Non-Gaussian noise assisted unmanned aerial vehicle covert communication method and system

Abstract

The embodiment of the invention relates to the technical field of unmanned aerial vehicle communication, in particular to a non-Gaussian noise assisted unmanned aerial vehicle covert communication method and system, and the method comprises the steps: building an unmanned aerial vehicle covert safety communication scene model assisted by an unmanned aerial vehicle jammer transmitting non-Gaussian noise; establishing an optimization problem in the established model by taking maximization of the average security hidden throughput of multiple users as a target and combining the concealment and power limitation constraint conditions; the optimization problem is converted into a multi-unmanned aerial vehicle cooperation Markov decision process; aiming at the Markov decision process obtained by conversion, using a combined attention mechanism and a standard multi-agent double-delay depth deterministic strategy gradient to optimize the multi-unmanned-aerial-vehicle trajectory to obtain an optimal multi-unmanned-aerial-vehicle trajectory; and instructing the unmanned aerial vehicle to execute a communication task based on the optimal multi-unmanned aerial vehicle trajectory. According to the method, the average security covert throughput in a non-Gaussian noise assisted covert security communication scene of the unmanned aerial vehicle node in the air can be well improved.

Description

Technical Field

[0001] The embodiments of the present application relate to the field of drone communication technology, and in particular to a non-Gaussian noise-assisted drone covert communication method and system. Background Art

[0002] Drones are widely used in the field of IoT (Internet of Things). Using drones for low-altitude flight to stabilize link connections can improve the efficiency of IoT data collection. Drones are also a viable solution for aviation communication services. Drones can provide support in scenarios where communication infrastructure needs to be quickly deployed, thereby achieving reliable communication coverage and data transmission. Compared with traditional communication systems, drones have better flexibility and effectiveness. The communication between drones and legitimate users on the ground is LoS (Line of Sight) channel communication, which has more reliable wireless transmission performance than ground-to-ground base station communication. The three-dimensional mobility of drones enables them to avoid obstacles and provide faster transmission rates and greater capacity for ground users. Due to their excellent maneuverability, flexible deployment capabilities and cost-effectiveness, drones have shown significant advantages in many application scenarios.

[0003] However, these advantages also bring new challenges. Although the aerial mobility of drones has great advantages over traditional ground base stations, hovering and moving in the air require additional propulsion energy. The limited onboard energy restricts the mobility of drones. Therefore, it is necessary to enhance communication performance and endurance through trajectory optimization and power allocation. In addition, potential security risks need to be considered in the future application of drone communication systems. Due to the LoS characteristics of drone air-to-ground communications, ensuring its communication security has become an important challenge.

[0004] Non-Gaussian noise-assisted technology uses non-Gaussian noise with pulse and tail characteristics, which makes it more difficult for eavesdroppers to separate the original signal from the mixed signal. It adds artificial interference signals to the transmission signal, allowing legitimate users to correctly decode confidential information with a small amount of interference, while eavesdroppers find it difficult to obtain any valid information from it. Its main advantage is to utilize the asymmetry of wireless channels, that is, the legitimate communicating parties usually enjoy better channel conditions than illegal eavesdroppers. Deploy friendly jammers near the enemy, let the friendly interference nodes send interference, and mix it with the useful information sent by the drone, thereby effectively hindering the activities of illegal eavesdroppers and monitors, and ensuring the security and concealment of communications between drones and legitimate users on the ground.

[0005] However, although the introduction of non-Gaussian noise technology improves security, it may also reduce communication efficiency. In the UAV network communication scenario, ensuring that the UAV maintains high communication transmission quality while maximizing the transmission throughput has become a challenging task. In the UAV network, this requires joint optimization of the flight trajectory and transmission power of the UAV, and considering the interference sending strategy. Therefore, in order to achieve covert and secure transmission of UAVs, it is particularly important to study how to effectively manage the interference caused by non-Gaussian noise assistance and optimize the trajectory of the UAV to ensure the security of communication. It is urgent to study the covert and secure transmission of UAVs assisted by non-Gaussian noise.

[0006] The application of drones as relay stations is also critical in covert communications. Drones can effectively improve the reliability of long-distance communications and reduce the probability of detection by dynamically adjusting their positions. Zhang et al. focused on drone-assisted covert communication networks, aiming to assist transmission and confuse the warden. They achieved covert transmission by calculating the optimal detection threshold, interruption probability expression, and power optimization. The results showed that cooperative interference and power trade-off can effectively ensure the security and concealment of communications. Wang et al. proposed a covert communication scheme that uses drones and IRS (Intelligent Reflecting Surface) to cooperate. By determining the optimal detection threshold and optimizing the transmission power, IRS phase, and drone position, effective covert transmission is achieved to protect it from the observation of the warden. Chen et al. studied how to use drones as relay nodes to assist covert wireless networks to improve communication performance and avoid detection by administrators.

[0007] In multi-UAV communication systems, reasonable resource allocation strategies, including power regulation, spectrum allocation, and spatial layout, are also the key to improving covert communication performance. The introduction of deep reinforcement learning technology provides UAVs with the ability to dynamically adapt to environmental changes, enabling them to optimize communication strategies in real time, thereby maintaining the concealment and efficiency of communication under evolving conditions. Li et al. considered the threat monitoring and detection scenario, and designed the UAV trajectory to maximize the transmission rate to the legitimate node. They adopted a double-delayed deep deterministic policy gradient method to effectively adaptively select the speed from the continuous action space. Numerical results verified the significant advantages of this method over the baseline. Hu et al. studied the covert communication in the scenario of a single UAV, a single user, and a single monitor. With the goal of maximizing the average effective covert rate of the legitimate user, the UAV trajectory and transmission power were jointly optimized through a deep reinforcement learning algorithm. The experimental results showed that its performance was significantly better than the baseline scheme, while ensuring the concealment of transmission and the convergence of the algorithm. Li et al. explored the application of cooperative UAV swarms in intelligent covert communication. By introducing a dynamic migration mechanism and a strategy based on a dual deep Q network, the scheduling, speed, and power of the UAV were jointly optimized to improve concealment and minimize the probability of detection errors.

[0008] Through the above analysis, the inventors of this application found that the current drone communication technology has the following defects:

[0009] First, there is currently little research on covert and secure transmission of UAVs assisted by non-Gaussian noise, especially research on the dynamic environment of UAVs, covert safety requirements, and UAV trajectory optimization, which increases the difficulty of designing transmission solutions.

[0010] Second, current research on optimization solutions for drone secure communication scenarios generally uses traditional optimization algorithms, but traditional optimization algorithms have limitations, such as local optimality, poor adaptation to dynamic environments, insufficient decision-making timeliness, and lack of transfer learning capabilities. These problems also bring difficulties to the design of transmission solutions. Summary of the invention

[0011] In view of this, the embodiments of the present application propose a non-Gaussian noise-assisted UAV covert communication method and system, develop a non-Gaussian noise-assisted UAV covert security transmission algorithm with better trajectory optimization performance and faster convergence speed, explore the use of attention mechanism and standard multi-agent double-delay deep deterministic policy gradient technology, optimize the trajectories of multiple UAVs in non-Gaussian noise-assisted UAV covert security transmission, and effectively improve the average security and covert throughput of aerial UAV nodes in non-Gaussian noise-assisted covert security communication scenarios.

