Multi-access-point covert communication federal optimization method for UAV-RIS system

Abstract

The invention discloses a multi-access-point covert communication federal optimization method for a UAV-RIS system. The multi-access-point covert communication federal optimization method comprises the following steps: (1) modeling aiming at UAV-RIS federal learning edge calculation; (2) modeling aiming at the UAV motion trail; (3) modeling is carried out for a UAV-RIS auxiliary hidden transmission channel; (4) formulating the problem; (5) decomposing non-convex problem form transformation and sub-problems; (6) carrying out splitting and form conversion on the sub-problems; (7) designing a dynamic cross optimization algorithm; according to the method, the covert communication federal learning has relatively high concealment and relatively high reliability.

Description

Technical Field

[0001] The present invention relates to the field of communication engineering technology, and in particular to a multi-access point covert communication federation optimization method for a UAV-RIS system. Background Art

[0002] With the rapid development of artificial intelligence and wireless communication technologies, Federated Learning (FL) has attracted widespread attention because it can achieve distributed model training while protecting data privacy. Federated learning calculates model gradients locally on user devices and uploads them to the server for model aggregation, effectively avoiding the privacy leakage risks caused by large-scale data transmission in traditional centralized training. However, frequent signal transmission during model aggregation may expose the existence and behavior patterns of user devices, thereby threatening the communication concealment and data security of the system.

[0003] As a key technology to improve communication privacy protection, covert communication achieves the concealment of communication behavior by disguising signal transmission in interference noise. However, in existing wireless communication systems, covert communication usually relies on transmission between fixed base stations or user devices, which is difficult to adapt to complex and dynamic scenario requirements, such as multi-user device distribution, physical isolation between base stations and users, etc. In addition, in federated learning, multiple devices participate in model training at the same time, which puts higher requirements on signal concealment and transmission efficiency. Existing covert communication technology is difficult to fully meet this demand. Unmanned Aerial Vehicle (UAV) has unique advantages in supporting complex communication scenarios due to its high flexibility and dynamic deployability. Combined with Reconfigurable Intelligent Surface (RIS) technology, UAV can optimize and enhance communication links by precisely controlling the phase and power of reflected signals. However, the covert transmission of federated learning models in the UAV-RIS system still faces the following technical challenges, including how to effectively optimize the transmission power of user equipment, the reflection parameters of RIS, the signal transmission path for multiple devices to access the UAV-RIS system, and the selection of user groups participating in federated learning, so as to improve the reliability and concealment performance of covert communication. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a multi-access point covert communication federation optimization method for UAV-RIS system, which realizes efficient covert transmission of model convergence signal by jointly optimizing communication resource allocation, reflection signal control, UAV flight trajectory planning and covert strategy design, so as to solve the problems existing in the background technology.

[0005] Technical solution: The multi-access point covert communication federation optimization method for a UAV-RIS system described in the present invention comprises the following steps: (1) Modeling UAV-RIS federated learning edge computing; (2) Modeling the UAV motion trajectory; (3) Modeling the channel for UAV-RIS-assisted covert transmission; (4) Set the maximum number of selected UEs and jointly design the UAV trajectory, UE power, base station beamforming, UAV-RIS reflection amplitude and phase offset to formulate the problem; (5) Decomposition of non-convex problems into transformations and sub-problems; (6) Split the sub-problems and transform their forms; (7) Design a dynamic cross optimization algorithm.

[0006] Furthermore, step (1) is specifically as follows: establish an edge computing model based on the assistance of UAV-RIS for training the global model of federated learning; use the channel gain and reflection matrix of UAV-RIS to optimize signal reception, calculate the mean square error MSE of the objective function, and use the mean square error as the performance indicator of the aggregation of the global model of federated learning; Furthermore, in step (2), the trajectory is represented by three-dimensional coordinates, including x, y, and z axis coordinates; and limits are imposed on the maximum flight distance, minimum flight altitude, maximum flight speed, and accumulated flight time of the drone.

[0007] Furthermore, in step (3), the detection performance is characterized based on the false alarm rate and missed detection rate, and the KL divergence is used as a concealment measurement indicator.

[0008] Furthermore, in step (4), the constraints include: concealment constraint, reflection amplitude and phase offset range, and maximum transmission power.

