A physical layer security-oriented dual-uav three-dimensional trajectory optimization method

Abstract

The application is a kind of physical layer security oriented dual-UAV three-dimensional trajectory optimization method, which is based on the optimization method of dual-UAV assisted secure data collection system. First, the optimization problem is constructed to maximize the total achievable secrecy rate of the system, involving the three-dimensional trajectory design of the UAV, the interference power of the interference UAV, the transmission power of the ground device and the transmission scheduling. Considering the existence of air eavesdroppers, we use the approximate lower bound to simplify the solving process of the non-convex optimization problem. Then, the original problem is decoupled into four sub-problems by BCD method, and each sub-problem is transformed into a manageable convex optimization problem by introducing relaxation variables and step-by-step convex approximation method. Numerical results verify the effectiveness of the proposed algorithm under various scenarios, indicating that the three-dimensional trajectory design of the UAV can significantly improve the average secrecy rate of the data collection system.

Description

TECHNICAL FIELD

[0001] The present application mainly relates to the field of unmanned aerial vehicle communication, and particularly relates to combining information security brought by physical layer security with the characteristics of unmanned aerial vehicle maneuverability and deployability, building a secure data collection communication system assisted by unmanned aerial vehicles, transmitting information from multiple ground users in an Internet of Things system to unmanned aerial vehicles under the consideration of probabilistic line-of-sight link communication, designing a three-dimensional (3D) flight trajectory of a double unmanned aerial vehicle facing physical layer security through theoretical derivation and simulation verification, and realizing transmission with maximum average secrecy rate. BACKGROUND

[0002] The statements in this section merely provide background information related to the present disclosure and can constitute the prior art. During the implementation of the present application, the inventors found at least the following problems in the prior art.

[0003] Unmanned Aerial Vehicles (UAVs) have become a revolutionary technology, with applications in various fields. Initially, they were designed and developed for military purposes, but today they have 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, intelligent logistics, law enforcement, disaster response, and pre-hospital emergency care. With the rapid progress of UAV technology, such as autonomous flight capabilities, payload capacity, and flight endurance, the widespread use of UAVs has been promoted globally. The development of these technologies not only brings new opportunities to various industries, but also brings a series of challenges. These challenges involve multiple aspects, including how to effectively regulate the use of UAVs, ensure flight safety, and effectively integrate UAV technology with existing infrastructure. Therefore, in-depth exploration and research in these areas are particularly important. Modifying the positioning or planning the flight path of the UAV can ensure a stable Line of Sight (LoS) connection with the ground node to achieve the best reliability. Therefore, the height and lateral position of the UAV play a crucial role in improving the efficiency of the UAV communication system. Trajectory design has become a key challenge that needs to be addressed. In the literature [Chen X, Sheng M, Li B, Zhao N. UAV communication for 6G: A review[J]. Journal of Electronics & Information Technology, 2022, 44(0): 1-9.], the successful commercialization of 5G has brought revolutionary changes to modern life, driving the development of the 6th generation of mobile communication technology. In the future 6G network, UAVs will play a key role, with application scenarios covering multiple fields, such as the construction of bee colony base stations, the deployment of holographic projections, long-distance relay communications, and data collection. To achieve these innovative applications, 6G networks will rely on a series of key technologies, including terahertz communication, ultra-large-scale antenna arrays, and endogenous artificial intelligence.

[0004] However, as we enter the era of 6G, there are still many challenges in UAV communication. The limited endurance of UAVs restricts their ability to perform long-duration tasks, and the need for network integration requires UAVs to operate flexibly in different network environments. The compatibility of intelligent reflecting surfaces also needs to be addressed to ensure that UAVs can effectively collaborate with emerging technologies. To address these challenges, we need interdisciplinary collaboration and continuous technological innovation. Currently, communication systems based on UAV trajectory design have been proposed and classified according to the different roles that UAVs play in wireless communication networks. These roles include base station UAV communication systems, relay UAV communication systems, and UAV-assisted communication systems for supporting aerial users. This classification method helps better understand the functions of UAVs in the network and promotes the further development of various applications. For example, a typical base station UAV proposed in [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 transmit power, UAV flight trajectory, and user scheduling coefficient. At the same time, the energy consumption of UAVs is also a point worth considering. To improve energy efficiency, [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.] formulates an energy minimization problem by jointly optimizing the UAV trajectory and communication time allocation, as well as the total task completion time, while meeting the communication throughput requirements of each ground node. [Lei H, Yang H, Park K-H, et al. Joint trajectory design and user scheduling for secure aerial underlay IoT systems[J]. IEEE Internet Things J., 2023, 10(15):13637-13648.] studies an aerial-assisted Internet of Things system with a single location-uncertain eavesdropper.The two-dimensional trajectory, transmit power and user scheduling of the cognitive unmanned aerial vehicle are jointly designed to maximize the average secrecy rate of cognitive users (CUs).

[0005] However, the existing research on unmanned aerial vehicle flight route design usually assumes that the unmanned aerial vehicle and the user or eavesdropper are in a line-of-sight channel, but this assumption is too simple and ignores factors such as the presence of obstacles and small-scale fading, so the flight route designed in this way may not meet the line-of-sight communication conditions in some sections due to the presence of obstacles, and is not suitable for actual use. In particular, when the unmanned aerial vehicle flies at a lower altitude, the shadow effect is significantly enhanced, and obstacles hinder the signal propagation between the unmanned aerial vehicle and the ground node, which will affect the communication quality. Therefore, recent technologies use a probabilistic line-of-sight channel model to solve this problem. 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.], a probabilistic line-of-sight (PLoS) channel model is proposed. Specifically, the probability of LoS communication with the ground node increases with the increase of the elevation angle, which can be achieved by moving the unmanned aerial vehicle horizontally close to the ground node or increasing its height. In the literature [Xu Y X, Cui M, Zhang G C, et al. Optimization Design of Unmanned Aerial Vehicle Secure Communication in Probabilistic Line-of-Sight Air-Ground Channel [J]. Computer Application Research, 2023, 40(02): 554-560.], the information transmission security of the unmanned aerial vehicle multi-user communication system is ensured at the physical layer, and the air-ground channel between the unmanned aerial vehicle and the ground node is modeled as a more realistic probabilistic line-of-sight channel. Under the constraints of unmanned aerial vehicle flight conditions and discrete user scheduling constraints, the three-dimensional flight trajectory of the unmanned aerial vehicle and the user scheduling are jointly designed to maximize the minimum average security rate of the user.

