A method and system for joint allocation of drone trajectory and user scheduling

Abstract

The present invention proposes a joint allocation method and system for drone trajectory and user scheduling. The present invention first selects drones, eavesdroppers and multiple ground users, calculates the maximum achievable confidentiality rate of the drone for each ground user at any horizontal position, then constructs a set of drone flight trajectory points, a set of user scheduling coefficients, and a set of hovering times, and then constructs optimization solution objectives and constraints. After initializing the optimization quantity set, the convex problem for each iteration solution is obtained by the convex approximation method, and the optimization solution for each iteration is obtained by iteration using the ellipsoid method. The execution is repeated until the change in the optimization solution target is less than the iteration threshold, and the optimal drone trajectory and user scheduling coefficient are obtained. The present invention constructs the optimal trajectory structure of a drone in a single drone-assisted secure communication scenario, which enhances system security while reducing algorithm complexity.

Description

Technical Field

[0001] The present invention relates to the field of unmanned aerial vehicle (UAV) secure communication, and in particular to a method and system for jointly allocating UAV trajectories and user scheduling. Background Art

[0002] Due to the advantages of high flexibility, efficient and rapid deployment, and line-of-sight-dominated air-to-ground channels, drones have been widely used in wireless communication networks, often acting as air base stations, air relays, air radio access points, etc. to improve communication quality. However, the openness of air-to-ground channels makes communication security difficult to guarantee. On the one hand, due to the inherent broadcast properties of wireless media in wireless communications, information can be easily obtained by unauthorized receivers, resulting in information leakage; on the other hand, drones are vulnerable to malicious interference and attacks when transmitting information. However, traditional encryption technology has high computational complexity and is not suitable for resource-constrained drone communication scenarios. Therefore, physical layer security has been widely studied in wireless communications as a computationally efficient and feasible technology.

[0003] The communication security is enhanced by taking advantage of the high flexibility of UAVs and adjusting their trajectories and resource allocation. However, the design of trajectories and resource allocation is usually coupled, which makes the design optimization problem intractable. G. Zhang et al. jointly designed the UAV trajectory and transmit power to maximize the average confidentiality rate under the constraints of average and peak transmit power and actual UAV mobility; F. Cheng et al. deployed UAVs as aerial relays and ensured the security performance of UAV relay wireless network cache by jointly optimizing UAV trajectory and time scheduling.

[0004] Although the existing designs have improved the security of drone communication systems to a certain extent, they mostly use time-division quantization to construct drone trajectories. Their actual performance depends on the quantization accuracy. When the quantization accuracy is improved, the algorithm complexity increases significantly, and this solution obtains suboptimal drone trajectories. The performance gap between the optimal solution and the existing suboptimal solution is still unclear. Secondly, the above studies mostly use the traditional Shannon capacity to define the theoretical upper limit of the communication rate under the additive Gaussian white noise channel. This scenario requires the use of infinitely long codewords for transmission to achieve error-free transmission or transmission with an infinitesimal error probability. In actual communication scenarios, random white noise cannot be well averaged out when the codeword is short, and the reliability of transmission is no longer infinite. Shannon's theorem cannot accurately describe the performance of the communication system in this scenario. Therefore, the security of drone communication scenarios under limited code length transmission still needs further research. Summary of the invention

[0005] The present invention provides a method for maximizing the maximum achievable confidentiality rate of users with the worst channel conditions by jointly optimizing UAV trajectory and user scheduling under limited code length domain transmission. The method aims to construct the optimal trajectory structure of UAVs in the dual-UAV assisted secure communication scenario to enhance system security and reduce algorithm complexity.

