A multi-unmanned aerial vehicle cooperative secure communication method based on wireless power transmission

Abstract

The application claims a kind of multi-unmanned aerial vehicle cooperative secure communication method based on wireless power transmission.The method constructs including uplink and downlink secure communication network, in the energy stage, by unmanned aerial vehicle to ground user transmission radio frequency energy, in transmission stage, by ground user with collection energy to communication unmanned aerial vehicle upload data, and by idle unmanned aerial vehicle as needed switch for interference unmanned aerial vehicle sends artificial noise.The method establishes channel model, security rate model, energy collection model and unmanned aerial vehicle energy consumption model, to maximize the original joint optimization problem (P) with security energy efficiency as target, joint optimization time slot division, unmanned aerial vehicle association, power allocation and flight trajectory and speed, and obtain scheduling result through time slot division algorithm based on Dingkelbach iteration and multi-unmanned aerial vehicle secure communication strategy iteration algorithm based on ground energy charging.The application can improve system security energy efficiency in energy limited scene while guaranteeing physical layer security.

Description

Technical Field

[0001] This invention relates to the fields of unmanned aerial vehicle (UAV) wireless communication, wireless power transmission, physical layer security, and resource optimization, and particularly to a multi-UAV cooperative secure communication method based on wireless power transmission. Background Technology

[0002] Drones, with their advantages of flexible deployment, high mobility, and ability to adjust their spatial position as needed, have been widely used in scenarios such as temporary coverage, data collection in remote areas, and emergency communications. In areas where ground infrastructure is limited or ground users are sparsely distributed, multiple drones can work together to provide communication services to ground terminals, thereby improving network coverage and link quality.

[0003] However, existing UAV-assisted communication systems still suffer from two prominent problems. First, ground users are typically powered by small-capacity batteries, making recharging difficult and limiting continuous data acquisition capabilities; the UAVs themselves also consume energy for flight propulsion and communication transmission, making system energy efficiency a key factor restricting the continuous operation of the network. Second, the wireless link between the UAV and ground users has open broadcast characteristics, which could allow ground eavesdropping nodes to intercept data uploaded by ground users to the UAV, leading to communication security risks.

[0004] Wireless power transfer technology can replenish energy for energy-constrained ground users using radio frequency energy. Combined with UAV communication, this allows UAVs to proactively fly to the user's vicinity to recharge. However, if UAVs only perform fixed communication, recharging, or jamming functions, the system struggles to dynamically adjust resources based on user energy status, channel changes, and eavesdropping threats, leading to insufficient energy utilization and secure transmission efficiency. Therefore, it is necessary to propose a multi-UAV cooperative communication method that jointly considers wireless power transfer, secure transmission, artificial noise interference, and UAV trajectory optimization.

[0005] The inventors' earlier application, CN121367939, discloses a trajectory and mode switching optimization method based on multi-UAV assisted low-altitude safe communication. First, a system model is constructed. Then, with maximizing system safety and energy efficiency as the optimization objective, an optimization problem is constructed with constraints on optimizing functional mode selection A, transmission power P, UAV trajectory Q, and UAV speed V. Next, the optimization problem is decomposed into three sub-problems concerning UAV functional mode selection, transmission power, and UAV trajectory and speed, and solved. Finally, overall iterative optimization is performed to find the overall optimal solution.

[0006] Compared to the aforementioned prior application, CN121367939 primarily targets multi-UAV-assisted low-altitude safe communication scenarios, focusing on resolving issues related to mode switching, transmission power allocation, trajectory design, and speed optimization between UAV communication and jamming functions. While this solution considers energy consumption during UAV flight and communication and optimizes resources with the goal of maximizing system safety and energy efficiency, its system model only considers ground users as legitimate communication users participating in safe transmission, failing to account for ground users' own energy limitations and the need for UAVs to provide wireless power transmission for recharging. Furthermore, this solution lacks a time-slot partitioning model between the UAV downlink wireless charging phase and the ground user uplink safe transmission phase, and does not introduce a ground user energy harvesting model, available energy constraints, or energy causal constraints. Therefore, when ground users have limited battery capacity and need to rely on UAV wireless charging to continuously upload data, this prior application struggles to address the joint optimization issues between user recharging, uplink safe transmission, artificial noise interference, and UAV energy consumption.

[0007] To address the aforementioned differences and shortcomings, this invention further introduces a wireless power transmission mechanism into the multi-UAV collaborative secure communication system. Each time slot is divided into a downlink wireless charging phase for the UAV and an uplink secure transmission phase for ground users. During the charging phase, the UAV transmits radio frequency energy to energy-constrained ground users. During the transmission phase, ground users use the collected energy to upload data to the communicating UAV. Simultaneously, idle UAVs can switch to jamming UAVs to transmit artificial noise to suppress eavesdropping nodes. This invention jointly considers time slot division, communication correlation, interference correlation, ground user transmission power, UAV power transmission power, UAV interference power, and UAV trajectory and speed within the same optimization framework. It also ensures the sustainability of the ground user's communication energy source through an energy harvesting model and energy causal constraints, thereby improving system security and energy efficiency in energy-constrained scenarios while guaranteeing secure uplink transmission. Summary of the Invention

[0008] This invention addresses the problems of insufficient battery life, susceptibility to eavesdropping, and low resource utilization caused by the fixed functions of multiple UAVs when energy-constrained ground users transmit data uplink over open wireless links. It proposes a multi-UAV cooperative secure communication method based on wireless power transmission.

[0009] The technical solution of the present invention is as follows:

[0010] A multi-UAV cooperative secure communication method based on wireless power transmission includes the following steps:

[0011] Step 1): Construct a multi-UAV-assisted uplink and downlink secure communication system model, and determine the system nodes, UAV functional modes, time allocation model, channel model, secure communication model, ground user energy harvesting and consumption model, and UAV energy consumption model;

[0012] Step 2): Based on the system model constructed in Step 1), construct the original joint optimization problem P with the goal of maximizing safety and energy efficiency, and determine the variables to be optimized and the constraints.

[0013] Step 3): To solve the original joint optimization problem P in Step 2), the fractional programming transformation and alternating iteration method are used to decompose problem P into four sub-problems: time slot partitioning, related variable and power optimization, communication UAV trajectory optimization, and interference UAV trajectory optimization, and then solve them.

[0014] Step 4): Based on the solution results of each sub-problem in Step 3), iteratively update the time slot division, UAV function scheduling, correlation, power allocation, UAV trajectory and speed, and output the multi-UAV cooperative safe communication strategy.

[0015] Furthermore, the total energy consumption of the drone is as follows.

