CN112533221A - Unmanned aerial vehicle anti-interference method combining trajectory planning and frequency spectrum decision - Google Patents

Abstract

The invention discloses an anti-jamming method for unmanned aerial vehicles with joint trajectory planning and spectrum decision-making. Aspects: Trajectory planning and spectrum decision-making; first use the solution method of convex optimization to plan the trajectory of the UAV user, then model the spectrum decision-making problem as a Stackelberg game, and solve the equilibrium solution through hierarchical learning, and finally realize the trajectory and spectrum. joint optimization. The invention can jointly optimize the above two dimensions of trajectory optimization and frequency decision-making, realize the anti-jamming goal of the UAV user, further improve the communication benefit of the UAV, and make the UAV user efficient in the case of limited flight energy consumption Complete the target communication task.

Description

A UAV anti-jamming method based on joint trajectory planning and spectrum decision making

technical field

The invention relates to the technical field of military communication countermeasures, in particular to an unmanned aerial vehicle anti-jamming method for joint trajectory planning and spectrum decision-making.

Background technique

In the context of contemporary UAV cluster operations, UAVs have developed rapidly and are widely used in communication, reconnaissance, information collection and other fields. The human-set task needs to move, so as to meet the communication needs in specific scenarios.

At the same time, drones also have certain shortcomings. Due to the limited load and load of a single UAV, its flight ability is poor and the data processing equipment it carries is insufficient. Therefore, under normal circumstances, a group of UAVs are required to act together to complete the task, and they are divided into host and wingman according to actual needs. When the host is running, it must transmit the data detected by it to the wingman to assist in sorting and analyzing the information data. Therefore, we need to realize the mutual communication between the UAV communication pairs, so as to efficiently complete the UAV mission.

For the anti-jamming problem of UAV swarms under external malicious interference, the existing research is based on a single frequency planning perspective. The optimal solution to the UAV anti-jamming problem is carried out in two dimensions. The goal of our UAV is to achieve a large amount of information transmission at a small cost of flight energy when multiple UAVs are flying at the same time in a fixed time. When considering trajectory optimization to achieve anti-jamming, it mainly involves the following aspects. On the one hand, our UAVs need to stay away from the interference source as much as possible, and on the other hand, we should avoid using the same frequency band of our UAVs too close, resulting in the same frequency. Finally, considering that the energy consumption caused by the flight distance has a greater impact on the UAV flight, the flight energy consumption also needs to be calculated in the trajectory optimization problem. For the trajectory optimization problem, there have been related researches before, but there are still some problems: (1) the internal interference problem of the UAV caused by the distance is too close; (2) the frequency conversion of the strong ground jammer causes the trajectory optimization to be segmented (3) The execution time of the UAV flight mission is limited, and it must go from the starting point to the end point within a limited time. Therefore, the trajectory design of each segment cannot be independent, and it is necessary to consider whether the follow-up UAV can fly to the end point in a limited time.

In terms of spectrum selection of UAV users, considering the competition between external malicious interference and mutual interference between users, the frequency decision problem of UAV users needs to be modeled as a Stackelberg game. Given the interference strategy, the underlying sub-game is an exact potential game, and there is at least one Nash equilibrium, according to which the above game model can be solved. And based on stochastic learning theory, an anti-jamming channel selection algorithm based on SLA is proposed in the lower sub-game, so as to achieve the goal of autonomous frequency decision-making by UAV users to avoid interference.

However, there is no existing literature that discloses how to combine the two schemes of trajectory planning and spectrum decision-making to optimize the anti-jamming of UAVs. The anti-jamming principles of the two schemes are completely different. How to realize the effective combination of the two is currently an urgent task. problem to be solved.

SUMMARY OF THE INVENTION

Aiming at the deficiencies in the prior art, the present invention provides an anti-jamming method for unmanned aerial vehicles that combines trajectory planning and spectrum decision-making, and jointly optimizes the above two dimensions of trajectory optimization and frequency decision-making, so as to achieve the anti-jamming goal of unmanned aerial vehicle users. , which further improves the communication benefits of UAVs, enabling UAV users to efficiently complete target communication tasks with limited flight energy consumption.

To achieve the above object, the present invention adopts the following technical solutions:

A UAV anti-jamming method for joint trajectory planning and spectrum decision-making, the UAV anti-jamming method is used for a plurality of UAV communication pairs starting from a starting point and heading to a destination at different flight heights in an intelligent jamming environment to perform the task on the fly, jointly optimize the frequency strategy and flight trajectory of all UAV communication pairs, and pursue to maximize the communication rate of the UAV communication pair; the anti-jamming method includes the following steps:

S1, model the loss and optimization problems of UAV users for actual communication scenarios;

S2, the optimization problem is divided into two aspects: trajectory planning and spectrum decision-making; first, the solution method of convex optimization is used to plan the trajectory of the UAV user, and then the spectrum decision-making problem is modeled as a Stackelberg game, which is carried out through hierarchical learning. Equilibrium solution, and finally realize the joint optimization of trajectory and spectrum.