[0006] To achieve the above object, the technical solution of the method of the present invention is:

[0007] A method for jointly allocating UAV trajectories and user scheduling comprises the following steps:

[0008] Step 1: Construct a dual-UAV assisted secure communication system model and calculate the maximum achievable confidentiality rate of the UAV to each ground user at any horizontal position;

[0009] Step 2: Construct optimization objectives and constraints, including UAV start and end point constraints, mission time constraints, mobility constraints, and user scheduling constraints, thereby establishing a joint optimization problem for UAV trajectory and user scheduling;

[0010] Step 3: Define the initial iterative trajectory point set of the UAV, the initial iterative hovering and turning time set of the UAV, and the initial scheduling coefficient set of the UAV for all ground users in the hovering point and flight segment;

[0011] Step 4: Obtain the lower bound concave approximation function of the maximum achievable confidentiality rate of the UAV to ground users at the hovering point and in the flight segment respectively through the convex approximation method; construct the convex constraint of the maximum achievable confidentiality rate after each iteration of convex approximation, and further construct the convex optimization solution target of the UAV in each iteration;

[0012] Step 5: According to the convex optimization solution target of each iteration of the UAV obtained in step 4, the optimization solution of each iteration is obtained by iterative solution using the ellipsoid method. Repeat the process until the change of the introduced auxiliary variables is less than the iteration threshold, and the optimal UAV trajectory and user scheduling coefficient are obtained.

[0013] Furthermore, the dual UAV assisted safety communication system model described in step 1 is as follows: establish a three-dimensional Cartesian coordinate system, deploy and fly at a fixed height H in a limited code length domain transmission scenario S The UAV UAV_S transmits information to K ground users, and introduces another UAV flying at a height of H J The UAV UAV_J sends interference to the ground, and there is an eavesdropper with a fixed position on the ground, where the position of the ground user is defined as w k =(w x,k ,w y,k ), the eavesdropper’s position is defined as w e =(w x,e ,w y,e); The flight trajectories of the two drones are q S ,q J , the transmission power is P S , P J .

[0014] Furthermore, the maximum achievable confidentiality rate of the drone described in step 1 to each ground user at any horizontal position is set to:

[0015]

[0016] Among them, β 0 is the channel gain per unit distance, σ 2 is the ambient noise power; represents the probability of information leakage, represents the information error rate of user k, m represents the code length, and the Q function is defined as d k (q S ), d e (q S ) represent the distances between UAV_S and user k and the eavesdropper respectively; d k (q J ), d e (q J ) represent the distances between UAV_J and user k and the eavesdropper respectively;

[0017] Due to the flight trajectories of the two drones q S (t), q J (t) contains continuous time variables, and K hovering points are introduced to reconstruct the continuous time trajectory into a continuous hovering flight trajectory, that is, the UAV hovers at the hovering point to transmit information, and the UAV flies at the maximum speed V between adjacent hovering points. max Flight, while introducing N turning points to fit the flight curve, the position of the i-th hovering point of the two UAVs is represented by q S,i ,q J,i , the position of the jth turning point after the i-th hovering point is denoted as q S,i,j ,q J,i,j The whole process trajectory of UAV_S can be expressed as:

[0018]

[0019] The whole process trajectory of UAV_J can be expressed as:

[0020]

[0021] Among them, the two drones fly at the same time, hover at the same time, and reach the turning point at the same time, so the set of moments in the drone flight phase is t = (t 1 ,t2 ,...,t 2i ,t 2i+1 ,...,t 2i+1 ,j,...,t 2K ), t 2i and t 2i+1 are the start and end time of the hovering at the ith hovering point, respectively, and t 2i+1,j is the turning point moment of the jth turning point after the ith hovering point;

[0022] Use a i,k represents the scheduling coefficient of UAV_S for user k at the i-th hovering point, a i,j,k represents the scheduling coefficient of UAV_S from the jth turning point to the j+1th turning point after the i-th hovering point. According to the flight sequence, the set a of user scheduling can be obtained. The maximum achievable confidentiality rate of user k during the entire flight process is expressed as:

[0023]

[0024] in,[·] + Represents [x] + =max{0,x}.

