A UAV trajectory design and power optimization method based on active eavesdropping

Abstract

The present invention discloses a method for drone trajectory design and power optimization based on active eavesdropping. Aiming at the existing two-hop illegal transmission links, the method optimizes the drone flight trajectory and interference power with the goal of maximizing the average eavesdropping rate. First, an optimization problem that meets the scenario is constructed. Then, based on the Block Coordinate Descent (BCD) method, the original problem is decoupled into several sub-problems. The sub-problems are solved using the continuous convex approximation (SCA) method. Finally, the sub-problems are iteratively solved to find a global optimal solution. Compared with other simple trajectory design or interference power optimization methods, the present invention has a better eavesdropping rate while ensuring successful eavesdropping.

Description

Technical Field

[0001] This application relates to the field of drones, specifically to utilizing the flexible maneuverability of drones to actively eavesdrop on illegal relay links, designing the drone's flight trajectory and interference power, and maximizing the active eavesdropping rate. Background Art

[0002] With the significant advancement of wireless technology, the industry has widely deployed wireless communication links that do not require infrastructure support to meet diverse application needs. However, these emerging infrastructure-free wireless communication technologies also bring potential security risks.

[0003] A simple approach to wireless information surveillance is passive eavesdropping, where a legitimate monitor simply listens to the wireless channel of any suspicious users to decode their transmitted information. However, this approach works only if the eavesdropping channel from the source to the legitimate monitor is better than the suspicious channel to the destination, so that information sent by the suspicious source can be reliably decoded on the legitimate monitor [Y. Zeng and R. Zhang, “Wireless information surveillance via proactive eavesdropping with spoofing relay,” IEEE J. Sel. Topics Signal Process., vol. 10, no. 8, pp. 1449-1461, Dec. 2016.].

[0004] Relay technology plays a vital role in wireless communication systems. It is a key technology to expand communication coverage and significantly improve the signal-to-noise ratio of the receiver.

[0005] In illegal cooperative communication systems, the presence of relay nodes provides illegal communicators with a wider communication range and higher reception quality, making illegal communication activities, which are already difficult to track and prevent, even more covert and difficult to detect. The paper [X. Jiang, H. Lin, C. Zhong, X. Chen, and Z. Zhang, "Proactive eavesdropping in relaying systems," IEEE Signal Process. Lett., vol. 24, no. 6, pp. 917-921, Jun. 2017.] studies the active eavesdropping problem in a two-hop system and maximizes the active eavesdropping rate by jointly optimizing beamforming and power allocation.

[0006] Drones are widely used in communications due to their flexible maneuverability. The literature [M.Huang, Y.Chen, and X.Tao, "Proactive eavesdropping in UAV systems via trajectory planning and power optimization," in Proc.2021IEEE Wireless Communications and Networking Conference Workshops (WCNCW), Nanjing, China, Mar.2021, pp.1-6.] studies how to maximize the eavesdropping rate by optimizing the unmanned flight trajectory and interference power under a single-hop link.

[0007] The above solutions have the following problems:

[0008] 1. Traditional passive monitoring cannot be used when the channel quality of the monitor is poor.

[0009] 2. Active eavesdropping on drones for traditional single-hop links cannot be applied to drone multi-hop links.

[0010] 3. When the starting point and end point of the drone's flight are not at the same altitude, traditional 2D trajectory design cannot be applied. Summary of the Invention

[0011] In response to the above problems, the present invention aims to address some of the problems in the prior art, or at least alleviate them. This invention provides a method and system for optimizing the flight trajectory and interference power of drones for active eavesdropping on relay links. This method jointly optimizes the flight trajectory and interference power of drones, maximizing the system's active eavesdropping rate.

[0012] The technical solution adopted by the present invention is a UAV trajectory design and power optimization method based on active eavesdropping, which includes the following steps:

[0013] Build a communication system model: Determine the locations of the illegal node S, illegal relay node R, and illegal receiving node D, as well as the starting and ending locations of the drone E. There is no direct link between S and D, and they can only be relayed through R. The information transmission between S and D is adaptive. E simultaneously receives link information from S and R and actively interferes with D, ultimately achieving active eavesdropping and maximizing the eavesdropping rate.