[0006] As in the patent application No. 202111058338.9 entitled "Unmanned aerial vehicle flight route offline and online hybrid optimization method for secure communication", the probabilistic line-of-sight channel model is used, which is closer to the actual communication environment, and the proposed three-dimensional unmanned aerial vehicle trajectory optimization further utilizes the additional degree of freedom of the vertical trajectory of the unmanned aerial vehicle to improve the security communication rate of the unmanned aerial vehicle. However, according to the applicant's research, because the energy of the unmanned aerial vehicle is limited and the introduction of the PLoS channel model increases the complexity of the solution, the above patent cannot maximize the system average security rate while ensuring the downlink communication with the ground user and suppressing the eavesdropping ability of the eavesdropper as much as possible. SUMMARY

[0007] In view of the above problems, the purpose of the present application is to solve some problems in the prior art, or at least alleviate these problems.

[0008] A physical layer security-oriented dual-unmanned aerial vehicle three-dimensional trajectory optimization method, comprising the following steps:

[0009] S1: Construct a communication system model: set up a dual-unmanned aerial vehicle assisted secure data collection system, wherein unmanned aerial vehicles U and J are respectively an aerial base station and an aerial friendly jammer of a data collection network, fly according to a certain initial trajectory, the communication link channel model of unmanned aerial vehicle U with a ground node is a PLoS model, the energy consumption of unmanned aerial vehicles U and J is limited, and meanwhile, an unmanned aerial vehicle E exists in the air as an eavesdropper to attempt to eavesdrop confidential information;

[0010] S2: Construct an optimization mathematical model: maximize the average security reachable rate of the system as the target, construct an optimization problem to maximize the average achievable secrecy rate of the system, and the optimization mathematical model involves GD transmission scheduling, the interference power of unmanned aerial vehicle J and the transmission power of GD, the horizontal flight trajectory of unmanned aerial vehicle U and the three-dimensional trajectory of unmanned aerial vehicle J, and the vertical flight trajectory of unmanned aerial vehicle U; the optimization mathematical model is as follows:

[0011]

[0012] wherein, is the average secrecy rate of the kth ground device (GD) in the nth time slot; A represents GD transmission scheduling, P represents the interference power of unmanned aerial vehicle J and the transmission power of GD, Q represents the horizontal flight trajectory of unmanned aerial vehicle U and the three-dimensional trajectory of unmanned aerial vehicle J, H represents the vertical flight trajectory of unmanned aerial vehicle U, and Θ represents the elevation angle of unmanned aerial vehicle U when flying with a ground user; N represents the number of time slots, n represents the nth time slot, and the whole time is discretized into α k [n] represents a binary variable, P k [n] represents the transmission power of unmanned aerial vehicle U, P J [n] represents the transmission power of unmanned aerial vehicle J; and respectively represent the maximum instantaneous power and the average power of GD in the transmission process, and respectively represent the maximum instantaneous power and the average power of unmanned aerial vehicle J in the transmission process; is the elevation angle between the kth GD and X, X∈{U,E}, q U [n], q E [n] and q J [n] respectively represent the horizontal positions of unmanned aerial vehicles U, E and J, and arctan(x) is a concave function; q i [n+1], qi [n] respectively represent the horizontal position of the UAV at the (n+1)th, nth time slot, z i [n+1], z i [n] respectively represent the vertical position of the UAV U and J at the (n+1)th, nth time slot; D min represents the minimum safe distance between the UAVs, H max and H min represent the maximum and minimum height of the UAVs; V xy and V z are the maximum horizontal and vertical speed of the UAVs in each time slot; δ t defines the length of each flight time slot of the UAV; q i [1], z i [1] represents the flight position of the UAV U and J in the horizontal direction and the vertical direction at the initial time, q i [N], z i [N] represents the flight position of the UAV U and J in the horizontal direction and the vertical direction at the final time; represents the horizontal energy consumption of the UAV U and J, represents the energy consumption of the UAV U and J in the vertical direction; represents the horizontal energy consumption of the UAV U and J in the nth time slot, represents the vertical energy consumption of the UAV U and J in the nth time slot; μ represents an additional signal attenuation factor in the NLoS environment;

[0013] S3: For the constructed optimization mathematical model, decoupling operation is carried out based on the BCD method, four sub-problems about GD transmission scheduling, interference power of the UAV J and transmission power of the GD, horizontal flight trajectory of the UAV U and three-dimensional trajectory of the UAV J, and vertical flight trajectory of the UAV U are obtained, and for each non-convex sub-problem, a convex approximation fitting method is adopted to convert it into a convex problem for solving;

[0014] The sub-problem about GD transmission scheduling is:

[0015]

[0016] wherein, η k is a relaxation variable introduced in the optimization problem ; the sub-problem is a typical LP linear programming problem, which is directly solved by using an optimization toolkit;

[0017] The sub-problem of the interference power of the UAV J and the transmission power of the GD is:

[0018]

[0019] The sub-problem of designing the horizontal flight trajectory of the UAV U and the three-dimensional flight trajectory of the UAV J is:

[0020]

[0021] wherein η k is the equivalent problem with the introduced slack variable;

[0022] The sub-problem of designing the vertical flight trajectory of the UAV U is:

[0023]

[0024] wherein δ t defines the length of each flight time slot of the UAV, η k is the equivalent problem with the introduced slack variable;

[0025] S4: solving the optimal GD transmission scheduling, the interference power of the UAV J and the transmission power of the GD, the horizontal flight trajectory of the UAV U and the three-dimensional trajectory of the UAV J, and the vertical flight trajectory of the UAV U by using an iterative algorithm.

[0026] Further, the sub-problem is approximated by successive convex approximations, and the steps are as follows:

[0027] The constraints C2-C4 of the sub-problem are all linear constraints, and first, the in the constraint C1 of the sub-problem is expressed as:

[0028]

[0029] Then, the non-convex expression in is converted to be convex by first-order Taylor expansion, and the following can be obtained:

[0030]

[0031] wherein represents a feasible point selected in the mth iteration; for this given feasible point, is a concave function about the optimization variables P k [n] and P J [n]; respectively 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 2denotes the variance of the additive white Gaussian noise; denote the channel coefficients of the LoS communication between the UAV U and the k GDs and the eavesdropper E, respectively, JE [n] denotes the channel coefficient between J and E in the nth time slot;

[0032] sub-problem is a standard convex optimization problem with respect to the optimization variable, which is solved by the interior point method.

