Double-unmanned aerial vehicle trajectory optimization method and system applied to coexistence scene of multiple eavesdroppers and no-fly zone

Abstract

The invention provides a dual unmanned aerial vehicle (UAV) trajectory optimization method and system applied to a multi-eavesdropper and no-fly zone coexistence scene. The method comprises the following steps: constructing a communication system model; constructing an optimized mathematical model with user scheduling, unmanned aerial vehicle beamforming and unmanned aerial vehicle flight path as constraints by taking maximization of the user safety rate as a target according to the communication system model; a block coordinate descent method is adopted to decouple the optimized mathematical model into sub-problems only about user scheduling, unmanned aerial vehicle beam forming and flight tracks of the unmanned aerial vehicle U and the unmanned aerial vehicle J; for each non-convex sub-problem, a convex approximation method is adopted to convert the non-convex sub-problem into a convex optimization form; an iterative algorithm is adopted to sequentially solve user scheduling, unmanned aerial vehicle wave beam occurrence and convex subproblems of flight paths of the user scheduling and the unmanned aerial vehicle wave beam occurrence, and finally successive approximation is carried out and a global optimal solution of an original overall optimization problem is obtained; according to the method, the waveform and the track are jointly optimized, and the eavesdropping capability of an eavesdropper is effectively interfered by using a radar signal, so that safe communication between the unmanned aerial vehicle and a ground user is ensured, and the method has obvious innovativeness and uniqueness in system design and application scenes.

Description

A method and system for optimizing the trajectory of dual unmanned aerial vehicles (UAVs) in scenarios involving multiple eavesdroppers and no-fly zones. Technical Field

[0001] This invention relates to the field of integrated communication and sensing, specifically to a method and system for optimizing the trajectory of dual unmanned aerial vehicles (UAVs) in scenarios where multiple eavesdroppers coexist with no-fly zones. Background Technology

[0002] Wireless sensing performance is a crucial development direction for future 6G, with communication and sensing technologies gradually converging. In wireless communication, communication security, from base stations to drones, has always been a significant issue, as potential eavesdroppers can compromise security. Drones, as core nodes in future mobile communication networks, have a wide range of applications and are attracting considerable attention from various industries.

[0003] In the literature [C. Chen, J. Yao, M. Jin, and Q. Guo, "Beamforming and computing capacity allocation for ISAC-assisted secure mobile edge computing," IEEE Wireless Commun. Lett., pp. 1-1, Sep. 2024.], multiple users transmit uplink information to a base station equipped with a mobile edge computing server for computation, while a potential eavesdropper is simultaneously eavesdropping. The duplex base station sends radar signals to interfere with the potential eavesdropper, achieving secure communication. In the literature [X. Liu, Y. Liu, Z. Liu, and TS Durrani, "Fair Integrated Sensing and Communication for Multi-UAV-Enabled Internet of Things: Joint 3-D Trajectory and Resource Optimization," IEEE Internet of Things Journal, vol. 11, no. 18, pp. 29546-29556, 2024.], multiple drones cooperate in the air to perform communication sensing tasks, maximizing the minimum communication rate. In [Z. Liu, X. Liu, Y. Liu, VCM Leung, and TS Durrani, "UAV assisted integrated sensing and communications for internet of things: 3Dtrajectory optimization and resource allocation," IEEE Transactions on Wireless Communications, vol. 23, no. 8, pp. 8654-8667, Aug. 2024.], the authors used a drone to send radar signals to sense targets, and then offloaded the received reflected radar information to a server without considering communication security.

[0004] The above solutions have the following problems: the security research on sensory integration has not been applied to multiple eavesdropping scenarios and no-fly zone scenarios; the problem of perception of multiple eavesdroppers has not been solved; and there is no security research on sensory integration under cognitive networks.