[0014] With the goal of maximizing the active eavesdropping rate, an optimization mathematical model is constructed with UAV interference power, UAV horizontal flight trajectory and UAV vertical flight trajectory as variables.

[0015] Determine whether to use 2D trajectory optimization or 3D trajectory optimization based on the starting and ending positions of the drone.

[0016] The BCD method is used to decouple the 2D optimization problem into two sub-problems: UAV horizontal flight trajectory optimization and UAV interference power optimization; the 3D optimization problem is decoupled into three sub-problems: UAV horizontal flight trajectory optimization, UAV vertical flight trajectory optimization, and UAV interference power optimization. For each sub-problem, the continuous convex optimization method is used to transform the non-convex sub-problem into a convex problem for solution; then the CVX toolbox is used to solve it.

[0017] The iterative algorithm is used to iterate the solved sub-problems to obtain the optimized flight trajectory and interference power. The solution of the previous sub-problem is used as the given value of the next sub-problem for alternating iterations, maximizing the eavesdropping rate while ensuring the success of eavesdropping.

[0018] The present invention also provides a communication system, including an illegal node S, an illegal relay node R, an illegal receiving node D and a drone E. There is no direct link between S and D, and they can only be relayed through R. The information transmission between S and D is adaptive. E simultaneously receives link information from S and R and actively interferes with D. The system can execute the above-mentioned drone trajectory design and power optimization method based on active eavesdropping.

[0019] Aiming at the actual situation of illegal relay links, the present invention plans and designs the interference power and flight trajectory of UAVs from the perspective of legal supervision, with the goal of maximizing the active eavesdropping rate.

[0020] Step 1: First, based on the actual situation of wireless communication and legal supervision, a wireless communication system model for active drone eavesdropping is constructed. In this system model, it is necessary to determine whether to perform 2D trajectory optimization or 3D trajectory optimization based on the starting and ending positions of the drone.

[0021] In step 2, due to the non-convexity of the model solution and the high coupling of optimization parameters, the BCD idea is used to decouple the original problem and break it down into several sub-problems.

[0022] In step 3, continuous convex approximation methods such as slack variables and first-order Taylor expansion are used to transform the non-convex subproblem into a convex problem, and finally CVX is used to solve it.

[0023] Based on the idea of ​​iteration, step 4 repeatedly iterates the sub-problem results obtained in steps 2 and 3, so that the final optimization result continuously approaches a fixed value, which is the target active eavesdropping rate.

[0024] Compared with other simple trajectory design or interference power optimization methods, the present invention has a better eavesdropping rate while ensuring the success of eavesdropping. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to make the purpose, technical solutions and beneficial effects of the present invention more clear, the present invention provides the following drawings for illustration:

[0026] Figure 1 is the communication system model of the present invention;

[0027] Figure 2 A flowchart of the operation of the present invention;

[0028] Figure 3 The optimal flight trajectory map for the UAV;

[0029] Figure 4 It is the algorithm iteration convergence graph;

[0030] Figure 5 This is a convergence verification diagram of the present invention. DETAILED DESCRIPTION

[0031] The preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings in the embodiments of the present invention.

[0032] (1) Construction of communication model: Figure 1 As shown in the figure, this paper mainly studies a UAV active eavesdropping communication system. In this system, there is an illegal relay communication link, and UAV E actively eavesdrops on this communication link by interference. It is assumed that the communication link of this system is a line-of-sight link, and the information transmission between the illegal transmitting node S and the illegal receiving node D is adaptive. S represents the horizontal position of the illegal transmitting node S, q R represents the horizontal position of the illegal relay node R, z R Represents the vertical position of the illegal relay node R. D Indicates the horizontal position of the illegal receiving node D. E represents the horizontal trajectory of UAV E, z E represents the vertical trajectory of UAV E.

[0033] The channel gain from S to E and R can be expressed as:

[0034]

[0035] β0 represents the channel reference gain. The channel gain from R to E and D and the channel gain from E to D can be expressed as:

[0036]

[0037] The information received by the illegal relay node R can be expressed as

[0038]

[0039] Among them, P S represents the transmission power of the illegal transmitting node S, x S Indicates the transmitted signal, n R represents Gaussian white noise.

