Double-unmanned aerial vehicle three-dimensional trajectory optimization method for physical layer security

Abstract

The invention relates to a physical layer security-oriented double-unmanned aerial vehicle three-dimensional trajectory optimization method, in particular to an optimization method based on a security data collection system assisted by double unmanned aerial vehicles. Firstly, an optimization problem is constructed to maximize the total achievable secrecy rate of the system, and three-dimensional trajectory design of the unmanned aerial vehicle, interference power interfering the unmanned aerial vehicle, transmission power of ground equipment and transmission scheduling are involved. In consideration of existence of an air eavesdropper, an approximate lower bound is adopted to simplify a solving process of a non-convex optimization problem. Thirdly, an original problem is decoupled into four sub-problems through a BCD method, and each sub-problem is converted into a manageable convex optimization problem through introduction of slack variables and a gradual convex approximation method; a numerical result verifies the effectiveness of the proposed algorithm in various scenes, and shows that the average secrecy rate of a data collection system can be remarkably improved by the three-dimensional trajectory design of the unmanned aerial vehicle.

Description

Technical Field

[0001] The present invention mainly relates to the field of UAV communication, specifically, to combine the information security brought by physical layer security with the characteristics of UAV mobility and deployability, to build a UAV-assisted secure data collection and communication system, and to transmit information to UAVs from multiple ground users in an Internet of Things system under the condition of probabilistic line-of-sight link communication. Through theoretical derivation and simulation verification, a three-dimensional (3D) flight trajectory of dual UAVs oriented to physical layer security is designed to achieve transmission with a maximized average confidentiality rate. Background Art

[0002] The statements in this section only provide background information related to the present disclosure, and these statements may constitute prior art. In the process of implementing the present invention, the inventors found that there are at least the following problems in the prior art.

[0003] Unmanned aerial vehicles (UAVs) have become a revolutionary technology that has been widely used in various fields. Initially, they were designed and developed for military use, but have now expanded to civilian and commercial fields, including agriculture, disaster management, surveillance, and aerial photography. These applications not only cover surveillance and monitoring, but also include aerial imaging, precision agriculture, smart logistics, law enforcement, disaster response, and pre-hospital emergency care. With the rapid advancement of drone technology, aspects such as autonomous flight capabilities, payload capacity, and flight endurance have been significantly improved, which has promoted the widespread use of drones around the world. The development of these technologies has not only brought new opportunities to various industries, but also brought a series of challenges. These challenges involve multiple aspects, including how to effectively regulate the use of drones, ensure flight safety, and how to effectively integrate drone technology with existing infrastructure. Therefore, in-depth exploration and research in these areas is particularly important. Modifying the positioning of drones or planning flight paths can ensure a stable Line of Sight (LoS) connection with ground nodes for optimal reliability. Therefore, the altitude and lateral position of drones play a vital role in improving the efficiency of drone communication systems. Trajectory design has become a key challenge that needs to be solved. In the literature [Chen Xinying, Sheng Min, Li Bo, Zhao Nan. A review of drone communications for 6G [J]. Journal of Electronics and Information Technology, 2022, 44(0): 1-9.] The commercial success of 5G has brought revolutionary changes to modern life and promoted the development of the 6th generation of mobile communication technology. In the future 6G network, drones will play a key role, and their application scenarios cover multiple fields, such as the construction of swarm base stations, the deployment of holographic projections, long-distance relay communications, and data collection. In order to realize these innovative applications, 6G networks will rely on a series of key technologies, including terahertz communications, ultra-large-scale antenna arrays, and endogenous artificial intelligence.

[0004] However, after entering the 6G era, UAV communications still face many challenges. The limitation of flight time restricts UAVs from performing long-term missions; the demand for network convergence requires UAVs to be able to operate flexibly in different network environments; and the compatibility of smart reflective surfaces also needs to be solved urgently to ensure that UAVs can work effectively with emerging technologies. To solve these challenges, we need interdisciplinary cooperation and continuous technological innovation. Currently, communication systems based on UAV trajectory design have been proposed and classified according to the different roles played by UAVs in wireless communication networks. These roles include base station UAV communication systems, relay UAV communication systems, and UAV auxiliary communication systems that provide support for aerial users. This classification method helps to better understand the functions of UAVs in the network and promote the further development of various applications. For example, the typical base station UAV proposed in the literature [Qingqing Wu, Yong Zeng, Rui Zhang. Joint trajectory and communication design for Multi-UAV enabled wireless networks [J]. IEEE Transactions on Wireless Communications, 2018, 17 (3): 2109-2121.] maximizes the system transmission rate by jointly optimizing the UAV transmission power, UAV flight trajectory and user scheduling coefficient. At the same time, the energy consumption of UAVs is also a point worth considering. In order to improve energy efficiency, the literature [Zeng Y, Xu J, Zhang R. Energy minimization for wireless communication with rotary-wing UAV [J]. IEEE Trans. Wireless Commun., 2019, 18 (4): 2329-2345.] formulated an energy minimization problem by jointly optimizing the UAV trajectory and communication time allocation as well as the total task completion time. The optimization goal is to minimize the total UAV energy consumption while meeting the communication throughput requirements of each ground node. The literature [Lei H, Yang H, Park KH, et al. Joint trajectory design and user scheduling for secure aerial underlay IoT systems [J]. IEEE Internet Things J., 2023, 10 (15): 13637-13648.] studied an aerial-assisted IoT system with a single position-uncertain eavesdropper.The 2D trajectory, transmit power, and user scheduling of cognitive UAVs are jointly designed to maximize the average confidentiality rate of cognitive users (CUs).

[0005] However, existing research on UAV flight route design usually assumes that there is a line-of-sight channel between the UAV and the user or eavesdropper. However, this assumption is too simple and ignores factors such as obstacles and small-scale fading. Therefore, the designed flight route may not meet the conditions of line-of-sight communication in some sections due to the existence of obstacles, and is not suitable for practical use. In particular, when the UAV flies at a lower altitude, the shadow effect is significantly enhanced, and obstacles hinder the signal propagation between the UAV and the ground node, which will affect the communication quality. Therefore, a recent technology uses a probabilistic line-of-sight channel model to solve this problem. The probabilistic line-of-sight (PLoS) channel model is proposed in the literature [Al-Hourani A, Kandeepan S, Lardner S. Optimal LAP Altitude for Maximum Coverage [J]. IEEE Wireless Commun. Lett., 2014, 3 (6): 569-572.]. Specifically, the probability of generating LoS communication with the ground node increases with the increase of the elevation angle, which can be achieved by moving the UAV horizontally closer to the ground node or increasing its altitude. Reference [Xu Yuxuan, Cui Miao, Zhang Guangchi, et al. Research on optimization design of UAV secure communication under probabilistic line-of-sight air-ground channel [J]. Computer Application Research, 2023, 40(02): 554-560.] Considering the information transmission security of the UAV multi-user communication system at the physical layer, the air-ground channel between the UAV and the ground node is modeled as a more realistic probabilistic line-of-sight channel. Under the constraints of the UAV flight conditions and discrete user scheduling, the minimum average safety rate of users is maximized by jointly designing the UAV's three-dimensional flight trajectory and user scheduling.