[0012] In the first aspect, an embodiment of the present application proposes a non-Gaussian noise-assisted UAV covert communication method, which includes the following steps: S1, establishing a UAV covert secure communication scenario model assisted by a UAV jammer that emits non-Gaussian noise; S2, in the established model, with the goal of maximizing the average secure covert throughput of multiple users, combined with concealment constraints and power limit constraints, an optimization problem is established; S3, the optimization problem is converted into a multi-UAV collaborative Markov decision process; S4, for the converted multi-UAV collaborative Markov decision process, the multi-UAV trajectory is optimized using a combination of attention mechanism and standard multi-agent double-delay deep deterministic policy gradient to obtain the optimal multi-UAV trajectory; S5, instructing the UAV to perform communication tasks based on the optimal multi-UAV trajectory.

[0013] Optionally, a drone covert secure communication scenario model assisted by a drone jammer that emits non-Gaussian noise is established, including: considering a drone covert secure communication scenario assisted by a drone jammer that emits non-Gaussian noise, the drone transmitter acts as an aerial mobile base station, and transmits signals to K assigned users in an environment where there are P eavesdroppers and a single monitor. The drone jammer keeps sending non-Gaussian noise while moving to protect the information transmission between the user and the drone transmitter from being eavesdropped and detected; the drone will optimize its own trajectory to ensure the service quality of the K assigned users. The drone's trajectory is divided into N time slots of equal time length on the time axis. The drone maintains a constant altitude during flight, and the drone transmitter and the drone jammer are set at altitudes H and H, respectively. a With H j In the above example, a and j represent the UAV transmitter and UAV jammer respectively. The user, monitor and eavesdropper are regarded as ground nodes. It is assumed that each UAV knows the location of the monitor, eavesdropper and user, but does not know the location of other UAVs. In the same time slot, at most one user receives the signal from the UAV transmitter. The eavesdropper steals information when the information is transmitted between the user and the UAV transmitter. The monitor is responsible for monitoring the information transmission between the user and the UAV transmitter.

[0014] Optionally, to consider adaptability, the transmission link between the drone transmitter and the user is regarded as a probabilistic LoS / NLoS channel link, and the path loss uses the probabilistic LoS / NLoS path loss model, which is expressed by the formula:

[0015]

[0016] Where PL(d,θ) represents the total path loss at distance d and elevation angle θ. Distance d is the straight-line distance between the UAV transmitter and the user, and elevation angle θ is the vertical angle between the UAV transmitter and the ground. represents the probability that the signal propagation path is a direct path at an elevation angle θ, τ and is an environmental parameter adjusted based on the environment, represents the probability that the signal propagation path is a non-direct path at the elevation angle θ;

[0017] For user k, the received signal is expressed as:

[0018]

[0019] in, represents the signal received by user k on the i-th channel, P a [n] represents the transmission power of the UAV transmitter, PL(d ak ,θ a ) represents the path loss between the UAV transmitter and user k, d ak represents the straight-line distance between the UAV transmitter and user k, θ a Indicates the vertical angle between the drone transmitter and the ground, X a (i) represents the signal transmitted by the UAV transmitter, P j [n] represents the transmission power of the UAV jammer, PL(d jk ,θ j ) represents the path loss from the UAV jammer to user k, d jk represents the straight-line distance between the UAV jammer and user k, θ j represents the vertical angle between the UAV jammer and the ground, χ j (i) represents the non-Gaussian noise emitted by the UAV jammer, n k (i) represents the Gaussian white noise received by user k;

[0020] For the eavesdropper p, the received signal is expressed as:

[0021]

[0022] in, represents the signal received by the eavesdropper p on the i-th channel, PL(d ap ,θ a ) represents the path loss between the drone transmitter and the eavesdropper p, d ap represents the straight-line distance between the drone transmitter and the eavesdropper p, PL(d jp ,θ j ) represents the path loss between the UAV jammer and the eavesdropper p, d jp represents the straight-line distance between the UAV jammer and the eavesdropper p, n p (i) represents the Gaussian white noise received by the eavesdropper p;

[0023] The monitor determines whether the drone transmitter is transmitting information based on the L received signals in each time slot. The signal received by the monitor is expressed as:

[0024]

[0025] Among them, H 0 represents the null hypothesis that the UAV transmitter does not transmit information, H 1 represents the alternative hypothesis of the UAV transmitter transmission information, PL(d jw ,θ j ) represents the path loss between the UAV jammer and the monitor, d jw represents the straight-line distance between the UAV jammer and the monitor, PL(d aw ,θ a ) represents the path loss between the UAV transmitter and the monitor, d aw represents the straight-line distance between the UAV transmitter and the monitor, n w (i) represents the Gaussian white noise received by the monitor.

[0026] Optionally, in the established model, with the goal of maximizing the average secure concealed throughput of multiple users, combined with the concealment constraint and the power limit constraint, an optimization problem is established, including:

[0027] Assume that the monitor's decision is divided into supporting H 0 D 0 and support H 1 D 1 There are two types, assuming that the false alarm probability and missed detection probability are P FA (t) and P MD (t) represents the total detection error probability ξ(t) is defined as ξ(t) = P FA (t)+P MD (t), the goal of the drone is to make ξ(t) in each time slot as close to 1 as possible, which can be expressed as:

[0028] ξ(t)=P FA (t)+P MD (t)≥1-ε

[0029] Among them, ε is a preset positive decimal close to 0 to ensure the confidentiality of communication;

[0030] In H 0 and H 1 Under the assumption that The likelihood functions are expressed as:

[0031]

[0032] Among them, CN(·) represents a complex function, represents the variance of the signal received by the monitor;

[0033] Assuming that the monitor knows the index information of the signal, the likelihood ratio of the best detection is expressed as:

[0034]

[0035] in, represents the likelihood ratio of the best detection;

[0036] The KL divergence is used to derive the lower limit of the minimum detection error probability. The lower limit of the minimum detection error probability is expressed as:

[0037]

[0038] Among them, ξ * [n] represents the lower limit of the minimum detection error probability, D 01 [n]≤2ε 2 represents the constraint of detection probability. When the constraint of detection probability is satisfied, the concealment constraint will also be satisfied. 01 [n] is expressed by the formula:

[0039]

[0040] Where I represents the identity matrix;

[0041] On the basis of the constraints of detection probability and concealment, the flight trajectory, transmission power and interference power of UAV transmitters and UAV jammers are optimized to maximize the average secure and covert throughput of multiple users. The UAV transmitter dynamically adjusts its position to provide high-quality services, and the UAV jammer adjusts its position to reduce the link quality of eavesdroppers and monitors, thus obtaining the optimization problem.

[0042] Optionally, the optimization problem is formulated as follows:

[0043]

[0044]

[0045] in, represents the average secure concealed throughput of multiple users, C1 represents the concealment constraint, ε2 represents the power constraint of the UAV transmitter, represents the maximum transmission power of the UAV transmitter, C3 represents the power constraint of the UAV jammer, represents the maximum transmission power of the UAV jammer, C4 represents the flight speed constraint of the UAV, q[n] and q[n+1] represent the positions of the UAV at sampling points n and n+1 respectively, and V max represents the maximum flight speed of the drone, T represents the time required for the drone to fly from q[n] to q[n+1], C5 represents the flight range constraint of the drone, and R D Indicates the scene space corresponding to the established model.

[0046] Optionally, the optimization problem is converted into a multi-UAV cooperative Markov decision process, including:

[0047] The UAV transmitter and UAV jammer are regarded as intelligent agents, forming a partially observable state space. The optimization problem is described by a five-tuple (S, A, Reward, PST, γ), where S represents the state space, A represents the action space, Reward represents the reward function, PST represents the state transition probability, and γ represents the discount factor.