[0025] Furthermore, the optimization problem in step 2 is solved to maximize the maximum achievable confidentiality rate of the user with the worst channel condition, which is expressed as:

[0026]

[0027] The starting and ending point constraints of the UAV are expressed as:

[0028] q S,0 =q 0 ,q S,F =q F ,q J,0 =q 0 ,q J,F =q F

[0029] The UAV mission time constraint is expressed as:

[0030] 0≤t 1 ≤...≤t 2K ≤T

[0031] The UAV mobility constraint is expressed as:

[0032] d(q S,2i,j )≤V max (t 2i,j+1 -t 2i,j ),d(q J,2i,j )≤Vmax (t 2i,j+1 -t 2i,j ),

[0033] The user scheduling coefficient constraint is expressed as:

[0034] 0≤a≤1

[0035]

[0036] Among them, q 0 and q F They represent the starting and ending points of the two drones, T represents the drone mission time, and V max Indicates the maximum flight speed of the drone.

[0037] Furthermore, the joint optimization problem of drone trajectory and user scheduling described in step 2 is:

[0038]

[0039] st:q S,0 =q 0 ,q S,F =q F ,q J,0 =q 0 ,q J,F =q F,

[0040] 0≤t 1 ≤...≤t 2K ≤T,

[0041] d(q S,2i,j )≤V(t 2i,j+1 -t 2i,j ),d(q J,2i,j )≤V(t 2i,j+1 -t 2i,j ),

[0042] 0≤a≤1,

[0043]

[0044] In order to facilitate problem solving, an auxiliary variable R is introduced and the optimization problem is transformed into:

[0045] max R

[0046] st:R k (q S ,q J ,t,a)≥R,

[0047] q S,0 =q 0 ,qS,F =q F ,q J,0 =q 0 ,q J,F =q F ,

[0048] 0≤t 1 ≤...≤t 2K ≤T,

[0049] d(q S,2i,j )≤V max (t 2i,j+1 -t 2i,j ),d(q J,2i,j )≤V max (t 2i,j+1 -t 2i,j ),

[0050] 0≤a≤1,

[0051]

[0052] Among them, max means maximization.

[0053] Furthermore, the initial iterative trajectory point set of the UAV described in step 3 is:

[0054]

[0055]

[0056] The initial iterative hovering time set of the drone is:

[0057]

[0058] Therefore, the initial time set of the drone can be obtained

[0059] The initial scheduling coefficient set of the UAV for all ground users is

[0060] Furthermore, step 4 uses a continuous convex optimization technique, i.e., a concave function of the lower bound of the maximum achievable confidentiality rate is obtained by a convex approximation method in each iteration;

[0061] Due to the presence of non-smooth operators [·] + First, the judgment matrix is ​​introduced in the hovering stage and the flight stage of the UAV and They are defined as:

[0062]

[0063]

[0064] The convex approximation of the maximum achievable confidentiality rate of the hovering segment described in step 4 is:

[0065]

[0066] The convex approximation of the maximum achievable confidentiality rate of the flight segment described in step 4 is:

[0067]

[0068] Where r represents the number of iterations, represents the concave function of the lower bound of the drone in the ith hovering segment, It represents the lower bound concave function of the UAV from the jth turning point to the j+1th turning point after the i-th hovering point;

[0069] The convex constraint of the maximum achievable confidentiality rate after the convex approximation described in step 4 is:

[0070]

[0071] The goal of each iteration of the UAV convex optimization solution described in step 4 is:

[0072]

[0073]

[0074] q S,0 =q 0 ,q S,F =q F ,q J,0 =q 0 ,q J,F =q F,

[0075] 0≤t 1 ≤...≤t 2K ≤T,

[0076] d(q S,2i,j )≤V max (t 2i,j+1 -t 2i,j ),d(q J,2i,j )≤V max (t 2i,j+1 -t 2i,j ),

[0077] 0≤a≤1,

[0078]

[0079] Among them, R (r) Represents the auxiliary variable introduced in the rth iteration.