[0006] For example, the patent application number 202111058338.9, entitled “Offline-online hybrid optimization method for drone flight routes for secure communications”, uses a probabilistic line-of-sight channel model, which is closer to the actual communication environment. At the same time, the proposed three-dimensional drone trajectory optimization further utilizes the additional degrees of freedom of the drone’s vertical trajectory to improve the drone’s secure communication rate. However, according to the applicant’s research, due to the limited energy of the drone and the complexity of the solution brought about by the introduction of the PLoS channel model, the above patent cannot maximize the system’s average secure rate while ensuring downlink communications with ground users and suppressing the eavesdropper’s eavesdropping capabilities as much as possible. Summary of the invention

[0007] In view of the above problems, the object of the present invention is to solve part of the problems in the prior art, or at least alleviate these problems.

[0008] A dual UAV three-dimensional trajectory optimization method for physical layer security includes the following steps:

[0009] S1: Construct a communication system model: Set up a dual-drone-assisted secure data collection system, where drones U and J serve as the air base station and air friendly jammer of the data collection network respectively, flying according to a certain initial trajectory. The communication link channel model between drone U and the ground node is a PLoS model. The energy consumption of drones U and J is limited. At the same time, there is a drone E in the air as an eavesdropper trying to eavesdrop on confidential information.

[0010] S2: Constructing an optimization mathematical model: With the goal of maximizing the average safe achievable rate of the system, an optimization problem is constructed to maximize the total achievable confidentiality rate of the system, involving the optimization mathematical model of GD transmission scheduling, the interference power of UAV J and the transmission power of GD, the horizontal flight trajectory of UAV U and the three-dimensional trajectory of UAV J, and the vertical flight trajectory of UAV U; the optimization mathematical model is:

[0011]

[0012] in, is the average confidentiality rate of the kth ground device (GD) in the nth time slot; A represents the GD transmission scheduling, P represents the interference power of UAV J and the transmission power of GD, Q represents the horizontal flight trajectory of UAV U and the three-dimensional trajectory of UAV J, H represents the vertical flight trajectory of UAV U, Θ represents the elevation angle of UAV U with the ground user during flight; N represents the number of time slots, n represents the nth time slot, α k [n] represents a binary variable, P k [n] represents the transmission power of UAV U, P J [n] represents the transmission power of UAV J; and They represent the maximum instantaneous power and average power of GD during transmission, and They represent the maximum instantaneous power and average power of UAV J during the transmission process respectively; Yes D k and the elevation angle between X, X∈{U,E},q U [n], q E [n] and q J [n] represents the horizontal position of UAVs U, E and J respectively, arctan(x) is a concave function; q i [n+1], q i[n] represents the horizontal position of the UAV at the n+1th and nth time slots, respectively, and z i [n+1], z i [n] represents the vertical positions of drones U and J at the n+1th and nth time slots, respectively; D min Indicates the minimum safe distance between drones, H max and H min Represents the maximum and minimum flight altitude of the drone; V xy and V z is the maximum horizontal and vertical speed that the UAV can fly in each time slot; δ t Defines the length of each flight time slot of the drone; q i [1] z i [1] represents the horizontal and vertical flight positions of UAVs U and J at the initial moment, q i [N], z i [N] represents the horizontal and vertical flight positions of UAVs U and J at the final moment; P i hor [n] represents the horizontal energy consumption of UAVs U and J, P i ver [n] represents the energy consumption of UAVs U and J in the vertical direction; represents the horizontal energy consumption of UAVs U and J in the nth time slot, represents the vertical energy consumption of UAVs U and J in the nth time slot; μ represents the additional signal attenuation factor in the NLoS environment; N represents the time slot, and the entire time is discretized as

[0013] Among them, the average confidentiality rate of the kth ground device (GD) in the nth time slot is approximately

[0014]

[0015] in also The G2A link is assumed to follow a probabilistic LoS channel model. This model takes into account the changing conditions that affect the visibility between the ground transmitter and the aerial receiver, thereby providing a probabilistic assessment of the link performance. This approach is essential to accurately describe the communication dynamics in scenarios where environmental factors may affect connectivity. In this context, the probability of a LoS connection in the nth time slot is expressed as:

[0016]

[0017] in Yes D kThe elevation angle between and X, a>0 and b>0 are constants specified by the actual environment. Accordingly, the NLoS probability can be expressed as Based on the LoS or NLoS state, at the same time X∈{U,E}, D in the nth time slot k The channel coefficient between and X is expressed as or Where ρ0 represents the channel gain per unit reference distance in the LoS environment, μ represents the additional signal attenuation factor in the NLoS environment, and α L and α N is the path loss exponent for LoS and NLoS scenarios, which usually satisfies α L ≤α N .

[0018] S3: For the constructed optimization mathematical model, decoupling operation is performed based on the BCD method to obtain four sub-problems about GD transmission scheduling, interference power of UAV J and transmission power of GD, horizontal flight trajectory of UAV U and three-dimensional trajectory of UAV J, and vertical flight trajectory of UAV U. For each non-convex sub-problem, a convex approximation fitting method is used to convert it into a convex problem for solution;

[0019] S4: Use the iterative algorithm to solve the optimal GD transmission scheduling, the interference power of UAV J and the transmission power of GD, the horizontal flight trajectory of UAV U and the three-dimensional trajectory of UAV J, and the vertical flight trajectory of UAV U.

[0020] The sub-problem about GD transmission scheduling A for:

[0021]

[0022] Among them, η k It is an optimization problem The slack variables introduced in the subproblem It is a typical LP linear programming problem, which can be solved directly using the optimization toolkit.

[0023] The sub-problem of the interference power of UAV J and the transmission power P of GD is for:

[0024]

[0025] Furthermore, the sub-problem To perform approximate fitting of continuous convex approximation, the steps are as follows:

[0026] Constraints C2 to C4 are all linear constraints. First, Expressed as:

[0027]

[0028] Again The non-convex formula in the equation can be converted to convex by first-order Taylor expansion:

[0029]

[0030] in, represents a feasible point selected in the mth iteration; for this given feasible point, It is about optimizing variable P k [n] and P J [n] is a concave function. This property is crucial for the subsequent optimization process. Replace the original We effectively transform the problem into a convex optimization problem. They represent the probability of generating a LoS link between the kth GD and the UAV U and the eavesdropper E in the nth time slot; σ 2 represents the variance of additive Gaussian white noise; h JE [n] represents the channel coefficient between J and E in the nth time slot.

[0031] Based on the above transformation, the subproblem It is a standard convex optimization problem about the optimization variable P, which can be solved by the interior point method.

[0032] The sub-problems of the horizontal flight trajectory of UAV U and the three-dimensional trajectory Q of UAV J are for:

[0033]

[0034] Among them, η k It is an equivalence problem The slack variables introduced.