In order to optimize the above technical solutions, the specific measures taken also include:

Further, in step S1, the process of modeling the loss of the UAV user and the optimization problem for the actual communication scenario includes the following steps:

c_M表示无人机用户对的可用信道，M为无人机通信对可用信道数，干扰信道集定义为c＝{c₁，c₂，…，c_J}，c_J为干扰可用信道，J为干扰可用信道数；S11, suppose the system includes N UAV communication pair users and one external malicious interference, the UAV user pair set is defined as Un ( _n =1, 2,...N), and the available channel set is defined as

c _M represents the available channels of the UAV user pair, M is the number of available channels for the UAV communication pair, the interference channel set is defined as c={c ₁ , c ₂ , ..., c _J }, c _J is the available channel for interference, J is the number of available channels for interference;

S12, divide the UAV communication pair into Z segments from the starting point to the end point, and solve the coordinates of each segment (x _{n, z} , _{yn, z} ), x _{n, z} represent the abscissa of the UAV n in the z-th segment, y _{n, z} represents the ordinate of the UAV in the z-th segment, thereby forming the coordinate set of the flight trajectory of the UAV communication pair n, namely: {(x _{n, 0} , y _{n, 0} ), (x _{n, 1} , yn _{, 1} ), (x _{n, 2} , yn _{, 2} ), ..., (x _{n, z} , yn _{, z} ), ..., (x _{n, Z} , yn _{, Z} )}, z=1,2,...,Z, where (xn _,0 ,yn _,0 ), (xn _,z ,yn _,z ), (xn _,Z ,yn _,Z ) respectively represent the starting coordinates of the UAV communication pair, the coordinates of the z-th segment and the end-point coordinates; remember that the vector formed by the abscissas of all users in the z segment is X, then X=[x _{1, z} , x _{1, z} ,...xn _,z ], remember that the vector formed by the ordinates of all users in the z segment is Y, then Y=[y1 _,z ,y1 _,z ,...yn _,z ];

S13, it is assumed that the combination of channel selection strategies of all users is a={a ₁ , a ₂ , ..., a _N }, a _-n ={a ₀ , a ₁ , ..., a _n-1 , a _n+1 , ... , a _N } represents the channel selection strategy combination of all users except user n;

Then the loss of the drone user in paragraph z is described as:

为用户n在z段遭受的期望加权和干扰，d_j，n，z为第z段无人机通信对用户n与干扰机j之间的距离，

d_k，n，z为无人机通信对用户n与无人机通信对用户k之间的距离，

为示性函数，a_n，z为用户n选择在第z段选择的信道，c_j，z为干扰机选择在第z段选的信道，d_n，z，z-1＝((x_n，z-x_n，z-1)²+(y_n，z-y_n，z-1)²)^1/2为用户n第z段的飞行距离，C₀为单位距离的飞行能耗，C₁为干扰水平和飞行能耗平衡因子；where p _n represents the transmit power of user n, p _j ′ represents the transmit power of jammer j,

is the expected weighted sum interference suffered by user n in segment z, d _{j, n, z} is the distance between user n and jammer j in the z-th segment of UAV communication,

d _{k, n, z} are the distances between the UAV communication pair user n and the UAV communication pair user k,

is an illustrative function, an _{n, z} is the channel selected by user n in the zth segment, c _{j, z} is the channel selected by the jammer in the zth segment, d _{n, z, z-1} = ((x _{n , z} -x _{n, z-1} ) ² +(y _{n, z} -y _{n, z-1} ) ² ) ^1/2 is the flight distance of the z-th segment of user n, C ₀ is the flight energy consumption per unit distance, C ₁ is the balance factor of interference level and flight energy consumption;

S14, by optimizing the user's horizontal and vertical coordinates and the frequency use strategy, in order to minimize the loss on each segment, thereby reducing the loss of the entire process, the optimization problem is described as:

Among them, x is the vector formed by the abscissa of the user, Y is the vector formed by the ordinate of the user, and o is the frequency usage policy of all users in the zth segment.

Further, in step S2, the process of using the convex optimization solution method to plan the trajectory of the UAV user includes the following steps:

S211, transform the loss modeling of user n into:

Among them, H _n and H _k are the flying heights of users n and k, x _{i, z} are the abscissas of user i in the zth segment, y _{i, z} are the ordinates of user i in the zth segment, x _j and y _j are the horizontal and vertical coordinates of the jammer, respectively;

S212, set the constraints as follows:

(1) Forward constraint

In order to ensure that the drone can fly to the destination, the following constraints are made:

Among them, d _z is the distance of the drone from the target position in the zth segment, d _max =V _max *T ₀ is the maximum flying distance of the drone in each segment, V _max is the maximum flying speed of the drone, and T ₀ for the flight time of each segment;

(2) Speed constraint

The maximum distance that constrains the UAV for each segment of flight is:

S213, describe the trajectory planning problem of the UAV as:

S214 , using the method of continuous convex approximation to solve the problem P1.

Further, in step S214, the process of solving the problem P1 by using the continuous convex approximation method includes the following steps:

S2141, note:

_Sk,n,z =(( _xk,z -xn _,z )2+(yk _,z -yn _,z ⁾ 2+( _Hn - _Hk ^{)2 ) -1}

Sn _{, z} = ((x _{n, z} - x _{n, z-1} ) ² +(y _{n, z} -y _{n, z-1} ) ² ) ^1/2

Transform problem P1 into:

S2142, scaling _Sn,z , Sn _,j,z , _Sk,n,z as follows:

S _{n, z} ≥ ((x _{n, z} -x _{n, z-1} ) ² +(y _{n, z} -y _{n, z-1} ) ² ) ^1/2

S _k,n,z ≥((x _k,z -x _n,z ) ² +(y _k,z -y _n,z ) ² +(H _n -H _k ) ² ) ^-1 ;

Transform P2 into:

S2143, using continuous convex approximation to approximate, get:

和

分别为x_k，z、x_n，z、y_k，z、y_n，z和S_n，z对应的一阶泰勒展开点，n，k＝1，2，…，N；n≠k；in

and

are the first-order Taylor expansion points corresponding to x _k,z , x _n,z , y _k,z , yn _,z and Sn _,z respectively, n,k=1,2,...,N; n≠k;

S2144, finally, by giving the initial Taylor expansion point, the problem P4 is iteratively solved, and the solution obtained by each iteration is used as a new Taylor expansion point, and the solution of the original problem P1 is obtained after multiple iterations.