[0009] Furthermore, in step (5), the MSE constraint is converted into the form of auxiliary variables, and the auxiliary variables are introduced using the interior point method in convex optimization, so that the solution of the optimal set of the original problem is transformed into the solution of a subset of the original solution; the original problem is decomposed into three sub-problems: trajectory optimization problem, hidden user equipment optimization selection problem, and hidden user equipment maximization transmission rate problem.

[0010] Furthermore, in step (6), the trajectory optimization problem is a separate problem, which independently optimizes the UAV trajectory and constrains the flight distance and altitude; the covert user device selection problem and the covert user device transmission rate maximization problem are a coupled problem that are split and solved; the convex substitution method is used in the device selection problem to replace the non-convex sparse objective function with a 1 norm to solve the user device priority; the covert transmission rate maximization problem adopts a bisection method to select the maximum set of covert user devices and optimize their transmission power and MSE; through convex recombination, matrix lifting, rank-one constraint processing and differential convex function regularization terms, the sub-problems are further decomposed into differential convex function forms.

[0011] Furthermore, step (7) includes the following steps: (71) Initialize communication parameters, including channel gain, RIS initial phase point, and preset threshold. UAV trajectory optimization parameters include: initial position, end position, maximum running time, and maximum speed; (72) Covert user equipment selection and priority calculation and UAV trajectory joint optimization; (73) Solving the maximum hidden user device set that minimizes MSE, including sorting the potential device set in ascending order, calculating the feasible user device set using a binary search method, and then solving the sub-problem; (74) Algorithm output: includes optimized hidden user equipment, optimized UAV trajectory and hidden transmission parameters.

[0012] An electronic device described in the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, it implements any one of the multi-access point covert communication federation optimization methods for a UAV-RIS system.

[0013] A storage medium described in the present invention stores a computer program, and when the computer program is executed by a processor, it implements any one of the multi-access point covert communication federation optimization methods for a UAV-RIS system.

[0014] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages: the covert signal transmission method of federated learning using UAV combined with RIS is used to reduce the physical isolation limitations of long-distance edge computing, and the covert transmission method is used to make the model aggregation process of federated learning undetectable; the present invention models and analyzes the target scene, designs a set of optimization processes and methods, disassembles and transforms the original complex problem, and finally designs a set of dynamic cross-optimization algorithms to optimize the system, including the flight trajectory of UAV, the covert user equipment selection strategy, and the transmission power of the equipment, the reflection parameters of RIS and many other parameters. The proposed method significantly improves the concealment and reliability of covert communication federated learning, and the proposed cross-optimization algorithm can be extended to a class of UAV covert communication federated learning scenarios. In summary, the multi-access point covert communication federated optimization method for the UAV-RIS system of the present invention can make the covert communication federated learning have the advantages of strong concealment and high reliability, and the proposed construction and analysis methods are highly universal. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is the application scenario of the present invention; Figure 2 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0016] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0017] The embodiment of the present invention provides a multi-access point covert communication federation optimization method for a UAV-RIS system, wherein the target scenario is as follows: Figure 1 The specific steps are as shown in Figure 2 As shown, the following steps are included: S1. UAV-RIS Federated Learning Edge Computing Modeling In this paper, a UAV-UAV-RIS-assisted edge computing model aggregation method is considered for training the global model of the federated learning system. The UAV-RIS-based edge computing method is similar to the uplink NOMA technology, which aims to effectively promote model aggregation from distributed user devices. , and denote the channel gains from user equipment i to the base station, from user equipment to UAV-RIS, and from UAV-RIS to the base station, respectively. It is assumed that the channel condition is flat and changes slowly within a transmission time slot. In addition, since there are many channel estimation schemes for UAV-RIS-assisted wireless transmission, perfect CSI (channel state information) is available. represents the diagonal reflection matrix of UAV-RIS, where represents the reflection amplitude, represents the phase offset of the nth element of UAV-RIS, Through the reflected signal of UAV-RIS, the signal received by the base station can be expressed as: (1) in, represents the transmission power of user equipment i, n represents Gaussian white noise, satisfying Aggregate beamforming at the base station After that, the objective function before post-processing is estimated as: (2) in represents the parameter used for denoising. Therefore, the global aggregation model of the base station can be obtained through the post-preprocessing function. In order to verify the aggregation performance of the global model in the federated learning edge computing, the mean square error (MSE) is used to calculate the aggregation model in the estimated value With target value The error between them is calculated as follows: (3) Among them, the transmission symbols follow an independent standard normal distribution, that is, Therefore, the transmission power of user equipment i is limited to Based on the above constraints, the performance of federated learning can be optimized.