[0035] Furthermore, the sub-problem To perform approximate fitting of continuous convex approximation, the steps are as follows:

[0036] First, we deal with the non-convex constraint C1, since is non-concave, so the optimization problem is non-convex and difficult to solve. as well as

[0037] therefore, It can be expressed as:

[0038]

[0039] in, ρ0 represents the channel power gain per unit reference distance in LoS environment; w k Indicates the horizontal position of GD; θ kX [n] is D k The elevation angle between and X; α L and α N is the path loss index for LoS and NLoS scenarios, where a>0 and b>0 are constants specified by the actual environment;

[0040] The new constraints are:

[0041]

[0042] Then, after performing SCA convex transformation on the left side of the above equation, we get

[0043]

[0044] in, Y (m) [n] represents Y[n] at the mth iteration; SCA is an optimization method designed to solve non-convex optimization problems. It converts non-convex problems into a series of convex optimization problems by constructing an approximation of a convex function near the current solution. In each iteration step, the algorithm gradually updates the solution by solving these convex problems and finally converges to a local optimal solution. The SCA method is flexible and efficient, and is widely used in fields such as machine learning, signal processing, and control systems, especially for optimization tasks with nonlinear or complex constraints.

[0045] This will lead to non-convex terms Perform Taylor expansion:

[0046]

[0047] in, and They represent x at the mth iteration respectively. k [n] and t kU [n], the expanded form is as follows:

[0048]

[0049] use Replace C1 Constraint C1 is a convex constraint;

[0050] Next, we deal with constraint C2 and relax it to the following form:

[0051]

[0052] It is worth noting that the function arctan(1 / x) is a convex function. Therefore, the right side of constraint C2 is relative to the expression ||q U [n]-w k || shows convexity. By applying the SCA method, the following convex constraints are obtained:

[0053]

[0054] in

[0055]

[0056] represents q at the mth iteration U [n];

[0057] Next, to handle constraint C3, first rewrite it as:

[0058]

[0059] The present invention applies the SCA method to obtain the lower bound of the above norm square function, which is specifically as follows:

[0060]

[0061] in, and represents the current estimated position and height of UAV J in the mth iteration; T represents the flight period. The present invention linearizes the objective function by introducing these iterative estimates, thereby simplifying the optimization problem.

[0062] Finally, constraint C7 is processed by introducing a slack variable λ i , rewrite constraint C7 as:

[0063]

[0064] For i∈{U,J}, v i [n] represents the flight speed of UAVs U and J, and: Among them, P0 and P1 are two constants, representing the inherent blade surface power and induced power respectively; U tip represents the tip speed of the rotor blade; d0 and ρ represent the body drag ratio and air density respectively; the average rotor induced speed is represented by v0; s and A represent the rotor stiffness and rotor disk area respectively;

[0065] This is a variable q i [n] and λ i [n] is a non-convex constraint. Taylor expansion is performed on the right side of the inequality to rewrite the constraint as follows:

[0066]

[0067] Based on the above transformation, the subproblem It is a standard convex optimization problem about the optimization variable Q, which can be solved by the interior point method.

[0068] The sub-problem about the vertical flight trajectory H of UAV U for:

[0069]

[0070] In the above formula, for i∈{U,J}, represents the horizontal energy consumption of UAVs U and J in the nth time slot, represents the vertical energy consumption of UAVs U and J in the nth time slot, z i [n+1], z i [n] represents the vertical position of drones U and J in the n+1th and nth time slots, respectively, and q i [n+1], q i [n] represents the horizontal position of the UAV at the n+1th and nth time slots, respectively, V xy Indicates the maximum horizontal speed of the drone, V z Indicates the maximum vertical speed of the drone, θ kX [n] represents the elevation angle between GD and X, w k Indicates the horizontal position of GD, H max and H min Represents the maximum and minimum flight altitude of the drone, q i [1] z i [1] represents the horizontal and vertical flight positions of UAVs U and J at the initial moment, q i [N], z i [N] represents the horizontal and vertical flight positions of UAVs U and J at the final moment, δ t Defines the length of each flight time slot of the UAV, η k It is an equivalence problem The slack variables introduced.

[0071] Furthermore, the sub-problem To perform approximate fitting of continuous convex approximation, the steps are as follows:

[0072] It is non-convex due to the existence of constraints C2 and C3. In addition, the constraint C1 Not only is it affected by H, but also by This interdependence increases the complexity of the problem, further leading to its non-convex nature. In short, non-convexity comes from specific constraints that do not satisfy the convex property and the complex relationships between the involved variables.

[0073] First we deal with the nonlinear constraint C2. We relax it to the following form:

[0074]

[0075] Among them, the function arctan(x) is a concave function; use SCA to transform the above formula into:

[0076]

[0077] in, and Indicates that in the mth iteration z U The value of [n];

[0078] Next, we process constraints C3 and rewrite them into the following form using SCA technology:

[0079]

[0080] Finally, we process constraint C1. Re-express it as:

[0081]

[0082] In the above formula Approximately:

[0083]

[0084] in, and They represent x at the mth iteration. k [n] and t kU [n]; will Replace with Constraint C1 is also rewritten as a convex constraint;

[0085] Based on the above transformation, the subproblem It is a standard convex optimization problem about the optimization variable H, which can be solved by the interior point method.

[0086] The interference signal emitted by the UAV J is a Gaussian pseudo-random sequence or a deterministic waveform similar to the desired signal structure.

[0087] A communication system includes K ground users and a UAV U serving in the air. During this process, an eavesdropper E in the air constantly attempts to eavesdrop on confidential information. Meanwhile, a friendly jammer J in the air suppresses the eavesdropper's eavesdropping ability. The system is capable of executing the dual-UAV three-dimensional trajectory optimization method for physical layer security.

[0088] The present invention has the following beneficial effects:

[0089] 1. In order to deal with the impact of shadow effect on communication quality, the present invention proposes an aerial communication network based on probabilistic line-of-sight links, focusing on physical layer security and maximizing the average safe achievable rate. By optimizing the three-dimensional flight trajectory of the drone, the present invention reduces the risk of signal eavesdropping and improves the confidentiality and reliability of the communication link. This solution shows the potential for wide application of drone technology in the field of communication security;

[0090] 2. The present invention is aimed at the actual situation under the PLoS channel model, which is more accurate than the LoS channel model. With the goal of maximizing the average safe rate of the system, the present invention dynamically plans and designs the aerial base station UAV U and the jamming UAV J of the data collection network, the GD transmission power and the jammer interference power P, the horizontal flight trajectory of UAV U and the three-dimensional flight trajectory Q of UAV J, and the vertical flight trajectory H of UAV U. Among them, the fair scheduling of the ground data collection network and the maximization of the average safe achievable rate of the system are the ultimate expected effects and goals of the present invention;

[0091] 3. The present invention aims to combine the flexibility and deployability of drones with limited energy consumption to build a drone-assisted wireless communication system. In this system, one drone is responsible for receiving signals, while the other drone acts as a jammer, specifically targeting eavesdroppers to interfere and improve the physical layer security of communications. By optimizing the three-dimensional flight trajectory of the dual drones, we maximize the average achievable rate and security of the system under the constraints of energy consumption and the power interference threshold of the primary user. Since the proposed optimization problem is a non-convex problem with multivariable coupling and involves complex probabilistic line-of-sight links, solving this optimization problem is challenging. To this end, we constructed an optimization mathematical model and decoupled it based on the block coordinate descent method to form four sub-problems about GD transmission scheduling, the interference power of drone J and the transmission power of GD, the horizontal flight trajectory of drone U and the three-dimensional trajectory of drone J, and the vertical flight trajectory of drone U. For non-convex sub-problems, we use convex approximation to convert them into convex problems for solution. Simulation results show that the proposed scheme has good convergence and effectiveness in improving system performance and security. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 A communication system model of the present invention;

