmanned aerial vehicle communication and improve network security.

Description

Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) communication technology, and particularly relates to a covert communication method and system for UAVs supported by a movable antenna. Background Technology

[0002] In recent years, unmanned aerial vehicles (UAVs) have attracted widespread attention as an effective means to overcome the physical transmission limitations of traditional terrestrial communication networks, due to their high probability of Loss of Service (LoS) links, high flexibility, and low cost. In particular, leveraging the high mobility and network design freedom of UAVs, through the joint design of UAV flight paths and resource allocation, can improve the quality of air-to-ground line-of-sight channels and further enhance communication performance.

[0003] Recently, drones have been considered a promising technology for next-generation networks due to their high flexibility, low cost, and especially their high-quality line-of-sight (LAS) communication. However, while the high-quality LAS link in drone communication networks can effectively improve network performance, it can also lead to serious covertness issues, as unauthorized surveillance can easily detect legitimate transmissions through open channels.

[0004] To meet the stealth requirements of UAV communication, UAV-supported stealth communication technology has become a research hotspot. This approach ensures low detection probability of unauthorized surveillance and protection of legitimate network communication activities. In 2022, Jiao et al. utilized the uncertainty of background noise to maximize the average stealth transmission rate by jointly optimizing UAV layout and resource allocation, thus ensuring the stealth of UAV-assisted communication. Subsequently, in 2023, Li et al. proposed a unified trajectory and resource optimization framework to further incorporate UAV maneuverability into stealth communication, achieving a balance between stealth and communication performance. Building on the above work, in 2025, Deng et al. introduced a fixed-position antenna into the UAV communication network and further improved the stealth communication performance through additional antenna beamforming design. It is worth noting that although the introduction of the antenna array significantly improved the stealth communication performance of the network, this work assumes that the antenna position is fixed. In recent years, with the development of movable antenna technology, the optimization of antenna position can introduce new spatial diversity gain to the system, thereby further improving the stealth of the network. However, the relevant research is still an open question, and further research is needed on UAV stealth communication methods and systems supported by movable antennas. Summary of the Invention

[0005] In view of the current situation where there is a lack of covert communication using the spatial degrees of freedom of movable antennas in UAV wireless communication networks, this invention proposes a UAV covert communication method and system supported by movable antennas for UAV downlink communication networks with multiple legitimate users and illegal surveillance, in order to improve the covertness of the network.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution:

[0007] A covert communication method for unmanned aerial vehicles supported by a movable antenna includes the following steps:

[0008] Based on the movable antenna communication scenario, the maximum communication rate of the legitimate user supported by the movable antenna is calculated based on the channel gain from the UAV to the legitimate user and the movable antenna turning vector from the UAV to the legitimate user.

[0009] Based on the movable antenna communication scenario, and using the channel gain from the UAV and jammer to the illegal guard, the movable antenna turning vector from the UAV to the illegal guard, and the likelihood ratio detection principle, the minimum detection error rate under multi-illegal guard cooperative detection is calculated.

[0010] Based on the maximum communication rate and minimum detection error rate, a joint optimization problem is established for time slot segmentation, beamforming, UAV trajectory and movable antenna position, including optimization objective and constraints, wherein the optimization objective is to maximize the minimum throughput of legitimate users while satisfying the covert communication constraints.

[0011] An iterative algorithm based on block coordinate descent and continuous convex approximation is used to obtain optimized time slot division, beamforming, UAV trajectory and movable antenna position parameters, and apply them to UAV covert communication.

[0012] Furthermore, the movable antenna communication scenario includes: a drone, multiple legitimate ground users, a friendly jammer, and a communication network of multiple cooperative illegal surveillance devices; the drone is equipped with a movable antenna array containing multiple antennas.

[0013] Furthermore, the expression for the drone's movable antenna turning vector towards the legitimate user is:

[0014]

[0015] The expression for the turning vector of the UAV toward the movable antenna of the illegal guard is:

[0016]

[0017] in, Representing the The time slot drone to the first The movable antenna steering vector of a legitimate user represent The One element; This represents the number of the movable antenna. This represents the total number of movable antennas; Represents the illegal guard number. The total number of illegal detentions; Representing the The first time slot The position of the movable antenna, Representing the The time slot drone to the first The tilt angle of a legitimate user; Representing the The time slot drone to the first The distance to a legitimate user Representing the The horizontal position of the drone in each time slot Representing the The horizontal position of a legitimate user Represents the drone's flight altitude; Representing the The time slot drone to the first The steering vector of an illegally guarded movable antenna. represent The One element, Representing the The time slot drone to the first An illegal guard's tilt angle; Representing the The time slot drone to the first The distance of an illegal guard, Representing the The horizontal position of an illegal guard; Represents the cosine value; Represents the signal wavelength, superscript Represents the transpose of a matrix; Represents the natural constant. Represents the imaginary unit. It represents pi.