[0040] The illegal relay node R adopts AF mode to amplify, and its amplification factor can be expressed as

[0041]

[0042] Among them, P R represents the power of illegal relay nodes, σ 2 represents the channel Gaussian noise, σ 2 ~(0,N).

[0043] The information received by the illegal receiving node D can be expressed as:

[0044]

[0045] P E is the interference power of UAV E, x AN Represents the interference signal emitted by the UAV, n D represents Gaussian white noise. Its signal-to-interference-noise ratio can be expressed as:

[0046]

[0047] The information received by UAV E can be expressed as

[0048]

[0049] n E represents Gaussian white noise, and the signal-to-interference-noise ratio of drone E is expressed as

[0050]

[0051] The information rate of the illegal receiving node D and the receiving rate of the drone E are expressed as

[0052] R D [n] = log2(1 + γ D [n])

[0053] R E [n] = log2(1 + γ E [n])

[0054] With the goal of maximizing the active eavesdropping rate, an optimization mathematical model is constructed with the UAV jamming power, the UAV horizontal flight trajectory, and the UAV vertical flight trajectory as variables. The optimization problem can be expressed as:

[0055]

[0056] stC1:R D [n]≤R E [n]

[0057] C2:q E [0] = q I ,q E [N] = q F

[0058] C3:z E [0]=H I ,z E [N]=H F

[0059]

[0060] The entire eavesdropping time is divided into N time slots, q E [n] represents the horizontal coordinate of UAV E in the nth time slot, P E [n] represents the interference power of the UAV in the nth time slot, z E [n] represents the vertical height of the UAV trajectory in the nth time slot, R D [n] is the information rate received in the nth time slot D, R E [n] is the information rate received in the nth time slot E, q E [0] represents the horizontal position of UAV E at time slot 0, q I represents the horizontal position of the starting point of the flight of UAV E, q E [N] represents the horizontal position of UAV E in the Nth time slot, q F Indicates the horizontal position of the flight endpoint of UAV E, z E [0] represents the flight altitude of UAV E at time slot 0, H I Indicates the altitude of the starting point of the flight of UAV E, z E [N] represents the flight altitude of UAV E in the Nth time slot, H F Indicates the altitude of the flight endpoint of UAV E, Indicates the maximum interference power of the UAV; Indicates the maximum interference power of the drone.

[0061] Condition C1 represents the prerequisite for successful eavesdropping. C2 and C3 are the constraints for the horizontal and vertical starting and ending positions, respectively. C4 represents the interference power constraint.

[0062] (2) Determine whether it is 2D trajectory optimization or 3D trajectory optimization based on the starting and ending altitudes of the drone.

[0063] When the starting and ending altitudes of the UAV are on the same horizontal plane or there is no need for 3D planning, a 2D optimization mathematical model is constructed with the UAV interference power and horizontal trajectory as variables, under the constraints of E eavesdropping success, UAV flight speed, acceleration, and interference power:

[0064]

[0065] stC1:R D [n]≤R E [n]

[0066] C2:q E [0] = q I ,q E [N] = q F

[0067]

[0068] C4:v xy [n+1]=v xy [n]+a xy [n]δ t

[0069] C5:v xy [0]=v xy [N]

[0070]

[0071] Where v xy [n] represents the horizontal flight speed of UAV E in the nth time slot, a xy [n] represents the horizontal acceleration of UAV E in the nth time slot, δ t Indicates time slot, Indicates the maximum horizontal flight speed, Indicates the maximum horizontal acceleration. v xy [0] represents the horizontal flight speed of the drone at time slot 0, v xy [N] represents the horizontal flight speed of the drone in the Nth time slot. C1 represents the constraint for successful eavesdropping; C2 represents the constraints on the drone's horizontal starting and ending positions; C3 and C4 represent the relationship between the drone's horizontal position, horizontal velocity, and horizontal acceleration; C5 represents the equality of the drone's horizontal starting and ending velocities; C6 represents the drone's maximum horizontal velocity and acceleration constraints; and C7 represents the interference power constraint.