Further, in step S2, the spectrum decision problem is modeled as a Stackelberg game, and the equilibrium solution is carried out through hierarchical learning, and the process of finally realizing the joint optimization of the trajectory and the spectrum includes the following steps:

其中，

表示无人机用户对集，

表示外部恶意干扰，

和

分别表示网内用户和干扰的策略集，

为无人机用户对的轨迹横坐标所采取的策略，

为无人机用户对的轨迹纵坐标所采取的策略，u_n和u_j分别表示无人机用户对n和干扰的效用函数；S221, the spectrum decision problem in step S1 is modeled as a Stackelberg game, expressed as

in,

represents the drone user pair set,

Indicates external malicious interference,

and

are the policy sets of users and interferences in the network, respectively,

The strategy adopted for the abscissa of the trajectory of the drone user pair,

is the strategy adopted for the trajectory ordinate of the UAV user pair, u _n and u _j represent the utility function of the UAV user pair n and interference, respectively;

S222, assuming that the interference is the leader and the drone user pair is the follower, model both the users in the network and the interference as game participants, and build a game model; for the drone user pair n, it hopes to achieve the least loss , thus, its utility function is defined as:

u _{n, z} (an _{, z} , a _{-n, z} , c _{j, z} , X, Y) = WE _{n, z}

where W is a predefined constant, and its value is determined by the user power in the environment, and the user's optimization problem for n is expressed as:

The lower-level user subgame is defined as:

干扰的优化问题被表示为c_j＝arg max u_j(a，c_j)；For interference, its goal is to maximize the interference utility function, which is defined as:

The optimization problem of interference is expressed as c _j =arg max u _j (a, c _j );

The upper-level disturbance subgame is defined as:

Among them, the strategy set is the interference channel set c;

的策略空间由离散的用频策略和连续的轨迹构成，将下层

子博弈分为两个子问题进行求解，以给出分层均衡。S223, lower game

The policy space of is composed of discrete frequency-use policies and continuous trajectories.

The subgame is solved in two subproblems to give a stratified equilibrium.

子博弈分为两个子问题进行求解，以给出分层均衡的过程包括：Further, in step S223, the lower layer

The subgame is divided into two subproblems to be solved to give a stratified equilibrium process including:

是一个精确势能博弈并且该博弈存在至少一个纳什均衡；同时在求得

的均衡解的情况下，将轨迹规划转化为凸问题，利用连续凸近似的方法进行求解；通过用频均衡点与轨迹优化不断的迭代，最终给出下层子博弈的策略；在博弈模型

中，在求解完成用户的策略后，干扰确定自己的干扰策略从而构成一个分层均衡。UAV communication adjusts the user's trajectory and frequency strategy. When the user's position is fixed, under the given interference strategy c _j , the lower-level UAV users constitute a game.

is an exact potential energy game and there is at least one Nash equilibrium in the game;

In the case of the equilibrium solution of , the trajectory planning is transformed into a convex problem, and the solution is solved by the method of continuous convex approximation; through the constant iteration of frequency equilibrium point and trajectory optimization, the strategy of the lower sub-game is finally given; in the game model

In , after solving the user's strategy, the interference determines its own interference strategy to form a hierarchical equilibrium.

中，在求解完成用户的策略后，干扰确定自己的干扰策略从而构成一个分层均衡的过程包括：Further, the in-game model

, after solving the user's strategy, the process of determining its own interference strategy to form a hierarchical equilibrium includes:

在轨迹调整完成后转变为至少存在一个纯策略纳什均衡的精确势能博弈

在博弈

中总存在NE(θ₀)，计算得到干扰的平稳策略

将

构成一个平稳意义上的分层均衡。Given an interference strategy θ ₀ , the game

After the trajectory adjustment is completed, it is transformed into an exact potential energy game with at least one pure-strategy Nash equilibrium.

in the game

There is always NE(θ ₀ ) in the

Will

It constitutes a stratified equilibrium in a stationary sense.

The beneficial effects of the present invention are:

By jointly optimizing the trajectory and frequency of the UAV user, the present invention can adjust the trajectory adaptively to avoid the jammer and avoid the interference frequency band by changing the frequency, so as to achieve the purpose of anti-jamming of the UAV. Frequency optimization and joint optimization can further improve the communication efficiency of UAV users and reduce the losses caused by external malicious interference.

Description of drawings

FIG. 1 is a schematic diagram of a communication confrontation scenario between a UAV and a jammer designed by the present invention.

Figure 2 shows a schematic diagram when the UAV flight trajectory is divided into 4 segments.

Figure 3 is a schematic diagram of the UAV flight trajectory when the jammer positions are different.

FIG. 4 is a schematic diagram corresponding to the frequency situation of the UAV under the situation of FIG. 2 .

Fig. 5 is a schematic diagram of the frequency and trajectory of the UAV obtained by selecting the middle sections of Fig. 2 and Fig. 3 numbered 47-48, respectively.

Figure 6 is a schematic diagram of the UAV flight trajectory when the jammer power is different.

Figure 7 is a comparison of the average UAV consumption per segment when the jammer positions are different.

Figure 8 is a comparison of the average consumption of UAVs under different segments.

Figure 9 is a comparison of the consumption of UAVs at different maximum flight speeds.

Figure 10 is the convergence curve of the proposed optimization problem.

11 is a flowchart of the UAV anti-jamming method for joint trajectory planning and spectrum decision-making according to the present invention.

Detailed ways

The present invention will now be described in further detail with reference to the accompanying drawings.

It should be noted that the terms such as "up", "down", "left", "right", "front", "rear", etc. quoted in the invention are only for the convenience of description and clarity, and are not used for Limiting the applicable scope of the present invention, the change or adjustment of the relative relationship shall be regarded as the applicable scope of the present invention without substantially changing the technical content.