[0005] For example, patent application number 202411870756.1, titled "A Three-Dimensional Trajectory Optimization Method for Dual UAVs Oriented to Physical Layer Security," while employing a dual-UAV collaborative approach to improve the average security rate of the data collection system, only considers the independent operation of the UAVs and does not utilize the communication capability between the base station UAV and the jamming UAV. Furthermore, it does not consider secure transmission issues or UAV power control within the UAV communication scenario. How to fully utilize the communication capability between dual UAVs while simultaneously addressing secure transmission and power control issues within the UAV communication scenario to achieve joint optimization of the integrated sensing waveform and UAV flight trajectory, ensuring secure communication between the UAV and the user, is a problem that needs to be solved. Summary of the Invention

[0006] To address the problems existing in the prior art, this invention proposes a dual-UAV trajectory optimization method for scenarios involving multiple eavesdroppers and no-fly zones. This method includes: constructing a communication system model; based on the communication system model and aiming to maximize user safety rate, constructing an optimization mathematical model constrained by user scheduling, UAV beamforming, and UAV flight trajectories; decoupling the optimization mathematical model using block coordinate descent into subproblems only concerning user scheduling, UAV beamforming, and UAV U and J flight trajectories; transforming each non-convex subproblem into a convex optimization form using a convex approximation method; and using an iterative algorithm to sequentially solve the convex subproblems of user scheduling, UAV beamforming, and their flight trajectories, ultimately approximating and obtaining the global optimal solution of the original overall optimization problem.

[0007] A dual-UAV trajectory optimization system for scenarios involving multiple eavesdroppers and no-fly zones, comprising: an initialization module, a mathematical model module, a mathematical model decoupling module, and an iterative solution module;

[0008] The initialization module considers a communication security system with multiple potential eavesdroppers (e) and m no-fly zones, sets up a drone (U) as a communication sensing base station, and initializes its flight trajectory to serve the ground-based [network / system]. To better increase the average safe rate of the system, the drone J performs jamming tasks to achieve the goal of secure communication.

[0009] The mathematical model module aims to maximize the average safe rate of the system and constructs an optimized mathematical model constrained by user scheduling, beamforming, and UAV flight trajectory.

[0010] The mathematical model decoupling module is used to decouple the mathematical model into sub-problems of user scheduling, beamforming, and UAV flight trajectory based on the BCD method. For each non-convex sub-problem, a convex approximation fitting method is used to convert it into a convex problem for solution. Specifically, when solving the non-convex problem related to beamforming, the SDR method that discards the rank-one constraint is used to convert the non-convex problem into a convex problem, and then the CVX toolbox is used for solution. Finally, the obtained solution is randomized through Gaussian to obtain a solution that satisfies the rank-one constraint.

[0011] The iterative solution module is used to solve the sub-problems of user scheduling, beamforming, and UAV flight trajectory using the SCA iterative algorithm.

[0012] A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the beamforming and trajectory optimization design method for a physical layer security-oriented dual unmanned aerial vehicle (UAV) ISAC system.

[0013] The beneficial effects of this invention are:

[0014] This invention is primarily applied to unmanned aerial vehicle (UAV)-assisted wireless communication scenarios. Addressing user communication security, it aims to improve communication security rates while also mitigating the impact of potential eavesdroppers on wireless communication quality and security. By combining the maneuverability of UAVs with the ability of strong radar signals to act as interference, a dual-UAV-assisted, integrated communication and sensing system is constructed. Through theoretical derivation and simulation verification, the integrated communication and sensing waveform and UAV flight trajectory are designed to maximize the system's security rate. This invention combines dual UAVs, beamforming, and integrated communication and sensing design, fully utilizing the communication capability between the two UAVs while simultaneously solving the problems of secure transmission and power control in UAV communication scenarios. It achieves joint optimization of the integrated communication and sensing waveform and UAV flight trajectory, ensuring secure communication between the UAV and the user, demonstrating high innovation and uniqueness. Attached Figure Description

[0015] Figure 1 is a model of the communication system of the present invention;

[0016] Figure 2 is a flowchart of the operation of this invention;

[0017] Figure 3 shows the optimal flight trajectory of the UAV;

[0018] Figure 4 shows the user scheduling strategy diagram;

[0019] Figure 5 is a convergence diagram of the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0021] To fully utilize the characteristics of dual UAV collaborative operation and simultaneously address the issues of secure transmission and power control in UAV communication scenarios, thereby achieving joint optimization of the integrated sensing waveform and UAV flight trajectory to ensure secure communication between the UAV and the user, as shown in Figure 1 or Figure 2, the applicant has designed a beamforming and trajectory optimization method for a dual UAV ISAC security system in a multi-eavesdropping-no-fly zone environment. With the goal of maximizing the system's security rate, the method dynamically plans and designs the user scheduling strategy, the integrated sensing waveform, and the UAV trajectory.