[0048] The state space S is defined as the current horizontal position of the UAV transmitter and the current horizontal position of the drone jammer

[0049] The action space is defined as the actions of the UAV transmitter and the actions of the drone jammer For the UAV transmitter, the action space includes the speed in the x-axis and y-axis directions and the magnitude of the transmission power. The action space of the UAV jammer includes the speed in the x-axis and y-axis directions and the magnitude of the jamming power.

[0050] In the UAV collaborative environment, the decision-making process involves each agent receiving an immediate reward based on the current state, the action performed, and the next state to be transferred to, and considering the termination signal. The reward mechanism includes penalties for the flight range, concealment, and distance of the UAV. The composition of the reward and penalty terms is as follows:

[0051] Secure and hidden throughput rewards, Incentivize drones to increase safe and covert throughput;

[0052] Boundary penalty, p b =1, if q[n]>R D ,else0, is applied when the drone exceeds the predetermined boundary to ensure that the drone operates within the specified area;

[0053] Hidden punishment, p ∈ =1, if D 01 [n]>∈ 2,else0, is applied when the minimum detection error probability of the monitor is lower than the threshold to ensure the concealment of communication;

[0054] Distance penalty,

[0055]

[0056] Among them, the distance penalty and They are used to encourage UAV transmitters and UAV jammers to fly around targets, encourage UAV transmitters to fly around users, and encourage UAV jammers to fly around eavesdroppers and monitors.

[0057] The overall reward function for the drone transmitter and the drone jammer is expressed as:

[0058]

[0059] Among them, α and β are coefficients that weigh the impact of different rewards and penalties, Ω 1 and Ω 2 is the weight of the corresponding penalty item;

[0060] In a UAV collaborative environment, the decisions and actions of each UAV will affect the overall system state. The state transition function describes the probability of the system reaching the next state given the current state and the UAV action, which is expressed by the formula:

[0061]

[0062] In this collaborative environment, there is no clear endpoint and the goal of the UAVs is to maximize the total communication capacity during the flight. The choice of the discount factor γ will reflect this long-term performance indicator.

[0063] Optionally, for the converted multi-UAV cooperative Markov decision process, the multi-UAV trajectory is optimized using a combination of an attention mechanism and a standard multi-agent double-delay deep deterministic policy gradient to obtain the optimal multi-UAV trajectory, including:

[0064] S41, initialize the network parameters of the Actor network, Critic network and attention network of the drone transmitter

[0065] S42, initialize the network parameters of the Actor network, Critic network and attention network of the drone jammer

[0066] S43, setting the network parameters of the target network to be the same as the network parameters of the main network, that is,

[0067] S44, if the convergence condition is met, go to S48, otherwise go to S44.1;

[0068] S44.1, UAV transmitter and UAV jammer observe their own status respectively and And select actions respectively and

[0069] S44.2, Execution Action in the environment;

[0070] S44.3, observe the next state The reward value r and the completion signal done are used to clarify s n+1 Whether it is a termination state;

[0071] S44.4, Storage In playback buffer B;

[0072] S44.5, if the drone flies out of the boundary, does not meet the concealment constraint, or the number of time slots reaches the upper limit, reset the environment state;

[0073] S44.6, when the preset number of updates is reached, set j=1 and proceed to S45, otherwise, proceed to S47;

[0074] S45, if j≤k, then enter,S45.1, otherwise, enter S47;

[0075] S45.1, randomly sample a small batch of samples of size SG from the playback buffer B;

[0076] S45.2, the target action calculated by the UAV transmitter is:

[0077]

[0078] S45.3, the target action calculated by the UAV jammer is:

[0079]

[0080] S45.4, calculate the target value y of the UAV transmitter A and the target value y of the UAV jammer J for:

[0081]

[0082] S45.5, by minimizing the loss, the network parameters of the Critic network and the attention network of the drone transmitter and the drone jammer are updated as follows:

[0083]

[0084] S45.6, if j is the time point of the policy update, then go to S46, otherwise, go to S47;

[0085] S46, using the gradient ascent method to update the Actor network of the drone transmitter and drone jammer is as follows:

[0086]

[0087] Gradually update the target network as follows:

[0088]

[0089] S47, ending the policy update cycle;

[0090] S48, obtain the optimal multi-UAV trajectory.

[0091] Through the above methods, this application establishes a drone covert secure communication scenario model assisted by a friendly drone jammer that emits non-Gaussian noise, with the goal of maximizing the average secure covert throughput of multiple users. Under the constraints of concealment and power limit, an optimization problem is established, and the optimization problem is converted into a multi-drone collaborative Markov decision process. The multi-drone trajectory is optimized using a combination of attention mechanism and standard multi-agent double-delay deep deterministic policy gradient, filling the gap in this field. The use of multi-agent deep reinforcement learning methods can effectively solve non-stationary problems, and the use of attention mechanisms can effectively capture key information and accelerate convergence, thereby improving the trajectory optimization performance of the algorithm. Compared with the currently proposed technologies, this application studies and explores the centralized decision-making problem in a multi-agent cooperative environment, emphasizing the importance of solving the centralized decision-making problem in a multi-agent cooperative environment in non-Gaussian noise-assisted drone covert secure transmission. Any drone covert secure transmission task involving non-Gaussian noise-assisted drones can be completed using the technical solution proposed in this application, which has better generalization ability and wider versatility.

[0092] In the second aspect, an embodiment of the present application proposes a non-Gaussian noise-assisted UAV covert communication system, the system comprising: a scenario model establishment module, used to establish a UAV covert secure communication scenario model assisted by a UAV jammer that emits non-Gaussian noise; an optimization problem establishment module, used to establish an optimization problem in the established model with the goal of maximizing the average secure covert throughput of multiple users, combined with concealment constraints and power limit constraints; a Markov conversion module, used to convert the optimization problem into a multi-UAV collaborative Markov decision process; a multi-UAV trajectory optimization module, used to optimize the multi-UAV trajectory for the converted multi-UAV collaborative Markov decision process, using a combination of attention mechanism and standard multi-agent double-delay deep deterministic policy gradient to obtain the optimal multi-UAV trajectory; a communication task execution module, used to instruct the UAV to perform the communication task based on the optimal multi-UAV trajectory.

[0093] In a third aspect, an embodiment of the present application proposes an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute a non-Gaussian noise-assisted drone covert communication method as described in the first aspect above.

[0094] In a fourth aspect, an embodiment of the present application proposes a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement a non-Gaussian noise-assisted drone covert communication method as described in the first aspect above.

[0095] It can be understood that the beneficial effects of the second to fourth aspects mentioned above can be found in the relevant description of the first aspect mentioned above, and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0096] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the related technologies, the drawings required for use in the embodiments of the present application or the related technical descriptions will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0097] Figure 1 is a flow chart of a non-Gaussian noise-assisted UAV covert communication method provided in one embodiment of the present application;

[0098] Figure 2 is a structural schematic diagram of a non-Gaussian noise-assisted UAV covert communication system provided in another embodiment of the present application;

[0099] Figure 3 It is a schematic diagram of the simulation experiment results of different algorithm convergence curves of a non-Gaussian noise-assisted drone covert security transmission system provided in another embodiment of the present application;

[0100] Figure 4 It is a structural schematic diagram of an electronic device provided in another embodiment of the present application. DETAILED DESCRIPTION

[0101] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the embodiments of the present application will be described in detail below in conjunction with the accompanying drawings. In the various embodiments of the present application, many technical details are proposed in order to make the reader better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical scheme claimed in the present application can also be implemented. The division of the following embodiments is only for the convenience of description, and the specific implementation mode of the present application should not constitute any limitation. The various embodiments can be combined with each other and referenced to each other under the premise of no contradiction.