[0016] Based on the time slot allocation, the total energy consumption of the UAV can be expressed as:

[0017]

[0018] UAV energy consumption includes flight propulsion energy consumption, wireless charging and transmission energy consumption, and artificial noise interference energy consumption. and These represent the coefficient factors for interference and transmission, respectively. Indicates the length of a single time slot. This represents the service association variable between the Kth UAV and the Mth ground user. This represents the interference correlation variable between the Kth UAV and the Nth ground eavesdropping node; This represents the power transmission power of the Kth UAV during the wireless power transmission phase. This represents the flight propulsion power of the Kth UAV in the t-th time slot. This represents the transmission power of the m-th ground user in time slot t.

[0019] Furthermore, in step 2): based on the system model constructed in step 1), a primal joint optimization problem P is constructed with the goal of maximizing safety and energy efficiency, and the variables to be optimized and constraints are determined, specifically including:

[0020] The system safety energy efficiency (SEE) is defined as the ratio of the amount of data safely transmitted by all ground users to the total energy consumption of the system during the mission cycle. The original joint optimization problem P aims to maximize SEE and jointly optimizes the time slot partitioning variables, communication-related variables, interference-related variables, ground user transmission power, UAV power transmission power, UAV interference power, and UAV flight trajectory and speed.

[0021] The original joint optimization problem P includes constraints on the minimum safe transmission rate of ground users, the maximum transmit power of ground users, the maximum energy transmission power and maximum interference power of UAVs, the minimum safe distance between UAVs, the maximum horizontal velocity of UAVs, the maximum vertical velocity of UAVs, the maximum acceleration of UAVs, the altitude range of UAVs, the energy causality constraint of ground users, and the functional mutual exclusion constraint of UAVs.

[0022] Furthermore, step 3) specifically includes:

[0023] First, the fractional problem of maximizing SEE is transformed into a subtraction problem using the Tinkelbach method, and the time slot partitioning subproblem is solved using an algorithm based on Tinkelbach iteration. Then, after obtaining the time slot partitioning results, an iterative algorithm for a multi-UAV safe communication strategy based on ground-based power supply is used to alternately update time slot partitioning, UAV scheduling, power allocation, UAV trajectory, and speed. Finally, each subproblem is solved by combining Big M reconstruction, variable relaxation, penalty terms, and continuous convex approximation methods until the SEE change between two adjacent iterations is less than a preset threshold or the number of iterations reaches a preset maximum. The Tinkelbach method includes: maximizing safety and energy efficiency... The divisibility objective is transformed into a subtraction problem with the objective of the difference between the product of the amount of securely transmitted data and the product of the security energy efficiency parameter and the total system energy consumption. Based on the current security energy efficiency parameter, the corresponding sub-problems are solved, and the security energy efficiency parameter is updated according to the solution results until the subtraction objective meets the convergence condition. The iterative algorithm of the multi-UAV secure communication strategy based on ground charging includes: initializing time slot partitioning, UAV scheduling, power allocation, UAV trajectory and speed, solving four sub-problems in sequence: time slot partitioning, related variable and power optimization, communication UAV trajectory optimization and interference UAV trajectory optimization, and calculating the system security energy efficiency according to the update results until the convergence condition is met.

[0024] The fractional programming parameters and the equivalent subtraction problem can be expressed as:

[0025] definition To maximize the SEE in solving the problem, the expression is:

[0026]

[0027] In the formula, The optimal time slot allocation index is the ratio of the amount of data safely transmitted within the task cycle to the total system energy consumption. Indicates time slot division The amount of securely transmitted data for all ground users during the next mission cycle. Indicates time slot division Total system energy consumption.

[0028] Using fractional programming theory, optimal energy efficiency is achieved if and only if the following equation holds:

[0029]

[0030] This equation represents the optimal equivalence condition in the Tinkelbach method;

[0031] Therefore, the original fractional optimization problem can be equivalently transformed into the following subtraction optimization problem:

[0032]

[0033] In the formula, This indicates the number of time slots included in the task cycle, where K represents the number of UAVs. This represents the safe transmission rate or lower bound of the safe transmission rate for the Kth UAV in the t-th time slot. This represents the time allocation factor for the t-th time slot. Indicates the length of a single time slot. This represents the safety energy efficiency parameter in the Tinkelbach iteration. Let represent the total energy consumption of the Kth UAV in the t-th time slot. The subtractive form facilitates solving the time slot division, associated power, and UAV trajectory subproblems separately within an alternating iterative framework.

[0034] Furthermore, the Tinkelbach method includes: transforming the fractional objective of maximizing safety energy efficiency into a subtraction problem with the objective of the difference between the product of the amount of safe transmitted data and the product of the safety energy efficiency parameters and the total energy consumption of the system; solving the corresponding sub-problems based on the current safety energy efficiency parameters; and updating the safety energy efficiency parameters according to the solution results until the subtraction objective meets the convergence condition; the iterative algorithm for multi-UAV safe communication strategy based on ground charging includes: initializing time slot partitioning, UAV scheduling, power allocation, UAV trajectory and speed; sequentially solving four sub-problems: time slot partitioning, related variable and power optimization, communication UAV trajectory optimization, and interference UAV trajectory optimization; and calculating the system safety energy efficiency according to the update results until the convergence condition is met.

[0035] Furthermore, in step 4), based on the solution results of each sub-problem in step 3), the time slot allocation, UAV function scheduling, correlation, power allocation, and UAV trajectory and speed are iteratively updated, and a multi-UAV cooperative safe communication strategy is output, specifically including:

[0036] In each iteration, the time slot partitioning subproblem is solved based on fixed UAV scheduling, power allocation, UAV trajectory, and speed. The correlation variable and power optimization subproblems are solved based on the updated time slot partitioning. The communication UAV trajectory optimization subproblem and the interference UAV trajectory optimization subproblem are further solved separately. The system safety energy efficiency is calculated based on the updated time slot partitioning, correlation, power, trajectory, and speed. The iteration stops when the difference in system safety energy efficiency between two adjacent iterations is less than a preset threshold or the number of iterations reaches a preset maximum. The system outputs the UAV operating mode, wireless charging time, safe uplink transmission time, communication correlation, interference correlation, ground user transmission power, UAV power transmission power, UAV interference power, UAV flight trajectory, and speed for each time slot.

[0037] Furthermore, the upper bound of the eavesdropping rate is determined based on the estimated location and uncertain radius of the eavesdropping node, so as to ensure the robustness of the security rate calculation when the actual location of the eavesdropping node is unknown.

