Method for joint resource allocation and trajectory design of unmanned aerial vehicles in the presence of eavesdroppers

Abstract

This invention discloses a method for joint resource allocation and trajectory optimization of unmanned aerial vehicles (UAVs) in eavesdropper environments, belonging to the field of UAV communication and physical layer security technology. It is implemented through the following technical solutions: constructing a system model of a base station, UAVs, target users, and eavesdroppers; establishing a rate model with dynamic power partitioning based on Shannon's formula; constructing an optimization problem with the goal of maximizing the minimum average security rate, integrating user scheduling, power allocation and partitioning, information causality, and UAV trajectory constraints; transforming the non-convex problem into a convex optimization problem using linear programming and quadratic transformation methods; alternately optimizing each sub-problem using a block coordinate descent framework, and solving for the optimal solution using the CVX toolbox. This invention achieves deep coordination of scheduling, power, and trajectory, improving communication security robustness and multi-user fairness, while also considering engineering practicality, and is suitable for UAV communication scenarios with high security requirements in 6G environments.

Description

Technical Field

[0001] This invention belongs to the field of UAV communication and physical layer security technology, specifically relating to a method for joint resource allocation and trajectory design of UAVs in an eavesdropper environment. Background Technology

[0002] With the evolution from 5G to 6G, integrated air-space-ground communication networks have become one of the core architectures for achieving full coverage, high-speed transmission, and emergency response. Unmanned aerial vehicles (UAVs), with their advantages of flexible deployment, high mobility, and a high proportion of line-of-sight links, have become the preferred solution for aerial communication platforms or mobile relay nodes. They are widely used in key scenarios such as capacity expansion in hotspot areas, emergency communication restoration in disaster scenarios, and data collection from IoT terminals, effectively compensating for the shortcomings of ground base station coverage blind spots and response delays.

[0003] However, while the line-of-sight transmission characteristics of UAV communication improve the quality of legitimate link channels, they also make transmitted signals vulnerable to interception by malicious eavesdroppers on the ground or in the air. This makes physical layer security a key bottleneck restricting the large-scale application of UAV communication. To address this challenge, physical layer security technology utilizes the randomness and variability of wireless channels to achieve information confidentiality without relying on upper-layer encryption protocols. Its core evaluation metric is the security rate (i.e., the difference between the capacity of the legitimate channel and the capacity of the eavesdropping channel), and it has become an important technical path for secure UAV communication.

[0004] Despite existing research on drone communication security, the following technical shortcomings still urgently need to be addressed: The isolation of variable optimization: Existing studies often optimize a single variable in UAV trajectory, power allocation or user scheduling, without fully considering the strong coupling relationship between the three, which makes it difficult to improve system safety performance and resource utilization efficiency in a coordinated manner; Insufficient adaptability of security mechanisms: Physical layer security technologies in drone scenarios mostly adopt fixed power split ratios or static anti-eavesdropping strategies, which cannot adapt to scenarios where the relative positions of drones, users, and eavesdroppers change dynamically, resulting in weak anti-eavesdropping robustness. The lack of modeling of actual constraints: Existing optimization schemes often ignore the information causal constraints of UAVs as mobile relays (i.e., the amount of forwarded information must not exceed the amount of received information), and do not fully integrate actual motion constraints such as UAV flight speed limits and position closed loops, resulting in insufficient feasibility and engineering applicability of the schemes; The solution efficiency of non-convex problems is low: The problem of joint resource allocation and trajectory optimization of UAVs is essentially a non-convex optimization problem. Existing transformation methods mostly use a single approximation method, which makes it difficult to achieve a balance between solution complexity and optimization accuracy, and cannot efficiently obtain the global optimal solution.

[0005] Therefore, in view of the shortcomings of existing technologies in joint variable optimization, dynamic security mechanisms, practical constraint modeling and non-convex problem solving, it is urgent to propose a joint resource allocation and trajectory optimization method for UAVs in eavesdropper environments, so as to achieve a synergistic improvement in system security performance and multi-user fairness, and provide technical support for 6G high security demand scenarios. Summary of the Invention

[0006] The purpose of this invention is to provide a method for joint resource allocation and trajectory design of UAVs in an eavesdropping environment, which solves the technical problem that existing UAV communication security technologies mostly adopt fixed power division ratios or static anti-eavesdropping strategies, which cannot adapt to scenarios where the relative positions of UAVs, users, and eavesdroppers change dynamically.