[0018] Furthermore, the calculation of the maximum communication rate of a legitimate user supported by the movable antenna includes:

[0019] The channel gain from the UAV to the legitimate user is calculated based on the location of the legitimate user and the location of the UAV. The channel gain from the UAV to the legitimate user is based on the distance between the UAV and the legitimate user, the air-to-ground channel power gain per unit distance, and the air-to-ground channel loss index.

[0020] Based on the channel gain from the UAV to the legitimate user and the steerable antenna from the UAV to the legitimate user, the maximum communication rate of the legitimate user supported by the steerable antenna is obtained through the beamforming vector and background noise power.

[0021] Furthermore, the expression for the maximum communication rate of a legitimate user supported by the movable antenna is:

[0022]

[0023] in, Represents the first under the support of movable antenna The first time slot The expression for the maximum communication rate of a legal user; Representing the Each time-slot beamforming vector represent The One element, Represents background noise power; superscript Represents the Hermitian transpose of a matrix; Representing the The time slot drone to the first Channel gain for each legitimate user Represents the air-to-ground channel power gain per unit distance. This represents the air-to-ground communication road damage index.

[0024] Furthermore, the calculation of the minimum detection error rate under multi-illegal-guard cooperative detection includes:

[0025] Calculate the channel gain from the drone to the unauthorized guard and the channel gain from the jammer to the unauthorized guard;

[0026] Based on the channel gain from the UAV to the illegal guard, the channel gain from the jammer to the illegal guard, and the turning vector of the movable antenna from the UAV to the illegal guard, the received signal power at the illegal guard location is obtained.

[0027] Based on the likelihood ratio detection principle, and based on the received signal power at the illegal guard post, the minimum detection error rate under the multi-illegal guard cooperative detection is obtained.

[0028] Furthermore, the expression for the minimum detection error rate under the multi-illegal-guard cooperative detection is:

[0029]

[0030] in, Representing the Minimum detection error rate under multi-times-slot illegal guard collaborative detection; It is the minimum value; This represents the joint probability density function of the power of the signal received by the watchdog when it is not communicating with the user. The joint probability density function representing the power of the signal received by the guard during communication between the UAV and the user. Representing the The probability density distribution parameters of the signal received by each guard.

[0031] Furthermore, the joint optimization problem is:

[0032]

[0033] in, Representatives jointly optimized time slot division Beamforming Drone trajectory and the position of the movable antenna Maximize communication throughput by minimizing the throughput of legitimate users; Representing the The first time slot The time slot segmentation coefficient for each legitimate user Represents the time slot length. Representing the The throughput of each legitimate user; This represents the first time slot position of the drone. Representing the first drone Each time slot position, Representing the The location of the drone in each time slot This represents the maximum speed of the drone; This represents the maximum size of the movable antenna. This represents the minimum distance between antennas. Representing the The first time slot The position of the movable antenna; This represents a given threshold for covert communication.

[0034] Furthermore, the block coordinate descent method and continuous convex approximation iterative algorithm are as follows:

[0035] Initialize the initial values ​​for time slot division, beamforming, UAV trajectory, and movable antenna position;

[0036] The following sub-steps are executed iteratively:

[0037] Solve the time slot division optimization subproblem when the beamforming, UAV trajectory, and local points of the movable antenna position are fixed.

[0038] Solve the beamforming optimization subproblem with fixed time slot division, UAV trajectory and local points of movable antenna position;

[0039] Solve the UAV trajectory optimization subproblem with fixed time slot division, beamforming, and local points of movable antenna position;

[0040] Solve the antenna position optimization subproblem when there is fixed time slot division, beamforming, and local points of UAV trajectory;

[0041] The iteration stops when the performance increase is less than a given threshold, and the optimized solution is output.