[0102] An embodiment of the present application proposes a non-Gaussian noise-assisted UAV covert communication method, which is applied to an electronic device, wherein the electronic device can be a terminal or a server. In this embodiment and the following embodiments, the electronic device is described using a server as an example. The implementation details of the non-Gaussian noise-assisted UAV covert communication method proposed in this embodiment are described below. The following content is only for the convenience of understanding the implementation details provided, and is not necessary for the implementation of this solution. The specific process of the non-Gaussian noise-assisted UAV covert communication method proposed in this embodiment is as follows: Figure 1 As shown, including:

[0103] S1, establishes a UAV covert secure communication scenario model assisted by a UAV jammer emitting non-Gaussian noise.

[0104] In the specific implementation, the server first establishes a drone covert secure communication scenario model assisted by a drone jammer that emits non-Gaussian noise, and the drone jammer that emits non-Gaussian noise is considered to be friendly.

[0105] In one example, when the server establishes a drone covert secure communication scenario model assisted by a drone jammer that emits non-Gaussian noise, a drone covert secure communication scenario assisted by a drone jammer that emits non-Gaussian noise is considered. The drone transmitter acts as an aerial mobile base station and transmits signals to the assigned K users (also called legal users, and users not in the allocation are illegal users) in an environment where there are P eavesdroppers and a single monitor. The drone jammer keeps sending non-Gaussian noise while moving to protect the information transmission between the user and the drone transmitter from being eavesdropped and detected. In order to ensure the service quality of the assigned K users, the drone will optimize its own trajectory. The drone's trajectory is divided into N time slots of equal time length on the time axis. The drone maintains a constant altitude during the flight. The drone transmitter and the drone jammer are set at altitudes H and H respectively. a With H j In the above example, a and j represent the UAV transmitter and UAV jammer, respectively. The user, monitor, and eavesdropper are regarded as ground nodes. It is assumed that each UAV knows the location of the monitor, eavesdropper, and user, but does not know the location of other UAVs (i.e., the UAV transmitter and the UAV jammer do not know each other's location). In the same time slot, at most one user receives the signal from the UAV transmitter. The eavesdropper steals information when the user and the UAV transmitter are transmitting information. The monitor is responsible for monitoring the information transmission between the user and the UAV transmitter.

[0106] In one example, to consider adaptability, the transmission link between the drone transmitter and the user is regarded as a probabilistic LoS / NLoS channel link, and the path loss uses the probabilistic LoS / NLoS path loss model, which is expressed by the formula:

[0107]

[0108] Where PL(d,θ) represents the total path loss at distance d and elevation angle θ. Distance d is the straight-line distance between the UAV transmitter and the user, and elevation angle θ is the vertical angle between the UAV transmitter and the ground. represents the probability that the signal propagation path is a direct path at an elevation angle θ, τ and ζ are environmental parameters adjusted based on the environment, It represents the probability that the signal propagation path is a non-direct path at the elevation angle θ.

[0109] Therefore, for user k, the received signal can be expressed as:

[0110]

[0111] in, represents the signal received by user k on the i-th channel, P a[n] represents the transmission power of the UAV transmitter, PL(d ak ,θ a ) represents the path loss between the UAV transmitter and user k, d ak represents the straight-line distance between the UAV transmitter and user k, θ a represents the vertical angle between the UAV transmitter and the ground, χ a (i) represents the signal transmitted by the UAV transmitter, P j [n] represents the transmission power of the UAV jammer, PL(d jk ,θ j ) represents the path loss from the UAV jammer to user k, d jk represents the straight-line distance between the UAV jammer and user k, θ j represents the vertical angle between the UAV jammer and the ground, χ j (i) represents the non-Gaussian noise emitted by the UAV jammer, n k (i) represents the Gaussian white noise received by user k.

[0112] For the eavesdropper p, the received signal can be expressed as:

[0113]

[0114] in, represents the signal received by the eavesdropper p on the i-th channel, PL(d ap ,θ a ) represents the path loss between the drone transmitter and the eavesdropper p, d ap represents the straight-line distance between the drone transmitter and the eavesdropper p, PL(d jp ,θ j ) represents the path loss between the UAV jammer and the eavesdropper p, d jp represents the straight-line distance between the UAV jammer and the eavesdropper p, n p (i) represents the Gaussian white noise received by the eavesdropper p.

[0115] In the covert communication scenario, the main task of the monitor is to detect whether the drone has established an information transmission connection with the ground user. In order to make a decision, the monitor determines whether the drone transmitter is transmitting information based on the L received signals in each time slot. In the nth time slot, the signal received by the monitor can be expressed as:

[0116]

[0117] Among them, H 0 represents the null hypothesis that the UAV transmitter does not transmit information, H 1represents the alternative hypothesis of the UAV transmitter transmission information, PL(d jw ,θ j ) represents the path loss between the UAV jammer and the monitor, d jw represents the straight-line distance between the UAV jammer and the monitor, PL(d aw ,θ a ) represents the path loss between the UAV transmitter and the monitor, d aw represents the straight-line distance between the UAV transmitter and the monitor, n w (i) represents the Gaussian white noise received by the monitor.

[0118] Non-Gaussian noise refers to noise whose probability distribution deviates from Gaussian distribution. Unlike Gaussian noise, non-Gaussian noise is characterized by heavy-tailed distribution and impulse, which means that the noise may contain high-amplitude burst interference. This noise is more common in many practical communication systems, especially in fields such as wireless communication and radar. The non-Gaussian noise model can make it more difficult for eavesdroppers to separate our signals from mixed signals due to the two characteristics of heavy-tailed distribution and impulse. This embodiment uses the α-stable distribution model, which is more difficult to separate in the non-Gaussian noise model.

[0119] The α-stable distribution model can make it more difficult for eavesdroppers to separate our signals from mixed signals. The α-stable distribution has a heavy-tail characteristic, and its probability density function may be high in the central area, but it is usually not close to 1 in most areas. Since the α-stable distribution does not have a simple closed form, its characteristic function shows that the distribution has a large uncertainty and a wide range of influence, which makes it difficult for its probability density function to approach 1 over a large range. Gaussian noise has a uniform power spectral density and simple statistical characteristics, which makes it easier for eavesdroppers to obtain signals.

[0120] The probability density function of the α-stable distribution has no closed form, but can be expressed by the characteristic function as follows:

[0121]

[0122] Among them, α is the characteristic index, β is the skew parameter, γ is the scale parameter, and δ is the location parameter. When α=2, the distribution degenerates into a Gaussian distribution. And the probability density function of the α-stable distribution has a serious tailing property, and the smaller the pulse index α, the more serious the tailing property. Since the α-stable distribution noise has a heavy tail characteristic, its noise power P n It is affected by heavy tails and extreme values, which makes the signal-to-noise ratio of the signal after the matched filter expressed as follows:

[0123]

[0124] in, is the variance of α-stable distributed noise, which is usually high and unstable, especially when α is small. In the background of Gaussian noise, the matched filter can effectively separate the signal and obtain the optimal output signal-to-noise ratio. However, in the background of α-stable distributed noise, due to the heavy tail and extreme value characteristics of the noise, the performance of the matched filter is significantly reduced, and the output signal-to-noise ratio is much lower than that of Gaussian noise. The statistical characteristics of Gaussian noise make signal separation relatively simple and efficient; while the α-stable distributed noise increases the difficulty of signal separation due to its complex statistical characteristics and extreme values.