[0007] The technical solution adopted in this invention is a method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in an eavesdropping environment, comprising the following steps: S1: Construct a communication system model that includes a base station, a drone, multiple target users, and at least one eavesdropper; S2: Establish a rate model for the communication system to obtain the reachable rate of the target user and the interception rate of the eavesdropper; S3: Construct an optimization problem with the goal of maximizing the minimum average security rate of the target users. The constraints of the optimization problem include user scheduling constraints, power allocation and power partitioning constraints, information causality constraints, and UAV trajectory constraints. S4: Transform the optimization problem into a tractable convex optimization problem; S5: The block coordinate descent framework is used to alternately optimize the subproblems of user scheduling, resource allocation and UAV trajectory, and the optimal resource allocation scheme and UAV trajectory are obtained by solving them.

[0008] The invention is further characterized by: The specific process of establishing the rate model of the communication system in S2 is as follows: Introducing power split ratio The drone's transmission power Separate signal power for information transmission and the power of artificial noise used to interfere with eavesdropping Based on the wireless channel power gain and Gaussian white noise power, the achievable speed from the base station to the UAV is calculated respectively. The reachability rate of the drone to the target user and the interception rate of eavesdroppers ; in, This is a time slot index.

[0009] The average confidentiality rate of the target user is the average of the confidentiality rates across all time slots. Within a single time slot, the scheduled target user... Confidentiality ,in, Schedule variables for users, Characterizing the UAV in the Time slot service target users , For drones to target users The achievable rate, To intercept target users for eavesdroppers The rate.

[0010] The user scheduling constraints are specifically: user scheduling variables. The value can be 0 or 1, where 0 indicates that the UAV does not serve the target user in the i-th time slot. 1 represents the target users of the service And the sum of the scheduling variables of all target users in any time slot i satisfies ,in The total number of target users.

[0011] The power allocation and power division constraints are as follows: Base station power constraints: Base station number Transmit power of time slot And the cumulative value of the base station transmit power in all time slots satisfies ,in The total number of time slots, This represents the average transmit power of the base station. Drone power constraints: Drone number Transmit power of time slot satisfy And the cumulative value of the UAV's transmit power across all time slots satisfies ,in, This represents the average transmit power of the drone. This represents the peak transmit power of the drone. Power split ratio constraint: Power split ratio To dynamically optimize parameters, each time slot adaptively adjusts based on the relative positions of the drone, target user, and eavesdropper, and satisfies... .

[0012] The specific causal constraints on information are as follows: For any target user The sum of the reachable rate of the user when scheduled across all time slots and the interception rate by the eavesdropper shall not exceed the sum of the reachable rates from the base station to the drone across all time slots. ,in The total number of time slots, Schedule variables for users.

[0013] The specific constraints on the drone trajectory are as follows: Position closed-loop constraint: UAV position coordinates in time slot 1 With the Time slot location coordinates Same, that is ,in For drones The horizontal coordinates of the time slot; Speed ​​limit constraint: The square of the UAV's position displacement between adjacent time slots shall not exceed the square of the product of the maximum speed and the time slot length, i.e. ,in, The maximum flight speed of the drone, The length of a single time slot. This represents the total number of time slots.

[0014] S4 employs a combination of linear programming simplification, quadratic transformation, concave-convex processes, and Taylor expansion to transform non-convex terms in the optimization objective, non-convex terms in the information causal constraints, and non-convex terms related to the UAV trajectory, ultimately yielding a convex optimization problem.