[0042] On the other hand, the present invention provides a covert communication system for unmanned aerial vehicles supported by a movable antenna, comprising:

[0043] Communication rate calculation module: It is used to calculate the maximum communication rate of the legitimate user supported by the movable antenna based on the channel gain from the UAV to the legitimate user and the movable antenna turning vector from the UAV to the legitimate user, according to the movable antenna communication scenario.

[0044] Detection error rate calculation module: It is used to calculate the minimum detection error rate under multi-illegal guard cooperative detection based on the channel gain from UAV and jammer to illegal guard, the turning vector of the movable antenna from UAV to illegal guard, and the likelihood ratio detection principle, according to the movable antenna communication scenario.

[0045] The optimization problem modeling module is used to establish a joint optimization problem of time slot segmentation, beamforming, UAV trajectory and movable antenna position based on the maximum communication rate and minimum detection error rate. The optimization objective is to maximize the minimum throughput of legitimate users while satisfying the covert communication constraints.

[0046] Joint optimization solution module: It is used to obtain optimized time slot division, beamforming, UAV trajectory and movable antenna position parameters by adopting an iterative algorithm based on block coordinate descent and continuous convex approximation, and apply it to the covert communication of UAVs.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] This invention proposes a covert communication method and system for unmanned aerial vehicles (UAVs) supported by movable antennas. This method maximizes the covertness of UAV wireless communication networks and effectively utilizes the high mobility of UAVs and the spatial diversity gain of movable antennas to significantly improve the channel for legitimate users while reducing the probability of legitimate communication behavior being detected by illegitimate users. It also enhances the ability to resist joint detection by multiple illegitimate users and meets the communication covertness requirements of next-generation UAV mobile communication networks. Attached Figure Description

[0049] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0050] Figure 1 This is a schematic diagram of a covert communication network for unmanned aerial vehicles supported by a movable antenna, according to an embodiment of the present invention.

[0051] Figure 2 This is a flowchart illustrating the method implemented in this invention;

[0052] Figure 3 Throughput comparison is designed for embodiments of the present invention. Detailed Implementation

[0053] 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 some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0054] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.

[0055] Example 1

[0056] Figure 1 A covert communication network for unmanned aerial vehicles (UAVs) supported by a movable antenna, as considered in a specific embodiment of the present invention, the network comprising a UAV, One legitimate ground user, one friendly jammer, and A collaborative illegal surveillance operation. The drone carries... One movable antenna array of the drone communicates with a legitimate ground user. Communication between the drone and the legitimate user is subject to cooperative detection by an unauthorized surveillance unit. Simultaneously, a friendly jammer transmits artificial noise to interfere with the unauthorized surveillance without disrupting legitimate communication. Let the drone's flight altitude be... Maximum flight speed is Maximum transmission power is The jammer's interference power is To improve the performance of covert security networks for drones, it is necessary to jointly design drone time slot division, beamforming, drone trajectory, and movable antenna positions to maximize throughput while minimizing the throughput of legitimate users. This problem is highly complex.

[0057] like Figure 2 The diagram shown is a flowchart of the method of the present invention. The implementation process includes the following steps:

[0058] Based on the movable antenna communication scenario, the maximum communication rate of the legitimate user supported by the movable antenna is calculated based on the channel gain from the UAV to the legitimate user and the movable antenna turning vector from the UAV to the legitimate user.

[0059] Based on the movable antenna communication scenario, and using the channel gain from the UAV and jammer to the illegal guard, the movable antenna turning vector from the UAV to the illegal guard, and the likelihood ratio detection principle, the minimum detection error rate under multi-illegal guard cooperative detection is calculated.

[0060] Based on the maximum communication rate and minimum detection error rate, a joint optimization problem is established for time slot segmentation, beamforming, UAV trajectory and movable antenna position, including optimization objective and constraints, wherein the optimization objective is to maximize the minimum throughput of legitimate users while satisfying the covert communication constraints.

[0061] An iterative algorithm based on block coordinate descent and continuous convex approximation is used to obtain optimized time slot division, beamforming, UAV trajectory and movable antenna position parameters, and apply them to UAV covert communication.