[0072] When the starting and ending altitudes of the drone are not on the same horizontal plane or other scenarios that require 3D planning, the following 3D optimization mathematical model is used, with the constraints of E eavesdropping success, drone flight speed, acceleration, and interference power as constraints, and drone interference power, horizontal trajectory, and vertical trajectory as variables:

[0073]

[0074] stC1:R D [n]≤R E [n]

[0075] C2:q E [0] = q I ,q E [N] = q F

[0076]

[0077] C4:v xy [n+1]=v xy [n]+a xy [n]δ t

[0078] C5:v xy [0]=v xy [N]

[0079]

[0080] C7:z E [0]=H I ,z E [N]=H F

[0081]

[0082] C9:v z [n+1]=v z [n]+a z [n]δ t

[0083] C10:v z [0]=v z [N]

[0084]

[0085] Where v z [n] represents the vertical flight speed of UAV E in the nth time slot, a z [n] represents the vertical acceleration of UAV E in the nth time slot, Indicates the maximum vertical flight speed, Indicates the maximum vertical acceleration. v z [0] represents the vertical flight speed of the UAV at time slot 0, v z [N] represents the vertical flight speed of the drone in the Nth time slot. C1 represents the eavesdropping success constraint; C2 represents the constraints on the drone's horizontal starting and ending positions; C3 and C4 represent the relationship between the drone's horizontal position, horizontal velocity, and horizontal acceleration; C5 represents the equality of the drone's horizontal starting and ending velocities; C6 represents the drone's maximum horizontal velocity and acceleration constraints; C7 represents the constraints on the drone's vertical starting and ending positions; C8 and C9 represent the relationship between the drone's vertical position, vertical velocity, and vertical acceleration; C10 represents the equality of the drone's vertical starting and ending velocities; C11 represents the drone's maximum vertical velocity and acceleration constraints; and C12 represents the interference power constraint.

[0086] (3) The optimization problem constructed by the present invention is a non-convex problem with multivariable coupling. The original optimization problem with multivariable coupling is decoupled into sub-problems related only to the power of the interfering UAV and the flight trajectory of the UAV 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.

[0087] For problem P1, the BCD method is used to decouple and obtain two sub-problems: horizontal trajectory optimization (P1.1) and interference power optimization (P1.2).

[0088] (3.1) The horizontal trajectory optimization (P1.1) can be expressed as:

[0089]

[0090] sqFt D [n]≤R E [n]

[0091] q E [0] = q I ,q E [N] = q F

[0092]

[0093] v xy [n+1]=v xy [n]+a xy [n]δ t

[0094] v xy [0]=v xy [N]

[0095]

[0096] For P1.1, the formula can be simplified to:

[0097] R E [n] = R E1 [n]-R E2 [n]

[0098]

[0099] d RE [n]=||q E [n]-q R || 2 +||z E -z R || 2 ,

[0100]

[0101] The above problem is difficult to solve, so we introduce slack variables. Substituting into the original formula we can get

[0102]

[0103] right Perform a first-order Taylor operation to obtain an upper bound

[0104]

[0105] Indicates that the slack variable Substitute R D The value obtained in [n], Indicates d ED Slack variables for [n], represents the jth iteration The value of express Upper bound of the first-order Taylor expansion.

[0106] right Perform a first-order Taylor operation to obtain the lower bound

[0107]

[0108] Indicates that the slack variable and Substitute R E1 The value obtained in [n], Indicates d RE Slack variables for [n], represents the jth iteration The value of Indicates d SE Slack variables for [n], represents the jth iteration d SE The value of [n], express The lower bound of the first-order Taylor expansion of , d SR represents the square of SR distance, ρ S Indicates the ratio of transmit power to channel noise.

[0109] right Perform a first-order Taylor operation to obtain the lower bound

[0110]

[0111] Indicates that the slack variable Substitute R E2 The value obtained in [n], express The lower bound of the first-order Taylor expansion of P E [n] represents the interference power of the UAV, represents the jth iteration The value of .