[0038] Furthermore, the correlation variable and power optimization subproblem are processed by the Big M reconstruction method to handle the product term of the binary correlation variable and the power variable, and the binary correlation variable is relaxed to a continuous variable between 0 and 1. At the same time, a penalty term is introduced to make the relaxed variable approach the binary value.

[0039] Furthermore, both the communication UAV trajectory optimization subproblem and the interference UAV trajectory optimization subproblem introduce auxiliary variables to handle distance-related terms, collision avoidance constraints, and flight propulsion energy consumption terms, and construct convex approximation problems through first-order Taylor expansion.

[0040] Furthermore, the multi-UAV collaborative safe communication strategy output process in step 4) includes: initializing time slot partitioning, UAV scheduling, power allocation, UAV trajectory and speed, and setting initial values ​​for system safety energy efficiency, convergence threshold and maximum number of iterations; in each iteration, fixing UAV scheduling, power allocation, UAV trajectory and speed, and using an algorithm based on Tinkelbach iteration to solve the time slot partitioning subproblem; solving the correlation variable and power optimization subproblems based on the updated time slot partitioning; solving the communication UAV trajectory and speed optimization subproblems and the interference UAV trajectory and speed optimization subproblems based on the updated time slot partitioning, correlation variables and power respectively; calculating the system safety energy efficiency based on the updated time slot partitioning, correlation, power allocation, UAV trajectory and speed; if the difference in system safety energy efficiency obtained from two adjacent iterations is not less than the preset threshold and the number of iterations has not reached the preset maximum number of iterations, then continue to execute the next iteration; otherwise, stop the iteration and output the multi-UAV collaborative safe communication strategy.

[0041] The advantages and beneficial effects of this invention are as follows:

[0042] This invention provides energy replenishment to energy-constrained ground users via wireless power transmission, enabling them to complete secure uplink transmissions using harvested energy and improving network continuity. Through dynamic switching of multiple UAV functions, idle UAVs can act as jamming UAVs to transmit artificial noise, enhancing the system's anti-eavesdropping capabilities. By jointly optimizing time slots, correlations, power, and trajectories, the system's security and energy efficiency are improved while satisfying constraints on energy causality, power, speed, altitude, and collision avoidance. By considering the uncertainty of eavesdropping node locations to calculate the upper bound of the eavesdropping rate, the security rate calculation and resource optimization results are robust.

[0043] The innovation of this invention is mainly reflected in the synergistic combination of steps 1 to 4 in claim 1: First, UAV wireless power transmission, ground user energy causal constraints, secure uplink transmission, artificial noise interference, and UAV flight energy consumption are considered simultaneously in the same system model; second, the charging stage and the secure transmission stage are coupled by dividing the time slots into variables, so that the available energy of ground users, transmission rate, and UAV energy consumption can all participate in secure energy efficiency optimization; third, by combining the Tinkelbach method, alternating iteration, Big M reconstruction, variable relaxation, and continuous convex approximation method, the original non-convex fractional optimization problem is decomposed into multiple solvable subproblems.

[0044] The above combination is not simply an overlay of conventional communication optimization steps, because there is a strong coupling relationship between wireless charging time, user upload power, UAV function switching, interference power and flight trajectory. Changes in any variable will simultaneously affect the available energy of ground users, the legitimate link rate, the eavesdropping link rate and the total system energy consumption.

[0045] By jointly optimizing the above variables, this invention can improve the continuous communication capability of ground users, enhance anti-eavesdropping performance, and improve system security and energy efficiency in scenarios with limited energy and eavesdropping threats. Attached Figure Description

[0046] Figure 1 This invention provides a preferred embodiment of a multi-UAV secure communication model diagram based on wireless power transmission. The diagram illustrates the spatial relationships between multiple UAVs, multiple energy-constrained ground users, and multiple ground eavesdropping nodes, as well as the collaborative working methods of UAVs in wireless power transmission, secure data reception, and artificial noise interference.

[0047] Figure 2 The graph showing the relationship between energy efficiency and iteration number provided in this embodiment of the invention illustrates the convergence change of the Safety Energy Efficiency (SEE) during the iteration process of the joint optimization algorithm, and is used to explain the convergence of the solution method of this invention.

[0048] Figure 3The 3D trajectory diagram of multiple UAVs based on EFSF provided in this embodiment of the invention shows the trajectory optimization results of multiple UAVs adjusting their flight altitude and spatial position according to the distribution of ground users and eavesdropping nodes during the mission cycle.

[0049] Figure 4 The EFSF-based two-dimensional trajectory diagram of multiple UAVs provided in this embodiment of the invention shows the trajectory planning results of multiple UAVs approaching ground users or approaching eavesdropping nodes to interfere in a horizontal plane.

[0050] Figure 5 The multi-UAV collaborative function scheduling diagram provided in this embodiment of the invention illustrates the process by which each UAV dynamically switches between communication mode and interference mode in different time slots.

[0051] Figure 6 The energy efficiency diagrams provided in this embodiment of the invention under different UAV power transmission powers illustrate the impact of changes in UAV wireless power transmission power on system safety and energy efficiency.

[0052] Figure 7 The energy efficiency diagrams provided in this embodiment of the invention under different energy conversion efficiencies illustrate the impact of changes in the energy conversion efficiency of ground users on the system's safety and energy efficiency.

[0053] Figure 8 The energy efficiency diagram provided in this embodiment of the invention for different numbers of users shows the impact of changes in the number of ground users on the system's safety and energy efficiency.

[0054] Figure 9 The graph showing the change in the total amount of confidential information under different task cycles provided in this embodiment of the invention illustrates the relationship between the total amount of confidential information in the method of this invention and the comparative scheme under different task execution times.

[0055] Figure 10 The diagram showing the change in safety energy efficiency (SEE) under different task cycles provided in this embodiment of the invention illustrates the relationship between the SEE of the method of the present invention and the comparative scheme under different task execution times. Detailed Implementation

[0056] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0057] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0058] Step 1: Construct a multi-UAV-assisted uplink and downlink secure communication system model, and determine the system nodes, UAV functional modes, time allocation model, channel model, secure communication model, ground user energy harvesting and consumption model, and UAV energy consumption model.

[0059] This invention constructs a multi-UAV-assisted uplink and downlink secure communication system model, which includes K UAVs, M energy-constrained ground users (GNs), and N ground eavesdropping nodes (ENs). The sets of UAVs, ground users, and eavesdropping nodes are represented as follows: , and In this system, drones transmit energy to ground users during the downlink phase via broadcast radio frequency signals, and ground users use the collected energy to upload confidential data to the corresponding drones during the uplink phase. Simultaneously, idle drones switch to jamming drones based on the risk of eavesdropping and send artificial noise to the eavesdropping nodes to reduce the quality of the eavesdropping link.