[0062] In this embodiment, calculating the maximum communication rate of a legitimate user supported by a movable antenna specifically includes:

[0063] First, based on the locations of the legitimate users and the UAV, calculate the channel gain from the UAV to the legitimate user and the expression for the movable antenna turning vector from the UAV to the legitimate user. Then, based on the channel gain and the expression for the movable antenna turning vector from the UAV to the legitimate user, obtain the expression for the maximum communication rate of the legitimate user supported by the movable antenna.

[0064] The channel gain from the drone to the legitimate user is:

[0065]

[0066] in Represents a valid user ID. Represents the time slot number. This represents the total number of time slots. Representing the The time slot drone to the first Channel gain for each legitimate user Represents the air-to-ground channel power gain per unit distance. Represents the air-to-ground communication road damage index; Representing the The time slot drone to the first The distance to a legitimate user Representing the The horizontal position of the drone in each time slot Representing the The horizontal position of a legitimate user.

[0067] The turning vector of the drone's movable antenna towards the legitimate user is:

[0068]

[0069] in Represents the number of the movable antenna; Representing the The time slot drone to the first The movable antenna steering vector of a legitimate user represent The One element; Representing the The first time slot The position of the movable antenna, Representing the The time slot drone to the first The tilt angle of a legitimate user Represents the signal wavelength, superscript Represents matrix transpose. Represents the natural constant. Represents the imaginary unit. It represents pi.

[0070] The expression for the maximum communication rate of a legal user supported by a movable antenna is:

[0071]

[0072] in Represents the first under the support of movable antenna The first time slot An expression for the maximum communication rate of a legal user. Representing the Each time-slot beamforming vector represent The One element, Represents background noise power; superscript This represents the Hermitian transpose of the matrix.

[0073] In this embodiment, calculating the minimum detection error rate under multi-illegal-guard cooperative detection specifically includes:

[0074] Based on the positions of the UAV, jammer, and guard, the channel gain expressions from the UAV and jammer to the illegal guard, as well as the movable antenna turning vector expression from the UAV to the illegal guard, are calculated. Furthermore, the expressions for the received signal and received signal power at the illegal guard's location are obtained. Then, based on the likelihood ratio detection principle, the expression for the minimum detection error rate under multi-illegal-guard cooperative detection is derived.

[0075] The channel gain expression for the drone to the illegal guard is:

[0076]

[0077] in Represents the illegal guard number. The total number of illegal guards. Representing the The time slot drone to the first The channel gain of an unauthorized guard; Representing the The time slot drone to the first The distance of an illegal guard, Representing the The horizontal position of an illegal guard.

[0078] The expression for the channel gain from the jammer to the unauthorized guard is:

[0079]

[0080] in Representing the jammer to the number Channel gain due to unauthorized guarding This represents the power gain of the ground channel per unit distance. Represents the ground road damage index; Representing the jammer to the number The distance of an illegal guard, This represents the horizontal position of the jammer. A complex Gaussian distribution with a mean of 0 and a variance of 1 represents small-scale fading.

[0081] The turning vector of the drone toward the movable antenna of the illegal guard is:

[0082]

[0083] in Representing the The time slot drone to the first The steering vector of an illegally guarded movable antenna. represent The One element, Representing the The time slot drone to the first An illegal guard's angle of elevation.

[0084] The signal received by the illegal detention center is represented by the following formula:

[0085]

[0086] in Represents the signal number. Represents the total number of signals in each time slot; Representing the The first time slot The first illegally received by the guard One signal, Representing the The first time-slot jammer sent the first... One interference signal, Representing the The drone delivered the first time slot One signal; This represents the assumption that drones do not have communication capabilities. This represents its alternative hypothesis.

[0087] The expression for the signal power received at the illegal detention center is:

[0088]

[0089] in Representing the The first time slot Signal power received at an unauthorized user location; The representative parameter is For an exponentially distributed random variable, its probability density function is... express; for Mapping random variables, their probability density functions are used express.

[0090] The expression for the minimum detection error rate under multi-illegal-guard cooperative detection is:

[0091]

[0092] in Representing the Minimum detection error rate under multi-times-slot illegal guard collaborative detection.

[0093] In this embodiment, establishing a joint optimization problem for time slot partitioning, beamforming, UAV trajectory, and movable antenna position in a UAV covert communication network supported by a movable antenna includes: first, constructing the objective of the optimization problem based on the expression for the maximum communication rate of legal users supported by the movable antenna; then, defining the mobility constraints, beamforming, antenna position, time slot partitioning, and covert communication constraints of the optimization problem; and finally, establishing a joint optimization problem for time slot partitioning, beamforming, UAV trajectory, and movable antenna position in a UAV covert communication network supported by a movable antenna based on the constructed objective and constraints.