[0018] S2. UAV motion trajectory modeling Assume that Figure 1 The scenario shown in Figure 1, where a group of user devices collaboratively generate data and train a global machine learning model, while a UAV equipped with a reconfigurable smart surface (UAV-RIS) continuously cruises to achieve wide-area model aggregation from the user devices. However, there is an attacker who attempts to detect the updated model parameters transmitted from the user devices to the UAV to eavesdrop on the information and recover the original data from the user devices. t At this moment, the trajectory information of UAV-RIS includes the coordinate information of the x-axis, y-axis and z-axis, which can be expressed as: (4) Taking into account the operational limitations of drones in actual scenarios, the motion limitations of UAV-RIS can be expressed by the following formula: (5) In the above formula, (6) Equation (5) limits the maximum flight distance in each iteration, while Equation (6) limits the minimum flight height. and denote the maximum speed and minimum flight altitude of the UAV, respectively, and T is the maximum cumulative flight time. The target endpoint is defined as .

[0019] S3, UAV-RIS assisted covert transmission modeling For the federated learning system based on covert communication mode, the present invention considers a finite number of channels as delay-constrained covert channels, which means that in some low-latency applications, the block length should be limited by the delay constraint. It is assumed that the channel state information (CSI) is available to the detection end (Willie), so that the detection end can identify a signal in all user devices. This assumption is valid because the detection end can detect the existence of federated learning information transmission. Specifically, The channel gain from the i-th user equipment to the detection end is recorded as , and the channel gain from UAV-RIS to the detection end is recorded as , where the detection end has only one antenna. In the invention, it is assumed that the detection end has strong detection performance, so the detection end can obtain accurate CSI, but in the system the detection end is regarded as a malicious user device for eavesdropping. Therefore, the basic performance gain that can be achieved by UAV-RIS in the context of covert communication can be described. The detection end detects the presence of transmission by making the following assumptions: (7) in, It indicates the signal received by the detection end when the k-th channel is used. represents the null hypothesis (the user device does not send information), represents the alternative hypothesis (the user equipment is sending information and aggregating it to the BS). represents the transmission power of the i-th user equipment, It means the mean is 0 and the variance is Gaussian white noise. Therefore, the false alarm rate of the detection end can be calculated and missed detection rate ,in and Indicates the information that the user equipment is transmitting or not transmitting. The detection error probability of the detection end The calculation formula is: (8) The detection end aims to minimize the probability of detection error , to identify whether the transmission of federated learning information exists. It is performed through likelihood ratio detection and can be expressed as: (9) (10) in, and Respectively represent the detection end in the assumption and Under this condition, the likelihood detection of L-th wireless channel is used. The present invention is expressed by the following formula: and The received signal Likelihood test: (11) (12) in, It means the mean is 0 and the variance is The complex Gaussian distribution of .

[0020] exist Assume that the signal received by the detection end contains only additive white Gaussian noise (AWGN). The likelihood function can be expressed as: (13) That is, the likelihood values ​​used by all channels are multiplied to obtain the total likelihood detection value. Assume that the signal received by the detection end contains only the hidden signal and additive white Gaussian noise. The likelihood function can be expressed as: (14) Although the optimal detection threshold at the detection end can be derived through hypothesis testing theory However, the formula The formal form of contains the gamma function, which makes optimization and solution challenging. To solve this problem, the present invention adopts The lower bound of is used as a constraint: (15) in, Indicates from arrive The Kullback-Leibler (KL) divergence of , for each user device i, is given by the following formula, based on the hypothesis test performance total variation distance bound and Pinsker inequality: (16) In the present invention, the hidden constraint is adopted ,in, Indicates the level of concealment, and a smaller value should be selected according to the specific requirements of the actual system. The model aggregation of federated learning may be affected by unfavorable wireless links, resulting in alignment errors and information leakage of transmission signals. Therefore, the present invention uses UAV-RIS to ensure the accuracy and security of federated learning during the aggregation process.