[0015] In S5, all subproblems of alternating optimization are convex optimization problems, specifically including: Scheduling subproblem: Given fixed resource allocation parameters and UAV trajectories, optimize user scheduling variables to maximize the minimum average security rate. ; Resource allocation subproblem: Optimize base station transmit power while fixing user scheduling variables and UAV trajectories. UAV launch power and power split ratio ; Trajectory optimization subproblem: With fixed user scheduling variables and resource allocation parameters, optimize the position coordinates of the UAV in each time slot. ; Each subproblem is solved iteratively until the optimization objective converges.

[0016] There is a coupling relationship between the drone trajectory and rate model: the drone's position coordinates By affecting the actual distance of the communication link This, in turn, changes the power gain of the wireless channel, ultimately affecting the achievable data rate from the base station to the drone. The reachability rate of the drone to the target user and the rate at which drones intercept eavesdroppers The calculation.

[0017] The beneficial effects of this invention are: This invention utilizes a block coordinate descent framework to deeply and jointly optimize user scheduling, power allocation, and UAV trajectory, effectively addressing the performance limitations caused by single-variable optimization in existing technologies. Through dynamic adaptation of these three elements, the UAV flight trajectory is precisely matched with the resource allocation strategy, significantly improving the average confidentiality rate of the worst-performing user while ensuring fairness in multi-user communication, thus filling a gap in existing technologies regarding variable coupling optimization.

[0018] This invention introduces a dynamic power split ratio, which adaptively adjusts the power ratio of information signals and artificial noise based on the real-time relative positions of the drone, target user, and eavesdropper. Compared to the fixed power split strategy in existing technologies, it can more flexibly address scenarios where the eavesdropper's position is uncertain. By using artificial noise to directionally interfere with the eavesdropping link, the rate difference between legitimate users and eavesdroppers is further widened, significantly improving the physical layer security robustness of the communication link.

[0019] This invention comprehensively models key constraints in practical engineering scenarios, such as information causal constraints, UAV flight speed limits, and position closed-loop constraints, ensuring that the amount of information forwarded by the UAV does not exceed the amount of information received from the base station, and that the flight trajectory conforms to the laws of physical motion. This design avoids the infeasibility problem caused by neglecting practical constraints in existing technologies, enabling the optimization results to be directly applied to actual UAV communication systems and reducing the difficulty of engineering implementation.

[0020] This invention employs a combined strategy of linear programming simplification, quadratic transformation, CCCP method, and Taylor expansion to transform a complex non-convex optimization problem into an efficiently solvable convex optimization problem. This solves the problem in existing technologies where a single transformation method struggles to balance solution accuracy and complexity. By combining the CVX toolbox with alternating optimization logic, the algorithm is ensured to converge quickly to the global optimum, reducing computational resource consumption and improving the real-time performance of the solution while maintaining optimization effectiveness.

[0021] This invention ensures that drones accurately serve individual users in each time slot through user scheduling constraints, and avoids resource waste by combining dynamic power allocation strategies, thus achieving efficient allocation of communication resources. This method is applicable to various drone communication scenarios such as capacity expansion in hotspot areas, emergency communication support, and IoT data collection, and is particularly well-suited to the high security and flexibility requirements of 6G communication, providing reliable technical support for the large-scale application of drones in scenarios with high confidentiality requirements. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the communication system model in the UAV joint resource allocation and trajectory design method for environments with eavesdroppers, as described in this invention; Figure 2 This is a schematic diagram of the optimized trajectory in the UAV joint resource allocation and trajectory design method for environments with eavesdroppers, as described in this invention; Figure 3 This is a schematic diagram illustrating the convergence of the minimum average security rate in the UAV joint resource allocation and trajectory design method for environments with eavesdroppers, as described in this invention. Detailed Implementation

[0023] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0024] Example 1 The UAV joint resource allocation and trajectory design method in an eavesdropping environment disclosed in this embodiment includes the following steps: S1: Construct a communication system model that includes a base station, a drone, K target users, and an eavesdropper; the drone acts as an airborne base station to assist in communication by transmitting signals to the K users, and the eavesdropper eavesdrops on the confidential information transmitted by the drone to the target users.