[0094] The goal of the optimization problem is:

[0095]

[0096] in Representing the The first time slot The time slot segmentation coefficient for each legitimate user Represents the time slot length. Representing the The throughput of each legitimate user. The above objective means achieving this through joint optimization of time slot allocation. Beamforming Drone trajectory and the position of the movable antenna Maximize communication throughput by minimizing the throughput of the minimum legitimate users.

[0097] The constraints include: mobility constraints, beamforming constraints (beamforming power does not exceed the maximum transmit power of the UAV), antenna position constraints, time slot division constraints, and covert communication constraints.

[0098] The mobility constraint for the optimization problem is:

[0099]

[0100] in This represents the first time slot position of the drone. Representing the first drone Each time slot position, Representing the The location of the drone in each time slot. The constraint means the position of the first time slot of the UAV and the position of the second time slot. The time slots are all at the same location, meaning the drone's trajectory is a closed curve. The constraint means that the speed of the drone is less than its maximum speed.

[0101] The beamforming constraint for the optimization problem is:

[0102]

[0103] The above constraint means that the beamforming power of the UAV should be less than its maximum transmit power.

[0104] The antenna position constraint for the optimization problem is:

[0105]

[0106] in This represents the maximum size of the movable antenna. This represents the minimum distance between antennas. Representing the The first time slot The position of the movable antenna; the above constraints mean that the position of the movable antenna should be within the specified size range, and the minimum distance between antennas should be greater than [missing information]. .

[0107] The time slot partitioning constraint for the optimization problem is:

[0108]

[0109] The meaning of the above constraints is as follows: The value of is between 0 and 1, and the sum of the time slot division coefficients of all legal users in any time slot must not be greater than 1.

[0110] The hidden communication constraint of the optimization problem is:

[0111]

[0112] in Representing a given covert communication threshold, the above constraint means that the minimum detection error rate under multi-illegal-user cooperative detection must be greater than the given threshold. This constraint can be equivalently transformed into:

[0113]

[0114] The joint optimization problem of time slot division, beamforming, UAV trajectory and movable antenna position in a covert UAV communication network supported by a movable antenna:

[0115]

[0116] In this embodiment, the above problems are solved based on the block coordinate descent method and the continuous convex approximation to obtain optimized solutions for time slot division, beamforming, UAV trajectory and movable antenna position.

[0117] The following is an iterative algorithm based on block coordinate descent and continuous convex approximation:

[0118] Initialize time slot division, beamforming, UAV trajectory, and initial values ​​for movable antenna position. And treat it as a local point of the iteration;

[0119] In each iteration, the first step is to focus on local points in beamforming, UAV trajectory, and movable antenna position. The joint optimization problem is transformed into a time slot segmentation optimization subproblem. This subproblem is solved using a convex optimization algorithm, and the optimized solution is used as a new local point for time slot segmentation. ;

[0120] Specifically, the time slot division optimization subproblem is as follows:

[0121]

[0122] The above problem is a linear convex problem, which can be solved efficiently using convex optimization algorithms to obtain new local points for time slot segmentation. .

[0123] Local points in time slot segmentation, UAV trajectory, and movable antenna location The joint optimization problem is transformed into a beamforming optimization subproblem. A continuous convex approximation method is used to approximate the beamforming optimization subproblem into a convex problem of the beamforming optimization subproblem. A convex optimization algorithm is then used to solve this convex problem, and the optimized solution is used as a new local beamforming point. ;

[0124] Specifically, the beamforming optimization sub-problem is:

[0125]

[0126] in represent The One element. Due to about Since it is not a concave function, the above problem is non-convex. This invention first utilizes a continuous convex approximation method to... It can be approximated by the following linear function, where :

[0127]

[0128] Where Re represents taking the real part of the complex number, represent An approximate linear function. Based on the above, a construction can be made. The lower concave approximation is:

[0129]

[0130] in Based on the above approximation, the convex problem of the beamforming optimization subproblem can be constructed as follows:

[0131]

[0132] The above problem is a convex problem, which can be solved efficiently using convex optimization algorithms to obtain new local beamforming points. .