[0112] At the same time, d ED [n] Using the first-order Taylor expansion, we can get

[0113]

[0114] Subproblem P1.1: Remove the successful eavesdropping constraint R D [n]≤R E [n], and introduce slack variables Transform Problem P1.1 into the following problem.

[0115]

[0116] q E [0] = q I ,q E [N] = q F ,

[0117]

[0118] v xy [0]=v xy [N],

[0119]

[0120] In the formula It is R D[n] Upper bound of the first-order Taylor expansion, R E =R E1 -R E2 . and R E1 and R E2 The lower bound of the first-order Taylor expansion, d SE [n],d RE [n] and d ED [n] is the square of the distance between SE, RE, and ED, Indicates d ED [n] Lower bound of the first-order Taylor expansion.

[0121] Q represents the set of horizontal flight positions of UAVs in all time slots {q E [n], n=0,...,N}, S1[n] represents R D [n] slack variable, S2[n] represents R E1 [n] slack variable, S3[n] represents R E2 Slack variables for [n], They are d SE [n],d RE [n] and d ED Slack variable for [n], q E [0] represents the horizontal position of the 0th time slot E, q I represents the horizontal position of the starting point of the flight of UAV E, q E [N] represents the horizontal position of the UAV in the Nth time slot, q F Indicates the horizontal position of the flight endpoint of UAV E, v xy [0] represents the horizontal flight speed of the drone at time slot 0, v xy [N] represents the horizontal flight speed of the UAV in the Nth time slot, Indicates the maximum horizontal flight speed, Indicates the maximum horizontal acceleration.

[0122] The above problem is a standard convex problem and can be solved directly using CVX.

[0123] The power optimization sub-problem can be expressed as:

[0124]

[0125] sqFt D [n]≤R E [n],

[0126]

[0127] RD [n] The lower bound is obtained by first-order Taylor expansion

[0128]

[0129] R D [n] = R D1 [n]-R D2 [n],

[0130]

[0131] R D1 [n] The upper bound is obtained by first-order Taylor expansion

[0132]

[0133] The original power optimization subproblem is transformed into the following problem:

[0134]

[0135] Represents R D The lower bound of [n], R D [n] = R D1 [n]-R D2 [n], Represents R D1 The upper bound of [n]. R D [n] is the information rate received in the nth time slot D, R E [n] is the information rate received in the nth time slot E. R D1 [n] and R D2 [n] represents the formula R D [n] = R D1 [n]-R D2 The minuend and subtrahend of [n].

[0136] The above problem is a standard convex problem and can be solved directly using CVX.

[0137] (3.2) For problem P2, the BCD method is used to decouple the problem, resulting in three sub-problems: horizontal trajectory optimization (P1.1), interference power optimization (P1.2), and vertical trajectory optimization (P2.1). The horizontal trajectory optimization sub-problem and the interference power optimization sub-problem have been explained in 3.1. The following mainly focuses on the vertical trajectory optimization sub-problem:

[0138]

[0139] stz E [0]=H I ,z E [N]=HF ,

[0140]

[0141] z E [n]≤H max ,z E [n]≥H min ,

[0142] v z [n+1]=v z [n]+a z [n]δ t ,n=0,1,...,N-1,

[0143] v z [0]=v z [N]

[0144]

[0145] The above problem is difficult to solve, so we introduce slack variables The above formula can be expanded to express as

[0146]

[0147] In the formula The variable Substitute R D The value obtained in [n], The variable and Substitute R E1 The value obtained in [n], The variable Substitute R E2 The value obtained in [n], is to set the slack variable z h [n] Substitute d ED The value obtained in [n], is to set the slack variable z h [n] Substitute d SE The value obtained in [n], is to set the slack variable z ER [n] Substitute d RE The value obtained in [n], z h [n] is the flight altitude of the drone z E [n] squared slack variable, z ER [n] is the flight altitude of the drone z E [n] and relay node R height z R The slack variable is the square of the difference between [n].