[0025] S2: Establish a rate model for the communication system based on Shannon's formula to obtain the achievable rate of the target user and the interception rate of the eavesdropper; S3: Construct an optimization problem with the goal of maximizing the minimum average confidentiality rate of the target user. The constraints of the optimization problem include user scheduling constraints, power allocation and power partitioning constraints, information causality constraints, and UAV trajectory constraints. S4: Transform the optimization problem into a tractable convex optimization problem; S5: The block coordinate descent framework is used to alternately optimize the subproblems of user scheduling, resource allocation and UAV trajectory. The CVX toolbox is used to solve the problem and obtain the optimal resource allocation scheme and UAV trajectory.

[0026] Example 2 Based on Example 1, the specific process of establishing the rate model of the communication system in S2 is as follows: Introducing power split ratio The drone's transmission power Separate signal power for information transmission and the power of artificial noise used to interfere with eavesdropping Then, the signal-to-noise ratio (SNR) is calculated using the obtained signal. Based on the wireless channel power gain and Gaussian white noise power, the achievable speed from the base station to the UAV is calculated. The reachability rate of the drone to the target user and the interception rate of eavesdroppers ;in, This is a time slot index.

[0027] Specifically: Solve for the signal-to-noise ratio in communication:

[0028] achievable speed from base station to drone :

[0029] achievable speed from drone to target user :

[0030] The interception rate of eavesdroppers :

[0031] in, It is Gaussian white noise.

[0032] Example 3 Based on Example 1, the average confidentiality rate of the target user is the average of the confidentiality rates of each time slot. In a single time slot, the scheduled target user... The confidentiality rate is:

[0033] In the formula: Schedule variables for users, Characterizing the UAV in the Time slot service target users , For drones to target users The achievable rate, To intercept target users for eavesdroppers The rate.

[0034] That is, the objective function of the optimization problem in S3, which aims to maximize the minimum average confidentiality rate of the target user, is:

[0035] Example 4 Based on Example 1, the user scheduling constraint (ensuring that the drone serves at most one user per time slot) is specifically defined as: user scheduling variable. The value can be 0 or 1, where 0 indicates that the UAV does not serve the target user in the i-th time slot. 1 represents the target users of the service And the sum of the scheduling variables of all target users in any time slot i satisfies ,in The total number of target users.

[0036] Furthermore, power allocation and power partitioning constraints (ensuring that the communication power allocated to users is neither too high nor too low, and that the system can adapt to uncertain scenarios such as imperfectly known eavesdropper locations, thus enhancing robustness) specifically include: Base station power constraints: Base station number Transmit power of time slot And the cumulative value of the base station transmit power in all time slots satisfies ,in The total number of time slots, This represents the average transmit power of the base station. Drone power constraints: Drone number Transmit power of time slot satisfy And the cumulative value of the UAV's transmit power across all time slots satisfies ,in, This represents the average transmit power of the drone. This represents the peak transmit power of the drone. Power split ratio constraint: Power split ratio To dynamically optimize parameters, each time slot adaptively adjusts based on the relative positions of the drone, target user, and eavesdropper, and satisfies... .

[0037] Furthermore, the information causal constraint (ensuring that the amount of information received by the drone is sufficient to forward to the user and to counter eavesdropping) specifically includes: For any target user The sum of the reachable rate of the user when scheduled across all time slots and the interception rate by the eavesdropper shall not exceed the sum of the reachable rates from the base station to the drone across all time slots. ,in The total number of time slots, Schedule variables for users.

[0038] Furthermore, the drone trajectory constraints (ensuring the start and end points are the same, and speed limits) are as follows: Position closed-loop constraint: UAV position coordinates in time slot 1 With the Time slot location coordinates Same, that is ,in For drones The horizontal coordinates of the time slot; Speed ​​limit constraint: The square of the UAV's position displacement between adjacent time slots shall not exceed the square of the product of the maximum speed and the time slot length, i.e. ,in, The maximum flight speed of the drone, The length of a single time slot. This represents the total number of time slots.

[0039] Example 5 Based on Example 1, S4 uses a combination of linear programming simplification, quadratic transformation, concave-convex process and Taylor expansion to transform the non-convex terms in the optimization objective, the non-convex terms in the information causal constraints and the non-convex terms related to the UAV trajectory, and finally obtains the convex optimization problem.