[0033] Further, the sub-problem is approximated by successive convex approximation, which is implemented as follows:

[0034] First, the non-convex constraint C1 of the sub-problem is relaxed by introducing a slack variable and Thus, can be expressed as:

[0035]

[0036] where, represents the channel power gain per unit reference distance in the LoS environment; w k denotes the horizontal position of the GD; θ kX [n] is the elevation angle between the kth GD and X; a L and a N are the path loss exponents for the LoS and NLoS scenarios, a > 0 and b > 0 are constants specified by the actual environment;

[0037] The new constraint is:

[0038]

[0039] where Y[n] is the slack variable introduced when dealing with the non-convex constraint C1;

[0040] Then, after the successive convex approximation (SCA) convex transformation of the left side of the new constraint, we obtain:

[0041]

[0042] where, Y (m) [n] denotes Y[n] at the mth iteration;

[0043] The non-convex term is Taylor expanded as:

[0044]

[0045] where, and denote the x k [n] and t kU [n] at the mth iteration, respectively, and the expansion is as follows:

[0046]

[0047] Using substitute the constraint C1 of the subproblem with The substituted constraint C1 is a convex constraint;

[0048] Next, handle the constraint C2 of the subproblem and relax it to the following form:

[0049]

[0050] where the function arctan(1 / x) is a convex function;

[0051] By applying the successive convex approximation (SCA) method, we obtain the following convex constraint:

[0052]

[0053] where

[0054] denote the q U [n] at the mth iteration;

[0055] Next, to handle the constraint C3 of the subproblem , first rewrite it as:

[0056]

[0057] Apply the successive convex approximation (SCA) method to obtain the lower bound of the squared norm function of the constraint C3 of the rewritten subproblem , which is as follows:

[0058]

[0059] where, and denote the current estimated position and altitude of the UAV J at the mth iteration; T denotes the flight period;

[0060] Finally, handle the constraint C7 of the subproblem by introducing a slack variable λ i and rewriting the constraint C7 of the subproblem as:

[0061]

[0062] for i∈{U,J}, v i [n] represents the flight speed of the UAVs U and J, and has: where 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 p represent the body drag ratio and air density respectively; the average rotor induced speed is represented by v0; s and A s represent the stiffness of the rotor and the rotor disc area respectively;

[0063] Rewriting the constraint further by Taylor expansion on the right side of the inequality:

[0064]

[0065] Sub-problem is a standard convex optimization problem about optimization variables, which is solved by using the interior point method.

[0066] Further, the sub-problem is approximated by continuous convex approximation, and the steps are as follows:

[0067] First, handle the nonlinear constraint C2 of the sub-problem , which is relaxed to the following form:

[0068]

[0069] where the function arctan(x) is a concave function; the above formula is converted to:

[0070]

[0071] where, and represent the value of z U [n] in the mth iteration;

[0072] Next, handle the constraint C3 of the sub-problem , which is rewritten to the following form by using the SCA technique:

[0073]

[0074] Finally, handle in the constraint C1 of the sub-problem , which is re-expressed as:

[0075]

[0076] in the above formula Approximately:

[0077]

[0078] where, and x k [n] and t kU [n] respectively; replace with The constraint C1 of the sub-problem is also rewritten as a convex constraint;

[0079] The sub-problem is a standard convex optimization problem with respect to optimization variables, which is solved by using an interior point method.

[0080] The interference signal emitted by the unmanned aerial vehicle J is a Gaussian pseudo-random sequence or a deterministic waveform similar to the structure of the required signal.

[0081] A communication system includes K ground users, serves the unmanned aerial vehicle U existing in the air, in the process, the air eavesdropper E tries to eavesdrop the confidential information at any time, and the air friendly jammer J suppresses the eavesdropping ability of the eavesdropper; the system can execute the physical layer security-oriented double unmanned aerial vehicle three-dimensional trajectory optimization method.

[0082] The present application has the following beneficial effects:

[0083] 1. To cope with the influence of shadow effect on communication quality, an air communication network based on a probabilistic line-of-sight link is proposed, which focuses on the maximization of physical layer security and average secure reachable rate. By optimizing the three-dimensional flight trajectory of the unmanned aerial vehicle, the present application reduces the risk of signal eavesdropping and improves the confidentiality and reliability of the communication link. This scheme shows the wide application potential of unmanned aerial vehicle technology in the field of communication security;

[0084] 2. The present application is aimed at the actual situation under the PLoS channel model which is more accurate than the LoS channel model, and takes the maximization of system average security rate as the target, dynamically plans and designs the air base unmanned aerial vehicle U and the interference unmanned aerial vehicle J of the data collection network, the GD transmission power and the interference power P of the jammer, the horizontal flight trajectory of the unmanned aerial vehicle U and the three-dimensional flight trajectory Q of the unmanned aerial vehicle J, and the vertical flight trajectory H of the unmanned aerial vehicle U. Among them, the fair scheduling of the ground data collection network and the maximization of the system average security reachable rate are the final expected effect and pursuit target of the present application;

[0085] 3, The application aims to combine the flexibility and deployability of UAVs with limited energy consumption to construct a UAV-aided wireless communication system. In this system, one UAV is responsible for receiving signals, while the other UAV acts as a jammer to interfere with eavesdroppers, thereby improving the physical layer security of communication. By optimizing the three-dimensional flight trajectory of the two UAVs, we maximize the average achievable rate and security of the system under the constraints of energy consumption and the power interference threshold of the main user. Since the proposed optimization problem is a multivariate coupled non-convex problem and involves complex probabilistic line-of-sight links, solving the optimization problem is challenging. Therefore, we construct an optimization mathematical model and decouple it based on the block coordinate descent method to form four sub-problems about the 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. For non-convex sub-problems, we convert them into convex problems for solving by using convex approximation. Simulation results show that the proposed scheme has good convergence and effectiveness in improving system performance and security. BRIEF DESCRIPTION OF DRAWINGS

[0086] Figure 1 The communication system model of the application;

[0087] Figure 2 The flow chart of the operation of the application;

[0088] Figure 3 The iterative convergence graph of different schemes;

[0089] Figure 4 The transmission scheduling graph under the algorithm proposed by the application;

[0090] Figure 5 The horizontal flight trajectory comparison graph of UAVs under different schemes;

[0091] Figure 6 The vertical flight trajectory comparison graph of UAVs under different schemes;

[0092] Figure 7 The vertical flight height change graph of UAVs over time under different schemes;

[0093] Figure 8 The power change graph of the algorithm proposed by the application in the flight cycle;

[0094] Figure 9 The power change graph of the comparative scheme in the flight cycle;

[0095] Figure 10 The achievable security rate comparison graph in the flight cycle under different schemes;

[0096] Figure 11 a horizontal flight speed variation diagram of the unmanned aerial vehicle under different schemes;

[0097] Figure 12 a vertical flight speed variation diagram of the unmanned aerial vehicle under different schemes;

[0098] Figure 13 a comparison diagram of average secure reachable rate of the system over time under different schemes. DETAILED DESCRIPTION

[0099] The embodiments of the present application are used for illustrating the present application but not limiting the present application, and various replacements and changes can be made according to the common technical knowledge and conventional means in the art without departing from the technical thought of the present application, which should be included in the scope of the present application.