[0060] This invention uses a three-dimensional Cartesian coordinate system to describe the positions of the drone, ground users, and eavesdropping nodes, and the drone (UAV) flies at an altitude of [missing information]. The horizontal coordinate of the k-th UAV in time slot t is represented as... The coordinates of the m-th ground user are represented as follows: ,in Let be the horizontal coordinate. The precise coordinates of the nth eavesdropping node are represented as follows: ,and This represents the horizontal coordinates. However, eavesdropping nodes conceal themselves to avoid detection, making their precise coordinates difficult for legitimate systems to obtain. Nevertheless, UAVs can still approximate their positions within a certain margin of error, satisfying... .in, This indicates the estimated location of the eavesdropping node. The radius of the circular uncertain region centered on the estimated location of the eavesdropping node is denoted as ...

[0061] The relevant channel model can be represented as:

[0062] Communication channel between the k-th UAV and the m-th ground user It can be represented as:

[0063]

[0064] in, This represents the channel gain at a reference distance d0 = 1 meter. This indicates the position of the k-th UAV within time slot t. This represents the location of the m-th ground user. This indicates the UAV's flight altitude.

[0065] Similarly, the interference channel between the k-th drone and the n-th eavesdropping node It can be represented as:

[0066]

[0067] in, This indicates the actual location of the nth eavesdropping node. This represents the estimated location of the nth eavesdropping node. The radius represents the uncertain location radius of the nth eavesdropping node; the meanings of other symbols are consistent with the aforementioned channel model.

[0068] The eavesdropping channel between the m-th ground user and the n-th eavesdropping node can be represented as:

[0069]

[0070] in, Indicates the path loss coefficient. This represents the small-scale Rayleigh fading power gain, and It follows an exponential distribution with a mean of 1.

[0071] The time allocation model is as follows:

[0072] Divide the task execution cycle into There are 1 time slots, and the set of time slots is represented as . Each time slot is [length missing] For the t-th time slot, the time slot partitioning variable is used. It is divided into two stages: pre- The timeframe is the wireless charging phase, during which the drone transmits radio frequency energy to ground users; afterwards... During the secure uplink transmission phase, ground users upload confidential data to the communication drone while simultaneously interfering with the drone by sending artificial noise. .

[0073] The unmanned aerial vehicle (UAV) function scheduling model and secure communication model are as follows:

[0074] Define communication-related variables Indicate whether the k-th UAV in the t-th time slot is receiving uplink data from the m-th ground user as a communication UAV; define interference correlation variables. This indicates whether the k-th drone in the t-th time slot sends artificial noise to the n-th eavesdropping node as a jamming drone. Any drone can serve at most one ground user or jam one eavesdropping node in the same time slot, and any ground user can associate with at most one communication drone in the same time slot. Furthermore, the same drone cannot act as both a communication drone and a jamming drone in the same time slot.

[0075] During the secure uplink transmission phase, the m-th ground user transmits at a power of Data is transmitted to the communication drone. The legitimate link rate is determined based on the received signal-to-noise ratio (SNR) of the legitimate link, and the eavesdropping link rate is determined based on the eavesdropping link from the ground user to the eavesdropping node and the artificial noise interfering with the drone's transmission. An upper bound on the eavesdropping rate is calculated within the region where the eavesdropping node's location is uncertain. The uplink secure rate is the non-negative portion of the difference between the legitimate link rate and the maximum eavesdropping link rate.

[0076] Legitimate link rate, eavesdropping link rate, and secure rate can be expressed as:

[0077] The achievable rate of transmission from the m-th ground user to UAV k can be expressed as:

[0078]

[0079] in, Let represent the transmission power of the m-th ground user in time slot t. The interference term is determined by the artificial noise transmitted by the UAV in interference mode and its corresponding channel. This indicates the interference power of the interfering UAV. This represents the power of additive white Gaussian noise.

[0080] Similarly, the eavesdropping rate from the m-th ground user to the n-th eavesdropping node can be expressed as:

[0081]

[0082] in, Represents a random variable The expected eavesdropping rate is determined by the eavesdropping channel from the m-th ground user to the n-th eavesdropping node, the ground user's transmission power, and the artificial noise that interferes with UAV transmission.

[0083] Due to the presence of eavesdropping, the secure rate received by UAV k is:

[0084]

[0085] in, This indicates that the non-negative part is taken, and the secure rate is determined by the difference between the rate achievable by the legitimate link and the rate of the eavesdropping link.

[0086] When considering the uncertain location of the eavesdropping node, the upper bound of the eavesdropping rate and the corresponding security rate can be rewritten as follows:

[0087] To account for the location estimation error of the eavesdropping node and the expected eavesdropping rate, the upper bound of the eavesdropping rate can be expressed as:

[0088]

[0089] The upper bound is used to make a conservative estimate of the eavesdropping capability when the actual location of the eavesdropping node is unknown.

[0090] Based on the aforementioned upper bound of the eavesdropping rate, the secure data rate received by UAV k can be rewritten as:

[0091]

[0092] The rewritten safe rate is used for subsequent time slot partitioning, correlation variables, and joint optimization of power and trajectory.

[0093] The ground user energy harvesting model, energy causal constraints, and UAV energy consumption model are as follows:

[0094] During the wireless charging phase, the energy collected by the m-th ground user is determined using a linear energy harvesting model. This harvested energy is related to the energy conversion efficiency, the time slot charging time, the UAV's power transmission capacity, and the channel gain from the UAV to the ground user. Considering the processing delay of the energy harvesting circuit, the energy used for uplink transmission by the ground user in the current time slot does not exceed the sum of its initial energy and the energy collected in previous time slots, thus satisfying the energy causality constraint.

[0095] The energy collected by ground users and the causal constraints on energy are as follows.

[0096] During the wireless power transfer (WPT) phase, the energy collected by the m-th ground user can be expressed as:

[0097]

[0098] The formula is used to calculate the energy collected by the m-th ground user during the wireless power transmission phase. The relevant symbols represent the energy conversion efficiency of the m-th ground user, the duration of the wireless charging phase within time slot t, the UAV power transmission power, and the channel gain from the UAV to the ground user.

[0099] Before the m-th ground user initiates uplink communication in the t-th time slot, the energy available for communication must satisfy the following constraints:

[0100]

[0101] This constraint limits the energy sources that the m-th ground user can access when making uplink transmissions in the current time slot, meaning that the current transmission energy consumption must not exceed its available energy.