In order to clearly illustrate the anti-jamming method for unmanned aerial vehicles proposed by the present invention, some symbols involved in the following embodiments and their corresponding value examples are first described. Table 1 is a summary table of the meanings of all symbols in the present invention, and Table 2 is an example table of values of some symbols.

Table 1 Symbol table

Table 2 The value table of some characters

With reference to FIG. 11 , the present invention refers to a UAV anti-jamming method for joint trajectory planning and spectrum decision-making. The UAV anti-jamming method is used for multiple UAV communication pairs from the Departure from the ground to the destination at different flight heights to perform tasks, jointly optimize the frequency strategy and flight trajectory of all UAV communication pairs, and pursue maximizing the communication rate of the UAV communication pairs; the anti-jamming method includes the following steps:

S1, the loss and optimization problem of UAV users are modeled for actual communication scenarios.

S2, the optimization problem is divided into two aspects: trajectory planning and spectrum decision-making; first, the solution method of convex optimization is used to plan the trajectory of the UAV user, and then the spectrum decision-making problem is modeled as a Stackelberg game, which is carried out through hierarchical learning. Equilibrium solution, and finally realize the joint optimization of trajectory and spectrum.

In an intelligent jamming environment, multiple UAV communication pairs start from the origin and travel to the destination at different flight altitudes to perform tasks. The goal is to jointly optimize the frequency strategy and flight trajectories of all UAV communication pairs, and pursue to maximize the communication rate of UAV communication pairs.

The system contains N drones communicating to users and one external malicious jammer. UAV communication requires real-time data transmission for users to complete the target communication task during the flight from the starting point to the end point. The pair set of UAV users is defined as Un ( _n =1, 2,...N), and the available channel set is defined as M={c ₁ , c ₂ ,..., c _M }, where c _M represents UAV users Pair of available channels, the number of available channels for M UAV communication pairs, and the set of interference channels is defined as, c={c ₁ , c ₂ , ..., c _J ), c _J is the available channel for interference, and J is the number of available channels for interference. In this system, the interference can sense the user's channel, it can adjust its interference strategy according to the user's strategy and environmental information, and pursues to maximize the interference utility. On the other hand, users are also intelligent, and they adopt flexible channel selection strategies to reduce the influence of mutual interference among users and external malicious interference. At the same time, UAV users can flexibly change the flight trajectory to reduce the impact of mutual interference and external interference between users. FIG. 1 is a system model diagram of the present invention, which includes N drone communication pairs for users and one external malicious interference, which reflects the process of drone communication for users flying from the starting point to the end point.

Divide the UAV communication pair into Z segments from the starting point to the end point, and solve the coordinates of each segment (x _{n, z} , y _{k, z} ), x _{n, z} represent the abscissa of UAV n in the z-th segment, y _{n, z} represent the ordinate of the UAV in the z-th segment. Thus, the coordinate set of the flight trajectory of the UAV communication pair n is formed, namely: {(x _{n, 0} , y _{n, 0} ), (x _{n, 1} , yn _{, 1} ), (x _{n, 2} , y _{n ,2} ),...,(xn _,z ,yn _,z ),...,(xn _,Z ,yn _,Z )},(z=1,2,...,Z) , where (x _{n, 0} , y _{n, 0} ), (x _{n, z} , y _{n, z} ), (x _{n, Z} , yn _{, Z} ) represent the starting coordinates of the UAV communication pair, the first The coordinates of the z segment and the coordinates of the end point. Note that the vector composed of the abscissas of all users in the z segment is X, then X=[x _{1, z} , x _{1, z} ,...x _{n, z} ], and the ordinates of all users in the z segment are composed. The vector of is Y, then Y=[y _{1, z} , y _{1, z} , ... y _{n, z} ].

It is assumed that the combination of channel selection strategies of all users is a={a ₁ , a ₂ , . . . , a _N }. a _-n ={a ₀ , a ₁ , . . . , a _n-1 , a _n+1 , . . . , a _N } represents the combination of channel selection strategies for all users except user n. For users, if two or more users select the same channel, mutual interference will occur. For interference, it selects 1 channel c _j for interference. Assuming that the available channels experience free space fading, the available channels for interference are the same as the set of available channels for users, and each user selects a channel for information transmission in a time slot.

At each stage z, it is assumed that the channels chosen by user n and the interferer are an ∈ M and c _j ∈ c, _respectively . The available rate of users for n can be expressed as

表示在第z段(段编号从z-1到z)的用户间互扰，

表示外部干扰，B表示信道带宽，N₀表示噪声功率谱密度，

表示用户对n的自由空间衰减。where p _n represents the transmit power of user n,

represents the mutual interference between users in segment z (segment numbers from z-1 to z),

represents external interference, B represents the channel bandwidth, N ₀ represents the noise power spectral density,

represents the user's free-space decay for n.

In this scenario, achieving efficient anti-jamming faces the following challenges: (1) Consider co-channel interference caused by frequency conflict; (2) Consider external malicious interference; (3) Consider flight paths to mitigate co-channel interference and malicious interference.

The expected weighted sum interference suffered by user n in segment z can be expressed as:

in,

d _{j, n, z} are the distances between user n and jammer j in the zth segment of UAV communication.

d _{k, n, z} are the distances between the UAV communication pair user n and the UAV communication pair user k.

f(x, y) is an indicative function, an _{n, z} are the channel selected by user n in the z-th segment, and c _{j, z} are the channel selected by the jammer in the z-th segment.

Due to the certain flight energy of UAV users, their flight distance is very limited, so the impact of flight energy consumption on UAV users cannot be ignored, and it needs to be included in the calculation of user losses.