[0093] Figure 2 A flowchart of the operation of the present invention;

[0094] Figure 3 Iterative convergence diagrams for different schemes;

[0095] Figure 4 It is a transmission scheduling diagram under the algorithm proposed by the present invention;

[0096] Figure 5 This is a comparison chart of the horizontal flight trajectory of the UAV under different schemes;

[0097] Figure 6 This is a comparison chart of the vertical flight trajectory of the UAV under different schemes;

[0098] Figure 7 This is a graph showing the change of the vertical flight height of the UAV over time under different schemes;

[0099] Figure 8 This is a power variation diagram of the algorithm proposed in the present invention during the flight cycle;

[0100] Fig. 9 The power variation diagram of the comparison scheme during the flight cycle;

[0101] Fig.10 The following is a comparison chart of the safe speeds that can be achieved during the flight cycle under different schemes;

[0102] Fig.11 This is the change diagram of the horizontal flight speed of the UAV under different schemes;

[0103] Fig.12 This is the vertical flight speed change diagram of the UAV under different schemes;

[0104] Fig.13 This is a comparison chart of the average safe achievable rate of the system under different schemes over time. DETAILED DESCRIPTION

[0105] The present invention is further described below in conjunction with the accompanying drawings. The embodiments of the present invention are only used to illustrate the present invention rather than to limit the present invention. Without departing from the technical idea of ​​the present invention, various substitutions and changes can be made according to common technical knowledge and customary means in the field, which should all be included in the scope of the present invention.

[0106] In view of the fact that drones are subject to a large shadow effect when flying at a relatively low altitude, the present invention proposes a dual-drone aerial data collection network under a probabilistic line-of-sight link. Taking into account the airborne energy consumption of drones and maximizing the average confidentiality rate of the system, the three-dimensional trajectory of the dual-drone flight is optimized to ensure downlink communication with ground users and to suppress the eavesdropper's eavesdropping ability as much as possible. This will maximize the average security rate of the system.

[0107] like Figure 1 As shown in 2, a dual UAV three-dimensional trajectory optimization method for physical layer security includes the following steps:

[0108] S1: Build a communication system model:

[0109] A dual-drone-assisted secure data collection system is set up, where drones U and J serve as the aerial base station and aerial friendly jammer of the data collection network respectively, flying according to a certain initial trajectory. The communication link channel model between drone U and the ground node is the PLoS model. The energy consumption of drones U and J is limited. At the same time, there is a drone E in the air as an eavesdropper trying to eavesdrop on confidential information.

[0110] Figure 1 This paper studies a dual-UAV-assisted secure data collection system, in which one UAV acts as a legitimate aerial base station U and collects confidential data from K ground devices (GD) in a time-division multiplexing mode during flight, marked as D k (k=1,…,K). At the same time, another drone E moves from its initial position Fly to final location As a potential eavesdropper during flight. To enhance the security of wireless communications, the jamming drone J weakens E's eavesdropping ability by generating artificial noise. Assume that the jamming signal emitted by the drone J is a Gaussian pseudo-random sequence or a deterministic waveform similar to the desired signal structure, so these jamming signals can be offset by the base station U. All devices are assumed to be equipped with a single antenna.

[0111] S2: Construct optimization mathematical model:

[0112] With the goal of maximizing the average safety rate of the system, an optimization mathematical model is constructed with the three-dimensional trajectory design of the dual UAVs, the jamming power of the jamming UAVs, the transmission power of the ground equipment, and the transmission scheduling as constraints.

[0113] Without loss of generality, the flight period T is divided into N time slots, and the entire time is discretized as The time interval of each time slot is Here N is large enough so that the position of the UAV in each time slot can be considered approximately constant. The positions of these nodes are represented by a Cartesian coordinate system. In the nth time slot, the horizontal positions of U, E, and J are denoted by q U [n] = [x U [n],y U [n]] T ,q E [n] = [x E [n],y E [n]] T and q J [n] = [x J [n],y J [n]] T Their vertical positions are z U [n], z E [n] and z J [n]. In addition, D k The horizontal coordinate of w is k =[x k ,y k ] T express.

[0114] In addition, U and J must satisfy the following mobility constraints:

[0115]

[0116] Where V xy δ t and V z δ t is the maximum horizontal and vertical distance that the drone can fly in each time slot, assuming its maximum speed is V xy and V z (unit: m / s), and Represent the initial and final horizontal positions of the UAV, and Then represents the initial and final vertical positions of the drone. In addition, in the nth time slot, D k The distance to the receiver X(X∈{U,E}) is expressed as:

[0117]

[0118] The air-to-air communication link between UAVs is modeled as a LoS channel. Therefore, the channel coefficient between J and E in the nth time slot is expressed as:

[0119]

[0120] In addition, all drones need to maintain a safe distance to ensure flight safety. The minimum safe distance is as follows:

[0121]

[0122] Among them, D min Indicates the minimum safe distance between drones. Define the scheduling variable a k [n], so that a k [n] = 1 means that the kth GD is active in the nth time slot and communicates with U, while all other nodes remain inactive. Conversely, if the kth GD does not communicate, then a k [n] = 0. Assume that only one GD can transmit data to U in each time slot. Therefore, the present invention defines:

[0123]

[0124] The present invention assumes that the G2A link follows a probabilistic line-of-sight (PLoS) channel model. This model takes into account the changing conditions that affect the visibility between the ground transmitter and the aerial receiver, thereby probabilistically evaluating the link performance. This approach is essential for accurately characterizing the communication dynamics, especially in scenarios where environmental factors (such as obstacles and meteorological conditions) may affect the connection. In this case, the probability of a LoS connection in the nth time slot is expressed as:

[0125]

[0126] in, is the elevation angle between the kth GD and X, a>0 and b>0 are constants specified by the actual environment. Accordingly, the NLoS probability can be expressed as Depending on the LoS or NLoS state, D in the nth time slot k The channel coefficient between and X can be expressed as or Where ρ0 represents the channel gain per unit reference distance in the LoS environment, μ represents the additional signal attenuation factor in the NLoS environment, and α L and α N are the path loss exponents for LoS and NLoS scenarios, respectively, usually conditional on α L ≤α N The present invention does not consider small-scale fading. Therefore, the expected achievable rate from the kth GD to U in the nth time slot can be expressed as follows:

[0127]

[0128] in, and Here, P k [n] represents the transmission power of the kth GD, σ 2 represents the variance of the additive white Gaussian noise. Similarly, the expected achievable rate of E in time slot n can be expressed as:

[0129]

[0130] in, And P J [n] represents the transmission power of J. Since the rate in the NLoS scenario is much lower than that in the LoS scenario, and in order to reduce the complexity of the solution, we only consider the expected rate under LoS conditions. Therefore, and The approximate lower bound of can be expressed as:

[0131]

[0132] in, They represent the channel coefficients of communication between the eavesdropper E and the kth GD in LoS and NLoS situations respectively.