[0022] Step one: First, based on the basic theories of wireless communication and physical layer security, construct a model of a drone-assisted wireless communication system.

[0023] Steps two, three, and four improved the mathematical theoretical derivation and problem-solving analysis in the model building process. In view of the non-convexity and high coupling of the optimization problem corresponding to the system model, the original optimization problem was decoupled and transformed by using the Block Coordinate Descent (BCD) algorithm and the approximate fitting method of continuous convex approximation.

[0024] Step 5: Based on the idea of ​​iteration, the sub-problems obtained in steps 2, 3, and 4 are iterated in a loop to make the system's safe rate continuously approach a fixed value. This fixed value is the maximum safe communication rate required by this invention.

[0025] The following are the specific steps and procedures.

[0026] S1, Construction of the communication model.

[0027] A communication system model is constructed: Considering a complex environment with e eavesdroppers and m no-fly zones, U is designated as the base station UAV, and J as the jamming UAV. The flight paths of U and J are initialized. To better serve the users on the ground, a user scheduling strategy is adopted. To ensure the security of information transmission, U detects eavesdropper E and sends the collected eavesdropping location information to J. J then emits radar waves to jam E, achieving secure communication.

[0028] As shown in Figure 1, this invention mainly studies a beamforming and trajectory optimization design method for a dual-UAV ISAC system oriented towards physical layer security. The base station UAV is a ground-based UAV. ground users ( Communication, marked as Meanwhile, U senses the eavesdropper E and marks it as... The collected eavesdropping location information is sent to jamming drone J, which then generates artificial noise to interfere with the eavesdropping user. Flight cycle Classified as There are 10 time slots, where the time interval between each time slot is 10 ... The horizontal position of the drone is represented as Their vertical positions are all represented as... .also and The horizontal coordinate is represented as , .

[0029] U and J represent the initial and final positions of the UAV, respectively. The distance between U and J is expressed as... , U and The distance between them is expressed as The distance between J and E is expressed as , The distance between the user and the distance is represented as .

[0030] The channel from UAV U to users k and e can be represented as:

[0031]

[0032] in, It is the channel fading coefficient per unit distance.

[0033]

[0034] Therefore, the steering vector is:

[0035]

[0036] The U-shaped drone is equipped with L transmitting antennas, and the communication signals it transmits are... The sensing signal is ,

[0037] Therefore, the total transmitted signal of the UAV U can be expressed as:

[0038]

[0039] in, This represents the transmit beamforming vector corresponding to user k. This represents the beamforming vector used for sensing. The signal received by a legitimate user k is:

[0040]

[0041] in, This represents additive white Gaussian noise (AWGN). The reachable rate of user k is expressed as:

[0042]

[0043] The signal-to-interference-plus-noise ratio is:

[0044]

[0045]

[0046] Similarly, the channel modeling between jammer J and eavesdropper e is as follows:

[0047]

[0048]

[0049] .

[0050] The interference signal emitted by the jammer J is:

[0051]

[0052] The signal received by eavesdropper e is:

[0053]

[0054] The corresponding eavesdropping rate is:

[0055]

[0056]

[0057]

[0058] .

[0059] Therefore, the average security rate (ASR) of the system is defined as:

[0060]

[0061] S2, construct an optimized mathematical model.

[0062] With the goal of maximizing user safety rate, an optimization mathematical model is constructed with constraints of user scheduling, UAV transmission power, integrated sensing waveform, and UAV flight trajectory.

[0063] The optimized mathematical model is as follows:

[0064]

[0065] In the formula Let represent the set of optimization variables, where These represent the communication rate between U and the user, and the eavesdropping rate of e, respectively. This refers to the user scheduling status of the UAV. It is the transmit power of the UAV. It is the sensing power of the U-type drone. It is the interference power of UAV J. It refers to the propulsion power of the U and J axes of the UAV. It is the horizontal propulsion power limitation of the drone. These are the U and J trajectories of the drone. , Indicate the starting and ending positions of U and J, respectively. The length of each flight time slot for U and J is defined. The maximum flight speeds U and J of the UAV at any given time are defined. These are the horizontal flight speeds U and J of the drone; , Drones were defined separately. The maximum transmission power of the UAV J and the maximum transmission power of the UAV J; The cognitive constraint threshold of the system was defined; This represents the system's average safe rate.