On the basis of expected weighting and interference, and considering the flight cost, let the UAV user's loss in the z-th segment be described as:

d _{n, z, z-1} = ((x _{n, z} - x _{n, z-1} ) ² +(y _{n, z} - y _{n, z-1} ) ² ) ^1/2 (7)

Among them, d _{n, z, z-1} is the flight distance of the zth segment of user n, C ₀ is the flight energy consumption per unit distance, and C ₁ is the balance factor of the interference level and the flight energy consumption.

By optimizing the user's horizontal and vertical coordinates and frequency use strategy, in order to minimize the loss on each segment, thereby reducing the loss of the entire process, the problem can be described as:

Among them, x is the vector formed by the abscissa of the user, Y is the vector formed by the ordinate of the user, and o is the frequency usage policy of all users in the zth segment.

Solve the problem of our drone users through the following steps:

其中，

表示无人机用户对集，

表示外部恶意干扰，

和

分别表示网内用户和干扰的策略集，

为无人机用户对的轨迹横坐标所采取的策略，

为无人机用户对的轨迹纵坐标所采取的策略，u_n和u_j分别表示无人机用户对n和干扰的效用函数。该模型中，无人机用户对为了有效应对抗干扰需要进行干扰检测，并假设干扰为领导者，无人机用户对为跟随者。将网内用户和干扰都建模为博弈参与者，构建博弈模型。对于无人机用户对n来说，它希望实现损失最小化。因而，在第z段其效用函数可定义为：Step 1: The above problem can be modeled as a Stackelberg game. Mathematically, it can be expressed as

in,

represents the drone user pair set,

Indicates external malicious interference,

and

are the policy sets of users and interferences in the network, respectively,

The strategy adopted for the abscissa of the trajectory of the drone user pair,

The strategy adopted for the trajectory ordinate of the UAV user pair, u _n and u _j represent the utility function of the UAV user pair n and interference, respectively. In this model, the UAV user pair needs to perform interference detection in order to effectively deal with the anti-jamming, and it is assumed that the interference is the leader and the UAV user pair is the follower. Both users and disturbances in the network are modeled as game participants, and a game model is constructed. For the drone user pair n, it wants to achieve loss minimization. Therefore, its utility function can be defined as:

u _{n, z} (an _{, z} , a _{-n, z} , c _{j, z} , X, Y) = WE _{n, z} (9)

Wherein W is a predefined constant, and its value is determined by the user power in the environment and can be adjusted freely. The user's optimization problem for n can be expressed as:

The lower-level user subgame is defined as:

For interference, its goal is to maximize the interference utility function, which can be defined as:

The optimization problem of interference can be expressed as:

c _j =arg max u _j (a, c _j ). (13)

The upper-level disturbance subgame can be defined as

Among them, the strategy set is the interference channel set

的策略空间由离散的用频策略和连续的轨迹构成，并且由式(6)(7)可知用户的轨迹与其他用户具有很强的耦合性，将下层

子博弈分为两个子问题进行求解，以给出分层均衡。lower game

The strategy space is composed of discrete frequency strategies and continuous trajectories, and it can be seen from equations (6) and (7) that the user's trajectory has a strong coupling with other users, and the lower layer

The subgame is solved in two subproblems to give a stratified equilibrium.

是一个精确势能博弈并且该博弈存在至少一个纳什均衡。同时在求得

的均衡解的情况下，将轨迹规划转化为凸问题，利用连续凸近似的方法进行求解。通过用频均衡点与轨迹优化不断的迭代，最终给出下层子博弈的策略。在博弈模型

中，在求解完成用户的策略后，干扰确定自己的干扰策略从而构成一个分层均衡。UAV communication adjusts the user's trajectory and frequency strategy. When the user's position is fixed, under the given interference strategy c _j , the lower-level UAV users constitute a game.

is an exact potential energy game and the game has at least one Nash equilibrium. while seeking

In the case of the equilibrium solution of , the trajectory planning is transformed into a convex problem, and the continuous convex approximation method is used to solve it. Through the constant iteration of frequency equilibrium point and trajectory optimization, the strategy of the lower sub-game is finally given. in game model

In , after solving the user's strategy, the interference determines its own interference strategy to form a hierarchical equilibrium.

Step 2:

As mentioned before, the loss for user n is modeled as:

Among them, H _n and H _k are the flying heights of users n and k, x _{i, z} are the abscissas of user i in the zth segment, y _{i, z} are the ordinates of user i in the zth segment, x _j and y _j are the abscissa and ordinate coordinates of the jammer, respectively.

The constraints are as follows:

(1) Forward constraint

In order to ensure that the drone can fly to the destination, the following constraints are made:

Among them, d _z is the distance of the drone from the target position in the zth segment, d _max =V _max *T ₀ is the maximum flying distance of the drone in each segment, V _max is the maximum flying speed of the drone, and T ₀ for the flight time of each segment. Figure 2 shows a schematic diagram of the UAV flight trajectory divided into 4 segments, the UAV trajectory is divided into 4 segments, 0·T ₀ =0 seconds to start flying, to 1·T ₀ =T ₀ seconds (that is, the first segment When the flight interval ends), the distance from the UAV to the end point should be less than 3*d _max , so that it can fly to the destination within the remaining 3T ₀ time; 1·T ₀ =T ₀ seconds to start flying, to 2.T ₀ = 2T ₀ seconds (ie, the end of the second flight interval), the position of the UAV from the end point should be less than 2*d _max .

(2) Speed constraint

Since the flying speed of the drone cannot be infinite, the maximum distance of each flight of the drone is constrained:

Therefore, the trajectory planning problem of UAV can be described as:

By taking the second derivative of P1 and analyzing it, we can see that the problem P1 is a non-convex problem.