[0102] The remaining energy after the m-th ground user completes communication in the current time slot can be expressed as:

[0103]

[0104] The formula is used to update the remaining energy after the m-th ground user communicates. This remaining energy is determined by the remaining energy of the previous time slot, the energy collected in the current time slot, and the energy consumed by communication in the current time slot, and serves as the input for the energy status of subsequent time slots.

[0105] Further combining the above available energy constraints and remaining energy update relationships, the following energy causal constraints can be obtained:

[0106]

[0107] This constraint means that the transmission energy consumption of the m-th ground user cannot exceed the energy available at the corresponding time, in order to ensure that ground users can carry out safe uplink transmission under energy-constrained conditions.

[0108] The total energy consumption of a drone includes flight propulsion energy consumption, wireless charging and transmission energy consumption, and artificial noise interference energy consumption. Flight propulsion energy consumption is determined by the drone's flight speed, acceleration, and rotor flight power model; wireless charging and transmission energy consumption is related to the transmission power and the duration of the charging phase; artificial noise interference energy consumption is related to the interference power and the duration of the secure uplink transmission phase.

[0109] The total energy consumption of the drone is as follows.

[0110] Based on the time slot allocation, the total energy consumption of the UAV can be expressed as:

[0111]

[0112] UAV energy consumption includes flight propulsion energy consumption, wireless charging and transmission energy consumption, and artificial noise interference energy consumption. and These represent the coefficient factors for interference and transmission, respectively.

[0113] Step 2: Based on the system model established in Step 1, construct the original joint optimization problem (P) with the goal of maximizing system safety and energy efficiency.

[0114] This embodiment aims to maximize Safety and Energy Efficiency (SEE), defined as the ratio of the amount of data safely transmitted by all ground users to the total energy consumption of the system during the mission cycle. The optimization variables of the original joint optimization problem (P) include time slot allocation variables, communication-related variables, interference-related variables, ground user transmission power, UAV power transmission power, UAV interference power, UAV flight trajectory, and speed. Constraints include minimum safe transmission rate constraints, power constraints, energy causality constraints, collision avoidance constraints, UAV speed constraints, acceleration constraints, and altitude range constraints. Step 2 is only used to complete the modeling of the original optimization problem (P), providing input for solving the problem in step 3.

[0115] This invention uses the ratio of the amount of data safely transmitted by all ground users to the total system energy consumption during the mission cycle as the system safety energy efficiency (SEE). With the goal of maximizing system safety energy efficiency, it jointly optimizes time slot partitioning variables, communication-related variables, interference-related variables, ground user transmission power, UAV power transmission power, UAV interference power, and UAV flight trajectory and speed. The constraints include minimum safe transmission rate constraints, power constraints, ground user energy causal constraints, UAV energy constraints, UAV speed constraints, altitude constraints, acceleration constraints, and collision avoidance constraints.

[0116] The original joint optimization problem (P) can be expressed as:

[0117]

[0118] The formula aims to maximize the system safety energy efficiency (SEE). The variables to be optimized include time slot division variables, communication-related variables, interference-related variables, ground user transmission power, UAV power transmission power, UAV interference power, and UAV flight trajectory and speed. The constraints C1-C12 correspond to UAV communication-related constraints, interference-related constraints, minimum safe rate constraints, ground user transmission power constraints, UAV power transmission and interference power constraints, UAV collision avoidance constraints, horizontal speed constraints, vertical speed constraints, acceleration constraints, flight altitude constraints, ground user energy causal constraints, and UAV function mutual exclusion constraints.

[0119] Therefore, step 2) completes the construction of the original optimization problem (P), that is, it clarifies the optimization objective, optimization variables and constraints; this step does not involve fractional transformation, subproblem decomposition or convex approximation of the problem (P).

[0120] Step 3: Solve the original joint optimization problem (P) in Step 2 using fractional programming transformation and alternating iteration method.

[0121] Since the original joint optimization problem (P) in step 2 simultaneously includes a fractional objective, binary variables, and non-convex constraints, this embodiment employs fractional programming transformation and alternating iteration methods for solving it. First, the Tinkelbach method is used to transform the safety and energy efficiency maximization problem into a subtraction problem. Second, the original problem is decomposed into four subproblems: time slot partitioning, related variable and power optimization, communication UAV trajectory optimization, and interference UAV trajectory optimization. Third, the Big M reconstruction method, variable relaxation, penalty terms, and continuous convex approximation methods are used to transform each subproblem into a solvable convex optimization problem. Finally, the four subproblems are iterated alternately until SEE converges.

[0122] The corresponding Tinkelbach fractional programming transformation formula is as follows:

[0123] The expression for maximizing the SEE in solving the problem is defined as follows:

[0124]

[0125] SEE stands for Security Energy Efficiency, which is the ratio of the amount of securely transmitted data to the total energy consumption of the system during the task cycle.

[0126] Using fractional programming theory, optimal energy efficiency is achieved if and only if the following equation holds:

[0127]

[0128] This equation represents the optimal equivalence condition in the Tinkelbach method.

[0129] Therefore, the original fractional optimization problem can be equivalently transformed into the following subtraction optimization problem:

[0130]

[0131] The subtraction form facilitates solving the time slot division, associated power, and UAV trajectory subproblems separately within an alternating iterative framework.

[0132] Furthermore, the solution process for the joint optimization problem includes the following specific implementation methods.

[0133] (1) Correlation variables and power optimization.

[0134] Under the conditions of fixed time slot division, UAV trajectory, and velocity, a joint optimization is performed on communication-related variables, interference-related variables, ground user transmission power, UAV power transmission power, and UAV interference power. This sub-problem can be expressed as:

[0135]

[0136] This formula is used to characterize the correlation variables and power allocation sub-problem under the conditions of fixed trajectory and fixed time slot division; the optimization variables include communication correlation variables, interference correlation variables, ground user transmission power, UAV power transmission in the WPT phase and UAV interference power in the secure transmission phase.

[0137] Since the binary correlation variables and power variables have a product term, this embodiment introduces an auxiliary variable and uses the Big M reconstruction method to transform the product coupling relationship into a set of linear constraints. Simultaneously, the binary correlation variables are relaxed to continuous variables between 0 and 1, and a penalty term is introduced to suppress deviations of the correlation variables from 0 or 1. After the above processing, the correlation variable and power optimization problem can be reconstructed as follows:

[0138]

[0139] The penalty term is used to constrain the communication-related variables and interference-related variables to approach binary values, and the auxiliary variable is used to carry out the product relationship between the related variables and the power variable, thereby avoiding the direct solution of the mixed integer nonlinear programming problem.