[0100] In view of the fact that the unmanned aerial vehicle will be affected by a larger shadow effect when flying at a relatively low height, the present application proposes a dual unmanned aerial vehicle air data collection network under a probabilistic line-of-sight link, considers the onboard energy consumption of the unmanned aerial vehicle, takes the maximization of the system average secure rate as the target, and ensures the downlink communication with the ground user and as much as possible suppresses the eavesdropping ability of the eavesdropper through the optimization design of the three-dimensional trajectory of the dual unmanned aerial vehicle flight. Further, the system average secure rate maximization is realized.

[0101] As shown in Figure 1 or 2, a dual unmanned aerial vehicle three-dimensional trajectory optimization method for physical layer security comprises the following steps:

[0102] S1: constructing a communication system model:

[0103] A dual unmanned aerial vehicle assisted secure data collection system is set, wherein the unmanned aerial vehicles U and J are respectively an air base station and an air friendly jammer of the data collection network, fly according to a certain initial trajectory, the communication link channel model of the unmanned aerial vehicle U with the ground node is a PLoS model, the energy consumption of the unmanned aerial vehicles U and J is limited, and meanwhile, there is an unmanned aerial vehicle E as an eavesdropper to attempt to eavesdrop the confidential information;

[0104] Figure 1 is a system model diagram of the whole scheme. The present application studies a dual unmanned aerial vehicle assisted secure data collection system, wherein one unmanned aerial vehicle is a legal air base station U, collects confidential data from K ground devices (GD) in a time division multiplexing mode during the flight process, and the confidential data is marked as D k (k = 1, …, K). Meanwhile, another unmanned aerial vehicle E flies from an initial position to a final position During the flight as a potential eavesdropper. To enhance the security of wireless communication, the jammer UAV J weakens the eavesdropping ability of E by generating artificial noise. It is assumed that the jamming signals emitted by the UAV J are Gaussian pseudo-random sequences or deterministic waveforms similar in structure to the desired signal, so these jamming signals can be canceled by the base station U. All devices are assumed to be equipped with a single antenna.

[0105] S2: Construct an optimization mathematical model:

[0106] With the goal of maximizing the system average safety rate, an optimization mathematical model is constructed with the constraints of three-dimensional trajectory design of the double UAVs, jamming power of the jammer UAV, transmission power and transmission scheduling of the ground device.

[0107] Without loss of generality, the flight period T is divided into N time slots, and the entire time is discretized as where the time interval of each time slot is Here N is large enough to make the position of the UAV in each time slot approximately constant. The positions of these nodes are represented in a Cartesian coordinate system. In the nth time slot, the horizontal positions of U, E and J are represented as 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], respectively. In addition, the horizontal coordinates of D k are represented by w k = [x k , y k ] T .

[0108] In addition, U and J must satisfy the following mobility constraints:

[0109]

[0110] where V xy δ t and V z δ t are the maximum horizontal and vertical distances that the UAV can fly in each time slot, assuming its maximum speed is V xy and Vz (Unit: m / s) and These represent the initial and final horizontal positions of the drone, respectively. and This represents the initial and final vertical positions of the drone. Furthermore, in the nth time slot, D... k The distance between the receiver X (X∈{U,E}) and the receiver X is expressed as:

[0111]

[0112] The air-to-air communication link between UAVs is modeled as a Loss-of-Speed ​​(LoS) channel. Therefore, the channel coefficient between J and E in the nth time slot is expressed as:

[0113]

[0114] In addition, all drones must maintain a safe distance to ensure flight safety. The minimum safe distance is as follows:

[0115]

[0116] Among them, D min This represents the minimum safe distance between drones. Define the scheduling variable 'a'. k [n], such that a k [n] = 1 indicates that the k-th GD is active and communicating with U in the n-th time slot, while all other nodes remain inactive. Conversely, if the k-th GD is not communicating, then a k [n] = 0. Assume that only one GD can transmit data to U in each time slot. Therefore, this invention defines:

[0117]

[0118] This invention assumes that the G2A link follows a probabilistic line-of-sight (PLoS) channel model. This model considers varying conditions affecting visibility between the ground transmitter and the air receiver, thus providing a probabilistic assessment of link performance. This method is crucial for accurately characterizing communication dynamics, especially in scenarios where environmental factors (such as obstacles and weather conditions) can affect connectivity. In this case, the probability of a LoS connection within the nth time slot is expressed as:

[0119]

[0120] in, Let be the elevation angle between the k-th GD and X, where a > 0 and b > 0 are constants specified by the actual environment. Correspondingly, the NLoS probability can be expressed as... According to the LoS or NLoS state, the channel coefficient between the nth time slot and D k The channel coefficient between D and X can be expressed as or where ρ0represents the channel gain per unit reference distance under LoS environment, μ represents the additional signal attenuation factor under NLoS environment, and α L and α N are the path loss exponents for LoS and NLoS scenarios, respectively, and the general condition is α L ≤ α N The present application does not consider small-scale fading. Therefore, the expected achievable rate of U in the nth time slot from the kth GD can be expressed as follows:

[0121]

[0122] where, and Here, P k [n] represents the transmission power of the kth GD, and σ 2 represents the variance of additive white Gaussian noise. Similarly, the expected achievable rate of E in time slot n can be expressed as:

[0123]

[0124] where, and P J [n] represents the transmission power of J. Since the rate under NLoS scenario is much lower than that under LoS scenario, and in order to reduce the complexity of the solution, we only consider the expected rate under LoS condition. Therefore, and The approximate lower bound of

[0125]

[0126] where, represent the channel coefficients for communication between the eavesdropper E and the kth GD under LoS and NLoS scenarios, respectively.

[0127] Then, the achievable secrecy rate of the kth ground device in n time slots can be approximately expressed as:

[0128]

[0129] where, The horizontal energy consumption of the UAV U and J is expressed as:

[0130]

[0131] where v i[n] represents the flight speed of U and J in hover state, and 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 p represent the fuselage drag ratio and air density, respectively, the average rotor induced speed is represented as v0, s and A represent the rotor stiffness and rotor disc area, respectively.