Note: _Sk,n,z =(( _xk,z -xn _,z )2+(yk _,z -yn _,z ⁾ 2+( _Hn - _Hk ^{)2 ) -1} (19)

Sn _{, z} = ((x _{n, z} - x _{n, z-1} ) ² +(y _{n, z} -y _{n, z-1} ) ² ) ^1/2 (21)

Then there are:

Scaling _Sn,z , Sn _,j,z , _Sk,n,z as follows:

S _{n, z} ≥ ((x _{n, z} - x _{n, z-1} ) ² +(y _{n, z} -y _{n, z-1} ) ² ) ^1/2 (23)

S _{k, n} , z ≥ ((x _{k, z -} x _{n, z} ) ² +(y _{k, z} -y _{n, z} ) ² +(H _n -H _k ) ² ) ^-1 (25)

It can be seen from (19), (20), (21) that when (23), (24), and (25) take equal signs, the scaling performed is equivalent relaxation, that is, P2 approaches the target minimum value. Then P2 will be transformed into:

Analysis of (23), (24), (25) shows that they are non-convex inequalities, so P3 is still a non-convex problem and cannot be solved directly. Therefore, using continuous convex approximation to approximate, we can get:

分别为x_k，z，x_n，z，y_k，z，y_n，z，S_n，z对应的一阶泰勒展开点。in

are the first-order Taylor expansion points corresponding to x _{k, z} , x _{n, z} , y _{k, z} , y _{n, z} , Sn _{, z} respectively.

Finally, by giving the initial Taylor expansion point, iteratively solve P4, and take the solution obtained by each iteration as a new Taylor expansion point, and the solution of the original problem P1 can be obtained after several iterations.

Step 3:

是一个精确势能博弈，并且该博弈

至少存在一个纳什均衡。因此给定一个干扰策略c_j，下层子博弈的势能函数可以构造为：Given an interference strategy c _j , the lower subgame

is an exact potential energy game, and the game

At least one Nash equilibrium exists. Therefore, given an interference strategy c _j , the potential energy function of the lower subgame can be constructed as:

in,

和

可得：Consider interference symmetry between user pairs. Take advantage of symmetry

and

Available:

In summary, Φ ₁ (a _n , a _-n , c _j ) can be reformulated as:

与a_n，z无关。in,

Has nothing to do with an _{, z} .

also,

与a_n，z无关。in,

Has nothing to do with an _{, z} .

Note that Φ ₃ (d _{n , z, z-1} ) is a function of distance, independent of an. Therefore, it can be obtained

是一个精确势能博弈。The above analysis shows that the change of the user's utility function caused by the unilateral change of the strategy by any user is the same as the change of the potential energy function.

It is an exact potential energy game.

In the proposed anti-jamming game, there is a stationary strategy for interference and a user's NE strategy to form a hierarchical equilibrium.

在轨迹调整完成后转变为精确势能博弈

由于精确势能博弈至少存在一个纯策略纳什均衡。因此，在给定干扰策略θ₀，在博弈

中总存NE(θ₀)。干扰的平稳策略可以表示为Given the interference strategy, the game

After the trajectory adjustment is completed, it is transformed into a precise potential energy game

Since there is at least one pure-strategy Nash equilibrium in exact potential games. Therefore, given the interference strategy θ ₀ , in the game

NE(θ ₀ ) is always stored in . The stationary policy of disturbance can be expressed as

构成一个平稳意义上的分层均衡。Every finite strategy game has a mixed strategy equilibrium, so

It constitutes a stratified equilibrium in a stationary sense.

Figure 3 shows the trajectories of UAV users with the same interference power in 3 available frequency bands of 6 users. It can be clearly found that when UAV users fly to the vicinity of interference, all UAV users are kept away from interference in order to maintain smooth communication. At the same time, due to the mutual interference of drones, the positions of drones are constantly being adjusted. For example, in the section of X-axis coordinate 80-400m of sub-graph a in Figure 3, UAV user 2 and UAV user 3 are very close at 80-200m, and far apart after 200-400m. The reason for this phenomenon is mainly to reduce mutual interference between users.

Figure 4 shows the frequency usage of each segment. It can be found that when the UAV and the jammer are located close to each other, the jammer can interfere with more users. Sub-picture a corresponds to the interference position (800, 130). In segments 10-18, the jammer can interfere with the most users every time, and there are available channels that are not used. Sub-picture b corresponds to the interference position (200, 30). In segments 2-7, the jammer can interfere with the most users every time, and there are available channels that are not used. The sub-picture c corresponds to the interference position (1600, 275). In segments 22-29, the jammer can interfere with the most users every time, and there are available channels that are not used. This phenomenon is because the user is closer to the jammer at this time, and the user first decides to jam and then decides. The interference is close to the user. In order to avoid the strong interference of the interference, the user abandons the interfered channel. Interference is intelligent. After the user makes a decision, in order to maximize its utility, the interference will interfere with the channel with the most users.

Figure 5 selects the frequency and trajectories of users numbered 47-48 in Figure 3 and Figure 4, so as to analyze the effect of the proposed algorithm in reducing mutual interference between users. Observing subgraphs a.1 and a.2, it can be found that the distance between user 1 and user 5 is close when the segment number is 47, but they use different channels. User 2, User 5, and User 6 use the same frequency and are therefore far apart. This phenomenon also exists in subgraphs b.1 and b.2 as well as in subgraphs c.1 and c.2. The reason for this phenomenon is that when using the same channel, the farther the distance is, the smaller the mutual interference, and the closer the distance is, the greater the mutual interference.

Figure 6 shows the user trajectories under different interference powers, and the subgraphs a and b correspond to the interference powers of 100w, 50w, and 25w, respectively. It can be found that the greater the interference, the farther the user is from the interference.