[0066] , These represent the center coordinates and radius of the no-fly zone, respectively.

[0067] In the above optimization problem, the optimization objective is to maximize the communication security rate. This indicates the scheduling constraints that base station drones impose on users. The transmit signal power of the base station U-type drone was constrained. The base station drone J's transmit signal power was constrained. and It is a semidefinite relaxation and rank-one constraint of the drone. The horizontal propulsion power of the drone was constrained. The start and end positions of the drone were restricted. and It is the speed constraint of the drone. It refers to the interference constraints on primary users in cognitive wireless networks. It is a no-fly zone constraint for drones.

[0068] To address the non-convexity and high coupling of the optimization problem corresponding to the system model, an approximate fitting method based on the BlockCoordinate Descent (BCD) algorithm and continuous convex approximation was adopted to decouple and transform the original optimization problem.

[0069] The problem of this invention will be solved according to the following steps, the specific steps of which are as follows:

[0070] S3. For the aforementioned optimized mathematical model, the problem is decoupled into subproblems based on the BCD method, focusing only on user scheduling, the transmit power of UAVs U and J, the integrated sensing waveform, and the flight trajectories of UAVs U and J. The BCD method is an efficient iterative optimization algorithm. Its core idea is to divide the optimization variables into multiple "blocks" and minimize the objective function by optimizing block by block (keeping other block variables fixed and only updating the current block).

[0071] Based on the Block Coordinate Descent (BCD) algorithm The problem is decoupled to obtain subproblems. , , , As shown below:

[0072]

[0073] Among them, sub-problems The optimization involves variables related to user scheduling. This problem is a standard convex optimization problem and can be solved directly.

[0074]

[0075] Subproblems The optimization involves variables related to beamforming;

[0076]

[0077] Subproblems Variables for optimizing the U-trajectory of unmanned aerial vehicles (UAVs);

[0078]

[0079] Subproblems The variables for optimizing the J-trajectory of the UAV.

[0080] S4. For each non-convex subproblem, a convex approximation fitting method is used to convert it into a convex problem for solution.

[0081] In response to the problem The first problem is a standard convex optimization problem that can be solved directly. For the remaining problems, we need to use the SCA method and introduce slack variables to approximate some non-convex constraints with convex values, thus transforming the original problem into a solvable convex optimization problem. The specific transformation method is as follows.

[0082] S41: Transformation Subproblem

[0083] Regarding the sub-problems The mathematical model after transforming the optimization objective and constraints into a convex problem using the successive approximation method (SCA) is as follows:

[0084]

[0085] S42: Transformation Subproblem

[0086] The following is the conversion and The specific steps.

[0087] Regarding the sub-problems and This sub-problem can be solved by introducing auxiliary variables:

[0088]

[0089] in , and These are introduced slack variables. and These are the flight altitudes of the U and J axes of the drone. and They are and The value in the t-th iteration.

[0090]

[0091]

[0092] In the above formula and This represents the flight speed of U and J when hovering. and This represents the introduced slack variable. and Represents the positional variables of U and J; constants and These represent the inherent power of the blade surface and the power generated by the rotor, respectively. Indicates the tip speed of the rotor blades, a variable. and Representing the drag ratio and air density, respectively, the average induced velocity of the rotor is expressed as... It means, and and These correspond to the rotor stiffness and the rotor disk area, respectively.

[0093] Regarding the sub-problems By introducing slack variables and the SCA algorithm, the problem is transformed into a convex optimization problem, including the following steps:

[0094] By introducing slack variables Rewritten as:

[0095]

[0096] in, It is Gaussian white noise. It is the channel fading coefficient per unit distance. The turning vector matrix from U to user k.