[0133] Then, the achievable confidentiality rate of the kth ground device in n time slots can be approximately expressed as:

[0134]

[0135] in, The horizontal energy consumption of UAVs U and J is expressed as:

[0136]

[0137] Where v i [n] represents the flight speed of U and J in the hovering state, and P0 and P1 are two constants, representing the inherent blade surface power and induced power, respectively. tip represents the tip speed of the rotor blade, d0 and ρ represent the fuselage drag ratio and air density respectively, the average rotor induced speed is denoted as v0, s and A represent the rotor stiffness and rotor disc area respectively.

[0138] The energy consumption of UAVs U and J in the vertical direction can be expressed as:

[0139]

[0140] Where W represents the weight of U and J. And v i Indicates the vertical flight speed of the drone, In addition, the drone does not consume power during the vertical descent. zWhen [n] < 0, P i ver [n]=0.

[0141] Construct the complete optimization problem:

[0142]

[0143] Among them, V xy and V z is the maximum horizontal and vertical speed that the drone can fly in each time slot. In the above formula, A represents the GD transmission scheduling, P represents the interference power of drone J and the transmission power of GD, Q represents the horizontal flight trajectory of drone U and the three-dimensional trajectory of drone J, H represents the vertical flight trajectory of drone U, and Θ represents the elevation angle of drone U with the ground user during flight. N represents the number of time slots, n represents the nth time slot, and α k [n] represents a binary variable, P k [n] represents the transmission power of UAV U, for i∈{U,J}, represents the horizontal energy consumption of UAVs U and J in the nth time slot, represents the vertical energy consumption of UAVs U and J in the nth time slot, z i [n+1], z i [n] represents the vertical position of drones U and J in the n+1th and nth time slots, respectively, and q i [n+1], q i [n] represents the horizontal position of the UAV at the n+1th and nth time slots, respectively, V xy Indicates the maximum horizontal speed of the drone, V z Indicates the maximum vertical speed of the drone. They represent the probability of generating a LoS link between the kth GD and the drone U and the eavesdropper E in the nth time slot, respectively. For X∈{U,E},d UX [n] represents the distance between GD and X in n time slots, α L and α N is the path loss exponent for LoS and NLoS scenarios. ρ0 represents the channel power gain with unit reference distance in LoS environment, σ 2 represents the variance of additive white Gaussian noise, μ represents the additional signal attenuation factor of the NLoS environment, and θ kX [n] represents the elevation angle between GD and X, w k Indicates the horizontal position of GD, and They represent the maximum instantaneous power and average power of GD during transmission, and They represent the maximum instantaneous power and average power of UAV J during transmission, H max and H min Represents the maximum and minimum flight altitude of the drone, q i [1] z i [1] represents the horizontal and vertical flight positions of UAVs U and J at the initial moment, q i [N], z i [N] represents the horizontal and vertical flight positions of UAVs U and J at the final moment, δ t Defines the length of each flight time slot of the drone.

[0144] Where C1 and C2 represent the constraints on the average and peak transmission power in each time slot, and Respectively represent D k C3 and C4 represent the constraints on the average and peak interference power in each time slot. and They represent the average and maximum interference power of J, and C5 represents D k C6 represents the safe separation distance constraint between all drones (U, J, E), C7 specifies the flight altitude constraint of drones U and J, H min and H max Represents the minimum and maximum vertical heights of U and J respectively, and C8 represents the maximum vertical height of the drone U and D k C9 and C10 represent the mobility constraints and the start and end position constraints of UAVs U and J, and C11 represents the propulsion energy consumption limit of U and J.

[0145] S3: For the constructed optimization mathematical model, decoupling operation is performed based on the BCD method to obtain four sub-problems about transmission scheduling, interference power of interfering UAVs and transmission power of ground equipment, horizontal flight trajectory of UAV U and three-dimensional flight trajectory design of UAV J, and vertical flight trajectory of UAV U. For each non-convex sub-problem, the convex approximation fitting method is used to convert it into a convex problem for solution.

[0146] S4: Use an iterative algorithm to solve the optimal GD transmission scheduling, the interference power of UAV J and the transmission power of GD, the horizontal flight trajectory of UAV U and the three-dimensional trajectory of UAV J, and the vertical flight trajectory of UAV U.

[0147] The proposed trajectory scheme for fair scheduling of energy-constrained aviation Internet of Things systems based on probabilistic line-of-sight links is a non-convex problem involving multivariable coupling of integer programming. The present invention utilizes Block Coordinate Descent (BCD) technology to decompose the original problem into multiple sub-problems. Specifically, given other variables A, P, Q and H are optimized in each sub-problem respectively. In addition, the non-convex constraints in the sub-problems are converted into convex constraints. The solution to this problem will be based on the following steps.

[0148] The specific steps are as follows:

[0149] (1) Based on the BCD algorithm The problem is decoupled and the three-dimensional trajectory design of the dual UAVs, the interference power of the interfering UAVs, the transmission power of the ground equipment and the transmission scheduling are transformed into four sub-problems: GD transmission scheduling A, the interference power of UAV J and the transmission power P of GD, the horizontal flight trajectory of UAV U and the three-dimensional trajectory Q of UAV J and the vertical flight trajectory H of UAV U. At the same time, the binary scheduling coefficient A is variable relaxed and the relaxation variable η is introduced k Replacement optimization problem The objective function in .

[0150] The specific questions are as follows:

[0151] Subproblem about GD transmission scheduling A η k It is an optimization problem The slack variables introduced in .

[0152]

[0153] Sub-problems about the interference power of UAV J and the transmission power P of GD

[0154]

[0155] About Us U Horizontal flight trajectory and drone J The subproblem of three-dimensional flight trajectory design Q

[0156]

[0157] Subproblem about the vertical flight trajectory H of UAV U

[0158]

[0159] (2) The subproblem obtained in step (1) is transformed into a convex problem, where the subproblem is a typical LP linear programming problem, which can be solved directly by existing optimization toolkits. and sub-problems It is a non-convex optimization problem that requires an approximate fit using continuous convex approximations.

[0160] For the sub-problem Among them, constraints C2 to C4 are all linear constraints. First, Expressed as:

[0161]

[0162] right The non-convex formula in the equation can be converted to convex by first-order Taylor expansion:

[0163]

[0164] represents a feasible point selected in the mth iteration. For this given feasible point, It is about optimizing variable P k [n] and P J [n] is a concave function. This property is crucial for the subsequent optimization process. Replace the original We effectively transform the problem into a convex optimization problem.

[0165] Based on the above transformation, the subproblem It is a standard convex optimization problem about the optimization variable P, which can be solved by the interior point method.

[0166] For the sub-problem First, we deal with the non-convex constraint C1, since is non-concave, so the optimization problem is non-convex and difficult to solve. as well as therefore, It can be expressed as:

[0167]

[0168] in The new constraints are:

[0169]

[0170] Then, after performing SCA convex transformation on the left side of the above equation, we get

[0171]

[0172] in Y (m)[n] represents Y[n] at the mth iteration. This will result in non-convex terms Perform Taylor expansion:

[0173]

[0174] in, and They represent x at the mth iteration respectively. k [n] and t kU [n], their expansions are as follows:

[0175]

[0176] use Replace C1 Constraint C1 is a convex constraint.

[0177] Next, we deal with constraint C2 and relax it to the following form:

[0178]

[0179] It is worth noting that the function arctan(1 / x) is a convex function. Therefore, the right side of constraint C2 is relative to the expression ||q U [n]-w k || shows convexity. By applying the SCA method, the following convex constraints are obtained:

[0180]

[0181] in

[0182]

[0183] and represents q at the mth iteration U [n].