[0140] Furthermore, the non-convex logarithmic difference in the safety rate is expressed as a combination of convex and concave functions, and a first-order Taylor expansion is performed at the current iteration point to obtain a solvable convex approximation problem:

[0141]

[0142] The convex approximation problem is used to update communication correlations, interference correlations, and various power variables in each iteration, and the solution results serve as input for subsequent UAV trajectory optimization.

[0143] (2) Communication UAV trajectory optimization.

[0144] Under the conditions of fixed time slot division, correlation variables, power allocation, and interference UAV trajectories, the flight trajectory and speed of a communication UAV are optimized. The trajectory optimization subproblem can be expressed as:

[0145]

[0146] This formula describes the trajectory and speed optimization problem of a communication UAV when receiving uplink confidential data from a ground user; the constraints include minimum safe rate constraint, ground user energy constraint, UAV collision avoidance constraint, speed constraint, acceleration constraint, and altitude constraint.

[0147] Since the legitimate link channel gain, ground user energy constraints, collision avoidance distance, and UAV propulsion energy consumption are all coupled with trajectory variables, this embodiment introduces auxiliary variables to handle distance-related terms, and uses a first-order Taylor expansion at the current iteration point to obtain the lower bound of the safe rate and the lower bound of the distance constraint. For example, the global lower bound of the rate-related term can be expressed as:

[0148]

[0149] The lower bound is used to transform the non-convex rate constraint in the UAV trajectory optimization into a convex constraint, so that the UAV can move closer to the service ground user while meeting the safety rate requirements, thereby improving the quality of the legitimate link.

[0150] For distance constraints and collision avoidance constraints, the following lower bound for distance can be constructed at the current trajectory point:

[0151]

[0152] This formula is used to transform the safety distance constraint and auxiliary distance constraint between UAVs into an affine lower bound, thereby maintaining the minimum safety distance between UAVs during trajectory iteration.

[0153] After auxiliary variable substitution and continuous convex approximation, the UAV trajectory optimization problem can be approximated as:

[0154]

[0155] This problem is a convex optimization problem, which can be used to update the trajectory and velocity of the communicating UAV and pass the update result to the trajectory optimization subproblem of the disturbing UAV.

[0156] (3) Optimization of UAV trajectory for interference.

[0157] Under the conditions of fixed time slot division, correlation variables, power allocation, and communication UAV trajectory, the flight trajectory and speed of the jamming UAV are optimized to allow it to approach eavesdropping nodes or key eavesdropping areas without disrupting legitimate communication links, thereby enhancing the effect of artificial noise jamming. The sub-problem of jamming UAV trajectory optimization can be expressed as:

[0158]

[0159] This formula describes the optimization problem of the trajectory and velocity of the disturbed UAV; the optimization objective is still the system SEE, and the constraints include safe rate constraints, UAV collision avoidance constraints, ground user energy constraints, velocity constraints, acceleration constraints, and flight altitude constraints.

[0160] To address the non-convex coupling between the interference UAV trajectory and the eavesdropping rate, this embodiment introduces relaxation variables and auxiliary variables, and performs a first-order Taylor expansion of the relevant convex function at the current iteration point. Its lower bound can be expressed as:

[0161]

[0162] The lower bound is used to transform the impact of the jamming UAV on the eavesdropping link into an iteratively solvable convex constraint, enabling the jamming UAV to dynamically adjust its jamming trajectory based on the uncertain location of the eavesdropping node.

[0163] After the above reconstruction, the problem of optimizing the trajectory of the disturbed UAV can be transformed into:

[0164]

[0165] The auxiliary variable set is used to characterize intermediate variables related to distance, speed, and propulsion energy consumption. Furthermore, following the Tinkelbach iteration method, the following subtractive convex problem can be solved at any reference point:

[0166]

[0167] The solution to this subtractive convex problem is used to update the trajectory and velocity of the interfering UAV, and participates in the next round of time slot division, joint update of correlation variables and power variables.

[0168] (4) Alternating iteration, convergence determination and complexity analysis.

[0169] This embodiment first selects an initial feasible solution that satisfies the constraints of power, energy, speed, altitude, and collision avoidance. Then, in each iteration, it sequentially solves the time slot partitioning subproblem, the correlation variable and power optimization subproblem, the communication UAV trajectory optimization subproblem, and the interference UAV trajectory optimization subproblem. The output of each subproblem serves as the input for the next subproblem and the next iteration.

[0170] Through the above alternating iterations, the system SEE remains monotonically constant during the iteration process, and the following convergence relationship can be obtained:

[0171]

[0172] This formula indicates that the objective function value of the system SEE does not decrease during adjacent iterations. Since the ground user transmission power, UAV power transmission power, UAV interference power, flight speed and mission duration are all constrained, the system SEE has an upper bound. Therefore, the alternating iteration process can converge to a stable solution.

[0173] The iteration stops when the difference in SEE between two consecutive iterations is less than a preset threshold, or when the number of iterations reaches a preset maximum. The overall time complexity of this algorithm can be expressed as:

[0174]

[0175] This complexity is jointly determined by the solution complexity of four sub-problems: time slot partitioning, correlation variable and power optimization, communication UAV trajectory optimization, and interference UAV trajectory optimization.

[0176] The joint optimization algorithm of this invention is as follows:

[0177] To solve the time slot allocation subproblem in step 3), this invention employs an algorithm based on Tinkelbach iteration. This algorithm takes UAV associated variables, transmission power, UAV trajectory, and velocity as input, and outputs the optimal UAV time slot allocation. Its pseudocode is shown in Table 1.

[0178] Algorithm 1: An algorithm based on Tinkelbach iteration 1: Input: UAV related variables Transmission power UAV trajectory and speed ; 2: Output: Optimal UAV time slot allocation ; 3: Initialization: UAV time slot indicators Energy efficiency Outer iterative index Inner iterative index Maximum number of iterations Threshold ; 4: for to do 5: for to do 6: In the known Solve the optimization problem (P1') under the given conditions to obtain the optimization variable values ​​for this iteration. ; 7: if then 8： , ; 9: break 10: else 11: Settings And update ; 12: end if 13: end for 14: if then 15： , ; 16: break 17: end if 18: end for

[0179] After obtaining the time slot allocation results, this invention further adopts an iterative algorithm for a multi-UAV secure communication strategy based on ground charging to alternately update the time slot allocation, UAV scheduling, power allocation, UAV trajectory and speed, and outputs the optimal energy efficiency. Its pseudocode is shown in Table 2.