[0097] via SCA Rewritten as:

[0098]

[0099] in, The turning vector matrix from U to the eavesdropper e. Based on the above transformation, a new optimization problem can be obtained, which is expressed as:

[0100]

[0101] S43: Transformation Subproblem

[0102] Regarding the sub-problems By introducing slack variables and the SCA algorithm, the problem is transformed into a convex optimization problem, including the following steps:

[0103] via SCA Rewritten as:

[0104]

[0105] Based on the above transformation, a new optimization problem can be obtained, which can be expressed as:

[0106]

[0107] Solve for S44.

[0108] Based on the iterative approach, the sub-problems obtained in steps two, three, and four are iteratively solved to continuously approach a fixed value for the system's safe communication rate. This fixed value is the maximum safe communication rate required by this invention. Therefore, an iterative algorithm is used to solve the convex problems of user scheduling, UAV transmission power, integrated sensing waveform, and UAV flight trajectory to obtain the global suboptimal solution to the entire optimization problem, as well as the optimal integrated sensing waveform and UAV flight trajectory.

[0109] The iterative algorithm flow is designed to connect the above convex optimization problems in series. The specific steps are shown in Table 1.

[0110] A dual-UAV trajectory optimization system for scenarios involving multiple eavesdroppers and no-fly zones includes the following modules:

[0111] Initialization module: Set U as a communication base station and J as a friendly jammer. At the same time, initialize their flight trajectories so that they can serve K users on the ground. In order to better increase the average security rate of the system, the UAV adopts a user scheduling and perception communication time-slot working strategy. At the same time, it considers the existence of a potential eavesdropper E to achieve the goal of secure communication.

[0112] The mathematical model module aims to maximize the average safe rate of the system by constructing an optimized mathematical model constrained by user scheduling, transmission power, integrated sensing waveform, and UAV flight trajectory.

[0113] The mathematical model decoupling module is used to decouple the mathematical model based on the BCD method into subproblems of user scheduling, transmit power, synesthetic waveform, and UAV flight trajectory. For each non-convex subproblem, a convex approximation fitting method is used to convert it into a convex problem for solution. Specifically, when solving the non-convex problem about the synesthetic waveform, the SDR method, which discards the rank-one constraint, is used to convert the non-convex problem into a convex problem. Then, the CVX toolbox is used for solution, and the obtained solution is Gaussian randomized to obtain a solution that satisfies the rank-one constraint.

[0114] The iterative solution module is used to solve sub-problems such as user scheduling, transmit power, integrated sensing waveform, and UAV flight trajectory using the SCA iterative algorithm.

[0115] Figure 3 shows the simulation verification of the proposed scheme. Through the process shown in Figure 2, the optimal flight trajectory of the UAV shown in Figure 3 is finally obtained.

[0116] Figure 4 shows the simulation verification of the user scheduling strategy of the present invention. As can be seen from the simulation diagram, the user scheduling strategy of the present invention first selects user 1, then user 2, and finally user 3. The rationality of the user scheduling strategy can be seen from the relationship between the user positions and the UAV trajectories.

[0117] Figure 5 shows the convergence of the proposed solution. The simulation results demonstrate the effectiveness of the algorithm proposed in this invention.

[0118] A computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the beamforming and trajectory optimization design method for a physical layer security-oriented dual unmanned aerial vehicle (UAV) ISAC system.

[0119] This invention presents a beamforming and trajectory optimization method for a dual-UAV ISAC security system in a multi-eavesdropping, no-fly zone environment. Addressing the scenario of potential eavesdroppers during downlink communication between a base station and a UAV, the method aims to maximize the average security rate for users by optimizing the integrated sensing waveform and UAV trajectory. First, an optimization problem fitting the scenario is constructed. Then, based on the Block Coordinate Descent (BCD) method, the original optimization problem is decoupled into subproblems concerning the integrated sensing waveform and the UAV flight trajectory. For each non-convex subproblem, a convex approximation is performed. Finally, an iterative algorithm is used to solve the problem, finding the global suboptimal solution and the optimal integrated sensing waveform and UAV flight trajectory.