[0133] Local points in time slot division, beamforming, and movable antenna location The joint optimization problem is transformed into a UAV trajectory optimization subproblem. A continuous convex approximation method is used to approximate the UAV trajectory optimization subproblem into a convex problem of the UAV trajectory optimization subproblem. A convex optimization algorithm is then used to solve this convex problem, and the optimized solution is used as a new local point on the UAV trajectory. ;

[0134] Specifically, the drone trajectory optimization sub-problem is:

[0135]

[0136] because about Since it is not a concave function, the above problem is non-convex. This invention utilizes a continuous convex approximation method to... It is approximated by the following concave function:

[0137]

[0138] in represent The approximate concave function, , This represents the approximation coefficient, and its values ​​are:

[0139]

[0140] in These are approximation coefficients, and their values ​​are:

[0141]

[0142] in, They represent The One element, They represent The Each element.

[0143] Based on the above approximation, the convex problem of the UAV trajectory optimization subproblem can be constructed as follows:

[0144]

[0145] in represent First-order Taylor expansion. The above problem is a convex problem, which can be efficiently solved using convex optimization algorithms to obtain new local points of the UAV trajectory. .

[0146] In time slot division, beamforming, and local points of UAV trajectory The joint optimization problem is transformed into an antenna position optimization subproblem. A continuous convex approximation method is used to approximate this subproblem into a convex problem of the antenna position optimization subproblem. A convex optimization algorithm is then used to solve this convex problem, and the optimized solution is used as a new local point for the antenna position. ;

[0147] Specifically, the antenna location optimization subproblem is:

[0148]

[0149] because about Since it is not a concave function, the above problem is non-convex. This invention utilizes a continuous convex approximation method to... It is approximated by the following concave function:

[0150]

[0151] in represent The approximate concave function, These are approximation coefficients, and their values ​​are:

[0152]

[0153] in This represents converting a vector into an equal-order diagonal matrix. , represent The One element, .

[0154] Based on the above approximation, the convex problem of the antenna position optimization subproblem can be constructed as follows:

[0155]

[0156] in represent First-order Taylor expansion. The above problem is a convex problem, which can be efficiently solved using convex optimization algorithms to obtain the new local antenna position. .

[0157] If the performance improvement in this iteration is less than a given threshold compared to the previous iteration, the iteration stops, and the local point of this iteration becomes the optimal solution to the problem; otherwise, it will be used as the local point for the next iteration, and the iteration will continue.

[0158] Figure 3 A comparison of the throughput of embodiments of the present invention is given, wherein the comparison schemes are a traditional single-antenna and a fixed-antenna scheme. It can be seen that under different... The proposed scheme outperforms traditional single-antenna and fixed-antenna schemes under the given values, which verifies the performance advantage of the proposed scheme.

[0159] Example 2

[0160] This embodiment provides a UAV-assisted coverage system based on continuous convex approximation, including:

[0161] The 3D non-convex optimization problem construction module is used in UAV communication scenarios with two ground nodes. It constructs the distance vector from the UAV to each node based on the coordinates of the two ground nodes, and establishes a 3D non-convex optimization problem in combination with antenna beam constraints.

[0162] The optimization problem dimensionality reduction module is used to calculate the node distance based on the coordinates of two ground nodes and construct equivalent nodes. Based on the distance vector from the UAV to the equivalent nodes, the dimensionality of the three-dimensional non-convex optimization problem is reduced to a two-dimensional planar coordinate positioning problem. The solution module is used to iteratively solve the two-dimensional planar coordinate positioning problem based on a continuous convex approximation algorithm to obtain a two-dimensional local optimum solution.

[0163] The restoration module is used to map and restore the two-dimensional local optimal solution to a three-dimensional coverage coordinate solution set of the UAV.

[0164] Variable function solving module: This module calculates the azimuth angle and downtilt angle variable functions of the UAV antenna based on the UAV's three-dimensional coverage coordinate solution set and ground node coordinates. A concealed UAV communication system supported by a movable antenna includes:

[0165] Communication rate calculation module: It is used to calculate the maximum communication rate of the legitimate user supported by the movable antenna based on the channel gain from the UAV to the legitimate user and the movable antenna turning vector from the UAV to the legitimate user, according to the movable antenna communication scenario.