[0132] The energy consumption of the UAVs U and J in the vertical direction can be represented as:

[0133]

[0134] where W represents the weight of U and J. And v i represents the vertical flight speed of the UAV, In addition, the UAV does not consume power during vertical descent. Therefore, when v z [n]<0, there is

[0135] Construct a complete optimization problem:

[0136]

[0137] where V xy and V z are the maximum horizontal and vertical speeds that the UAVs can fly in each time slot, A in the above formula represents the GD transmission scheduling, P represents the interference power of the UAV J and the transmission power of the GD, Q represents the horizontal flight trajectory of the UAV U and the three-dimensional trajectory of the UAV J, H represents the vertical flight trajectory of the UAV U, and Θ represents the elevation angle of the UAV U when flying with the ground user. N represents the number of time slots, n represents the nth time slot, and a k [n] represents a binary variable, P k [n] represents the transmission power of the UAV U, and for i∈{U,J}, represents the horizontal energy consumption of the UAVs U and J in the nth time slot, represents the vertical energy consumption of the UAVs U and J in the nth time slot, z i [n+1], z i [n] represent the vertical positions of the UAVs U and J in the nth+1, nth time slots, respectively, q i [n+1], q i [n] represent the horizontal positions of the UAVs in the nth+1, nth time slots, respectively, V xy represents the maximum horizontal speed of the UAV, V z represents the maximum vertical speed of the UAV, respectively represent the probability of the k-th GD establishing a LoS link with the drone U and the eavesdropper E in the n-th time slot, for X ∈ {U, E}, d UX [n] denotes the distance between the GD and X in the n-th time slot, α L and α N are the path loss exponents in LoS and NLoS scenarios, respectively. ρ0represents the channel power gain with unit reference distance in LoS environment, σ 2 denotes the variance of additive white Gaussian noise, μ represents the additional signal attenuation factor in NLoS environment, θ kX [n] represent the elevation angle between the GD and X, respectively, w k denotes the horizontal position of the GD, and represent the maximum instantaneous power and average power of the GD during transmission, respectively, and represent the maximum instantaneous power and average power of the drone J during transmission, respectively, H max and H min represent the maximum and minimum altitudes of the drone, q i [1], z i [1] represent the initial horizontal and vertical positions of the drones U and J, q i [N], z i [N] represent the final horizontal and vertical positions of the drones U and J, δ t defines the length of each flight time slot of the drone.

[0138] where C1and C2represent the constraints on the average and peak transmission power in each time slot, and represent the average and maximum transmission power of D k , respectively, C3and C4represent the constraints on the average and peak interference power in each time slot, and represent the average and maximum interference power of J, respectively, C5represents the elevation angle constraint between D k and U, C6represents the safety separation distance constraint between all drones (U, J, E), C7specifies the flight altitude constraint of the drones U and J, H min and H max represent the minimum and maximum vertical altitudes of U and J, respectively, C8represents the transmission scheduling constraint between the drone U and D k , C9and C10represent the mobility constraints and the start and end position constraints of the drones U and J, and C11represents the propulsion energy consumption limit of U and J.

[0139] S3: For the constructed optimization mathematical model, decoupling operation is performed based on the BCD method to obtain four sub-problems: transmission scheduling, interference power of the interfering UAV 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, a convex approximation fitting method is used to convert it into a convex problem for solution.

[0140] S4: Use an iterative algorithm to solve for the optimal GD transmission scheduling, the interference power of UAV J and the transmission power of GD, the horizontal flight trajectory of UAV U, the three-dimensional trajectory of UAV J, and the vertical flight trajectory of UAV U.

[0141] The trajectory scheme for fair scheduling in an energy-constrained aviation IoT system based on probabilistic line-of-sight links proposed in this invention is a multivariate coupled non-convex problem involving integer programming. Solving the primal problem... This invention utilizes the Block Coordinate Descent (BCD) technique to decompose the original problem into multiple subproblems. Specifically, for given variables A, P, Q, and H, optimization is performed in each subproblem. Furthermore, non-convex constraints in the subproblems are transformed into convex constraints. The solution to this problem will follow these steps.

[0142] The specific steps are as follows:

[0143] (1) Based on the BCD algorithm The problem is decoupled by transforming the 3D trajectory design of the two UAVs, the interference power of the interfering UAV, the transmission power of the ground equipment, and the transmission scheduling into four subproblems: GD transmission scheduling A, the interference power of UAV J and the transmission power of GD P, the horizontal flight trajectory of UAV U, the 3D trajectory of UAV J Q, and the vertical flight trajectory of UAV U H. Simultaneously, the binary scheduling coefficient A is relaxed, and the relaxation variable η is introduced. k Replacement optimization issues The objective function in [the context].

[0144] The specific issues are as follows:

[0145] Subproblems related to GD transmission scheduling A η k It's an optimization problem. The slack variables introduced in the process.

[0146]

[0147] Subproblems concerning the interference power of UAV J and the transmission power P of GD

[0148]

[0149] Sub-problem on horizontal flight trajectory of UAV U and three-dimensional flight trajectory design Q of UAV J

[0150]

[0151] Sub-problem on vertical flight trajectory H of UAV U

[0152]

[0153] (2) Perform convex problem conversion on the sub-problem obtained in step (1), wherein the sub-problem is a typical LP linear programming problem, which can be directly solved by existing optimization toolboxes. The sub-problem and the sub-problem is a non-convex optimization problem, which needs to be approximated by continuous convex approximation.

[0154] For the sub-problem wherein the constraints C2-C4 are all linear constraints, first express in the constraint C1 as:

[0155]

[0156] Perform first-order Taylor expansion conversion on the non-convex formula in to obtain:

[0157]

[0158] denotes a feasible point selected in the mth iteration. For this given feasible point, is a concave function with respect to the optimization variables P k [n] and P J [n]. This feature is crucial for the subsequent optimization process. By replacing the original with we effectively convert the problem into a convex optimization problem.

[0159] Based on the above transformation, the sub-problem is a standard convex optimization problem with respect to the optimization variable P, which can be solved by the interior point method.

[0160] For the sub-problem first handle the non-convex constraint C1. Since is non-concave, the optimization problem is non-convex and difficult to solve. Introduce an auxiliary variable and Thus, can be expressed as

[0161]

[0162] where The new constraint is

[0163]

[0164] Then, after performing the SCA convex transformation on the left side of the above equation, we get

[0165]

[0166] where Y (m) [n] represents Y[n] at the mth iteration. The term is non-convex. We perform Taylor expansion on it as follows:

[0167]

[0168] where, and represent x k [n] and t kU [n] at the mth iteration, respectively, whose expanded forms are as follows:

[0169]

[0170] Using to replace in C1, the constraint C1 becomes a convex constraint.

[0171] Next, we deal with the constraint C2, which is relaxed to the following form:

[0172]

[0173] It is worth noting that the function arctan(1 / x) is a convex function. Therefore, the right side of the constraint C2 with respect to the expression U [n]-w k || shows convexity. By applying the SCA method, we get the following convex constraint:

[0174]

[0175] where

[0176]

[0177] And represents q U[n].