[0080] Furthermore, the optimal solution for each iteration described in step 5 is:

[0081]

[0082] in, and They represent the trajectory points of the two UAVs in the rth iteration, t (r) represents the set of UAV hovering turning moments of the rth iteration, a (r) represents the scheduling coefficient of the hovering and flying segments of the UAV for all ground users in the rth iteration;

[0083] The above process is repeated until the change in the auxiliary variable is less than the iteration threshold. The judgment process of whether the change in the auxiliary variable introduced in step 5 is less than the iteration threshold is as follows:

[0084] R (r) -R (r-1) <ε

[0085] Among them, R (r) represents the auxiliary variable introduced in the rth iteration, R (r-1) represents the auxiliary variable introduced in the r-1th iteration, and ε represents the iteration threshold;

[0086] The optimal UAV trajectory point, the optimal UAV hovering turning point set, the optimal UAV hovering segment and flight segment scheduling coefficient set for all ground users described in step 5

[0087] In another aspect, the present invention provides a drone trajectory and user scheduling joint allocation system, comprising:

[0088] Module 1 is used to build a dual-UAV assisted secure communication system model and calculate the maximum achievable confidentiality rate of the UAV to each ground user at any horizontal position;

[0089] Module 2 is used to construct optimization solution objectives and constraints, including UAV start and end point constraints, mission time constraints, mobility constraints, and user scheduling constraints, so as to establish the joint optimization problem of UAV trajectory and user scheduling;

[0090] Module three is used to define the initial iterative trajectory point set of the drone, the initial iterative hovering and turning time set of the drone, and the initial scheduling coefficient set of the drone for all ground users in the hovering point and flight segment;

[0091] Module 4 is used to obtain the lower bound concave approximate function of the maximum achievable confidentiality rate of the drone to ground users at the hovering point and in the flight segment respectively through the convex approximation method; construct the convex constraint of the maximum achievable confidentiality rate after each iteration of convex approximation, and further construct the convex optimization solution target of the drone in each iteration;

[0092] Module five is used to solve the convex optimization target of each iteration of the UAV obtained in module four, obtain the optimal solution of each iteration through the iterative solution of the ellipsoid method, and repeat the execution until the change of the introduced auxiliary variable is less than the iteration threshold, so as to obtain the optimal UAV trajectory and user scheduling coefficient.

[0093] Compared with the prior art, the present invention has the following beneficial effects:

[0094] The present invention provides a joint design method for drone trajectory and user scheduling for secure communication under limited code length transmission, which maximizes the maximum achievable confidentiality rate of ground users with the worst channel conditions under the constraints of drone mobility, mission time and user scheduling coefficient. This scheme constructs the optimal trajectory of drones in this scenario, significantly improving system security while reducing algorithm complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 : A UAV communication scenario model diagram for secure communication in an embodiment of the present invention;

[0096] Figure 2 : A flow chart of a joint design method of drone trajectory and user scheduling for secure communication in an embodiment of the present invention;

[0097] Figure 3 : Simulation diagram of the trajectory of the drone according to the embodiment of the present invention; DETAILED DESCRIPTION

[0098] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians of the present invention without making creative work are within the scope of protection of the present invention.

[0099] Example 1

[0100] like Figure 1 As shown, the present invention considers the limited code length transmission scenario, establishes a three-dimensional Cartesian coordinate system, and deploys a flight at a fixed height H in the limited code length domain transmission scenario. S = 30m UAV_S transmits information to K ground users, and introduces another UAV flying at a height of HJ = The UAV UAV_J at a distance of 40m sends interference to the ground, where there is an eavesdropper at a fixed position.

[0101] Combination Figure 2 The specific design method is as follows:

[0102] Step 1: Construct a dual-UAV assisted secure communication system model and calculate the maximum achievable confidentiality rate of the UAV to each ground user at any horizontal position;

[0103] The number of ground users in step 1 is K=4, and the position of the ground user is defined as w k =(w x,k ,w y,k ), the eavesdropper’s position is defined as w e =(w x,e ,w y,e ); The flight trajectories of the two drones are q S ,q J , the transmission power is P S =10, P J =10.