[0120] This invention first constructs a system model integrating communication and sensing functions, and then establishes an optimization problem model aimed at improving physical layer security. For this non-convex optimization problem, the Block Coordinate Descent (BCD) method is used to decouple it into sub-problems such as integrated sensing waveform design and UAV flight trajectory optimization. The integrated sensing waveform sub-problem is transformed into a solvable convex optimization problem using semidefinite relaxation (SDR) technology; the UAV flight trajectory sub-problem is approximated using sequential convex approximation (SCA) through iteration. Finally, an efficient iterative algorithm is designed to solve the sub-problems alternately to obtain a globally suboptimal solution, achieving joint optimization of the integrated sensing waveform and UAV flight trajectory. This patent's dual UAVs, through joint waveform and trajectory optimization, use radar signals to interfere with the eavesdropper's eavesdropping rate, achieving the goal of secure communication between the UAV and the user. The communication-sensing waveform and UAV trajectory design, achieving physical layer security, possess high innovation and uniqueness.

[0121] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the trajectory of two unmanned aerial vehicles (UAVs) in a scenario where multiple eavesdroppers coexist with a no-fly zone, characterized in that, include: Construct a communication system model; Based on the communication system model with the goal of maximizing user safety rate, an optimization mathematical model is constructed with user scheduling, UAV beamforming, and UAV flight trajectory as constraints. The optimization mathematical model is decoupled into subproblems only concerning user scheduling, UAV beamforming, and UAV U and J flight trajectories using the block coordinate descent method. For each non-convex subproblem, a convex approximation method is used to transform it into a convex optimization form. An iterative algorithm is then used to solve the convex subproblems of user scheduling, UAV beamforming, and their flight trajectories sequentially, ultimately approximating and obtaining the global optimal solution of the original overall optimization problem.

2. The dual-UAV trajectory optimization method according to claim 1, applicable to scenarios with multiple eavesdroppers and no-fly zones, is characterized in that... The communication system model is constructed as follows: U is set as the base station U, and U is set as the jamming U. There are multiple potential eavesdroppers E on the ground. U detects the eavesdroppers E and sends the collected eavesdropping location information to the jamming U. J jams E by emitting radar waves.

3. The dual-UAV trajectory optimization method according to claim 1, applicable to scenarios with multiple eavesdroppers and no-fly zones, is characterized in that... Optimization of mathematical models includes: ;in, Let represent the set of optimization variables, where These represent the communication rate between U and the user, and the eavesdropping rate of e, respectively. This refers to the user scheduling status of the UAV. It is the transmit power of the UAV. It is the sensing power of the U-type drone. It is the interference power of UAV J. It refers to the propulsion power of the U and J axes of the UAV. It is the horizontal propulsion power limitation of the drone. These are the U and J trajectories of the drone. 、 Indicate the starting and ending positions of U and J, respectively. The length of each flight time slot for U and J is defined. The maximum flight speeds U and J of the UAV at any given time are defined. These are the horizontal flight speeds U and J of the drone; 、 Drones were defined separately. The maximum transmission power of the UAV J and the maximum transmission power of the UAV J; The cognitive constraint threshold of the system was defined; This represents the system's average safe rate; ， These represent the center coordinates and radius of the no-fly zone, respectively.

4. The dual-UAV trajectory optimization method according to claim 3, applicable to scenarios with multiple eavesdroppers and no-fly zones, is characterized in that... The optimization mathematical model is decoupled to obtain subproblems. 、 、 、 For: Subproblems for: Subproblems for: Subproblems for: Subproblems for: Where A is the optimized scheduling coefficient. For the system's safe speed, C is constraint problem 1, where K is the number of users. Here, is the scheduling coefficient, and n is the nth time slot. For the first One user; W is the optimized beamforming variable. For the trace-finding operation, C2 represents constraint problem 2. Let E be the beamforming variable from U to user k, and E be the number of eavesdroppers. For the beamforming variables from U to the eavesdropper e, Let U be the maximum transmission power, and e be the e-th eavesdropper. Beamforming variables from J to the eavesdropper e, Let J be the maximum transmit power, and C3 be constraint problem 3. To find the rank of the matrix, Let U be the beamforming variable from U to the primary user r, where r is the primary user, C4 be constraint problem 4, C5 be constraint problem 5, and N be the number of time slots. For the channel from U to r, Q is the threshold for interference to the primary user in a cognitive network. U For user U's horizontal position variable, For the horizontal propulsion power of U, For horizontal propulsion power threshold, This is the actual starting position of the drone. The starting position of the drone is set. This is the actual starting position of the drone. Here, J represents the starting position of the drone, and J represents the jamming drone. For the drone's horizontal speed, The time slot length, For the horizontal speed threshold of the drone, Let J be the coordinates at time j. The center of the no-fly zone, Q is the square of the radius of the no-fly zone; J Let J be the horizontal position variable. For the horizontal propulsion power of J, J is the horizontal propulsion power threshold.