[0184] Next, to handle constraint C3, we first rewrite it as:

[0185]

[0186] The present invention applies the SCA method to obtain the lower bound of the above norm square function, which is specifically as follows:

[0187]

[0188] in, and represents the current estimated position and height of UAV J in the mth iteration. The present invention linearizes the objective function by introducing these iterative estimates, thereby simplifying the optimization problem.

[0189] Finally, constraint C7 is processed by introducing a slack variable λ i , rewrite constraint C7 as:

[0190]

[0191] For i∈{U,J}, v i [n] represents the flight speed of UAVs U and J, and: Among them, P0 and P1 are two constants, representing the inherent blade surface power and induced power respectively; U tip represents the tip speed of the rotor blade; d0 and ρ represent the body drag ratio and air density respectively; the average rotor induced speed is represented by v0; s and A represent the rotor stiffness and rotor disk area respectively. This is a variable q i [n] and λ i [n] is a non-convex constraint. Taylor expansion is performed on the right side of the inequality to rewrite the constraint as follows:

[0192]

[0193] Based on the above transformation, the subproblem It is a standard convex optimization problem about the optimization variable Q, which can be solved by the interior point method.

[0194] For the sub-problem It is non-convex due to the existence of constraints C2 and C3. In addition, the constraint C1 Not only is it affected by H, but also by This interdependence increases the complexity of the problem, further leading to its non-convex nature. In short, non-convexity comes from specific constraints that do not satisfy the convex property and the complex relationships between the involved variables.

[0195] First, we deal with the nonlinear constraint C2. We relax it to the following form:

[0196]

[0197] It is worth noting that the function arctan(x) is a concave function. However, CVX does not include arctan(x). CVX is a MATLAB toolbox specifically designed for modeling and solving convex optimization problems. It provides an intuitive way to define optimization problems, allowing users to model in a form close to mathematical expression without having to deeply understand the underlying solution algorithm, so we use SCA to transform the above formula into:

[0198]

[0199] in, and Indicates that in the mth iteration z U The value of [n].

[0200] Next, we process constraints C3 and rewrite them into the following form using SCA technology:

[0201]

[0202] Finally, we process constraint C1. Re-express it as:

[0203]

[0204] In the above formula Approximately:

[0205]

[0206] in, and They represent x at the mth iteration. k [n] and t kU [n] Replace with Constraint C1 is also rewritten as a convex constraint.

[0207] Based on the above transformation, the subproblem It is a standard convex optimization problem about the optimization variable H, which can be solved by the interior point method.

[0208] (3) Design an iterative algorithm flow to serially connect the convex optimization problems obtained in step (2). For specific steps, see Table 1.

[0209] Table1 Iterative Algorithm

[0210]

[0211] (4) Proof of algorithm convergence:

[0212] 1. In the first step of the algorithm, the problem It is a standard LP linear programming that can solve A m+1 , so: R(A m ,P m ,Θ m ,H m ,Q m )≤R(A m+1 ,P m ,Θ m ,H m ,Q m ).

[0213] 2. In the second step of the algorithm, the problem It is a convex optimization problem, which can be solved by the optimization solver P m+1 , so: R(A m+1 ,P m ,Θ m ,H m ,Q m )≤R(A m+1 ,P m+1 ,Θ m ,H m ,Q m ).

[0214] 3. In the third step of the algorithm, in the second step of the algorithm, by fitting the convex approximation of the optimization variable Q, we can get:

[0215] R(A m+1 ,P m+1 ,Θ m ,H m ,Q m )=R lb (A m+1 ,P m+1 ,Θ m ,H m ,Q m )

[0216] ≤R lb (A m+1 ,P m+1 ,Θ m ,H m ,Q m+1 )

[0217] ≤R(A m+1 ,P m+1 ,Θ m ,H m ,Q m+1 )

[0218] Similarly, in the fourth step of the algorithm, the above relationship is also satisfied, so we can get that the function value R(A) in the whole program algorithm process is m ,P m ,Θ m ,H m ,Q m ) must be a non-decreasing function, and R(A m ,P m ,Θ m ,H m ,Q m ) approaches a fixed constant, which is the optimal sum rate of the entire system.

[0219] Step 1: First, based on the basic theories of wireless communication and PLoS channel model, a wireless communication system model assisted by energy-constrained UAVs is constructed. In this system model, the energy of the UAV must be limited and the complexity of the solution brought by the introduction of the PLoS channel model must be reduced, so the optimization goal of the problem needs to be converted into its approximate lower bound to reduce the difficulty of solution.

[0220] Steps 2 and 3 improve the mathematical theory derivation and problem solving analysis in the process of model building. In view of the non-convexity and high coupling of the optimization problem corresponding to the system model, an approximate fitting method based on the Block Coordinate Descent (BCD) algorithm and continuous convex approximation is used to decouple and transform the original optimization problem. BCD is an efficient optimization method, and its Chinese name is block coordinate descent method. It simplifies the solution process of complex problems through block optimization strategy and is widely used in many fields. It is particularly excellent in dealing with optimization problems with block structures. (For the specific process, please refer to the specific implementation method of the present invention).

[0221] Step 4 adopts the idea of ​​iteration, and iterates the sub-problems obtained in steps 2 and 3 in a loop, so that the system security transmission rate continuously approaches a constant value, which is the maximum system average safe achievable rate required by the present invention.

[0222] This paper proposes an optimization method for a dual-drone-assisted secure data collection system. First, an optimization problem is constructed to maximize the total achievable confidentiality rate of the system, involving four optimization problems: GD transmission scheduling, the interference power of drone J and the transmission power of GD, the horizontal flight trajectory of drone U and the three-dimensional trajectory of drone J, and the vertical flight trajectory of drone U. Considering the existence of aerial eavesdroppers, we use an approximate lower bound to simplify the solution process of non-convex optimization problems. Then, the original problem is decoupled into four sub-problems by the BCD method, and each sub-problem is transformed into a manageable convex optimization problem by introducing slack variables and the stepwise convex approximation method.

[0223] In order to prove the effectiveness of the proposed algorithm, that is, the improvement of performance, the following benchmark solutions are listed for comparison:

[0224] Baseline scheme 1: The system only considers a single UAV to collect information without interference assistance, and jointly optimizes the 3D trajectory of U, the transmission power of GD, and user scheduling. It is worth noting that the energy consumption under this scheme is the sum of the energy consumption of the two UAVs in the proposed scheme.

[0225] Baseline 2: Given the trajectories of U and J, the transmission power of GD, and the interference power of J, the provided trajectory is used as the initial trajectory of the proposed scheme, while the provided power remains fixed and is taken as and

[0226] Baseline 3: All UAVs fly at the lowest altitude and jointly optimize the 2D trajectories of U and J, the interference power of J, the transmission power of GD, and user scheduling.

[0227] Figure 2 It is a flow chart 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.