[0148] right Use first-order Taylor expansion to obtain the upper bound

[0149]

[0150] right Use first-order Taylor expansion to obtain the lower bound

[0151]

[0152] right Use first-order Taylor expansion to obtain the lower bound

[0153] right Use first-order Taylor expansion to obtain the lower bound

[0154]

[0155] The final formula can be expressed as

[0156]

[0157] S4[n]≤S5[n]-S6[n],

[0158]

[0159] z ER [n]≥(z E [n]-z R ) 2 ,

[0160] z E [0]=H I ,z E [N]=H F

[0161]

[0162] v z [n+1]=v z [n]+a z [n]δ t

[0163] v z [0]=v z [N]

[0164]

[0165] Where Z represents the set of vertical flight heights of all time slots UAVs {z E[n], n=0,...,N}, S2 represents the set of slack variables S4[n], S5[n], S6[n] Z1 represents the slack variable z h [n],z ER The collection of [n] v z represents the vertical flight speed, a z Indicates vertical flight acceleration. S4[n] indicates R D Slack variables for [n], yes The upper bound of the first-order Taylor expansion, S5[n] represents R E1 The slack variables, express The lower bound of the first-order Taylor expansion, S6[n] represents R E2 The slack variables, express The lower bound of the first-order Taylor expansion, z h [n] represents z E The slack variable of [n] squared, represents z E The lower bound of the first-order Taylor expansion of the square of [n], z R [n] represents the height of relay node R, z ER [n] represents the flight altitude of the drone z E [n] and the vertical height z of the relay node R R The slack variable is the square of the difference between [n]. This is a standard convex problem and can be solved directly.

[0166] (4) Use iterative algorithm to solve the UAV interference power and UAV flight trajectory.

[0167] An iterative algorithm process is designed to connect the above convex optimization problems in series. The 2D steps are shown in Table 1, and the 3D steps are shown in Table 2.

[0168]

[0169] Table 1

[0170]

[0171] Table 2

[0172] Figure 2 This is a flowchart of the overall and initialization parts of the iterative algorithm proposed by the present invention for solving the optimization problem. Its detailed process corresponds to the specific solution steps of the above optimization problem.

[0173] Figure 3The flowchart of the 2D iterative algorithm and 3D iterative algorithm proposed by the present invention for solving the optimization problem. The detailed process corresponds to the specific solution steps of the above optimization problem.

[0174] Figure 4 This invention is based on the simulation verification of the proposed solution. Figure 3 The process finally results in Figure 4 The optimal flight trajectory of the drone is shown.

[0175] Figure 5 The simulation verifies the convergence of the scheme of the present invention. It can be seen from the simulation diagram that the algorithm proposed in the scheme of the present invention is effective.

Claims

1. A UAV trajectory design and power optimization method based on active eavesdropping, characterized in that: The following steps are involved: Build a communication system model: Determine the locations of the illegal node S, illegal relay node R, and illegal receiving node D, as well as the starting and ending locations of the active eavesdropping drone E. There is no direct link between S and D, and they can only be relayed through R. The information transmission between S and D is adaptive. E simultaneously receives link information from S and R and actively interferes with D, ultimately achieving active eavesdropping and maximizing the eavesdropping rate. With the goal of maximizing the active eavesdropping rate, an optimization mathematical model is constructed with the UAV jamming power, the UAV horizontal flight trajectory, and the UAV vertical flight trajectory as variables: s.t.C1:R D [n]≤R E [n] C2:q E [0]=q I ,q E [N]=q F C3:z E [0]=H I ,With E [N]=H F The entire eavesdropping time is divided into N time slots, q E [n] represents the horizontal coordinate of UAV E in the nth time slot, P E [n] represents the interference power of the UAV in the nth time slot, z E [n] represents the vertical height of the UAV trajectory in the nth time slot, R D [n] is the information rate received in the nth time slot D, R E [n] is the information rate received in the nth time slot E, q E [0] represents the horizontal position of UAV E at time slot 0, q I represents the horizontal position of the starting point of the flight of UAV E, q E [N] represents the horizontal position of UAV E in the Nth time slot, q F Indicates the horizontal position of the flight endpoint of UAV E, z E [0] represents the flight altitude of UAV E at time slot 0, H I Indicates the altitude of the starting point of the flight of UAV E, z E [N] represents the flight altitude of UAV E in the Nth time slot, H F Indicates the altitude of the flight endpoint of drone E; represents the maximum interference power of the drone; C1 represents the prerequisite for successful eavesdropping, C2 and C3 are the constraints of the horizontal and vertical starting and ending positions respectively, and C4 represents the interference power constraint; Determine whether to use 2D trajectory optimization or 3D trajectory optimization based on the starting and ending positions of the drone; The BCD method is used to decouple the 2D optimization problem into two sub-problems: UAV horizontal flight trajectory optimization and UAV interference power optimization. The 3D optimization problem is decoupled into three sub-problems: UAV horizontal flight trajectory optimization, UAV vertical flight trajectory optimization, and UAV interference power optimization. For each sub-problem, the continuous convex optimization method is used to transform the non-convex sub-problem into a convex problem for solution. The iterative algorithm is used to iterate the solved sub-problems to obtain the optimized flight trajectory and interference power, maximizing the eavesdropping rate while ensuring the success of eavesdropping.