[0104] The maximum achievable confidentiality rate of the drone described in step 1 to each ground user at any horizontal position is set to:

[0105]

[0106] Among them, the channel gain per unit distance is defined as β 0 =-30dB, the ambient noise power is defined as σ 2 =-30dBm, the information leakage probability is defined as The information error rate of the kth user is defined as The code length is defined as m = 100;

[0107] K = 4 hovering points and N = 1 turning point are introduced to reconstruct the continuous time trajectory into a continuous hovering flight trajectory. The position of the i-th hovering point of the two UAVs is represented by q S,i ,q J,i , the position of the jth turning point after the i-th hovering point is denoted as q S,i,j ,q J,i,j Taking UAV_S as an example, the whole process trajectory of the UAV can be expressed as

[0108]

[0109] Use a i,k represents the scheduling coefficient of UAV_S for user k at the i-th hovering point, a i,j,krepresents the scheduling coefficient of UAV_S from the jth turning point to the j+1th turning point after the i-th hovering point. According to the flight order, the set a of user scheduling can be obtained. The maximum achievable confidentiality rate of user k during the entire flight process is expressed as

[0110]

[0111] in,[·] + Represents [x] + =max{0,x}.

[0112] Step 2: Construct optimization objectives and constraints, including UAV start and end point constraints, mission time constraints, mobility constraints, and user scheduling constraints, thereby establishing a joint optimization problem for UAV trajectory and user scheduling;

[0113] The optimization problem in step 2 aims to maximize the maximum achievable confidentiality rate of the user with the worst channel condition, which can be expressed as:

[0114]

[0115] The starting and ending point constraints of the UAV are expressed as:

[0116] q S,0 =q 0 ,q S,F =q F ,q J,0 =q 0 ,q J,F =q F

[0117] The UAV mission time constraint is expressed as:

[0118] 0≤t 1 ≤...≤t 2K ≤T

[0119] The UAV mobility constraint is expressed as:

[0120] d(q S,2i,j )≤V max (t 2i,j+1 -t 2i,j ),d(q J,2i,j )≤V max (t 2i,j+1 -t 2i,j ),

[0121] The user scheduling coefficient constraint is expressed as:

[0122] 0≤a≤1

[0123]

[0124] Among them, q 0 and q F They represent the starting and ending points of the two drones, T represents the drone mission time, and V max Indicates the maximum flight speed of the drone.

[0125] Furthermore, the joint optimization problem of drone trajectory and user scheduling described in step 2 is:

[0126]

[0127] st:q S,0 =q 0 ,q S,F =q F ,q J,0 =q 0 ,q J,F =q F,

[0128] 0≤t 1 ≤...≤t 2K ≤T,

[0129] d(q S,2i,j )≤V(t 2i,j+1 -t 2i,j ),d(q J,2i,j )≤V(t 2i,j+1 -t 2i,j ),

[0130] 0≤a≤1,

[0131]

[0132] Among them, max means maximization; in order to facilitate problem solving, an auxiliary variable R is introduced, and the optimization problem is transformed into:

[0133] max R

[0134] st:R k (q S ,q J ,t,a)≥R,

[0135] q S,0 =q 0 ,q S,F =q F ,q J,0 =q 0 ,q J,F =q F,

[0136] 0≤t 1 ≤...≤t 2K ≤T,

[0137] d(q S,2i,j )≤V max (t 2i,j+1 -t 2i,j ),d(q J,2i,j )≤V max (t 2i,j+1 -t 2i,j ),

[0138] 0≤a≤1,

[0139]

[0140] Step 3: Define the initial iterative trajectory point set of the UAV, the initial iterative hovering and turning time set of the UAV, and the initial scheduling coefficient set of the UAV for all ground users in the hovering point and flight segment;

[0141] The initial iterative trajectory point set of the UAV described in step 3 is:

[0142]

[0143]

[0144] The initial iterative hovering time set of the UAV is:

[0145]

[0146] Therefore, the initial time set of the drone can be obtained

[0147] The initial scheduling coefficient set of the UAV for all ground users is

[0148] Step 4: Obtain the convex problem of each iteration through the convex approximation method;

[0149] Step 4 uses a continuous convex optimization technique, i.e., a concave function of the lower bound of the maximum achievable confidentiality rate obtained by a convex approximation method in each iteration;