[0178] Next, to handle constraint C3, we first rewrite it as:

[0179]

[0180] The present application applies the SCA method to obtain a lower bound of the norm square function of the above equation, as follows:

[0181]

[0182] where, and denote the current estimated position and altitude of UAV J at the mth iteration. The present application linearizes the objective function by introducing these iterative estimates, thereby simplifying the optimization problem.

[0183] Finally, handle constraint C7 by introducing a slack variable λ i Rewrite constraint C7 as:

[0184]

[0185] For i∈{U,J}, v i [n] represents the flight speed of UAVs U and J, and has: where P0 and P1 are two constants representing the inherent blade surface power and induced power, respectively; U tip denotes the tip speed of the rotor blade; d0 and p represent the body drag ratio and air density, respectively; the average rotor induced speed is denoted by v0; s and A s represent the stiffness of the rotor and the rotor disc area, respectively. This is a non-convex constraint on the variables q i [n] and λ i [n], and the constraint is rewritten as:

[0186]

[0187] Based on the above transformation, the subproblem is a standard convex optimization problem with respect to the optimization variable Q, which can be solved by the interior point method.

[0188] For the subproblem is non-convex due to the presence of constraints C2 and C3. In addition, the in constraint C1 is not only affected by H, but also by This interdependence increases the complexity of the problem, further leading to its non-convexity. In summary, the non-convexity arises from specific constraints that do not satisfy the convexity property and the complex relationship between the variables involved.

[0189] First, we deal with the nonlinear constraint C2. We relax it to the following form:

[0190]

[0191] It is worth noting that the function arctan(x) is a concave function. However, CVX does not contain arctan(x), CVX is a MATLAB toolbox dedicated to 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 expressions without deep understanding of the underlying solution algorithm, so we use SCA to convert the above formula to:

[0192]

[0193] where, And represents the value of z U [n] in the mth iteration.

[0194] Next, we deal with the constraints C3, using SCA technology, we rewrite them as follows:

[0195]

[0196] Finally, we deal with in constraint C1, re-express it as:

[0197]

[0198] Approximate in the above formula as:

[0199]

[0200] where, and represent x k [n] and t kU [n] in the mth iteration, respectively. Replace with Constraint C1 is also rewritten as a convex constraint.

[0201] Based on the above transformation, the subproblem is a standard convex optimization problem about optimization variable H, which can be solved by interior point method.

[0202] (3) Design the iterative algorithm process, connect the convex optimization problems obtained in step (2) in series, see Table 1 for specific steps.

[0203] Table1 Iterative Algorithm

[0204]

[0205] (4) Algorithm convergence proof:

[0206] 1. In the first step of the algorithm, the problem is a standard LP linear programming problem that can be solved for A m+1 , thus: R(A m , P m , Θ m , H m , Q m ) ≤ R(A m+1 , P m , Θ m , H m , Q m ).

[0207] 2. In the second step of the algorithm, the problem is a convex optimization problem that can be solved for P m+1 by an optimization solver, thus: 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 ).

[0208] 3. In the third step of the algorithm, in the second step of the algorithm, by fitting a convex approximation to the optimization variable Q, we can get:

[0209] 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 )

[0210] ≤ R lb (A m+1 , P m+1 , Θ m , H m , Q m+1 )

[0211] ≤ R(A m+1 , P m+1 , Θm ,H m ,Q m+1 )

[0212] Similarly, in the fourth step of the algorithm, the above relationship is also satisfied, so that the function value R(A m ,P m ,Θ m ,H m ,Q m ) is a non-decreasing function throughout the algorithm process, and R(A m ,P m ,Θ m ,H m ,Q m ) can be approximated to a fixed constant through continuous iteration of the program, and the constant is the optimal sum rate of the entire system.

[0213] Step one, according to the basic theory of wireless communication and PLoS channel model, a model of energy-limited unmanned aerial vehicle assisted wireless communication system is constructed. In this system model, the energy-limited unmanned aerial vehicle needs to be guaranteed, and the complexity of solving the PLoS channel model is introduced, that is, the optimization objective of the problem needs to be transformed into its approximate lower bound to reduce the solving difficulty.

[0214] Steps two and three perfect the mathematical theory derivation and problem solving analysis in the model building process. In view of the non-convexity and high coupling of the optimization problem corresponding to the system model, the approximate fitting method based on Block Coordinate Descent (BCD) algorithm and continuous convex approximation is used to decouple and transform the original optimization problem. BCD is a high-efficiency optimization method, which is a block coordinate descent method in Chinese, and simplifies the solving process of complex problems through block optimization strategy, and is widely used in many fields, especially in dealing with optimization problems with block structure. (For details, see the specific embodiments of the present application).

[0215] Step four uses the idea of iteration to make the system safety transmission rate approach a fixed value through the way of loop iteration of the sub-problems obtained in steps two and three, and the fixed value is the maximum system average safety reachable rate required by the present application.

[0216] The application proposes an optimization method of a secure data collection system based on dual unmanned aerial vehicle assistance. First, an optimization problem is constructed to maximize the total achievable secrecy rate of the system, involving four optimization problems of GD transmission scheduling, the interference power of unmanned aerial vehicle J and the transmission power of GD, the horizontal flight trajectory of unmanned aerial vehicle U and the three-dimensional trajectory of unmanned aerial vehicle J, and the vertical flight trajectory of unmanned aerial vehicle U. Considering the existence of an aerial eavesdropper, we use an approximate lower bound to simplify the solving process of the non-convex optimization problem. 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 a relaxation variable and a step-by-step convex approximation method.

[0217] In order to prove the effectiveness of the proposed algorithm, i.e. the performance improvement, the following several benchmark schemes are listed for comparison:

[0218] Benchmark scheme 1: the system only considers a single unmanned aerial vehicle collecting information without the assistance of interference, jointly optimizing 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 unmanned aerial vehicles in the proposed scheme.

[0219] Benchmark scheme 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, and the provided power remains fixed, taking the values of and

[0220] Benchmark scheme 3: all unmanned aerial vehicles fly at the lowest height, jointly optimizing the 2D trajectory of U and J, the interference power of J, the transmission power of GD and user scheduling.

[0221] Figure 2 is the flowchart of the iterative algorithm proposed by the application to solve the optimization problem. The detailed process corresponds to the specific solving steps of the above optimization problem.