[0040] Specifically: The linear programming with user scheduling constraints is simplified to... Transforming the information causal constraint Taylor expansion into ,in yes The upper bound of the first-order Taylor expansion at the reference point yes The lower bound of the first-order Taylor expansion at the reference point.

[0041] Constraints on confidentiality , Transformation It is an auxiliary variable that is introduced.

[0042] Example 6 Based on Example 1, each sub-problem in S5 that is alternately optimized is a convex optimization problem, specifically including: Scheduling subproblem: Given fixed resource allocation parameters and UAV trajectories, optimize user scheduling variables to maximize the minimum average security rate. ; Resource allocation subproblem: Optimize base station transmit power while fixing user scheduling variables and UAV trajectories. UAV launch power and power split ratio ; Trajectory optimization subproblem: With fixed user scheduling variables and resource allocation parameters, optimize the position coordinates of the UAV in each time slot. ; Each subproblem is solved iteratively until the optimization objective converges.

[0043] Specifically: First, fix P and Q, then optimize B: define a set of user scheduling. ,power Drone trajectory The optimization problem can be expressed as: Objective function:

[0044] Constraint 1:

[0045] Constraint 2:

[0046] Constraint 3:

[0047] Constraint 4:

[0048] Constraint 3 refers to the condition that in any discrete time slot... Within this problem, the sum of all users' scheduling variables does not exceed 1. The user scheduling subproblem is clearly a convex optimization problem, which can be solved using CVX.

[0049] Then, fixing B and Q, optimize P: The optimization problem can be expressed as: Objective function:

[0050] Constraint 1:

[0051] Constraint 2:

[0052] Constraint 3: , , , ; Constraint 4:

[0053] The convex lower bound constraint of the safe rate, where It is a non-convex DC function. (Using...) Obtained through CCCP and Taylor expansion Convex lower bound replacement . We can obtain Constraint 2 is a power split ratio constraint, which directly affects the variables. This represents the proportion of power allocated to useful information signals, which is a key control knob for achieving physical layer security. It's not a fixed value, but rather in each time slot. This can be optimized. It allows the system to dynamically adjust weights based on the real-time relative positions of the drone, the user, and the eavesdropper. Constraint 3 is a hard limit on system resources, ensuring the solution is physically feasible. Constraint 4 is the core constraint for the drone's specific role as a mobile relay; it stipulates that for any user... The total amount of information that the drone forwards to the user, including the portion received by the legitimate user and the portion that is being eavesdropped on, cannot exceed the total amount of information it receives from the base station.

[0054] This problem is a mixed nonconvex integer problem, due to the nonconvexity of the constraints and the presence of binary constraints. Two auxiliary variables are introduced. and , replace the original variable and , making , . Legal user rate and eavesdropper rate Represented by a new variable:

[0055]

[0056] The confidentiality rate expression at this time is:

[0057] Safe Rate Item It is a concave function minus a concave function, belonging to the DC structure, and is non-convex overall.

[0058] make , can be written as ,in, and All are concave functions.

[0059] At the reference point Perform a first-order Taylor expansion and replace it with its global upper bound. :

[0060] The gradient is calculated as follows:

[0061] get convex lower bound .

[0062] Information causal constraints:

[0063] left It is a concave function, and its upper bound is obtained by expanding it at the reference point. ,right yes The concave function, in The lower bound is obtained by expanding the area. After the replacement, the constraint becomes convex:

[0064] Therefore, the optimization problem can be restated as:

[0065] Since the objective function is concave and all constraints are linear or convex, this optimization problem is transformed into a convex optimization problem, which can be solved using the standard convex optimization solver (CVX).

[0066] Finally, fix B and P, and optimize Q: The optimization problem can be expressed as:

[0067] Rate expression:

[0068]

[0069] in, It is about The function is convex, but its reciprocal appears within the logarithmic function, resulting in overall non-convexity. A quadratic transformation is applied to extract the fractional terms from the logarithmic function, transforming it into a workable form. In the fraction, introduce auxiliary variables :

[0070] right In the fraction, introduce auxiliary variables :

[0071] For a given , The maximization problem becomes about and A linear function, but It is still about Non-convex. (The sentence appears to be incomplete and requires further context.) and It is approximately a convex function.