2. The method for UAV trajectory design and power optimization based on active eavesdropping according to claim 1, characterized in that: The 2D optimization problem is s.t.C1:R D [n]≤R E [n] C2:q E [0]=q I ,q[N]=q F C4:v xy [n+1]=v xy [n]+a xy [n]δ t C5:v xy [0]=v xy [N] Where v xy [n] represents the horizontal flight speed of the UAV in the nth time slot, a xy [n] represents the horizontal acceleration of the UAV in the nth time slot, δ t Indicates time slot, Indicates the maximum horizontal flight speed, represents the maximum horizontal acceleration, v xy [0] represents the horizontal flight speed of the drone at time slot 0, v xy [N] represents the horizontal flight speed of the UAV in the Nth time slot; C1 represents the constraint on successful eavesdropping; C2 represents the constraints on the starting and ending positions of the UAV in the horizontal direction; C3 and C4 represent the relationship between the UAV's horizontal position, horizontal speed, and horizontal acceleration; C5 represents that the UAV's horizontal starting speed and horizontal ending speed are equal; C6 represents the UAV's horizontal maximum speed and acceleration constraints; and C7 represents the interference power constraint.

3. The method for UAV trajectory design and power optimization based on active eavesdropping according to claim 2, characterized in that: The 3D optimization problem is s.t.C1:R D [n]≤R E [n] C2:q E [0]=q I ,q E [N]=q F C4:v xy [n+1]=v xy [n]+a xy [n]δ t C5:v xy [0]=v xy [N] C7:z E [0]=H I ,z E [N]=H F C9:v z [n+1]=v z [n]+a z [n]δ t C10:v z [0]=v z [N] Where v z [n] represents the vertical flight speed of the UAV in the nth time slot, a z [n] represents the vertical acceleration of the UAV in the nth time slot, Indicates the maximum vertical flight speed, represents the maximum vertical acceleration, v z [0] represents the vertical flight speed of the UAV at time slot 0, v z [N] represents the vertical flight speed of the UAV in the Nth time slot; C1 represents the constraint on successful eavesdropping; C2 represents the constraint on the starting and ending positions of the UAV in the horizontal direction; C3 and C4 represent the relationship between the UAV's horizontal position, horizontal velocity and horizontal acceleration; C5 represents the equality of the UAV's horizontal starting velocity and horizontal ending velocity; C6 represents the UAV's horizontal maximum velocity and acceleration constraints; C7 represents the constraint on the starting and ending positions of the UAV in the vertical direction; C8 and C9 represent the relationship between the UAV's vertical position, vertical velocity and vertical acceleration; C10 represents the equality of the UAV's vertical starting velocity and vertical ending velocity; C11 represents the UAV's vertical maximum velocity and acceleration constraints; C12 represents the constraint on interference power.