[0166] Detection error rate calculation module: It is used to calculate the minimum detection error rate under multi-illegal guard cooperative detection based on the channel gain from UAV and jammer to illegal guard, the turning vector of the movable antenna from UAV to illegal guard, and the likelihood ratio detection principle, according to the movable antenna communication scenario.

[0167] The optimization problem modeling module is used to establish a joint optimization problem of time slot segmentation, beamforming, UAV trajectory and movable antenna position based on the maximum communication rate and minimum detection error rate. The optimization objective is to maximize the minimum throughput of legitimate users while satisfying the covert communication constraints.

[0168] Joint optimization solution module: It is used to obtain optimized time slot division, beamforming, UAV trajectory and movable antenna position parameters by adopting an iterative algorithm based on block coordinate descent and continuous convex approximation, and apply it to the covert communication of UAVs.

[0169] It should be understood that any parts not described in detail in this specification belong to the prior art.

[0170] It should be understood that the above description of preferred embodiments is quite detailed, but this should not be construed as limiting the scope of protection of this invention. It is neither necessary nor possible to exhaustively describe all possible embodiments. Those skilled in the art, guided by this invention, can make substitutions or modifications without departing from the scope of the claims, all of which fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

Claims

1. A method for covert communication of a drone supported by a mobile antenna, characterized in that, The method comprises the following steps: According to the movable antenna communication scenario, the maximum communication rate of the legitimate user supported by the movable antenna is calculated based on the channel gain from the UAV to the legitimate user and the movable antenna steering vector from the UAV to the legitimate user; The movable antenna steering vector from the UAV to the legitimate user is expressed as: The movable antenna steering vector from the UAV to the guard is expressed as: wherein represents the number of time slots, represents the number of movable antennas, represents the movable antenna steering vector from the drone to the legitimate user, represents the element of ; represents the number of time slots, represents the number of movable antennas, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the element of ; represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the number of time slots, represents the cosine value; represents the signal wavelength, the superscript represents the matrix transpose; represents the natural constant, represents the imaginary unit, represents the circle constant; The calculation of the maximum communication rate of the legitimate user supported by the movable antenna comprises: According to the position of the legitimate user and the position of the UAV, the channel gain from the UAV to the legitimate user is calculated, which is based on the distance between the UAV and the legitimate user, the air-ground channel power gain per unit distance, and the air-ground channel path loss index; According to the channel gain from the UAV to the legitimate user and the movable antenna steering vector from the UAV to the legitimate user, the maximum communication rate of the legitimate user supported by the movable antenna is obtained through the beamforming vector and the background noise power; The maximum communication rate of the legitimate user supported by the movable antenna is expressed as: in, Represents the first under the support of movable antenna The first time slot The expression for the maximum communication rate of a legal user; Representing the Each time-slot beamforming vector represent The One element, Represents background noise power; superscript Represents the Hermitian transpose of a matrix; Representing the The time slot drone to the first Channel gain for each legitimate user Represents the air-to-ground channel power gain per unit distance. Represents the air-to-ground communication road damage index; The maximum communication rate of the legitimate user supported by the movable antenna is expressed as: wherein represents the maximum communication rate of the kth legitimate user in the nth time slot under the support of the movable antenna, represents the maximum communication rate of the kth legitimate user in the nth time slot under the support of the movable antenna, represents the maximum communication rate of the kth legitimate user in the nth time slot under the support of the movable antenna, represents the beamforming vector of the kth time slot, represents the kth element of the vector represents the kth element of the vector represents the kth element of the vector represents the kth element of the vector represents the background noise power; the superscript represents the matrix Hermitian transpose; represents the channel gain from the UAV to the kth legitimate user in the nth time slot, represents the channel gain from the UAV to the kth legitimate user in the nth time slot, represents the channel gain from the UAV to the kth legitimate user in the nth time slot, represents the channel gain from the UAV to the kth legitimate user in the nth time slot, represents the channel gain from the UAV to the kth legitimate user in the nth time slot. According to the movable antenna communication scenario, the minimum detection error rate under multi-guard cooperative detection is calculated based on the channel gain from the UAV and the jammer to the guard, the movable antenna steering vector from the UAV to the guard, and the likelihood ratio detection principle; The calculation of the minimum detection error rate under multi-guard cooperative detection comprises: The channel gain from the UAV to the guard and the channel gain from the jammer to the guard are calculated; Based on the channel gain from the UAV to the guard and the channel gain from the jammer to the guard and the movable antenna steering vector from the UAV to the guard, the received signal power at the guard is obtained; According to the likelihood ratio detection principle, based on the received signal power at the guard, the minimum detection error under the multi-guard cooperative detection is obtained; The minimum detection error rate under the multi-guard cooperative detection is expressed as: wherein, represent the minimum detection error rate under the cooperative detection of the is the minimum value; represent the joint distribution probability density function of the guard received signal power when the UAV is not in communication with the user, represent the joint distribution probability density function of the guard received signal power when the UAV is in communication with the user, represent the probability density distribution parameters of the guard received signal, Based on the maximum communication rate and the minimum detection error rate, a joint optimization problem of time slot segmentation, beamforming, UAV trajectory and movable antenna position is established, including an optimization objective and constraint conditions, wherein the optimization objective is to maximize the minimum throughput of the legal user under the condition of satisfying the covert communication constraint.​ An iterative algorithm based on block coordinate descent and successive convex approximation is used to obtain the optimized time slot segmentation, beamforming, UAV trajectory, and movable antenna position parameters, which are applied to the covert communication of the UAV. 2.The method of claim 1, wherein, The movable antenna communication scenario comprises a communication network of one UAV, multiple ground legitimate users, one friendly jammer, and multiple cooperative guards; the UAV is equipped with a movable antenna array comprising multiple antennas. 3.The method of claim 1, wherein, The joint optimization problem is: in, Representatives jointly optimized time slot allocation Beamforming Drone trajectory and the position of the movable antenna Maximize communication throughput by minimizing the throughput of legitimate users; Representing the The first time slot The time slot segmentation coefficient for each legitimate user Represents the time slot length. Representing the The throughput of each legitimate user; This represents the first time slot position of the drone. Representing the drone Each time slot position, Representing the The location of the drone in each time slot This represents the maximum speed of the drone; This represents the maximum size of the movable antenna. This represents the minimum distance between antennas. Representing the The first time slot The position of the movable antenna; This represents a given threshold for covert communication.