[0072] definition: and

[0073] Both functions are convex at the reference point. Performing a first-order Taylor expansion at this point yields the global lower bound:

[0074]

[0075]

[0076]

[0077] lower bound distance d and Substituting into the expression after the second transformation:

[0078]

[0079] At this point, for fixed , and reference trajectory , and It is about Convex function. The lower bound for the safe rate is:

[0080] The information causal constraint also includes It depends on .right At the reference point Performing a first-order Taylor expansion at that point yields the lower bound. .

[0081] Replace the causal constraint with: .

[0082] The trajectory optimization subproblem is transformed into: Objective function:

[0083] Constraint 1:

[0084] Constraint 2:

[0085] Constraint 3:

[0086] Constraint 4:

[0087] The original form of the safety rate lower bound constraint requires that the average safety rate for each user is not lower than the target value. .in With position Highly nonconvex correlation. Through quadratic transformation and first-order Taylor expansion, we obtain information about the trajectory. lower bound of concave functions The constraint becomes Constraint 2 requires that the UAV's starting and ending positions be the same in the discrete time series. Constraint 3 limits the maximum displacement of the UAV between adjacent time slots. Constraint 4 ensures that the UAV does not plan a trajectory that is far away from the base station for a long time and only focuses on high-speed forwarding to the user.

[0088] This optimization problem is transformed into a convex optimization problem, which can be solved using a standard convex optimization solver.

[0089] Example 7 Based on Example 1, there is a coupling relationship between the UAV trajectory and the rate model: the UAV's position coordinates By affecting the actual distance of the communication link This, in turn, changes the power gain of the wireless channel, ultimately affecting the achievable data rate from the base station to the drone. The reachability rate of the drone to the target user and the rate at which drones intercept eavesdroppers The calculation.

[0090] Based on the above embodiments 1-7, specific embodiments are now given: like Figure 1 As shown, the security issues of UAV-assisted communication are studied in a three-dimensional (3D) coordinate system. The communication system includes a ground base station (BS), a UAV repeater, an eavesdropping device, and K users. ∈ K ={1,2,…K}. All information is transmitted from the BS to the UAV via the BS-UAV link, and then to the UAV-user link. Simultaneously, an eavesdropping device can capture confidential information transmitted to the end user via the UAV-Eve link. To improve the security of the UAV-user link, an AN signal is introduced to interfere with the eavesdropper's reception, thereby maximizing the minimum average confidentiality rate for all users.

[0091] BS is located at the origin O= Place. A number of terminal users are randomly distributed on the xoy plane, among which users The horizontal coordinate is Considering the limited flight cycle of drones The UAV flies at a fixed altitude H, ignoring takeoff and landing phases. The horizontal position of the UAV at time t is denoted as... The horizontal coordinates of the eavesdropper are Then, the cycle Discretized Each time slot ,in This represents a sufficiently small time slot length. Therefore, the drone in each time slot The horizontal position is denoted as To enhance the security of information transmission, the drone's flight path should be as close as possible to the business unit (BS) and users, while maintaining a safe distance from potential eavesdroppers. To ensure users receive more confidential information, the drone should first take off from its origin, fly past each end user, and then complete its mission at its destination.

[0092] make and Let represent the origin and destination of the drone, respectively. Then the constraint is:

[0093]

[0094] in, This is the maximum speed of the drone.

[0095] In the time slot During this period, the channel power gain of the UAV-User and UAV-Eve links follows a free-space path loss model. This channel model is expressed as...

[0096] In the formula, Indicates reference distance Channel power gain at =1m Indicates the first The distance between the drone and the user within each time slot. Indicates in time slot The distance from the BS to the drone. Indicates in time slot The distance from the drone to the end user Indicates in time slot The distance between the drone and the eavesdropper.