[0125] The heavy-tailed characteristics of non-Gaussian noise and the probability density function without a closed form make it difficult to apply traditional signal processing methods. Extreme value and high peak interference significantly affect the signal separation effect. Non-Gaussian noise Using non-Gaussian noise in communication systems can significantly improve the security and concealment of communication links, and increase the difficulty for eavesdroppers to separate and steal information. By using non-Gaussian noise, especially α-stable distribution noise, the anti-interference ability and information security of the communication system can be effectively improved, preventing eavesdroppers from obtaining useful information.

[0126] S2, in the established model, with the goal of maximizing the average secure concealed throughput of multiple users, an optimization problem is established by combining the concealment constraints and the power limit constraints.

[0127] In the specific implementation, after the server establishes a drone covert secure communication scenario model assisted by a drone jammer that emits non-Gaussian noise, it can establish an optimization problem in the established model with the goal of maximizing the average secure covert throughput of multiple users, combining the concealment constraints and the power limit constraints.

[0128] In one example, suppose the monitor's decision is divided into supporting H 0 D 0 and support H 1 D 1 There are two types, assuming that the false alarm probability and missed detection probability are P FA (t) and P MD (t) represents the total detection error probability ξ(t) is defined as ξ(t) = P FA (t)+P MD (t), the goal of the drone is to make ξ(t) in each time slot as close to 1 as possible, which can be expressed as:

[0129] ξ(t)=P FA (t)+P MD (t)≥1-ε

[0130] Among them, ε is a preset positive decimal close to 0 to ensure the confidentiality of communication.

[0131] In H0 and H 1 Under the assumption that The likelihood functions are expressed as:

[0132]

[0133] Among them, CN(·) represents a complex function, Represents the variance of the signal received by the monitor.

[0134] Assuming that the monitor knows the index information of the signal, the likelihood ratio of the best detection is expressed as:

[0135]

[0136] in, represents the likelihood ratio for the best detection.

[0137] exist Based on this, the minimum detection error probability ξ can be derived * , however, due to the incomplete gamma function involved in ξ * This brings difficulties to further analysis. Therefore, we turn to using KL divergence to derive the lower limit of the minimum detection error probability. The lower limit of the minimum detection error probability is expressed as:

[0138]

[0139] Among them, ξ * [n] represents the lower limit of the minimum detection error probability, D 01 [n]≤2ε 2 represents the constraint on the detection probability. When the constraint on the detection probability is satisfied, the concealment constraint will also be satisfied.

[0140] D 01 [n] is expressed by the formula:

[0141]

[0142] Here, I represents the identity matrix. Thus, an effective method for evaluating the covert communication effect is provided, which ensures the concealment of UAV communication and simplifies the analysis of the monitor's detection behavior.

[0143] Based on the constraints of detection probability and concealment, the server can optimize the flight trajectory, transmission power and interference power of the UAV transmitter and UAV jammer to maximize the average secure and covert throughput of multiple users. The UAV transmitter dynamically adjusts its position to provide high-quality services, and the UAV jammer adjusts its position to reduce the link quality of the eavesdropper and monitor, thereby solving the optimization problem.

[0144] In an example, the optimization problem established can be expressed by the following formula:

[0145]

[0146] in, represents the average secure concealed throughput of multiple users, C1 represents the concealment constraint, C2 represents the power constraint of the UAV transmitter, represents the maximum transmission power of the UAV transmitter, C3 represents the power constraint of the UAV jammer, represents the maximum transmission power of the UAV jammer, C4 represents the flight speed constraint of the UAV, q[n] and q[n+1] represent the positions of the UAV at sampling points n and n+1 respectively, and V max represents the maximum flight speed of the drone, T represents the time required for the drone to fly from q[n] to q[n+1], C5 represents the flight range constraint of the drone, and R D It represents the scene space corresponding to the established model. It is worth noting that C2 and C3 are determined by the hardware and energy limitations of the UAV transmitter and the UAV jammer.

[0147] S3, converts the optimization problem into a multi-UAV collaborative Markov decision process.

[0148] In a specific implementation, after the server establishes the optimization problem, it can convert the optimization problem into a multi-UAV collaborative Markov decision process.

[0149] In one example, when the server converts the optimization problem into a multi-UAV collaborative Markov decision process, it first regards the UAV transmitter and the UAV jammer as intelligent agents to form a partially observable state space, and describes the optimization problem by a quintuple (S, A, Reward, PST, γ), where S represents the state space, A represents the action space, Reward represents the reward function, PST represents the state transition probability, and γ represents the discount factor.

[0150] The state space S is defined as the current horizontal position of the UAV transmitter and the current horizontal position of the drone jammer

[0151] The action space is defined as the actions of the UAV transmitter and the actions of the drone jammer For the UAV transmitter, the action space includes the speed in the x-axis and y-axis directions and the magnitude of the transmission power. The action space of the UAV jammer includes the speed in the x-axis and y-axis directions and the magnitude of the jamming power.

[0152] In the UAV collaborative environment, the decision-making process involves each agent receiving an immediate reward based on the current state, the action performed, and the next state to be transferred to, and considering the termination signal. The reward mechanism includes penalties for the flight range, concealment, and distance of the UAV. The composition of the reward and penalty terms is as follows:

[0153] Secure and hidden throughput rewards, Incentivize drones to increase security covert throughput.

[0154] Boundary penalty, p b =1, if q[n]>R D ,else0,is applied when the drone exceeds the predetermined boundary to ensure that the drone operates within the specified area.

[0155] Hidden punishment, p ∈ =1, if D 01 [n]>∈ 2 ,else0,is applied when the minimum detection error probability of the monitor is lower than the threshold to ensure the concealment of communication.

[0156] Distance penalty,

[0157]

[0158] Among them, the distance penalty and They are respectively used to motivate drone transmitters and drone jammers to fly around targets, encourage drone transmitters to fly around users, and encourage drone jammers to fly around eavesdroppers and monitors.

[0159] The overall reward function for the drone transmitter and the drone jammer is expressed as:

[0160]

[0161] Among them, α and β are coefficients that weigh the impact of different rewards and penalties, Ω 1 and Ω 2 is the weight of the corresponding penalty item.

[0162] In a UAV collaborative environment, the decisions and actions of each UAV will affect the overall system state. The state transition function describes the probability of the system reaching the next state given the current state and the UAV action, which is expressed by the formula:

[0163] In this collaborative environment, there is no clear endpoint and a smaller discount factor γ will not be set. The goal of the drone is not to reach a certain location as quickly as possible, but to maximize the total communication capacity during the flight. Therefore, the choice of the discount factor γ will reflect this long-term performance indicator rather than the short-term fastest arrival time.

[0164] S4, for the converted multi-UAV collaborative Markov decision process, uses the combination of attention mechanism and standard multi-agent double-delay deep deterministic policy gradient to optimize the multi-UAV trajectory and obtain the optimal multi-UAV trajectory.

[0165] In the specific implementation, the server optimizes the multi-UAV trajectory for the converted multi-UAV cooperative Markov decision process using a combination of attention mechanism and standard multi-agent double-delay deep deterministic policy gradient to obtain the optimal multi-UAV trajectory, which can be achieved through the following steps:

[0166] S41, initialize the network parameters of the Actor network, Critic network and attention network of the drone transmitter

[0167] S42, initialize the network parameters of the Actor network, Critic network and attention network of the drone jammer

[0168] S43, setting the network parameters of the target network to be the same as the network parameters of the main network, that is,

[0169] S44: If the convergence condition is met, go to S48; otherwise, go to S44.1.