[0228] Figure 3 and Figure 4 This is a simulation verification based on the proposed solution of the present invention. Figure 3 and Figure 4 The simulation results of the iterative convergence of various schemes and the transmission scheduling of the proposed scheme are shown. Figure 3 It can be observed that the proposed scheme has convergence in jointly optimizing the transmission scheduling coefficient, the transmission power of the UAV and the 3D flight trajectory of the UAV. In addition, other comparison schemes also have good convergence. The results show that the proposed scheme has the highest confidentiality rate, which shows the effectiveness and superiority of the proposed algorithm. In addition, from Figure 4 It can be observed that the transmission scheduling results of the proposed scheme, the simulation results show that all GDs are alternately in the service state, which means that U can only communicate with one user in each cycle, and the unscheduled users remain silent at this time. When multiple GDs participating in the scheduling meet the access requirements, the user with the highest security rate will be selected for scheduling. Subsequently, the average security rate of the aerial IoT system is maximized.

[0229] Figure 5 and Figure 6 Demonstrated the horizontal trajectory and 3D trajectory simulation results in different schemes. W, as well as from Figure 5 It can be observed that the horizontal trajectory of UAV U in the OUWJ scheme is different from that in the other schemes. In the OUWJ scheme, U first flies to D2, while in the other schemes, U initially flies in the direction of D1. This is because compared with the other schemes, the OUWJ scheme has no interference assistance, and the interception capability of the eavesdropper E is not suppressed. Since D1 is closer to the launch point of E, in order to increase the safety rate of the system, U first flies to D2, and only turns to D1 when E is farther away. Compared with other schemes, this increases the flight time between GD, which affects the achievable rate of the system. Figure 6As shown in Figure 2, compared with the 2D scheme, the proposed scheme enables the UAV to have greater trajectory flexibility. During the flight between GD, U can increase the flight altitude to form a larger elevation angle with GD, thereby improving the reachability rate. At the same time, J can adjust the flight altitude to minimize the eavesdropping ability of E.

[0230] Figure 7 The simulation shows the vertical height change under different schemes. When U leaves GD, it first rises to a higher altitude and then dives to get a better elevation angle. In the proposed scheme, J first rises to 80 meters, maintains the same flight altitude as the eavesdropper E, and then adjusts the altitude to maintain the minimum safe distance from E, thereby maximally suppressing E's eavesdropping ability.

[0231] Figure 8 and Fig. 9 The simulation verifies the power variation of the proposed scheme and the 2D scheme throughout the flight cycle. It can be observed that J’s transmission power is relatively high at the beginning and before the end of the flight cycle. This is because at these two moments, U is far away from GD, and in order to ensure secure communication, J increases the suppression of E’s eavesdropping ability. In addition, it can be seen from the above figure that when U flies between GD, the 2D scheme maintains a relatively low elevation angle during this period, which has a negative impact on the communication rate with GD. Therefore, during the time when U flies between GD in the 2D scheme, GD’s transmission power is low. In order to increase the average rate, the 2D scheme allocates more power when U hovers directly above GD.

[0232] Fig.10 The simulation shows that when U hovers above GD in the 2D scheme, it receives more power, resulting in a higher achievable safe rate than the proposed scheme. However, when U flies between GDs, the power allocation is significantly reduced, resulting in a much lower achievable safe rate than the proposed scheme. Therefore, from the average rate of the entire cycle, the proposed scheme is better than the 2D scheme.

[0233] Fig.11 and Fig.12 The simulation shows the horizontal and vertical flight speed curves of different UAV schemes. It can be observed that the OUWJ scheme has more propulsion power, enabling it to hover above the GD, while the other schemes have less propulsion power, resulting in continuous hovering throughout the flight to control energy consumption.

[0234] Fig.13The simulation shows that the average achievable security rate changes with the flight period T under different schemes. It can be seen that the average confidentiality rate obtained by the proposed algorithm based on BCD and SCA is better than other schemes. Compared with the OUWJ scheme without the assistance of the jammer, the simultaneous optimization of the trajectories of the two drones can effectively suppress the eavesdropper's eavesdropping ability. Compared with the 2D scheme with a fixed vertical flight altitude, the optimization of the 3D trajectory of the two drones can make U increase the elevation angle with GD to increase the information transmission rate, and J can fly closer to E to suppress its eavesdropping ability to the greatest extent. These two points combined bring about an improvement in the system security rate, which also reflects that the scheme proposed in this paper can maximize the security performance of the system under consideration.

[0235] The above numerical results verify the effectiveness of our proposed algorithm in various scenarios and show that the three-dimensional trajectory design of UAVs can significantly improve the average confidentiality rate of the data collection system.

[0236] The present invention has a wide range of applications in drone-assisted communication systems, and is particularly suitable for eavesdropping protection scenarios related to data collection and physical layer security. In an environment where sensitive data needs to be collected in real time, drones can be quickly deployed and provide flexible communication support to ensure the secure transmission of information. By introducing a more realistic probabilistic line-of-sight model for modeling, the accuracy of information transmission in the communication system under interference conditions can be significantly improved. In the eavesdropping protection scenario, the drone is not only responsible for data transmission, but also can effectively interfere with potential eavesdroppers and enhance the physical layer security of communications through optimized flight trajectory design. The dual-drone three-dimensional trajectory optimization for physical layer security can achieve efficient data transmission under limited energy consumption, meeting the strict requirements for information security and privacy protection.

[0237] The present invention also provides a communication system, including K ground users, serving a UAV U in the air, during which an eavesdropper E in the air constantly attempts to eavesdrop on confidential information, and a friendly jammer J in the air suppresses the eavesdropper's eavesdropping ability. The system can execute the above-mentioned UAV three-dimensional trajectory optimization method based on probabilistic line-of-sight links.