In FIG. 7 , the corresponding interference positions of loc1, loc2, loc3 and loc4 are (800, 130), (200, 30), (1600, 275) and (1000, 130), respectively. It can be found that no matter where the jamming is located, the larger the jamming power, the greater the draw consumption, because in order to compare the jamming, the UAV will fly farther.

It can be seen from Figure 8 that when the maximum flight speed is greater, the loss of the UAV is smaller, because the greater the maximum flight speed, the greater the degree of freedom that the UAV trajectory can be adjusted. In other words, it can reduce the co-frequency mutual interference between UAVs.

Figure 9 shows the comparison between the algorithm designed under different interference power and other algorithms. The ratio of using frequency random trajectory uniformity to using frequency optimization trajectory uniformity shows that the loss of using frequency optimization is less; compared with the joint solution, the joint solution loss is smaller when using frequency optimization trajectory uniformity. On the whole, the proposed algorithm has the least loss, that is, its performance is the best.

Convergence curves for the proposed optimization problem are provided in Figure 10. The iteration stops if the preset objective function tolerance is met or the number of iterations reaches the maximum value. Specifically, when solving by frequency, the probability of using frequency is required to be > ^1-0.001 , and the maximum number of iterations is 1000. When planning the trajectory, it is required that the relative change between the two times before and after is less than 10-4 and the maximum number of iterations is 100 times. It can be seen from the figure that the convergence time of the algorithm designed in this patent is less than 200 times, which shows the effectiveness of the designed algorithm.

The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions that belong to the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those skilled in the art, some improvements and modifications without departing from the principle of the present invention should be regarded as the protection scope of the present invention.

Claims (7)

1. An unmanned aerial vehicle anti-interference method combining trajectory planning and frequency spectrum decision is characterized in that the unmanned aerial vehicle anti-interference method is used for executing tasks on a plurality of unmanned aerial vehicle communication pairs starting from a starting place and going to a destination at different flight heights in an intelligent interference environment, jointly optimizing frequency utilization strategies and flight trajectories of all unmanned aerial vehicle communication pairs and pursuing maximization of communication rate of the unmanned aerial vehicle communication pairs; the anti-interference method comprises the following steps:

s1, modeling the loss and optimization problem of the unmanned aerial vehicle user aiming at the actual communication scene;

s2, the optimization problem is divided into two aspects: trajectory planning and spectrum decision making; firstly, a convex optimization solving method is used for planning the track of an unmanned aerial vehicle user, then a frequency spectrum decision problem is modeled into a Stackelberg game, balanced solution is carried out through layered learning, and finally the joint optimization of the track and the frequency spectrum is realized.

2. The unmanned aerial vehicle anti-jamming method based on joint trajectory planning and spectrum decision of claim 1, wherein in step S1, the process of modeling the loss and optimization problem of the unmanned aerial vehicle user for the actual communication scenario includes the following steps:

s11, the system comprises N unmanned aerial vehicle communication pairs and a malicious interference outside, and the unmanned aerial vehicle user pair set is defined as U_n(N ═ 1, 2.. N), and the available channel set is defined as

c_MRepresenting available channels of unmanned aerial vehicle user pairs, M being the number of available channels of unmanned aerial vehicle communication pairs, and the set of interference channels being defined as

c_JJ is the number of interference available channels;

s12, dividing the unmanned aerial vehicle communication pair into Z sections from the starting point to the end point, and solving the coordinate (x) of each section_n,z,y_n,z)，x_n,zDenotes the abscissa, y, of drone n in the z-th segment_n,zThe ordinate of the drone in the z-th segment, forming a set of coordinates of the flight trajectory of the drone communication pair n, namely: { (x)_n,0,y_n,0),(x_n,1,y_n,1),(x_n,2,y_n,2),...,(x_n,z,y_n,z),...,(x_n,Z,y_n,Z) 1,2, Z, wherein (x)_n,0,y_n,0),(x_n,z,y_n,z),(x_n,Z,y_n,Z) Respectively representing the initial coordinate, the z-th segment coordinate and the end point coordinate of the unmanned aerial vehicle communication pair; note that the vector formed by the abscissa of all users in the z segment is X, and X ═ X_1,z,x_1,z,...x_n,z]If the vector formed by the vertical coordinates of all users in the z segment is Y, Y ═ Y_1,z,y_1,z,...y_n,z]；

S13, assuming that the combination of the channel selection policies of all users is a ═ a₁,a₂,…,a_N}，a_-n＝{a₀,a₁,…,a_n-1,a_n+1,…,a_NRepresents the channel selection strategy combination of all users except the user n;

the loss of the drone user in the z-th segment is described as:

wherein p is_nRepresenting the transmission power, p, of user n_j' denotes the transmit power of the jammer j,

for the expectation that user n suffers in section zWeight and interference, d_j,n,zFor the distance between user n and jammer j for the z-th drone communication pair,

d_k,n,zfor the distance between drone communication pair user n and drone communication pair user k,

as an indicative function, a_n,zSelecting the channel selected in the z-th segment for user n, c_j,zSelecting the channel selected in the z-th segment for the jammer, d_n,z,z-1＝((x_n,z-x_n,z-1)²+(y_n,z-y_n,z-1)²)^1/2For the flight distance of the nth segment of the user, C₀Energy consumption per unit distance, C₁Interference level and flight energy consumption balance factors;

s14, the optimization problem is described as follows, by optimizing the horizontal and vertical coordinates of the user and the frequency strategy to minimize the loss on each segment, thereby reducing the loss of the whole process:

wherein, X is a vector formed by the abscissa of the user, Y is a vector formed by the ordinate of the user, and O is a frequency utilization strategy of all users in the z-th section.