[0170] S44.1, UAV transmitter and UAV jammer observe their own status respectively and And select actions respectively and

[0171] S44.2, Execution Action In the environment.

[0172] S44.3, observe the next state The reward value r and the completion signal done are used to clarify s n+1 Whether it is a terminated state.

[0173] S44.4, Storage In playback buffer B.

[0174] S44.5, if the drone flies out of the boundary, does not meet the concealment constraint, or the number of time slots reaches the upper limit, reset the environment state.

[0175] S44.6, when the preset number of updates is reached, set j=1 and enter S45, otherwise, enter S47.

[0176] S45, if j≤k, then enter, S45.1, otherwise, enter S47.

[0177] S45.1, randomly sample a mini-batch of size SG from the playback buffer B.

[0178] S45.2, the target action calculated by the UAV transmitter is:

[0179]

[0180] S45.3, the target action calculated by the UAV jammer is:

[0181]

[0182] S45.4, calculate the target value y of the UAV transmitter A and the target value y of the UAV jammer J for:

[0183]

[0184] S45.5, by minimizing the loss, the network parameters of the Critic network and the attention network of the drone transmitter and the drone jammer are updated as follows:

[0185]

[0186] S45.6, if j is the time point of the policy update, proceed to S46, otherwise, proceed to S47.

[0187] S46, using the gradient ascent method to update the Actor network of the drone transmitter and drone jammer is as follows:

[0188]

[0189] Gradually update the target network as follows:

[0190]

[0191] S47, ending the policy update cycle;

[0192] S48, obtain the optimal multi-UAV trajectory.

[0193] S5, instructs the UAV to perform the communication task based on the optimal multi-UAV trajectory.

[0194] In the specific implementation, after the server obtains the optimal multi-UAV trajectory, it can instruct the UAV transmitter and the UAV jammer to perform communication tasks based on the optimal multi-UAV trajectory.

[0195] In this embodiment, a UAV covert secure communication scenario model assisted by a friendly UAV jammer emitting non-Gaussian noise is established. With the goal of maximizing the average secure covert throughput of multiple users, an optimization problem is established under the constraints of concealment and power limit, and the optimization problem is converted into a multi-UAV collaborative Markov decision process. The multi-UAV trajectory is optimized using a combination of attention mechanism and standard multi-agent double-delay deep deterministic policy gradient, which fills the gap in UAV covert communication assisted by non-Gaussian noise. The use of multi-agent deep reinforcement learning methods can effectively solve non-stationary problems, and the use of attention mechanisms can effectively capture key information and accelerate convergence, thereby improving the trajectory optimization performance of the algorithm. Compared with the currently proposed technologies, this embodiment studies and explores the centralized decision-making problem in a multi-agent cooperative environment, and emphasizes the importance of solving the centralized decision-making problem in a multi-agent cooperative environment in non-Gaussian noise-assisted UAV covert secure transmission. Any UAV covert secure transmission task involving non-Gaussian noise assistance can be completed using the technical solution of this embodiment, which has better generalization ability and wider versatility.

[0196] The step division of the above methods is only for clear description. When implemented, they can be combined into one step or some steps can be split and decomposed into multiple steps. As long as they include the same logical relationship, they are all within the scope of protection of this application; adding insignificant modifications to the algorithm or process or introducing insignificant designs without changing the core design of the algorithm and process are all within the scope of protection of this application.

[0197] Another embodiment of the present application proposes a non-Gaussian noise-assisted UAV covert communication system. The implementation details of the non-Gaussian noise-assisted UAV covert communication system proposed in this embodiment are specifically described below. The following content is only for the convenience of understanding the implementation details provided, and is not necessary for the implementation of this example. Figure 2 It is a structural diagram of a non-Gaussian noise-assisted UAV covert communication system proposed in this embodiment, which includes: a scene model establishment module 601, an optimization problem establishment module 602, a Markov conversion module 603, a multi-UAV trajectory optimization module 604 and a communication task execution module 605.

[0198] The scenario model building module 601 is used to build a drone covert secure communication scenario model assisted by a drone jammer that emits non-Gaussian noise.

[0199] The optimization problem establishment module 602 is used to establish an optimization problem in the established model with the goal of maximizing the average secure concealed throughput of multiple users, combined with concealment constraints and power limit constraints.

[0200] The Markov conversion module 603 is used to convert the optimization problem into a multi-UAV collaborative Markov decision process.

[0201] The multi-UAV trajectory optimization module 604 is used to optimize the multi-UAV trajectory based on the converted multi-UAV collaborative Markov decision process, using a combination of attention mechanism and standard multi-agent double-delay deep deterministic policy gradient to obtain the optimal multi-UAV trajectory.

[0202] The communication task execution module 605 is used to instruct the UAV to execute the communication task based on the optimal multi-UAV trajectory.

[0203] It is worth mentioning that all modules involved in this embodiment are logic modules. In practical applications, a logic unit can be a physical unit, a part of a physical unit, or a combination of multiple physical units. In addition, in order to highlight the innovative part of this application, this embodiment does not introduce units that are not closely related to solving the technical problems proposed by this application, but this does not mean that there are no other units in this embodiment.

[0204] It is not difficult to find that this embodiment is a system embodiment corresponding to the above method embodiment, and this embodiment can be implemented in conjunction with the above method embodiment. The relevant technical details and technical effects mentioned in the above embodiments are still valid in this embodiment, and in order to reduce repetition, they are not repeated here. Accordingly, the relevant technical details mentioned in this embodiment can also be applied in the above embodiments.

[0205] In another embodiment, in order to evaluate the performance of the non-Gaussian noise-assisted UAV covert communication method and system proposed in this application, we conducted relevant simulation experiments. In the simulation experiment, a non-Gaussian noise-assisted UAV covert security transmission system is considered. The specific parameters of the simulation experiment are as follows: Consider a UAV communication system consisting of three users, and assume that there are two eavesdroppers trying to intercept the communication content, and the concealment constraint ∈ is set to 0.05. The maximum speed of the UAV transmitter and the UAV jammer are both set to To simulate a fast-moving aerial environment. The optimization algorithm used in training is the adam algorithm, the playback buffer pool is set to 10000, the discount factor is set to 0.99, the learning rate is set to 0.001, and the noise exploration space is set to 5%. In the reward function, Ω 1 Set to 1,Ω 2Set to 100, the reward coefficient α is set to 2, and β is set to 20. The range boundary of the drone's flight is set from -100 to 600 on the x-axis and y-axis, which indicates the flight area limit of the drone on these two axes. The noise is set to 5% of the action space;

[0206] Figure 3 The convergence curves of different algorithms are shown. Figure 3 It can be seen that the combination of attention mechanism and standard multi-agent double-delayed deep deterministic policy gradient (i.e. AM-MATD3) is significantly better than other algorithms in both learning speed and final benefits, especially in the initial stage, showing a faster learning speed. As the training progresses, it also shows a stable reward growth and smaller fluctuations, which reflects the stability of its learning process. This fast and stable convergence shows that AM-MATD3 can effectively learn effective strategies in the environment and optimize these strategies to obtain higher long-term returns. In a multi-agent environment, collaboration between agents is the key to improving overall performance. The AM-MATD3 algorithm introduces an attention mechanism to allow each agent to more effectively learn how to interact and collaborate with other agents in the face of dynamic changes within the group. This is in stark contrast to the single-agent TD3 algorithm, where agents are trained independently and cannot capture the behavioral strategies of other agents. Therefore, in a multi-agent setting, the performance of single-agent TD3 is limited and cannot achieve the same effect as collaborative learning. The attention mechanism strengthens the interaction between agents, and this interaction enables the AM-MATD3 algorithm to achieve excellent performance in complex multi-agent environments. By introducing the attention mechanism, each agent can pay more attention to environmental factors and the behaviors of other agents that are critical to the success of the strategy. This centralized learning method is very valuable in a multi-agent environment, which can promote collaboration and speed up the learning process. Therefore, the trajectory optimization performance of the algorithm proposed in this application is better than the currently proposed algorithm methods, and the simulation experiment verifies the superiority of the algorithm proposed in this application.