4. The method of claim 3, wherein the UAV is a mobile antenna supported UAV. The iterative algorithm based on block coordinate descent and successive convex approximation is as follows: Initial values of time slot segmentation, beamforming, UAV trajectory, and movable antenna position are initialized; The following sub-steps are iteratively executed: When the beamforming, UAV trajectory, and movable antenna position local points are fixed, a time slot segmentation optimization sub-problem is solved; When the time slot segmentation, UAV trajectory, and movable antenna position local points are fixed, a beamforming optimization sub-problem is solved; When the time slot segmentation, beamforming, and movable antenna position local points are fixed, a UAV trajectory optimization sub-problem is solved; When the time slot segmentation, beamforming, and UAV trajectory local points are fixed, an antenna position optimization sub-problem is solved; When the performance increment is less than a given threshold, the iteration is stopped, and the optimization solution is output.

5. A drone concealed communication system supported by a mobile antenna, characterized in that, The method comprises: a communication rate calculation module configured to calculate a maximum communication rate of a legitimate user under the movable antenna support according to a movable antenna communication scenario based on a channel gain from the UAV to the legitimate user and a movable antenna steering vector from the UAV to the legitimate user; a detection error rate calculation module configured to calculate a minimum detection error rate under multi-guard collaboration detection according to the movable antenna communication scenario based on a channel gain from the UAV and the jammer to the guard, a movable antenna steering vector from the UAV to the guard, and a likelihood ratio detection principle; an optimization problem modeling module configured to establish a joint optimization problem of time slot segmentation, beamforming, UAV trajectory, and movable antenna position based on the maximum communication rate and the minimum detection error rate, including an optimization objective and constraint conditions, wherein the optimization objective is to maximize the minimum throughput of the legitimate user under the condition of satisfying the covert communication constraint; a joint optimization solution module configured to obtain optimized time slot segmentation, beamforming, UAV trajectory, and movable antenna position parameters by using an iterative algorithm based on block coordinate descent and successive convex approximation, and apply them to the covert communication of the UAV; the movable antenna supported UAV covert communication system is configured to perform the steps of the movable antenna supported UAV covert communication method of any one of claims 1-4.

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