[0021] S4. Problem Formulation The objective function of the present invention is to maximize the number of selected user devices, and the present invention jointly designs the operation trajectory of the UAV, the transmission power of the user equipment, the receiving beamforming of the base station, the phase offset and reflection amplitude of the UAV-RIS, while satisfying the mean square error requirements and concealment constraints.

[0022] P1: (17) (18) (19) (20) (twenty one) (twenty two) Among them, (17) is the concealment constraint, (18) is the federated learning MSE constraint, that is, only when the rated signal threshold is met can the federated learning be participated in. The constraint in (19) means that the reflection amplitude of each UAV-RIS reflection unit is in the range of [0,1], and the phase offset is In the range, (20) represents the maximum transmission power of the user equipment. The optimization problem P1 is a mixed integer programming problem. Since the integer variables in the objective function Sum and integer variables I and continuous variables a, , The associated non-convex MSE constraint makes this problem very difficult to solve. In addition, due to the KL divergence and The tight coupling and hiddenness constraint (17) is non-convex.

[0023] S5. Non-convex problem transformation and sub-problem decomposition In order to solve this problem, the original constraints must be transformed into non-convex constraints: (twenty three) in, The present invention introduces an auxiliary variable s and uses the interior point method to transform the problem of maximizing the number of user devices into minimizing non-zero Therefore, based on solving the subset, the original problem is converted into a sparse optimization problem: P2: (twenty four) (25) (26) (19), (20), (21), (22) In the above formula, yes A subset of This problem is still very complicated, so it needs to be converted into three sub-problems for solution, namely, trajectory optimization problem, optimal concealment user device group selection problem and concealed user device maximum transmission rate problem.

[0024] (a1) Trajectory optimization subproblem The trajectory optimization sub-problem can be split separately and expressed as: P3: (27)

[0025] (a2) Hidden user device optimization selection problem For the user device selection problem, the non-convex sparse objective function 0-norm is replaced by 1-norm as a convex alternative, which can be solved by CVX toolbox. The problem with 1-norm objective can be expressed as follows: P4: (28)

[0026] By solving the above problems, we can get the value , which represents the priority of the i-th user device selection, and then turns to the second sub-problem to identify the feasibility of federated learning to conceal user device selection.

[0027] (a3) Problem of maximizing transmission rate of hidden user equipment The result of the above sub-problem P4 represents the mean square error (MSE) of user equipment i, but cannot meet the MSE and concealment requirements at the same time. Sort in ascending order in, Representing a collection The i-th smallest element in P2. This sorting ensures that the priorities of the user equipment are arranged according to the result of P4(a). The present invention adopts a binary search method to determine the maximum user equipment set j that meets the feasible selection conditions in P2. For a given set , check its feasibility to minimize Therefore, combined with the results of P4, the maximum concealment user equipment set is selected using the dichotomy method to minimize the MSE of the selected user equipment. The process is as follows: P5: (29)

[0028] If for the collection If the target value of solving problem P4 is less than the MSE requirement, then the optimal concealment set of user equipment can be obtained, including the transmission power of the user equipment, the aggregate beamforming of the base station, and the reflection amplitude and phase offset of the UAV-RIS.

[0029] S7. Sub-problem splitting and form conversion (b1) Sub-problem P4 is split into: First, note that for the nonconvex hidden constraint (15) , which can be equivalently transformed into: (30) in, , ,and . Auxiliary variables satisfy . is a scalar, which means that both the user equipment and Willie are configured with a single antenna. In addition, if , then expression (30) can be rewritten as a quadratic form ,in (31) Based on the above transformations and a series of convex transformation methods, problem P4 is decomposed into problems P4(a) and P4(b) through convex reorganization and matrix lifting methods. First, define , , Problem P4 (i.e., Formula (28)) can be restated as follows: P4(a) : (32)

[0030] (33)

[0031] (34)

[0032] (35)

[0033] (36) in, is the auxiliary variable for convex optimization, ,and .

[0034] If the transmission power matrix p and the convex optimization auxiliary variable U are fixed, the original subproblem is transformed into an alternating optimization subproblem. For variables s and a, problem P4 can be simplified to a reflection beamforming matrix The feasibility identification problem. By defining , as well as , Problem P4(a) can be restated as: Solve for V

[0035] (37) (38) Where “V” represents the feasible set of UAV-RIS reflection amplitudes and phase offsets, which satisfies the constraints given the general characteristics of UAV-RIS. , similarly, referring to equations (30) and (31), the above problem can be restated as: P4(b): Solve for V (39) (40) (41) (42) In the above formula, (43) At this point, subproblem P4 has been split into two secondary subproblems P4(a) and P4(b). Next, subproblem P5 will be disassembled.