3. The unmanned aerial vehicle anti-jamming method based on joint trajectory planning and spectrum decision of claim 2, wherein in step S2, the process of planning the trajectory of the unmanned aerial vehicle user by using the convex optimization solution method includes the following steps:

s211, modeling and transforming the loss of user n into:

wherein H_n、H_kIs the flight height, x, of the user n, k_i,zFor user i on the abscissa, y, of segment z_i,zFor user i in the z-th segment, x_jAnd y_jRespectively an abscissa and an ordinate of the jammer;

s212, setting the constraint conditions as follows:

(1) forward motion restraint

In order to ensure that the unmanned aerial vehicle can fly to the destination, the following constraints are made:

wherein d is_zFor the distance of the unmanned plane from the target position in the z-th segment, d_max＝V_max*T₀For maximum flight distance, V, of each segment of the drone_maxFor maximum flight speed, T, of the unmanned aerial vehicle₀Is the time of flight of each segment;

(2) speed constraint

The maximum distance for restricting each flight of the unmanned aerial vehicle is as follows:

s213, describing the trajectory planning problem of the unmanned aerial vehicle as follows:

s214, the problem P1 is solved by using the continuous convex approximation method.

4. The unmanned aerial vehicle anti-jamming method based on joint trajectory planning and spectrum decision of claim 3, wherein in step S214, the process of solving the problem P1 by using the continuous convex approximation method includes the following steps:

s2141, note:

S_k,n,z＝((x_k,z-x_n,z)²+(y_k,z-y_n,z)²+(H_n-H_k)²)^-1

S_n,z＝((x_n,z-x_n,z-1)²+(y_n,z-y_n,z-1)²)^1/2

problem P1 was converted into:

s2142, to S_n,z、S_n,j,z、S_k,n,zThe following scaling was performed:

S_n,z≥((x_n,z-x_n,z-1)²+(y_n,z-y_n,z-1)²)^1/2

S_k,n,z≥((x_k,z-x_n,z)²+(y_k,z-y_n,z)²+(H_n-H_k)²)^-1；

converting P2 to:

s2143, approximation is performed by using continuous convex approximation, and the following is obtained:

wherein

And

are respectively x_k,z、x_n,z、y_k,z、y_n,zAnd S_n,zA corresponding first-order taylor expansion point, N, k being 1, 2. n is not equal to k;

s2144, the problem P4 is solved iteratively by giving out an initial Taylor expansion point, the solution obtained by each iteration is used as a new Taylor expansion point, and the solution of the original problem P1 is obtained through multiple iterations.

5. The unmanned aerial vehicle anti-interference method combining trajectory planning and spectrum decision making according to claim 2, wherein in step S2, the spectrum decision problem is modeled as a Stackelberg game, equilibrium solution is performed through layered learning, and finally, the process of achieving joint optimization of trajectory and spectrum comprises the following steps:

s221, modeling the spectrum decision problem in the step S1 into a Stackelberg game, which is expressed as

Wherein,

representing a set of pairs of drone users,

indicating an external malicious disturbance that may be present,

and

respectively representing the set of policies for in-network users and interference,

the strategy adopted for the trajectory abscissa of the drone user pair,

strategy adopted for the trajectory ordinate of the unmanned aerial vehicle user pair, u_nAnd u_jRespectively representing utility functions of the unmanned aerial vehicle user on n and interference;

s222, assuming that the interference is a leader and the unmanned aerial vehicle user pair is a follower, modeling both users and the interference in the network as game participants, and constructing a game model; for drone user pair n, it wants to achieve loss minimization, and thus its utility function is defined in segment z as:

u_n,z(a_n,z,a_-n,z,c_j,z,X,Y)＝W-E_n,z

where W is a predefined normal number whose value depends on the user power in the environment, and the user's optimization problem for n is expressed as:

the lower level user sub-game is defined as:

for interference, its goal is to achieve a maximization of the interference utility function, which is defined as:

the optimization problem of the interference is denoted c_j＝argmaxu_j(a,c_j)；

The upper level disturbing sub-game is defined as:

wherein the strategy set is an interference channel set

S223, lower layer game

The strategy space of (A) is composed of discrete frequency strategy and continuous track, and the lower layer is

The sub-game is divided into two sub-problems to solve to give hierarchical equilibrium.

6. The unmanned aerial vehicle anti-jamming method based on joint trajectory planning and spectrum decision of claim 5, wherein in step S223, the lower layer is processed

The sub game is divided into two sub problems to be solved, and the process of giving hierarchical equilibrium comprises the following steps:

the unmanned aerial vehicle communication adjusts the user in two aspects of track and frequency strategy, and the user position is fixed under the given interference strategy c_jLower, lower-layer unmanned aerial vehicle user pair composition game

Is an accurate potential energy game and the game has at least one nash equilibrium; at the same time obtain

Under the condition of the equilibrium solution, converting the trajectory planning into a convex problem, and solving by using a continuous convex approximation method; through continuous iteration of frequency balance points and track optimization, a strategy of a lower-layer sub game is finally given; game playing model

After the strategy of the user is solved, the interference determines the own interference strategy so as to form layered balance.

7. The unmanned aerial vehicle anti-jamming method based on joint trajectory planning and spectrum decision of claim 6, wherein the game model is

After the strategy of the user is solved, the process of interference determining the own interference strategy so as to form hierarchical equilibrium comprises the following steps:

given interference strategy θ₀Game of chance

After the track adjustment is completed, the method is changed into the method that at least one pure object existsStrategic Nash balanced accurate potential energy gaming

On game

In the presence of NE (theta)₀) Calculating a stationary strategy for interference

Will be provided with

A hierarchical equalization in the sense of stationarity is formed.

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