[0180] Algorithm 2: Iterative Algorithm for Secure Communication Strategy of Multiple UAVs Based on Ground-Powered Charging 1: Input: Time slot allocation UAV scheduling Power distribution UAV trajectory and speed ; 2: Output: Optimal energy efficiency ; 3: Initialization: Energy Efficiency Number of iterations ; 4: while and do 5: Based on fixed , , and Solving the problem (P1') using Algorithm 1 yields the following results. ; 6: Based on , , , and Solve the problem (P2''') to obtain... and ; 7: Based on , , , and Solve the problem (P3') to obtain... and ; 8: Based on , , , , , and Solve the problem (P4'') to obtain... and ; 9: According to , , , and Calculate energy efficiency ; 10: ; 11: end while

[0181] Step 4: Based on the solution results of each sub-problem obtained in Step 3, iteratively update the time slot division, UAV function scheduling, correlation, power allocation, UAV trajectory and speed, and output the multi-UAV cooperative safe communication strategy.

[0182] Specifically, in each iteration, the time slot partitioning subproblem is solved based on fixed UAV scheduling, power allocation, UAV trajectory, and speed. The correlation variable and power optimization subproblems are then solved based on the updated time slot partitioning. Further subproblems for optimizing communication UAV trajectories and interfering UAV trajectories are solved separately. System safety efficiency is calculated based on the updated time slot partitioning, correlation relationships, power, trajectory, and speed. Iteration stops when the difference in system safety efficiency between two adjacent iterations is less than a preset threshold or the number of iterations reaches a preset maximum. The system then outputs the UAV operating mode, wireless charging time, safe uplink transmission time, communication correlation relationships, interference correlation relationships, ground user transmission power, UAV power transmission power, UAV interference power, UAV flight trajectory, and speed for each time slot.

[0183] To further illustrate the beneficial effects of the technical solution of this invention, a simulation experiment was conducted in this embodiment. The simulation compares the functional switching scheme based on ground charging (EFSF) of this invention with the fixed time slot allocation scheme (TAS), the fixed jamming UAV scheme (FJS), and the greedy association scheme (GAS). In TAS, time slots are evenly divided into energy transmission and communication phases; in FJS, dedicated jamming UAVs are deployed to continuously transmit jamming signals; and in GAS, a greedy assignment method is used to select the UAV resource with the highest current rate. Specific simulation parameter settings are as follows:

[0184] In this embodiment, the ground simulation area is set to 1000×1000 m², and all ground users and eavesdropping nodes are distributed in this ground area. UAVs perform wireless charging, secure data reception and artificial noise interference tasks above this area.

[0185] The channel and energy-related parameters are set as follows: the received noise power spectral density of both UAV and eavesdropping node is -173 dBm / Hz, the channel power gain at the reference distance is -30 dB, the time slot length is 1 s, the channel bandwidth is 1 MHz, the energy conversion efficiency of ground users is 0.6, and the path loss index is 2.

[0186] The UAV flight and power-related parameters are set as follows: maximum UAV power transmission is 30 dBm, maximum ground user transmit power is 20 dBm, UAV wireless charging power is 10 W, maximum UAV acceleration is 3 m / s², minimum safe distance between UAVs is 15 m, blade tip speed is 120 m / s, air density is 1.225 kg / m³, rotor disk area is 0.503 m², rotor blade related parameters are 0.05, rotor flight power parameters are 79.86 W, transmission energy consumption coefficient is 0.5, and convergence threshold is 10^-3.

[0187] The above parameters are used to uniformly set the channel conditions, wireless charging conditions, UAV flight constraints, and convergence determination conditions for the EFSF scheme and the comparison scheme; under the same parameter conditions, the security efficiency and confidential information transmission capabilities of each scheme are compared to verify the effectiveness of the joint optimization strategy of the present invention.

[0188] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions.

[0189] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0190] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A multi-UAV cooperative secure communication method based on wireless power transmission, characterized in that, Includes the following steps: Step 1): Construct a multi-UAV-assisted uplink and downlink secure communication system model, and determine the system nodes, UAV functional modes, time allocation model, channel model, secure communication model, ground user energy harvesting and consumption model, and UAV energy consumption model; Step 2): Based on the system model constructed in Step 1), construct the original joint optimization problem P with the goal of maximizing safety and energy efficiency, and determine the variables to be optimized and the constraints. Step 3): To solve the original joint optimization problem P in Step 2), the fractional programming transformation and alternating iteration method are used to decompose problem P into four sub-problems: time slot partitioning, related variable and power optimization, communication UAV trajectory optimization, and interference UAV trajectory optimization, and then solve them. Step 4): Based on the solution results of each sub-problem in Step 3), iteratively update the time slot division, UAV function scheduling, correlation, power allocation, UAV trajectory and speed, and output the multi-UAV cooperative safe communication strategy.

2. The multi-UAV cooperative secure communication method based on wireless power transmission according to claim 1, characterized in that, The total energy consumption of the drone is as follows: Based on the time slot allocation, the total energy consumption of the UAV can be expressed as: UAV energy consumption includes flight propulsion energy consumption, wireless charging and transmission energy consumption, and artificial noise interference energy consumption. and These represent the interference and transmission coefficients, respectively. Indicates the length of a single time slot. This represents the service association variable between the Kth UAV and the Mth ground user. This represents the interference correlation variable between the Kth UAV and the Nth ground eavesdropping node; This represents the power transmission power of the Kth UAV during the wireless power transmission phase. This represents the flight propulsion power of the Kth UAV in the t-th time slot. This represents the transmission power of the m-th ground user in time slot t.

3. The multi-UAV cooperative secure communication method based on wireless power transmission according to claim 1, characterized in that, Step 2): Based on the system model constructed in Step 1), construct the original joint optimization problem P with the goal of maximizing safety and energy efficiency, and determine the variables to be optimized and the constraints, specifically including: The system safety energy efficiency (SEE) is defined as the ratio of the amount of data safely transmitted by all ground users to the total energy consumption of the system during the mission cycle. The original joint optimization problem P aims to maximize SEE and jointly optimizes the time slot partitioning variables, communication-related variables, interference-related variables, ground user transmission power, UAV power transmission power, UAV interference power, and UAV flight trajectory and speed. The original joint optimization problem P includes constraints on the minimum safe transmission rate of ground users, the maximum transmit power of ground users, the maximum energy transmission power and maximum interference power of UAVs, the minimum safe distance between UAVs, the maximum horizontal velocity of UAVs, the maximum vertical velocity of UAVs, the maximum acceleration of UAVs, the altitude range of UAVs, the energy causality constraint of ground users, and the functional mutual exclusion constraint of UAVs.