[0036] (b2) Subproblem P4 conversion In the present invention, when performing user device selection based on the hidden federated learning framework, it is very important to detect the rank-one constraint in the non-convex quadratic constraint. , the rank-one constraint can be rewritten as: (44) in represents the i-th singular value of matrix A. In addition, if the trace norm and spectral norm are defined as: (45) Then the rank-one constraint can be equivalent to: (46) in Therefore, the rank-one constraint can be handled using the Convex Function Difference (DC) regularization term. The DC regularization term expression for problem P4(a) is described as follows: P6: (47) (48) (49) (50) (51) in, and represents the regularization factor. Therefore, when the DC regularization part is equal to zero, the rank-one constraint of the matrix can be satisfied. In addition, by By performing Cholesky decomposition, a feasible aggregated beamforming vector a can be calculated. Furthermore, the original problem P4(b) can also be transformed into a DC form, which can be converted to: P7: (52) (53) (54) (55) If the target value of P7 becomes zero, it can also be decomposed by Cholesky Compute a feasible solution of rank one .make , further based on Get the reflection beamforming matrix of RIS.

[0037] (b3) Splitting of subproblem P5 Similar to the above processing method, the original problem P5 can be split. First, define and , transforming the original problem P5 into two low-rank matrix optimization problems, the first sub-problem can be expressed as: P5(a):

[0038] (56) (57) (58) (59) On the other hand, assuming that the transmission power of the user equipment is and the aggregated beamforming vector a, the second sub-problem can be obtained as: Solve for V (60) (61) (62) (63) Furthermore, the above low-rank problem (60) can be transformed into: solving V (64) (65) (66) (b4) Subproblem P5 conversion Problems P5(a) and P5(b) are structurally transformed into convex function difference forms to ensure feasible rank-one constraints and hidden constraints. Subproblem P5(a) can be converted to: P8:

[0039] (67) (68) (69) Subproblem P5(b) can be transformed into: P9:

[0040] (70) (71) (72) Problems P8 and P9 can be solved by designing efficient algorithms using subgradient linearization one by one.

[0041] S6. Dynamic cross optimization algorithm design Based on the above problems P3, P6, P7, P8, and P9, dynamic optimization is performed to solve the problem. In order to solve the problem, the present invention proposes a dynamic cross optimization algorithm, and its specific process is as follows: S61: Initialization Step 1.1 Initialize communication parameters, including: Channel gain: , RIS initial phase point , and preset thresholds .

[0042] Step 1.2 Initialize UAV trajectory optimization parameters: initial position , the end position , maximum runtime , maximum speed , define the position of each time slot .

[0043] S62: Hidden user device selection and priority calculation and UAV trajectory joint optimization Step 2.1 Update , and start the cycle; Step 2.2 Given , solve problem P6 to update .

[0044] Step 2.3 Given ， Solve problem P7 to update .

[0045] Step 2.4 Trajectory optimization initialization: for arrive : Randomly generate federated learning user devices Location within the region. Based on the initial location Calculate the initial mean square error . Define the target location and all user devices as direction nodes. Find the distance in the quadrant The nearest direction node sets the direction of the nearest user device as the flight direction of the UAV.

[0046] Step 2.5 Trajectory optimization loop: For arrive : UAV For the interval, from Fly to .calculate ,save and If the UAV reaches the target location , then exit the loop. If the flight time ≥ , then exit the loop.

[0047] Step 2.6 Until the target value of problem P4 is less than , you can get .

[0048] S63: Solving the maximum hidden user equipment set that minimizes MSE Step 3.1 In ascending order Sorting: .

[0049] Step 3.2 Use the binary search method to calculate the feasible user equipment set : set up Repeat the following steps: Update .

[0050] Step 3.3 Given , solve problem P8 and calculate If the maximum ,but ,save , and exit the loop. Otherwise, if the maximum ,but , .

[0051] Step 3.4 Given and , solve problem P9 and calculate Until the target value of problem P5 is less than and .

[0052] Step 3.5 The loop ends and we get , and select User Device Set .