[0222] Figure 3 and Figure 4 is the simulation verification based on the proposed scheme of the application, Figure 3 and Figure 4 show the simulation results of the transmission scheduling of the proposed scheme and the iterative convergence of the system under various schemes. From Figure 3 it can be observed that the proposed scheme has convergence in jointly optimizing the transmission scheduling coefficient, the unmanned aerial vehicle transmission power and the unmanned aerial vehicle 3D flight trajectory, and other comparative schemes also have good convergence. The results show that the secrecy rate of the proposed scheme is the highest, which illustrates the effectiveness and superiority of the proposed algorithm. In addition, from Figure 4It can be observed that the transmission scheduling results of the proposed schemes, the simulation results show that all GDs are alternately in service state, which indicates that U can only communicate with one user in each cycle, and the unscheduled users remain silent. When multiple GDs participating in 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 Internet of Things system is maximized.

[0223] Figure 5 and Figure 6 The horizontal trajectory, 3D trajectory simulation results of different schemes are demonstrated, in which

[0224] W, and From Figure 5 It can be observed that the horizontal trajectory of the UAV U under the OUWJ scheme is different from that of other schemes. In the OUWJ scheme, U first flies towards D2, while in other schemes, U initially flies towards D1. This is because, compared with other schemes, the OUWJ scheme has no interference assistance, and the interception ability of the eavesdropper E is not suppressed. Since D1 is closer to the transmission point of E, in order to improve the security rate of the system, U first flies towards D2, and only when E is farther away will it turn to D1. This makes the flight time between GDs increase compared with other schemes, thereby affecting the achievable rate of the system. As Figure 6 shown, compared with the 2D scheme, the proposed scheme makes the UAV have greater trajectory flexibility. During the flight between GDs, U can increase the flight height, thereby forming a larger elevation angle with GDs, thereby improving the achievable rate. At the same time, J can adjust the flight height to minimize the eavesdropping ability of E.

[0225] Figure 7 The simulation shows the change in vertical height under different schemes. When U leaves GD, it first rises to a higher height, and then dives to obtain a better elevation angle. In the proposed scheme, J first rises to 80 meters, maintains the same flight height as the eavesdropper E, and then adjusts the height to maintain the minimum safe distance from E, thereby maximally suppressing the eavesdropping ability of E.

[0226] Figure 8 and Figure 9The power variations of the proposed scheme and the 2D scheme are verified in the whole flight period. It can be observed that the transmission power of J is relatively high at the beginning and end of the flight period. This is because at these two time instants, U is far away from GD, and in order to ensure safe communication, J increases the suppression of the eavesdropping ability of E. In addition, it can be seen from the above figure that when U flies between GD, the 2D scheme relatively maintains a low elevation angle during this period, which has a negative impact on the communication rate with GD. Therefore, the transmission power of GD is low during the time when U flies between the GD in the 2D scheme. In order to improve the average rate, the 2D scheme allocates more power when U directly hovers above GD.

[0227] Figure 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 GD, the power allocation is significantly reduced, resulting in a much lower achievable safe rate than the proposed scheme. Therefore, in terms of the average rate throughout the cycle, the proposed scheme is superior to the 2D scheme.

[0228] Figure 11 and Figure 12 The simulation shows the horizontal and vertical flight speed variation curves of different UAV schemes. It can be observed that the OUWJ scheme has more propulsion power, enabling it to hover above GD, while the propulsion power of other schemes is less, resulting in continuous hovering to control energy consumption throughout the flight.

[0229] Figure 13 The simulation illustrates the variation of the average achievable secure rate with the flight period T under different schemes. It can be seen that the average secure rate obtained by the proposed algorithm based on BCD and SCA is superior to other schemes. Compared with the OUWJ scheme without the assistance of the interferer, optimizing the trajectories of both UAVs can effectively suppress the eavesdropping ability of the eavesdropper, and compared with the 2D scheme with a fixed vertical flight height, optimizing the 3D trajectory of both UAVs can enable U to increase the elevation angle with GD to improve the information transmission rate, and J can fly to a position closer to E to maximize its eavesdropping ability. The combination of these two points brings an improvement in the system security rate, which also reflects that the proposed scheme can maximize the security performance of the considered system.

[0230] The above numerical results verify the effectiveness of the algorithm we proposed in various scenarios, indicating that the three-dimensional trajectory design of the UAV can significantly improve the average secure rate of the data collection system.

[0231] The application has wide application in unmanned aerial vehicle assisted communication system, and is particularly suitable for data collection and eavesdropping protection scenarios related to physical layer security. In an environment requiring real-time collection of sensitive data, unmanned aerial vehicles can be quickly deployed and provide flexible communication support to ensure the safe transmission of information. By introducing a more realistic probabilistic line-of-sight model for modeling, the accuracy of information transmission of the communication system under interference conditions can be significantly improved. In the eavesdropping protection scenario, the unmanned aerial vehicle not only takes charge of data transmission, but also effectively interferes with potential eavesdroppers through optimized flight trajectory design, enhancing the physical layer security of communication. The three-dimensional trajectory optimization of the dual unmanned aerial vehicle for physical layer security can achieve efficient data transmission under limited energy consumption, meeting the strict requirements for information security and privacy protection.

[0232] The application also provides a communication system comprising K ground users, a service unmanned aerial vehicle U existing in the air, an air eavesdropper E trying to eavesdrop confidential information at all times during the process, and a friendly jammer J existing in the air to suppress the eavesdropping ability of the eavesdropper. The system can perform the above-mentioned unmanned aerial vehicle three-dimensional trajectory optimization method based on the probabilistic line-of-sight link.