[0150] Due to the presence of non-smooth operators [·] + First, the judgment matrix is ​​introduced in the hovering stage and the flight stage of the UAV and They are defined as:

[0151]

[0152]

[0153] The convex approximation of the maximum achievable confidentiality rate of the hovering segment described in step 4 is:

[0154]

[0155] The convex approximation of the maximum achievable confidentiality rate of the flight segment described in step 4 is:

[0156]

[0157] Where r represents the number of iterations, represents the concave function of the lower bound of the drone in the ith hovering segment, It represents the lower bound concave function of the UAV from the jth turning point to the j+1th turning point after the i-th hovering point;

[0158] The convex constraint of the maximum achievable confidentiality rate after the convex approximation described in step 4 is:

[0159]

[0160] The goal of each iteration of the UAV convex optimization solution described in step 4 is:

[0161]

[0162]

[0163] q S,0 =q 0 ,q S,F =q F ,q J,0 =q 0 ,q J,F =q F ,

[0164] 0≤t 1 ≤...≤t 2K ≤T,

[0165] d(q S,2i,j )≤V max (t 2i,j+1 -t 2i,j ),d(q J,2i,j )≤V max (t 2i,j+1 -t 2i,j ),

[0166] 0≤a≤1,

[0167]

[0168] Among them, R (r) Represents the auxiliary variable introduced in the rth iteration.

[0169] Step 5: According to the convex problem solved in each iteration obtained in step 4, the optimal solution for each iteration is obtained by iterative solution using the ellipsoid method. Repeat the process until the change in the introduced auxiliary variables is less than the iteration threshold, and the optimal UAV trajectory and user scheduling coefficient are obtained.

[0170] The optimal solution for each iteration described in step 5 is:

[0171]

[0172] in, and They represent the trajectory points of the two UAVs in the rth iteration, t (r) represents the set of UAV hovering turning moments of the rth iteration, a (r) represents the scheduling coefficient of the hovering and flying segments of the UAV for all ground users in the rth iteration;

[0173] The above process is repeated until the change in the auxiliary variable is less than the iteration threshold. The judgment process of whether the change in the auxiliary variable introduced in step 5 is less than the iteration threshold is as follows:

[0174] R (r) -R (r-1) <ε

[0175] Among them, R (r) represents the auxiliary variable introduced in the rth iteration, R (r-1) represents the auxiliary variable introduced in the r-1th iteration, and ε represents the iteration threshold;

[0176] The optimal UAV trajectory point, the optimal UAV hovering turning point set, the optimal UAV hovering segment and flight segment scheduling coefficient set for all ground users described in step 5

[0177] In this embodiment, Figure 3 This is a simulation diagram of the trajectory of a drone according to an embodiment of the present invention.

[0178] Example 2

[0179] This embodiment provides a drone trajectory and user scheduling joint allocation system, including:

[0180] Module 1 is used to build a dual-UAV assisted secure communication system model and calculate the maximum achievable confidentiality rate of the UAV to each ground user at any horizontal position;

[0181] Module 2 is used to construct optimization solution objectives and constraints, including UAV start and end point constraints, mission time constraints, mobility constraints, and user scheduling constraints, so as to establish the joint optimization problem of UAV trajectory and user scheduling;

[0182] Module three is used to define the initial iterative trajectory point set of the drone, the initial iterative hovering and turning time set of the drone, and the initial scheduling coefficient set of the drone for all ground users in the hovering point and flight segment;

[0183] Module 4 is used to obtain the lower bound concave approximate function of the maximum achievable confidentiality rate of the drone to ground users at the hovering point and in the flight segment respectively through the convex approximation method; construct the convex constraint of the maximum achievable confidentiality rate after each iteration of convex approximation, and further construct the convex optimization solution target of the drone in each iteration;

[0184] Module five is used to solve the convex optimization target of each iteration of the UAV obtained in module four, obtain the optimal solution of each iteration through the iterative solution of the ellipsoid method, and repeat the execution until the change of the introduced auxiliary variable is less than the iteration threshold, so as to obtain the optimal UAV trajectory and user scheduling coefficient.