[0053] S64: Output result: Optimized hidden user device: , ; Optimized UAV trajectory: , ; Hidden transmission parameters: .

[0054] An embodiment of the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the computer program is loaded into the processor, the computer program implements any one of the multi-access point covert communication federation optimization methods for a UAV-RIS system.

[0055] An embodiment of the present invention further provides a storage medium storing a computer program. When the computer program is executed by a processor, the computer program implements any one of the multi-access point covert communication federation optimization methods for a UAV-RIS system.

Claims

1. A multi-access point covert communication federation optimization method for UAV-RIS system, characterized in that: The following steps are involved: (1) Modeling UAV-RIS federated learning edge computing; (2) Modeling the UAV motion trajectory; (3) Modeling the channel for UAV-RIS-assisted covert transmission; (4) Set the maximum number of selected UEs and jointly design the UAV trajectory, UE power, base station beamforming, UAV-RIS reflection amplitude and phase offset to formulate the problem; (5) Decomposition of non-convex problems into transformations and sub-problems; (6) Split the sub-problems and transform their forms; (7) Design a dynamic cross optimization algorithm.

2. A method for optimizing the multi-access point covert communication federation of a UAV-RIS system according to claim 1, characterized in that: Step (1) is as follows: establish an edge computing model based on UAV-RIS assistance to train the global model of federated learning; use the channel gain and reflection matrix of UAV-RIS to optimize signal reception, calculate the mean square error (MSE) of the objective function, and use the mean square error as the performance indicator of the global model aggregation of federated learning.

3. The multi-access point covert communication federation optimization method for UAV-RIS system according to claim 1, characterized in that: In step (2), the trajectory is represented by three-dimensional coordinates, including x, y, and z axis coordinates; and limits the maximum flight distance, minimum flight altitude, maximum flight speed, and cumulative flight time of the drone.

4. The multi-access point covert communication federation optimization method for UAV-RIS system according to claim 1, characterized in that: In step (3), the detection performance is characterized based on the false alarm rate and missed detection rate, and the KL divergence is used as a concealment measure.

5. The multi-access point covert communication federation optimization method for UAV-RIS system according to claim 1, characterized in that: In step (4), the constraints include: concealment constraint, reflection amplitude and phase offset range, and maximum transmission power.

6. The method for optimizing the multi-access point covert communication federation of a UAV-RIS system according to claim 1, characterized in that: In step (5), the MSE constraint is converted into the form of auxiliary variables, and the auxiliary variables are introduced using the interior point method in convex optimization, so that the solution of the optimal set of the original problem is transformed into the solution of a subset of the original solution; The original problem is decomposed into three sub-problems: trajectory optimization problem, hidden user device optimization selection problem, and hidden user device maximization transmission rate problem.

7. The multi-access point covert communication federation optimization method for UAV-RIS system according to claim 1, characterized in that: In step (6), the trajectory optimization problem independently optimizes the UAV trajectory, constraining the flight distance and altitude; the hidden user equipment selection problem and the hidden user equipment transmission rate maximization problem are coupled problems that are split and solved; The convex substitution method is used in the device selection problem to replace the non-convex sparse objective function with the 1 norm to solve the user device priority. The bisection method is used to select the maximum hidden user device set for the hidden transmission rate maximization problem to optimize its transmission power and MSE. The sub-problems are further decomposed into differential convex function forms through convex recombination, matrix lifting, rank-one constraint processing and differential convex function regularization terms.

8. The multi-access point covert communication federation optimization method for UAV-RIS system according to claim 1, characterized in that: Step (7) includes the following steps: (71) Initialize communication parameters, including channel gain, RIS initial phase point, and preset threshold. UAV trajectory optimization parameters include: initial position, end position, maximum running time, and maximum speed; (72) Covert user equipment selection and priority calculation and UAV trajectory joint optimization; (73) Solving the maximum hidden user device set that minimizes MSE, including sorting the potential device set in ascending order, calculating the feasible user device set using a binary search method, and then solving the sub-problem; (74) Algorithm output: includes optimized hidden user equipment, optimized UAV trajectory and hidden transmission parameters.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the computer program is loaded into the processor, it implements the multi-access point covert communication federation optimization method for the UAV-RIS system according to any one of claims 1 to 8.

10. A storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, a multi-access point covert communication federation optimization method for a UAV-RIS system is implemented according to any one of claims 1 to 8.

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