[0207] Another embodiment of the present application provides an electronic device, the structure of which can be as follows: Figure 4 As shown, it includes: at least one processor 701; and a memory 702 that is communicatively connected to the at least one processor 701; wherein the memory 702 stores instructions that can be executed by the at least one processor 701, and the instructions are executed by the at least one processor 701 so that the at least one processor 701 can execute a non-Gaussian noise-assisted UAV covert communication method described in the above-mentioned method embodiments.

[0208] Among them, the memory and the processor can be connected in a bus manner, and the bus can include any number of interconnected buses and bridges, and the bus connects various circuits of one or more processors and memories together. The bus can also connect various other circuits such as peripherals, voltage regulators, and power management circuits together, which are all well known in the art and will not be repeated in this article. The bus interface provides an interface between the bus and the transceiver. The transceiver can be one element or multiple elements, such as multiple receivers and transmitters, providing a unit for communicating with various other devices on a transmission medium. The data processed by the processor is transmitted on the wireless medium through the antenna, and further, the antenna also receives the data and transmits the data to the processor.

[0209] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. Memory can be used to store data used by the processor when performing operations.

[0210] Another embodiment of the present application relates to a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement the non-Gaussian noise-assisted drone covert communication method described in the above method embodiments.

[0211] That is, those skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a program, and the program is stored in a storage medium, including a number of instructions to enable a device (which can be a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, ROM (Read-Only Memory), RAM (Random Access Memory), disk or optical disk and other media that can store program codes.

[0212] Those skilled in the art will appreciate that the above embodiments are specific embodiments for implementing the present application, and in actual applications, various changes may be made thereto in form and detail without departing from the spirit and scope of the present application.

Claims

1. A non-Gaussian noise-assisted UAV covert communication method, characterized in that: include: S1, establishes a UAV covert secure communication scenario model assisted by a UAV jammer emitting non-Gaussian noise; S2, in the established model, with the goal of maximizing the average secure concealed throughput of multiple users, combined with the concealment constraint and the power limit constraint, an optimization problem is established; S3, converts the optimization problem into a multi-UAV collaborative Markov decision process; S4, for the converted multi-UAV cooperative Markov decision process, uses the combined attention mechanism and the standard multi-agent double-delay deep deterministic policy gradient to optimize the multi-UAV trajectory and obtain the optimal multi-UAV trajectory; S5, instructs the UAV to perform the communication task based on the optimal multi-UAV trajectory.

2. The non-Gaussian noise-assisted UAV covert communication method according to claim 1 is characterized in that: A UAV covert secure communication scenario model assisted by a UAV jammer emitting non-Gaussian noise is established, including: Consider a drone covert secure communication scenario assisted by a drone jammer that emits non-Gaussian noise. The drone transmitter acts as an aerial mobile base station and transmits signals to K assigned users in an environment where there are P eavesdroppers and a single monitor. The drone jammer keeps sending non-Gaussian noise while moving to protect the information transmission between the user and the drone transmitter from being eavesdropped and detected. To ensure the service quality of the K assigned users, the drone will optimize its own trajectory. The drone's trajectory is divided into N time slots of equal length on the time axis. The drone maintains a constant altitude during the flight. The drone transmitter and drone jammer are set at altitudes H and H respectively. a With H j In the above figure, a and j represent the UAV transmitter and UAV jammer respectively, and the user, monitor, and eavesdropper are regarded as ground nodes. It is assumed that each UAV knows the location of the monitor, eavesdropper, and user, but does not know the location of other UAVs. In the same time slot, at most one user receives the signal from the drone transmitter. The eavesdropper steals information when information is transmitted between the user and the drone transmitter, and the monitor is responsible for monitoring the information transmission between the user and the drone transmitter.

3. The non-Gaussian noise-assisted UAV covert communication method according to claim 2 is characterized in that: In order to consider adaptability, the transmission link between the drone transmitter and the user is regarded as a probabilistic LoS / NLoS channel link, and the path loss uses the probabilistic LoS / NLoS path loss model, which is expressed by the formula: Where PL(d,θ) represents the total path loss at distance d and elevation angle θ. Distance d is the straight-line distance between the UAV transmitter and the user, and elevation angle θ is the vertical angle between the UAV transmitter and the ground. represents the probability that the signal propagation path is a direct path at an elevation angle θ, τ and ζ are environmental parameters adjusted based on the environment, represents the probability that the signal propagation path is a non-direct path at the elevation angle θ; For user k, the received signal is expressed as: in, represents the signal received by user k on the i-th channel, P a [n] represents the transmission power of the UAV transmitter, PL(d ak ,θ a ) represents the path loss between the UAV transmitter and user k, d ak represents the straight-line distance between the UAV transmitter and user k, θ a represents the vertical angle between the UAV transmitter and the ground, χ a (i) represents the signal transmitted by the UAV transmitter, P j [n] represents the transmission power of the UAV jammer, PL(d jk ,θ j ) represents the path loss from the UAV jammer to user k, d jk represents the straight-line distance between the UAV jammer and user k, θ j represents the vertical angle between the UAV jammer and the ground, χ j (i) represents the non-Gaussian noise emitted by the UAV jammer, n k (i) represents the Gaussian white noise received by user k; For the eavesdropper p, the received signal is expressed as: in, represents the signal received by the eavesdropper p on the i-th channel, PL(d ap ,θ a ) represents the path loss between the drone transmitter and the eavesdropper p, d ap represents the straight-line distance between the drone transmitter and the eavesdropper p, PL(d jp ,θ j ) represents the path loss between the UAV jammer and the eavesdropper p, d jp represents the straight-line distance between the UAV jammer and the eavesdropper p, n p (i) represents the Gaussian white noise received by the eavesdropper p; The monitor determines whether the drone transmitter is transmitting information based on the L received signals in each time slot. The signal received by the monitor is expressed as: Among them, H0 represents the null hypothesis that the UAV transmitter does not transmit information, H1 represents the alternative hypothesis that the UAV transmitter transmits information, and PL(d jw ,θ j ) represents the path loss between the UAV jammer and the monitor, d jw represents the straight-line distance between the UAV jammer and the monitor, PL(d aw ,θ a ) represents the path loss between the UAV transmitter and the monitor, d aw represents the straight-line distance between the UAV transmitter and the monitor, n w (i) represents the Gaussian white noise received by the monitor.