[0185] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present invention.

[0186] Obviously, those skilled in the art can make various changes and modifications to the embodiments of the present invention without departing from the spirit and scope of the embodiments of the present invention. Thus, if these modifications and variations of the embodiments of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

[0187] Other parts not described in detail are all prior art.

Claims

1. A joint allocation method of drone trajectories and user scheduling, characterized in that: The steps include: Step 1: Construct a dual-UAV assisted secure communication system model and calculate the maximum achievable confidentiality rate of the UAV to each ground user at any horizontal position; Step 2: Construct optimization objectives and constraints, including UAV start and end point constraints, mission time constraints, mobility constraints, and user scheduling constraints, thereby establishing a joint optimization problem for UAV trajectory and user scheduling; Step 3: Define the initial iterative trajectory point set of the UAV, the initial iterative hovering and turning time set of the UAV, and the initial scheduling coefficient set of the UAV for all ground users in the hovering point and flight segment; Step 4: Obtain the lower bound concave approximation function of the maximum achievable confidentiality rate of the UAV to ground users at the hovering point and in the flight segment respectively through the convex approximation method; construct the convex constraint of the maximum achievable confidentiality rate after each iteration of convex approximation, and further construct the convex optimization solution target of the UAV in each iteration; Step 4 uses a continuous convex optimization technique, i.e., a concave function of the lower bound of the maximum achievable confidentiality rate obtained by a convex approximation method in each iteration; Due to the presence of non-smooth operators First, the judgment matrix is ​​introduced in the hovering stage and the flight stage of the UAV and , respectively defined as: The convex approximation of the maximum achievable confidentiality rate of the hovering segment described in step 4 is: The convex approximation of the maximum achievable confidentiality rate of the flight segment described in step 4 is: in, represents the number of iterations, Indicates that the drone is The lower bound of the hovering segment is concave function, Indicates that the drone is After the hover point The turning point to The lower bound of the turning point is a concave function; The convex constraint of the maximum achievable confidentiality rate after the convex approximation described in step 4 is: The goal of each iteration of the UAV convex optimization solution described in step 4 is: in, Indicates Auxiliary variables introduced in the iteration; Step 5: According to the convex optimization solution target of each iteration of the UAV obtained in step 4, the optimization solution of each iteration is obtained by iterative solution using the ellipsoid method. Repeat the process until the change of the introduced auxiliary variables is less than the iteration threshold, and the optimal UAV trajectory and user scheduling coefficient are obtained.

2. A method for joint allocation of drone trajectories and user scheduling according to claim 1, characterized in that: The dual UAV assisted safety communication system model described in step 1 is as follows: establish a three-dimensional Cartesian coordinate system, deploy and fly at a fixed height in a limited code length domain transmission scenario UAV_S A ground user transmits information, and at the same time another aircraft flying at a high altitude is introduced The UAV UAV_J sends interference to the ground, and there is an eavesdropper with a fixed position on the ground. The position of the ground user is defined as , the eavesdropper position is defined as ; The flight trajectories of the two drones are , The transmission powers are , .

3. A method for joint allocation of drone trajectories and user scheduling according to claim 2, characterized in that: The maximum achievable confidentiality rate of the drone described in step 1 to each ground user at any horizontal position is set to: in, is the channel gain per unit distance, is the ambient noise power; represents the probability of information leakage, Indicates user The information error rate, represents the code length, and the Q function is defined as ; , Respectively represent UAV_S and user The distance between you and the eavesdropper; , Represents UAV_J and user The distance between you and the eavesdropper; Due to the flight trajectories of the two drones , Contains continuous time variables, introducing The continuous time trajectory is reconstructed into a continuous hovering flight trajectory by using the hovering points. That is, the UAV hovers at the hovering points to transmit information, and the UAV flies at the maximum speed between the adjacent hovering points. Flying, while introducing The turning points are used to fit the flight curve. The position of the hover point is represented by , , No. The first hover point after The position of the turning point is expressed as , The whole process trajectory of UAV_S can be expressed as: The whole process trajectory of UAV_J can be expressed as: Among them, the two drones fly at the same time, hover at the same time, and reach the turning point at the same time, so the set of moments in the drone flight phase is , and Respectively The hover start and end times at the hover points, For the After the hover point a turning point; a turning point; use Indicates that UAV_S is in The user is The scheduling coefficient, Indicates that UAV_S is in After the hover point The turning point to The scheduling coefficient of the turning point segment can be obtained according to the flight order. ,user The maximum achievable confidentiality rate during the entire flight process is expressed as: in, express .