[0097] Their calculation formulas are:

[0098]

[0099]

[0100] Therefore, the channel gains of the BS-UAV, UAV-User, and UAV-Eve links in time slot i are respectively:

[0101]

[0102]

[0103] In the drone-user link, the drone sends confidential information to an end user in each time slot. We introduce a binary variable. This represents user scheduling. When When the drone communicates with user k, otherwise... To ensure that the drone serves at most one user per time slot, the following constraint is obtained:

[0104]

[0105] set up and Indicates time slot The transmission power of the BS and the drone. We will It is divided into two parts: one part is represented as The information signal, the other part is represented as The AN is used to interfere with eavesdroppers.

[0106] in, This indicates the power split ratio that meets the requirements. The range of values ​​for is:

[0107] The end user can eliminate the AN, but the eavesdropper may not be able to eliminate it. Therefore, the transmit power constraint is:

[0108]

[0109]

[0110]

[0111] in, and These represent the average transmission power of the base station and the drone, respectively. This represents the peak power budget. The signal-to-noise ratio (SNR) of the BS-UAV link is expressed as...

[0112] For ease of calculation, a new variable is introduced. ,in Representing the power of the noise, then the first... The achievable rate of a time-slotted BS-UAV link is:

[0113] Then time slot The signal-to-noise ratio of the UAV-User link is:

[0114] when At that time, the reachability rate from the drone to end user k is:

[0115] Similarly, time slots The signal-to-noise ratio (SINR) of the UAV-Eve link can be expressed as:

[0116] Meanwhile, the eavesdropper in the The achievable rate of intercepting terminal user k in one time slot is expressed as:

[0117] The reachability rate from the drone to the end user k and the eavesdropper in the 1st... The achievable rate of intercepting terminal user k in the first time slot can be obtained from the 1st time slot. The security rate of the UAV-User link in each time slot is:

[0118] In addition, end user k in The average confidentiality rate achieved during this period was:

[0119] The drone forwards the information received from the BS to the end user; therefore, the achievable rate of the BS-UAV link is greater than the sum of the rates of the UAV-User link and the UAV-Eve link. Therefore, in the preceding... Within each time slot, the following information causal relationship constraints are introduced:

[0120] Since the objective function is concave and all constraints are linear or convex, this optimization problem is transformed into a convex optimization problem, which can be solved using a standard convex optimization solver. Figure 2 As shown, with the increase of the number of flight cycles, the minimum average security level of the optimized UAV communication significantly improves, eventually reaching a stable level. The minimum average security level is highest when the number of flight cycles is 80. Figure 3 As shown, the optimized drone trajectory moves towards the ideal position and satisfies the constraints.

[0121] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, 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 a process, method, article, or apparatus. Without further limitations, 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.

[0122] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0123] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for joint resource allocation and trajectory design of unmanned aerial vehicles (UAVs) in an eavesdropping environment, characterized in that, Includes the following steps: S1: Construct a communication system model that includes a base station, a drone, multiple target users, and at least one eavesdropper; S2: Establish the rate model of the communication system to obtain the reachable rate of the target user and the interception rate of the eavesdropper; S3: Construct an optimization problem with the objective of maximizing the minimum average security rate of the target user. The constraints of the optimization problem include user scheduling constraints, power allocation and power partitioning constraints, information causality constraints, and UAV trajectory constraints. S4: Transform the optimization problem into a tractable convex optimization problem; S5: The block coordinate descent framework is used to alternately optimize the subproblems of user scheduling, resource allocation and UAV trajectory, and the optimal resource allocation scheme and UAV trajectory are obtained by solving them.

2. The method for joint resource allocation and trajectory design of unmanned aerial vehicles in an eavesdropping environment according to claim 1, characterized in that, The specific process of establishing the rate model of the communication system in S2 is as follows: Introducing power split ratio The drone's transmission power Separate signal power for information transmission and the power of artificial noise used to interfere with eavesdropping Based on the wireless channel power gain and Gaussian white noise power, the achievable speed from the base station to the UAV is calculated respectively. The reachability rate of the drone to the target user and the interception rate of eavesdroppers ; in, This is a time slot index.