5. The dual-UAV trajectory optimization method according to claim 4, applicable to scenarios with multiple eavesdroppers and no-fly zones, is characterized in that... Regarding the sub-problems The mathematical model after transforming the optimization objective and constraints into a convex problem using the successive approximation method is as follows: ;in, It is the expression for the communication rate from U drone U to user k after one transformation via SCA; It is the expression for the eavesdropping rate after one transformation by SCA.

6. The dual-UAV trajectory optimization method according to claim 4, applicable to scenarios with multiple eavesdroppers and no-fly zones, is characterized in that... Regarding the sub-problems and This sub-problem can be solved by introducing auxiliary variables: ;in , and These are introduced slack variables. and These are the flight altitudes of the U and J drones. and They are and The value at the t-th iteration; ； ;in, and This represents the flight speed of U and J when hovering. and This represents the introduced slack variable. and Represents the position variables of U and J, constants and These represent the inherent power of the blade surface and the power generated by the rotor, respectively. Indicates the tip speed of the rotor blades, a variable. and Representing the drag ratio and air density, respectively, the average induced velocity of the rotor is expressed as... It means, and and These correspond to the rotor stiffness and the rotor disk area, respectively.

7. The dual-UAV trajectory optimization method according to claim 4, applicable to scenarios with multiple eavesdroppers and no-fly zones, is characterized in that... Regarding the sub-problems By introducing slack variables and the SCA algorithm, the problem is transformed into a convex optimization problem. Specifically, this includes: introducing slack variables to transform... Rewritten as: ; via SCA Rewritten as: Based on the above transformation, a new optimization problem is obtained, which is expressed as: ;in, It is Gaussian white noise. It is the channel fading coefficient per unit distance. The turning vector matrix from U to user k; The turning vector matrix from U to the eavesdropper e.

8. The dual-UAV trajectory optimization method according to claim 4, applicable to scenarios with multiple eavesdroppers and no-fly zones, is characterized in that... Regarding the sub-problems The problem is transformed into a convex optimization problem by introducing slack variables and the SCA algorithm; specifically: the SCA algorithm is used to transform... Rewritten as: Based on the above transformation, a new optimization problem is obtained, which is expressed as: ;in, The Taylor expansion of the eavesdropping rate from U to e, For the channel from U to e, Beamforming variables from U to user k It is Gaussian white noise. For channel coefficients, For the expanded values ​​of the introduced slack variables, The steering vector from J to e, Assign beamforming variables to user J to e. This is a slack variable that is introduced.

9. A dual-UAV trajectory optimization system for scenarios involving multiple eavesdroppers and no-fly zones, the system being used to execute the dual-UAV trajectory optimization method for scenarios involving multiple eavesdroppers and no-fly zones as described in any one of claims 1 to 8, characterized in that... include: The module includes an initialization module, a mathematical model module, a mathematical model decoupling module, and an iterative solution module. The initialization module is based on a communication security system with multiple potential eavesdroppers (e) and m no-fly zones. It sets up the UAV U as a communication sensing base station, initializes its flight trajectory, and enables it to serve the ground-based [unclear] network. A user, UAV J, performs interference tasks to achieve the goal of secure communication. The mathematical model module aims to maximize the system's average safe rate and constructs an optimized mathematical model constrained by user scheduling, beamforming, and UAV flight trajectory. The mathematical model decoupling module decouples the mathematical model into sub-problems of user scheduling, beamforming, and UAV flight trajectory based on the BCD method. For each non-convex sub-problem, a convex approximation fitting method is used to convert it into a convex problem for solution. The iterative solution module uses the SCA iterative algorithm to solve the sub-problems of user scheduling, beamforming, and UAV flight trajectory.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the dual-UAV trajectory optimization method described in any one of claims 1 to 8, applicable to scenarios where multiple eavesdroppers coexist with no-fly zones.

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