4. A method for jointly allocating drone trajectories and user scheduling according to claim 1, characterized in that: The optimization problem in step 2 aims to maximize the maximum achievable confidentiality rate of the user with the worst channel condition, which can be expressed as: The starting and ending point constraints of the UAV are expressed as: The UAV mission time constraint is expressed as: The UAV mobility constraint is expressed as: The user scheduling coefficient constraint is expressed as: in, and Respectively represent the starting and ending points of the two drones, Indicates the drone mission time, Indicates the maximum flight speed of the drone.

5. A method for jointly allocating drone trajectories and user scheduling according to claim 4, characterized in that: The joint optimization problem of drone trajectory and user scheduling described in step 2 is: In order to facilitate problem solving, auxiliary variables are introduced , the optimization problem is transformed into: in, Indicates maximization.

6. A method for joint allocation of drone trajectories and user scheduling according to claim 5, characterized in that: The initial iterative trajectory point set of the UAV described in step 3 is: The initial iterative hovering time set of the drone is: Therefore, the initial time set of the drone can be obtained ; The initial scheduling coefficient set of the UAV for all ground users is: .

7. A method for jointly allocating drone trajectories and user scheduling according to claim 6, characterized in that: The optimal solution for each iteration described in step 5 is: in, and Respectively represent The trajectory point set of the two drones in the iteration, Indicates The first iteration of the drone hovering transition moment collection, Indicates The scheduling coefficients of the hovering and flying segments of the UAV for all ground users in the iteration; The above process is repeated until the change in the auxiliary variable is less than the iteration threshold. The judgment process of whether the change in the auxiliary variable introduced in step 5 is less than the iteration threshold is as follows: in, Indicates Auxiliary variables introduced in the iteration, Indicates Auxiliary variables introduced in the iteration, represents the iteration threshold; The optimal UAV trajectory point, the optimal UAV hovering turning point set, the optimal UAV hovering segment and flight segment scheduling coefficient set for all ground users described in step 5 .

8. A UAV trajectory and user scheduling joint allocation system, characterized in that: include: Module 1 is used to build a dual-UAV assisted secure communication system model and calculate the maximum achievable confidentiality rate of the UAV to each ground user at any horizontal position; Module 2 is used to construct optimization solution objectives and constraints, including UAV start and end point constraints, mission time constraints, mobility constraints, and user scheduling constraints, so as to establish the joint optimization problem of UAV trajectory and user scheduling; Module three is used to define the initial iterative trajectory point set of the drone, the initial iterative hovering and turning time set of the drone, and the initial scheduling coefficient set of the drone for all ground users in the hovering point and flight segment; Module 4 is used to obtain the lower bound concave approximate function of the maximum achievable confidentiality rate of the drone to ground users at the hovering point and in the flight segment respectively through the convex approximation method; construct the convex constraint of the maximum achievable confidentiality rate after each iteration of convex approximation, and further construct the convex optimization solution target of the drone in each iteration; Module 5 is used to solve the convex optimization target of each iteration of the UAV obtained in module 4, obtain the optimal solution of each iteration through the iterative solution of the ellipsoid method, and repeat the execution until the change of the introduced auxiliary variable is less than the iteration threshold, so as to obtain the optimal UAV trajectory and user scheduling coefficient; The UAV trajectory and user scheduling joint allocation system is used to execute the steps in the UAV trajectory and user scheduling joint allocation method described in any one of claims 1-7.

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