3. The method for joint resource allocation and trajectory design of unmanned aerial vehicles in an eavesdropping environment according to claim 1, characterized in that, The average confidentiality rate of the target user is the average of the confidentiality rates of each time slot. In a single time slot, the scheduled target user... Confidentiality rate ,in, Schedule variables for users, Characterizing the UAV in the Time slot service target users , For drones to target users The achievable rate, To intercept target users for eavesdroppers The rate.

4. The method for joint resource allocation and trajectory design of unmanned aerial vehicles in an eavesdropping environment according to claim 1, characterized in that, The user scheduling constraints specifically refer to: user scheduling variables. The value can be 0 or 1, where 0 indicates that the UAV does not serve the target user in the i-th time slot. 1 represents the target users of the service And the sum of the scheduling variables of all target users in any time slot i satisfies ,in The total number of target users.

5. The method for joint resource allocation and trajectory design of unmanned aerial vehicles in an eavesdropping environment according to claim 1, characterized in that, The power allocation and power partitioning constraints are specifically as follows: Base station power constraints: Base station number Transmit power of time slot And the cumulative value of the base station transmit power in all time slots satisfies ,in The total number of time slots, This represents the average transmit power of the base station. Drone power constraints: Drone number Transmit power of time slot satisfy And the cumulative value of the UAV's transmit power across all time slots satisfies ,in, This represents the average transmit power of the drone. This represents the peak transmit power of the drone. Power split ratio constraint: Power split ratio To dynamically optimize parameters, each time slot adaptively adjusts based on the relative positions of the drone, target user, and eavesdropper, and satisfies... .

6. The method for joint resource allocation and trajectory design of unmanned aerial vehicles in an eavesdropping environment according to claim 1, characterized in that, The aforementioned information causal constraint specifically refers to: For any target user The sum of the reachable rate of the user when scheduled across all time slots and the interception rate by the eavesdropper shall not exceed the sum of the reachable rates from the base station to the drone across all time slots. ,in The total number of time slots, Schedule variables for users.

7. The method for joint resource allocation and trajectory design of unmanned aerial vehicles in an eavesdropping environment according to claim 1, characterized in that, The specific constraints on the drone trajectory are as follows: Position closed-loop constraint: UAV position coordinates in time slot 1 With the Time slot location coordinates Same, that is ,in For drones The horizontal coordinates of the time slot; Speed ​​limit constraint: The square of the UAV's position displacement between adjacent time slots shall not exceed the square of the product of the maximum speed and the time slot length, i.e. ,in, The maximum flight speed of the drone, The length of a single time slot. This represents the total number of time slots.

8. The method for joint resource allocation and trajectory design of unmanned aerial vehicles in an eavesdropping environment according to claim 1, characterized in that, S4 employs a combination of linear programming simplification, quadratic transformation, concave-convex processes, and Taylor expansion to transform non-convex terms in the optimization objective, non-convex terms in the information causal constraints, and non-convex terms related to the UAV trajectory, ultimately yielding a convex optimization problem.

9. The method for joint resource allocation and trajectory design of unmanned aerial vehicles in an eavesdropping environment according to claim 1, characterized in that, In S5, all subproblems of alternating optimization are convex optimization problems, specifically including: Scheduling subproblem: Given fixed resource allocation parameters and UAV trajectories, optimize user scheduling variables to maximize the minimum average security rate. ; Resource allocation subproblem: Optimize base station transmit power while fixing user scheduling variables and UAV trajectories. UAV launch power and power split ratio ; Trajectory optimization subproblem: With fixed user scheduling variables and resource allocation parameters, optimize the position coordinates of the UAV in each time slot. ; Each subproblem is solved iteratively until the optimization objective converges.

10. The method for joint resource allocation and trajectory design of unmanned aerial vehicles in an eavesdropping environment according to claim 1, characterized in that, The UAV trajectory and velocity model are coupled: the UAV's position coordinates By affecting the actual distance of the communication link This, in turn, changes the power gain of the wireless channel, ultimately affecting the achievable data rate from the base station to the drone. The reachability rate of the drone to the target user and the rate at which drones intercept eavesdroppers The calculation.

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