Claims

1. A dual-UAV 3D trajectory optimization method for physical layer security, characterized in that, Includes the following steps: S1: Construct a communication system model: Set up a dual-UAV-assisted security data collection system, in which UAVs U and J serve as the airborne base station and the airborne friendly jammer of the data collection network, respectively, flying along a certain initial trajectory. The communication link channel model between UAV U and the ground node is a PLoS model. The energy consumption of UAVs U and J is limited. At the same time, there is UAV E in the air as an eavesdropper attempting to eavesdrop on confidential information. S2: Constructing an Optimization Mathematical Model: With the objective of maximizing the system's average achievable secure rate, an optimization problem is constructed to maximize the system's average achievable secure rate. This involves optimizing mathematical models for GD transmission scheduling, the interference power of UAV J and the transmission power of GD, the horizontal flight trajectory of UAV U, the three-dimensional trajectory of UAV J, and the vertical flight trajectory of UAV U. The optimization mathematical model is as follows: in, Let A represent the average security rate of the k-th ground device (GD) in the n-th time slot; A represents the GD transmission schedule; 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 between UAV U and the ground user during flight; N represents the number of time slots; n represents the n-th time slot; and the entire time is discretized into... α k [n] represents a binary variable, P k [n] represents the transmission power of the UAV U, P J [n] represents the transmission power of UAV J; and These represent the maximum instantaneous power and average power of GD during transmission, respectively. and These represent the maximum instantaneous power and average power of UAV J during transmission, respectively. It is the elevation angle between the k-th GD and X, where X∈{U,E}, q U [n]、q E [n] and q J [n] represents the horizontal positions of U, E, and J of the drones, respectively, and arctan(x) is a concave function; q i [n+1]、q i [n] represents the horizontal position of the UAV in the (n+1)th and nth time slots, respectively, z i [n+1]、z i [n] represents the vertical positions of UAVs U and J in the (n+1)th and nth time slots, respectively; D min H represents the minimum safe distance between drones. max and H min This represents the maximum and minimum flight altitude of the drone; V xy and V z These are the maximum horizontal and vertical speeds that the drone can fly in each time slot; δ t The length of each flight time slot of the UAV is defined; q i [1]、z i [1] represents the initial horizontal and vertical flight positions of U and J, respectively, 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 U and J drones. This indicates the energy consumption of U and J in the vertical direction for the drones; This represents the horizontal energy consumption of UAVs U and J in the nth time slot. denoted by , representing the vertical energy consumption of UAVs U and J in the nth time slot; μ represents the additional signal attenuation factor under NLoS environment; S3: For the constructed optimization mathematical model, decoupling operation is performed based on the BCD method to obtain four sub-problems: 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. The sub-problem concerning GD transmission scheduling for: Where, η k It's an optimization problem. The slack variables introduced in the process; the subproblem This is a typical LP linear programming problem, which can be solved directly using an optimization toolkit; The subproblems of the interference power of the UAV J and the transmission power of the GD for: The sub-problems of designing the horizontal flight trajectory of UAV U and the three-dimensional flight trajectory of UAV J. for: Where, η k It is an equivalence problem Introduced slack variables; The subproblem of the vertical flight trajectory of the UAV U for: Where, δ t The length of each flight time slot of the UAV is defined, η. k It is an equivalence problem Introduced slack variables; S4: Use an iterative algorithm to solve for the optimal GD transmission schedule, the interference power of UAV J and the transmission power of GD, the horizontal flight trajectory of UAV U, 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, characterized in that, The sub-problem The approximate fitting of continuous convex approximation is performed as follows: Subproblems Constraints C2 to C4 are all linear constraints. First, the subproblems are... In constraint C1 Expressed as: Again The non-convex expression is transformed into a convex expression by a first-order Taylor expansion, resulting in: in, This represents a feasible point selected in the m-th iteration; for this given feasible point, It concerns the optimization variable P. k [n] and P J A concave function of [n]; σ represents the probability of a Loss of Sight (LoS) link being established between the k-th GD in the nth time slot and the drone U and the eavesdropper E, respectively; 2 This represents the variance of additive white Gaussian noise; Let h represent the channel coefficients for LoS communication between the drone U and the eavesdropper E and k GDs, respectively. JE [n] represents the channel coefficient between J and E in the nth time slot; Subproblems This is a standard convex optimization problem concerning the optimization variables, which is solved using the interior point method.

3. The dual-UAV three-dimensional trajectory optimization method for physical layer security according to claim 1, characterized in that, The sub-problem The approximate fitting of continuous convex approximation is performed as follows: First, address the subproblems. Non-convex constraint C1: Introducing slack variables as well as therefore, This can be expressed as: in, ρ0 represents the channel power gain per unit reference distance in a LoS environment; w k θ represents the horizontal position of GD; kX [n] is the elevation angle between the k-th GD and X; α L and α N It is the path loss exponent for LoS and NLoS scenarios, where a > 0 and b > 0 are constants specified by the actual environment; The new constraints are: Where Y[n] is the relaxation 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 newly added constraint, we obtain: in, Y (m) [n] represents Y[n] in the m-th iteration; This will result in a non-convex term. Perform a Taylor expansion: in, and Let x represent the value of x in the m-th iteration. k [n] and t kU [n], expanded as follows: use Sub-problem of substitution In constraint C1 The replaced constraint C1 is a convex constraint; Next, we will address the subproblems. The constraint C2 is relaxed to the following form: Here, the function arctan(1 / x) is a convex function; By applying the successive convex approximation (SCA) method, the following convex constraints are obtained: in q represents the value at the m-th iteration. U [n]; Next, in order to deal with the subproblems Constraint C3 is first rewritten as: Applying the successive convex approximation (SCA) method to obtain the rewritten subproblems The lower bound of the constrained C3 norm square function is as follows: in, and The m-th iteration represents the estimated position and altitude of UAV J; T represents the flight period. Finally, handle the subproblem. The constraint C7 is addressed by introducing a slack variable λ. i Subproblems Constraint C7 is rewritten as: For i∈{U,J}, v i [n] represents the flight speeds of drones U and J, and we have: Where P0 and P1 are two constants, representing the inherent blade surface power and the induced power, respectively; U tip The tip velocity of the rotor blades is represented by d0 and ρ, respectively, which represent the drag ratio and air density. The average rotor induced velocity is represented by v0; s and A s These represent the rotor stiffness and rotor disk area, respectively. Performing a Taylor expansion on the right side of the inequality, the rewritten constraints are further rewritten as follows: Subproblems This is a standard convex optimization problem concerning the optimization variables, which is solved using the interior point method.

4. The dual-UAV three-dimensional trajectory optimization method for physical layer security according to claim 1, characterized in that, The sub-problem The approximate fitting of continuous convex approximation is performed as follows: First, address the subproblems. The nonlinear constraint C2 is relaxed to the following form: Here, the function arctan(x) is a concave function; using SCA, the above equation can be transformed into: in, and In the m-th iteration, z U The value of [n]; Next, we will address the subproblems. Constraint C3, using the SCA technique, can be rewritten in the following form: ‖q J [n]-q U [n]‖ 2 +|z J [n]-z U [n]| 2 ‖q U [n]-q E [n]‖ 2 +|z U [n]-z E [n]| 2 Finally, handle the subproblem. In constraint C1 Reexpress it as: In the above formula Approximately: in, and Let x represent x in the m-th iteration. k [n] and t kU [n]; will Replace with Subproblems The constraint C1 was also rewritten as a convex constraint; Subproblems This is a standard convex optimization problem concerning the optimization variables, which is solved using the interior point method.

5. The dual-UAV three-dimensional trajectory optimization method 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.

6. A communication system comprising K ground users and an aerial unmanned aerial vehicle (UAV) U, wherein an aerial eavesdropper E constantly attempts to eavesdrop on confidential information, while a friendly jammer J in the air suppresses the eavesdropper's eavesdropping capability; 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 1-5.

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