4. The non-Gaussian noise-assisted UAV covert communication method according to claim 3 is characterized in that: In the established model, with the goal of maximizing the average secure concealed throughput of multiple users, combined with the concealment constraints and power limit constraints, an optimization problem is established, including: Assume that the monitor's decision is divided into two types: D0 supporting H0 and D1 supporting H1. Assume that the false alarm probability and missed detection probability are represented by P FA (t) and P MD (t) represents the total detection error probability ξ(t) is defined as ξ(t) = P FA (t)+P MD (t), the goal of the drone is to make ξ(t) in each time slot as close to 1 as possible, which can be expressed as: ξ(t)=P FA (t)+P MD (t)≥1-ε Among them, ε is a preset positive decimal close to 0 to ensure the confidentiality of communication; Under the assumptions of H0 and H1, The likelihood functions are expressed as: Among them, CN(·) represents a complex function, represents the variance of the signal received by the monitor; Assuming that the monitor knows the index information of the signal, the likelihood ratio of the best detection is expressed as: in, represents the likelihood ratio of the best detection; The KL divergence is used to derive the lower limit of the minimum detection error probability. The lower limit of the minimum detection error probability is expressed as: Among them, ξ * [n] represents the lower limit of the minimum detection error probability, D 01 [n]≤2ε 2 represents the constraint of detection probability. When the constraint of detection probability is satisfied, the concealment constraint will also be satisfied. 01 [n] is expressed by the formula: Where I represents the identity matrix; On the basis of the constraints of detection probability and concealment, the flight trajectory, transmission power and interference power of UAV transmitters and UAV jammers are optimized to maximize the average secure and covert throughput of multiple users. The UAV transmitter dynamically adjusts its position to provide high-quality services, and the UAV jammer adjusts its position to reduce the link quality of eavesdroppers and monitors, thus obtaining the optimization problem.

5. The non-Gaussian noise-assisted UAV covert communication method according to claim 4 is characterized in that: The optimization problem established is expressed by the following formula: in, represents the average secure concealed throughput of multiple users, C1 represents the concealment constraint, C2 represents the power constraint of the UAV transmitter, represents the maximum transmission power of the UAV transmitter, C3 represents the power constraint of the UAV jammer, represents the maximum transmission power of the UAV jammer, C4 represents the flight speed constraint of the UAV, q[n] and q[n+1] represent the positions of the UAV at sampling points n and n+1 respectively, and V max represents the maximum flight speed of the drone, T represents the time required for the drone to fly from q[n] to q[n+1], C5 represents the flight range constraint of the drone, and B D Indicates the scene space corresponding to the established model.

6. The non-Gaussian noise-assisted UAV covert communication method according to claim 5, characterized in that: The optimization problem is converted into a multi-UAV cooperative Markov decision process, including: The UAV transmitter and UAV jammer are regarded as intelligent agents, forming a partially observable state space. The optimization problem is described by a five-tuple (S, A, Reward, PST, γ), where S represents the state space, A represents the action space, Reward represents the reward function, PST represents the state transition probability, and γ represents the discount factor. The state space S is defined as the current horizontal position of the UAV transmitter and the current horizontal position S of the UAV jammer n J ={x j (n),y j (n)}; The action space is defined as the actions of the UAV transmitter and the actions of the drone jammer For the UAV transmitter, the action space includes the speed in the x-axis and y-axis directions and the magnitude of the transmission power. The action space of the UAV jammer includes the speed in the x-axis and y-axis directions and the magnitude of the jamming power. In the UAV collaborative environment, the decision-making process involves each agent receiving an immediate reward based on the current state, the action performed, and the next state to be transferred to, and considering the termination signal. The reward mechanism includes penalties for the flight range, concealment, and distance of the UAV. The composition of the reward and penalty terms is as follows: Secure and hidden throughput rewards, Incentivize drones to increase safe and covert throughput; Boundary penalty, p b =1, ifq[n]>R D ,else0, is applied when the drone exceeds the predetermined boundary to ensure that the drone operates within the specified area; Hidden punishment, p ∈ =1, if D 01 [n]>∈ 2 ,ekse0, is applied when the minimum detection error probability of the monitor is lower than the threshold to ensure the concealment of communication; Distance penalty, Among them, the distance penalty and They are used to encourage drone transmitters and drone jammers to fly around targets, encourage drone transmitters to fly around users, and encourage drone jammers to fly around eavesdroppers and monitors. The overall reward function for the drone transmitter and the drone jammer is expressed as: Among them, α and β are coefficients that weigh the impact of different rewards and penalties, and Ω1 and Ω2 are the weights of the corresponding penalty terms; In a UAV collaborative environment, the decisions and actions of each UAV will affect the overall system state. The state transition function describes the probability of the system reaching the next state given the current state and the UAV action, which is expressed by the formula: In this collaborative environment, there is no clear endpoint and the goal of the UAVs is to maximize the total communication capacity during the flight. The choice of the discount factor γ will reflect this long-term performance indicator.

7. The non-Gaussian noise-assisted UAV covert communication method according to claim 6, characterized in that: For the converted multi-UAV cooperative Markov decision process, the multi-UAV trajectory is optimized by combining the attention mechanism and the standard multi-agent double-delay deep deterministic policy gradient to obtain the optimal multi-UAV trajectory, including: S41, initialize the network parameters of the Actor network, Critic network and attention network of the drone transmitter S42, initialize the network parameters of the Actor network, Critic network and attention network of the drone jammer S43, setting the network parameters of the target network to be the same as the network parameters of the main network, that is, S44, if the convergence condition is met, go to S48, otherwise go to S44.1; S44.1, UAV transmitter and UAV jammer observe their own status respectively and And select actions respectively and S44.2, Execution Action in the environment; S44.3, observe the next state The reward value r and the completion signal done are used to clarify s n+1 Whether it is a termination state; S44.4, Storage In playback buffer B; S44.5, if the drone flies out of the boundary, does not meet the concealment constraint, or the number of time slots reaches the upper limit, reset the environment state; S44.6, when the preset number of updates is reached, set j=1 and proceed to S45, otherwise, proceed to S47; S45, if j≤k, then enter,S45.1, otherwise, enter S47; S45.1, randomly sample a small batch of samples of size SG from the playback buffer B; S45.2, the target action calculated by the UAV transmitter is: S45.3, the target action calculated by the UAV jammer is: S45.4, calculate the target value y of the UAV transmitter A and the target value y of the UAV jammer J for: S45.5, by minimizing the loss, the network parameters of the Critic network and the attention network of the drone transmitter and the drone jammer are updated as follows: S45.6, if j is the time point of the policy update, then go to S46, otherwise, go to S47; S46, using the gradient ascent method to update the Actor network of the drone transmitter and drone jammer is as follows: Gradually update the target network as follows: S47, ending the policy update cycle; S48, obtain the optimal multi-UAV trajectory.

8. A non-Gaussian noise-assisted UAV covert communication system, characterized in that: include: A scenario model building module, used to build a UAV covert secure communication scenario model assisted by a UAV jammer emitting non-Gaussian noise; An optimization problem establishment module is used to establish an optimization problem in the established model with the goal of maximizing the average secure concealed throughput of multiple users, combined with concealment constraints and power limit constraints; Markov transformation module, used to transform the optimization problem into a multi-UAV collaborative Markov decision process; The multi-UAV trajectory optimization module is used to optimize the multi-UAV trajectory based on the converted multi-UAV collaborative Markov decision process, using the combined attention mechanism and the standard multi-agent double-delay deep deterministic policy gradient to obtain the optimal multi-UAV trajectory; The communication task execution module is used to instruct the UAV to perform the communication task based on the optimal multi-UAV trajectory.

9. An electronic device, characterized in that: include: at least one processor; and, a memory communicatively coupled to the at least one processor; Wherein, the memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute the non-Gaussian noise-assisted drone covert communication method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, it is capable of implementing the non-Gaussian noise-assisted drone covert communication method as described in any one of claims 1 to 7.

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