4. The method for UAV trajectory design and power optimization based on active eavesdropping according to claim 2 or 3, characterized in that: The UAV horizontal flight trajectory optimization sub-problem is 5. The method for UAV trajectory design and power optimization based on active eavesdropping according to claim 4, characterized in that: Subproblem (P1.1): Remove the successful eavesdropping constraint R D [n]≤R E [n], and introduce slack variables Convert P1.1 to: S1[n]≤S2[n]-S3[n], q E [0]=q I ,q E [N]=q F , v xy [0]=v xy [N], In the formula It is R D [n] Upper bound of the first-order Taylor expansion, and R E1 and R E2 The lower bound of the first-order Taylor expansion, d SE [n],d RE [n] and d ED [n] is the square of the distance between SE, RE, and ED, Indicates d ED [n] The lower bound of the first-order Taylor expansion, Q represents the set of horizontal flight positions of all time slots of the UAV {q E [n], n=0,...,N}, S1[n] represents R D [n] slack variable, S2[n] represents R E1 [n] slack variable, S3[n] represents R E2 Slack variables for [n], They are d SE [n],d RE [n] and d ED Slack variable for [n], q E [0] represents the horizontal position of the 0th time slot E, q I represents the horizontal position of the starting point of the flight of UAV E, q E [N] represents the horizontal position of the UAV in the Nth time slot, q F Indicates the horizontal position of the flight endpoint of UAV E, v xy [0] represents the horizontal flight speed of the drone at time slot 0, v xy [N] represents the horizontal flight speed of the UAV in the Nth time slot, Indicates the maximum horizontal flight speed, Indicates the maximum horizontal acceleration, for R E [n] According to R E [n] = R E1 [n]-R E2 [n] form, R E1 [n] and R E2 [n] represents the formula R E [n] = R E1 [n]-R E2 Minuend and subtrahend in [n].

6. The method for UAV trajectory design and power optimization based on active eavesdropping according to claim 2 or 3, characterized in that: The UAV interference power optimization sub-problem is 7. The method for UAV trajectory design and power optimization based on active eavesdropping according to claim 6, characterized in that: Transform subproblem (P1.2) into the following question: Where P represents the set of UAV interference powers in all time slots {P E [n],n=0,...,N}, Represents R D The lower bound of [n], R D [n] = R D1 [n]-R D2 [n], Represents R D1 The upper bound of [n], R D [n] is the information rate received in the nth time slot D, R E [n] is the information rate received in the nth time slot E, R D1 [n] and R D2 [n] represents the formula R D [n] = R D1 [n]-R D2 The minuend and subtrahend of [n].

8. The method for UAV trajectory design and power optimization based on active eavesdropping according to claim 3, characterized in that: The sub-problem of optimizing the vertical flight trajectory of the UAV is:

9. The method for UAV trajectory design and power optimization based on active eavesdropping according to claim 8, characterized in that: Introducing slack variables, Convert subproblem (P2.1) into a convex problem and solve it: S4[n]≤S5[n]-S6[n], z ER [n]≥(z E [n]-z R ) 2 , z E [0]=H I ,z E [N]=H F v z [n+1]=v z [n]+a z [n]δ t v z [0]=v z [N] Where Z represents the set of vertical flight heights of all time slots UAVs {z E [n], n=0,...,N}, S2 represents the set of slack variables S4[n], S5[n], S6[n] Z1 represents the slack variable z h [n],z ER [n], the set v z represents the vertical flight speed, a z represents vertical flight acceleration, S4[n] represents R D Slack variables for [n], It is R D [n] is the upper bound of the first-order Taylor expansion, S5[n] represents R E1 The slack variables, Represents R E1 The lower bound of the first-order Taylor expansion, S6[n] represents R E2 The slack variables, Represents R E2 The lower bound of the first-order Taylor expansion, z h [n] represents z E The slack variable of [n] squared, represents z E The lower bound of the first-order Taylor expansion of the square of [n], z R [n] represents the height of relay node R, z ER [n] represents the flight altitude of the drone z E [n] and the vertical height z of the relay node R R The slack variable is the square of the difference between [n].

10. A communication system, characterized in that: The system includes an illegal node S, an illegal relay node R, an illegal receiving node D and a drone E. There is no direct link between S and D, and they can only be relayed through R. The information transmission between S and D is adaptive. E receives the link information of S and R at the same time, and actively interferes with D. The system can execute the drone trajectory design and power optimization method based on active eavesdropping as described in any one of claims 1 to 9.

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