4. The multi-UAV cooperative secure communication method based on wireless power transmission according to claim 1, characterized in that, Step 3) specifically includes: First, the fractional problem of maximizing SEE is transformed into a subtraction problem using the Tinkelbach method, and the time slot partitioning subproblem is solved using an algorithm based on Tinkelbach iteration. Then, after obtaining the time slot partitioning results, an iterative algorithm for a multi-UAV secure communication strategy based on ground-based power supply is used to alternately update time slot partitioning, UAV scheduling, power allocation, UAV trajectory, and speed. Finally, the subproblems are solved by combining Big M reconstruction, variable relaxation, penalty terms, and continuous convex approximation methods until the SEE change between two adjacent iterations is less than a preset threshold or the number of iterations reaches a preset maximum. The Tinkelbach method is an iterative transformation method for solving fractional programming problems, which transforms the "ratio of securely transmitted data to total system energy consumption" in the secure energy efficiency maximization problem into a problem with secure energy efficiency parameters. The reduction target, and through continuous updating The goal is to converge the subtractive objective to zero, thereby obtaining the corresponding optimal safety energy efficiency. The iterative algorithm for multi-UAV safe communication strategy based on ground charging refers to solving four sub-problems in sequence: time slot division, related variable and power optimization, communication UAV trajectory optimization, and interference UAV trajectory optimization, based on the initial time slot division, UAV scheduling, power allocation, UAV trajectory and speed. The solution results of each sub-problem are used as the input for the next round of alternating updates until the system safety energy efficiency meets the convergence condition. The fractional programming parameters and the equivalent subtraction problem can be expressed as: definition To maximize the SEE in solving the problem, the expression is: In the formula, The optimal time slot allocation index is the ratio of the amount of data safely transmitted within the task cycle to the total system energy consumption. Indicates time slot division The amount of securely transmitted data for all ground users during the next mission cycle. Indicates time slot division Total system energy consumption; Using fractional programming theory, optimal energy efficiency is achieved if and only if the following equation holds: This equation represents the optimal equivalence condition in the Tinkelbach method; Therefore, the original fractional optimization problem can be equivalently transformed into the following subtraction optimization problem: In the formula, This indicates the number of time slots included in the task cycle, where K represents the number of UAVs. This represents the safe transmission rate or lower bound of the safe transmission rate for the Kth UAV in the t-th time slot. This represents the time allocation factor for the t-th time slot. Indicates the length of a single time slot. This represents the safety energy efficiency parameter in the Tinkelbach iteration. Let represent the total energy consumption of the Kth UAV in the tth time slot; where the subtractive form facilitates solving the time slot division, associated power, and UAV trajectory subproblems separately under the alternating iterative framework.

5. A multi-UAV cooperative secure communication method based on wireless power transmission according to claim 4, characterized in that, The Tinkelbach method includes: transforming the fractional objective of maximizing safety energy efficiency into a subtraction problem with the objective of the difference between the product of the amount of safe transmitted data and the product of the safety energy efficiency parameters and the total energy consumption of the system; solving the corresponding sub-problems based on the current safety energy efficiency parameters; and updating the safety energy efficiency parameters according to the solution results until the subtraction objective meets the convergence condition; the iterative algorithm for multi-UAV safe communication strategy based on ground charging includes: initializing time slot partitioning, UAV scheduling, power allocation, UAV trajectory and speed; solving four sub-problems in sequence: time slot partitioning, related variable and power optimization, communication UAV trajectory optimization and interference UAV trajectory optimization; and calculating the system safety energy efficiency according to the update results until the convergence condition is met.

6. A multi-UAV cooperative secure communication method based on wireless power transmission according to claim 4, characterized in that, Step 4): Based on the solution results of each sub-problem in Step 3), iteratively update the time slot division, UAV function scheduling, correlation, power allocation, and UAV trajectory and speed, and output a multi-UAV cooperative safe communication strategy, specifically including: In each iteration, the time slot partitioning subproblem is solved based on fixed UAV scheduling, power allocation, UAV trajectory, and speed. The correlation variable and power optimization subproblems are solved based on the updated time slot partitioning. The communication UAV trajectory optimization subproblem and the interference UAV trajectory optimization subproblem are further solved separately. The system safety energy efficiency is calculated based on the updated time slot partitioning, correlation, power, trajectory, and speed. The iteration stops when the difference in system safety energy efficiency between two adjacent iterations is less than a preset threshold or the number of iterations reaches a preset maximum. The system outputs the UAV operating mode, wireless charging time, safe uplink transmission time, communication correlation, interference correlation, ground user transmission power, UAV power transmission power, UAV interference power, UAV flight trajectory, and speed for each time slot.

7. A multi-UAV cooperative secure communication method based on wireless power transmission according to claim 1, characterized in that, The upper bound of the eavesdropping rate is determined based on the estimated location and uncertain radius of the eavesdropping node, so as to ensure the robustness of the security rate calculation when the actual location of the eavesdropping node is unknown.

8. A multi-UAV cooperative secure communication method based on wireless power transmission according to claim 1, characterized in that, The correlation variables and power optimization subproblems are processed by the Big M reconstruction method to handle the product terms of binary correlation variables and power variables, and the binary correlation variables are relaxed to continuous variables between 0 and 1. At the same time, a penalty term is introduced to make the relaxed variables approach binary values.

9. A multi-UAV cooperative secure communication method based on wireless power transmission according to claim 1, characterized in that, Both the communication UAV trajectory optimization subproblem and the interference UAV trajectory optimization subproblem introduce auxiliary variables to handle distance-related terms, collision avoidance constraints, and flight propulsion energy consumption terms, and construct convex approximation problems through first-order Taylor expansion.

10. A multi-UAV cooperative secure communication method based on wireless power transmission according to claim 1, characterized in that, The multi-UAV collaborative safe communication strategy output process in step 4) includes: initializing time slot partitioning, UAV scheduling, power allocation, UAV trajectory and speed, and setting initial values ​​for system safety energy efficiency, convergence threshold and maximum number of iterations; in each iteration, fixing UAV scheduling, power allocation, UAV trajectory and speed, and using an algorithm based on Tinkelbach iteration to solve the time slot partitioning subproblem; solving the correlation variable and power optimization subproblems based on the updated time slot partitioning; solving the communication UAV trajectory and speed optimization subproblems and the interference UAV trajectory and speed optimization subproblems based on the updated time slot partitioning, correlation variables and power respectively; calculating the system safety energy efficiency based on the updated time slot partitioning, correlation, power allocation, UAV trajectory and speed; if the difference in system safety energy efficiency obtained from two adjacent iterations is not less than the preset threshold and the number of iterations has not reached the preset maximum number of iterations, then continue to execute the next iteration; otherwise, stop the iteration and output the multi-UAV collaborative safe communication strategy.

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