Claims

1. A dual-UAV three-dimensional trajectory optimization method for physical layer security, characterized in that: The following steps are involved: S1: Construct a communication system model: Set up a dual-drone-assisted secure data collection system, where drones U and J serve as the air base station and air friendly jammer of the data collection network respectively, flying according to a certain initial trajectory. The communication link channel model between drone U and the ground node is a PLoS model. The energy consumption of drones U and J is limited. At the same time, there is a drone E in the air as an eavesdropper trying to eavesdrop on confidential information. S2: Constructing an optimization mathematical model: With the goal of maximizing the average safe and achievable rate of the system, an optimization problem is constructed to maximize the average achievable confidentiality rate of the system, involving the optimization mathematical model of GD transmission scheduling, the interference power of UAV J and the transmission power of GD, the horizontal flight trajectory of UAV U and the three-dimensional trajectory of UAV J, and the vertical flight trajectory of UAV U; the optimization mathematical model is: in, is the average confidentiality rate of the kth ground device (GD) in the nth time slot; A represents the GD transmission scheduling, P represents the interference power of UAV J and the transmission power of GD, Q represents the horizontal flight trajectory of UAV U and the three-dimensional trajectory of UAV J, H represents the vertical flight trajectory of UAV U, Θ represents the elevation angle of UAV U with the ground user during flight; N represents the number of time slots, n represents the nth time slot, α k [n] represents a binary variable, P k [n] represents the transmission power of UAV U, P J [n] represents the transmission power of UAV J; and They represent the maximum instantaneous power and average power of GD during transmission, and They represent the maximum instantaneous power and average power of UAV J during the transmission process respectively; Yes D k and the elevation angle between X, X∈{U,E},q U [n], q E [n] and q J [n] represents the horizontal position of UAVs U, E and J respectively, arctan(x) is a concave function; q i [n+1], q i [n] represents the horizontal position of the UAV at the n+1th and nth time slots, respectively, and z i [n+1], z i [n] represents the vertical positions of drones U and J at the n+1th and nth time slots, respectively; D min Indicates the minimum safe distance between drones, H max and H min Represents the maximum and minimum flight altitude of the drone; V xy and V z is the maximum horizontal and vertical speed that the UAV can fly in each time slot; δ t Defines the length of each flight time slot of the drone; q i [1] z i [1] represents the horizontal and vertical flight positions of UAVs U and J at the initial moment, q i [N], z i [N] represents the horizontal and vertical flight positions of UAVs U and J at the final moment; P i hor [n] represents the horizontal energy consumption of UAVs U and J, P i ver [n] represents the energy consumption of UAVs U and J in the vertical direction; represents the horizontal energy consumption of UAVs U and J in the nth time slot, represents the vertical energy consumption of UAVs U and J in the nth time slot; μ represents the additional signal attenuation factor in the NLoS environment; N represents the time slot, and the entire time is discretized as S3: For the constructed optimization mathematical model, decoupling operation is performed based on the BCD method to obtain four sub-problems about GD transmission scheduling, interference power of UAV J and transmission power of GD, horizontal flight trajectory of UAV U and three-dimensional trajectory of UAV J, and vertical flight trajectory of UAV U. For each non-convex sub-problem, a convex approximation fitting method is used to convert it into a convex problem for solution; S4: Use the iterative algorithm to solve the optimal GD transmission scheduling, the interference power of UAV J and the transmission power of GD, the horizontal flight trajectory of UAV U and the three-dimensional trajectory of UAV J, and the vertical flight trajectory of UAV U.

2. The dual UAV three-dimensional trajectory optimization method for physical layer security according to claim 1 is characterized in that: The sub-problem about GD transmission scheduling A for: Among them, η k It is an optimization problem The slack variables introduced in the subproblem It is a typical LP linear programming problem, which can be solved directly using the optimization toolkit.

3. The dual-UAV three-dimensional trajectory optimization method for physical layer security according to claim 1 is characterized in that: The sub-problem of the interference power of UAV J and the transmission power P of GD is for:

4. The dual UAV three-dimensional trajectory optimization method for physical layer security according to claim 3 is characterized in that: The sub-problem To perform approximate fitting of continuous convex approximation, the steps are as follows: Constraints C2 to C4 are all linear constraints. First, Expressed as: Again The non-convex formula in the equation can be converted to convex by first-order Taylor expansion: in, represents a feasible point selected in the mth iteration; for this given feasible point, It is about optimizing variable P k [n] and P J A concave function of [n]; They represent the probability of generating a LoS link between the kth GD and the UAV U and the eavesdropper E in the nth time slot; σ 2 represents the variance of additive Gaussian white noise; They represent the channel coefficients of LoS communication between UAV U and eavesdropper E and k GDs, respectively, and h JE [n] represents the channel coefficient between J and E in the nth time slot; Based on the above transformation, the subproblem It is a standard convex optimization problem about the optimization variable P, which can be solved by the interior point method.

5. The method for optimizing dual UAV three-dimensional trajectories for physical layer security according to claim 1 is characterized in that: The horizontal flight trajectory of UAV U and the three-dimensional flight trajectory of UAV J are designed as sub-problems of Q for: Among them, η k It is an equivalence problem The slack variables introduced.

6. The method for optimizing the dual UAV three-dimensional trajectories for physical layer security according to claim 5 is characterized in that: The sub-problem To perform approximate fitting of continuous convex approximation, the steps are as follows: First deal with the non-convex constraint C1: Introduce slack variables as well as therefore, It can be expressed as: in, ρ0 represents the channel power gain per unit reference distance in LoS environment; w k Indicates the horizontal position of GD; θ kX [n] is the elevation angle between the kth GD and X; α L and α N is the path loss index for LoS and NLoS scenarios, where a>0 and b>0 are constants specified by the actual environment; The new constraints are: Among them, Y[n] is the slack variable introduced when dealing with the non-convex constraint C1; Then, after performing a successive convex approximation (SCA) convex transformation on the left side of the above equation, we get: in, Y (m) [n] represents Y[n] at the mth iteration; This will lead to non-convex terms Perform Taylor expansion: in, and They represent x at the mth iteration respectively. k [n] and t kU [n], the expanded form is as follows: use Replace C1 Constraint C1 is a convex constraint; Next, we deal with constraint C2 and relax it to the following form: Among them, the function arctan(1 / x) is a convex function; By applying the SCA method, the following convex constraints are obtained: in represents q at the mth iteration U [n]; Next, to handle constraint C3, first rewrite it as: The present invention applies the SCA method to obtain the lower bound of the above norm square function, which is specifically as follows: in, and represents the current estimated position and altitude of UAV J in the mth iteration; T represents the flight period; Finally, constraint C7 is processed by introducing a slack variable λ i , rewrite constraint C7 as: For i∈{U,J}, v i [n] represents the flight speed of UAVs U and J, and: Among them, P0 and P1 are two constants, representing the inherent blade surface power and induced power respectively; U tip represents the tip speed of the rotor blade; d0 and ρ represent the body drag ratio and air density respectively; the average rotor induced speed is represented by v0; s and A represent the rotor stiffness and rotor disk area respectively; Taylor expansion is performed on the right side of the inequality, and the constraint is rewritten as: Based on the above transformation, the subproblem It is a standard convex optimization problem about the optimization variable Q, which can be solved by the interior point method.

7. The method for optimizing dual UAV three-dimensional trajectories for physical layer security according to claim 1, characterized in that: The sub-problem about the vertical flight trajectory H of UAV U for: Among them, δ t Defines the length of each flight time slot of the UAV, η k It is an equivalence problem The slack variables introduced.

8. The method for optimizing the three-dimensional trajectories of dual UAVs for physical layer security according to claim 7, characterized in that: The sub-problem To perform approximate fitting of continuous convex approximation, the steps are as follows: First, the nonlinear constraint C2 is processed and relaxed into the following form: Among them, the function arctan(x) is a concave function; use SCA to transform the above formula into: in, and Indicates that in the mth iteration z U The value of [n]; Next, we process constraints C3 and rewrite them into the following form using SCA technology: Finally, we process constraint C1. Re-express it as: In the above formula Approximately: in, and They represent x at the mth iteration. k [n] and t kU [n]; will Replace with Constraint C1 is also rewritten as a convex constraint; Based on the above transformation, the subproblem It is a standard convex optimization problem about the optimization variable H, which can be solved by the interior point method.

9. The method for optimizing dual UAV three-dimensional trajectories for physical layer security according to claim 1, characterized in that: The interference signal emitted by the UAV J is a Gaussian pseudo-random sequence or a deterministic waveform similar to the desired signal structure.

10. A communication system, including K ground users, serving U drones in the air, during which an eavesdropper E in the air constantly attempts to eavesdrop on confidential information, and a friendly jammer J in the air suppresses the eavesdropper's eavesdropping ability; characterized in that: The system is capable of executing the dual-UAV three-dimensional trajectory optimization method for physical layer security as described in any one of claims 1-9.

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