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

Unmanned aerial vehicle anti-interference method combining trajectory planning and frequency spectrum decision Download PDF

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CN112533221A
CN112533221A CN202011290216.8A CN202011290216A CN112533221A CN 112533221 A CN112533221 A CN 112533221A CN 202011290216 A CN202011290216 A CN 202011290216A CN 112533221 A CN112533221 A CN 112533221A
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aerial vehicle
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CN112533221B (en
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刘钢
徐子默
黄赞奇
王梅
刘一甲
李兆智
戚楠
吴启晖
王可为
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Nanjing University of Aeronautics and Astronautics
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/18—Network planning tools
    • H04W16/20—Network planning tools for indoor coverage or short range network deployment
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04K—SECRET COMMUNICATION; JAMMING OF COMMUNICATION
    • H04K3/00—Jamming of communication; Counter-measures
    • H04K3/80—Jamming or countermeasure characterized by its function
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/22—Traffic simulation tools or models
    • H04W16/225—Traffic simulation tools or models for indoor or short range network
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W84/00—Network topologies
    • H04W84/02—Hierarchically pre-organised networks, e.g. paging networks, cellular networks, WLAN [Wireless Local Area Network] or WLL [Wireless Local Loop]
    • H04W84/04—Large scale networks; Deep hierarchical networks
    • H04W84/08—Trunked mobile radio systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W84/00—Network topologies
    • H04W84/18—Self-organising networks, e.g. ad-hoc networks or sensor networks
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Abstract

The invention discloses an unmanned aerial vehicle anti-interference method combining track planning and frequency spectrum decision, which 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. The invention can jointly optimize the two dimensions of the trajectory optimization and the frequency utilization decision, realizes the anti-interference target of the unmanned aerial vehicle user, further improves the communication benefit of the unmanned aerial vehicle, and enables the unmanned aerial vehicle user to efficiently complete the target communication task under the condition of limited flight energy consumption.

Description

Unmanned aerial vehicle anti-interference method combining trajectory planning and frequency spectrum decision
Technical Field
The invention relates to the technical field of military communication countermeasure, in particular to an unmanned aerial vehicle anti-interference method combining trajectory planning and frequency spectrum decision.
Background
Under the background of the contemporary unmanned aerial vehicle clustering combat, the unmanned aerial vehicle is developed rapidly, is widely applied to the fields of communication, investigation, information collection and the like, and has the main characteristics of small volume, strong mobility and low cost, and can move according to the task requirement set by people, thereby meeting the communication requirement under a specific scene.
Meanwhile, the unmanned aerial vehicle also has certain defects. When a single unmanned aerial vehicle executes a task, the flight capacity is poor due to the fact that the load is limited, and the carried data processing equipment is insufficient. Therefore, in a common situation, a group of unmanned aerial vehicles is required to act together to complete a task, and the unmanned aerial vehicles are divided into a host and a wing plane according to actual demands, and the data detected by the host during operation must be transmitted to the wing plane to assist in the consolidation and analysis of information data. Therefore, the mutual communication between the unmanned aerial vehicle communication pairs needs to be realized by the people, so that the unmanned aerial vehicle task is efficiently completed.
For the unmanned aerial vehicle cluster anti-interference problem under the external malicious interference, the existing research is based on a single frequency planning angle, and the unmanned aerial vehicle anti-interference problem is optimally solved by combining two dimensions of a space track and a frequency in consideration of the influence of the flight track of the unmanned aerial vehicle on the interference. The goal of the unmanned aerial vehicle of our party is to obtain a larger information transmission amount at a smaller flight energy cost when a plurality of unmanned aerial vehicles fly simultaneously within a fixed time. When the track optimization is considered to realize anti-interference, the method mainly relates to the following aspects that on one hand, the unmanned aerial vehicle of one party needs to be far away from an interference source as far as possible, on the other hand, the unmanned aerial vehicle of the other party using the same frequency band is prevented from being too close to cause same frequency interference, and finally, the flight energy consumption also needs to be calculated in the track optimization problem because the energy consumption brought by the flight distance has great influence on the flight of the unmanned aerial vehicle. For the trajectory optimization problem, there have been related studies before, but there still exist certain problems: (1) the problem of internal interference of the unmanned aerial vehicle caused by too close distance; (2) the track optimization must be performed in a segmented manner due to frequency conversion of the ground strong jammer; (3) the unmanned aerial vehicle has limited flight mission execution time and must fly to the terminal from the starting point in limited time, so that the track design of each section cannot be independent, and the problem of whether the subsequent unmanned aerial vehicle can fly to the terminal in limited time is considered.
In the aspect of selecting the frequency spectrum of the user of the unmanned aerial vehicle, the frequency use decision problem of the user of the unmanned aerial vehicle needs to be modeled into a Stackelberg game in consideration of competition of two levels of external malicious interference and mutual interference among users. And under the condition of a given interference strategy, the lower-layer sub game is an accurate potential energy game, and at least one Nash equilibrium exists, so that the game model can be solved in an equilibrium manner. And based on a random learning theory, an anti-interference channel selection algorithm based on SLA is provided in the lower-layer sub game, so that the goal that the unmanned aerial vehicle user decides to avoid interference from the main frequency is achieved.
At present, no existing literature discloses how to combine two schemes of trajectory planning and frequency spectrum decision to perform anti-interference optimization on the unmanned aerial vehicle, the anti-interference principles of the two schemes are completely different, and how to realize effective combination of the two schemes is a problem which needs to be solved urgently at present.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides the unmanned aerial vehicle anti-interference method combining track planning and frequency spectrum decision, the two dimensions of track optimization and frequency decision are jointly optimized, the anti-interference target of an unmanned aerial vehicle user is realized, the communication benefit of the unmanned aerial vehicle is further improved, and the unmanned aerial vehicle user can efficiently complete the target communication task under the condition of limited flight energy consumption.
In order to achieve the purpose, the invention adopts the following technical scheme:
an unmanned aerial vehicle anti-interference method combining trajectory planning and frequency spectrum decision is used for executing tasks by starting from a starting place to a destination at different flight heights by a plurality of unmanned aerial vehicle communication pairs under 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.
In order to optimize the technical scheme, the specific measures adopted further comprise:
further, in step S1, the process of modeling the loss and optimization problem of the drone user for the actual communication scenario includes the following steps:
s11, the system includes N unmanned aerial vehicles to communicate with the user and an external malicious interference, the unmanned aerial vehicles useThe family pair set is defined as Un(N ═ 1, 2.. N), and the available channel set is defined as
Figure BDA0002782048100000022
cMRepresenting available channels of unmanned aerial vehicle user pairs, wherein M is the number of available channels of unmanned aerial vehicle communication pairs, and the interference channel set is defined as c ═ c1，c2，…，cJ}，cJJ 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 sectionn，z，yn，z)，xn，zDenotes the abscissa, y, of drone n in the z-th segmentn，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，yn，0)，(xn，1，yn，1)，(xn，2，yn，2)，...，(xn，z，yn，z)，...，(xn，Z，yn，Z) 1,2, Z, wherein (x)n，0，yn，0)，(xn，z，yn，z)，(xn，Z，yn，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 ═ X1，z，x1，z，…xn，z]If the vector formed by the vertical coordinates of all users in the z segment is Y, Y ═ Y1，z，y1，z，...yn，z]；
S13, assuming that the combination of the channel selection policies of all users is a ═ a1，a2，…，aN}，a-n＝{a0，a1，…，an-1，an+1，…，aNRepresents 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:
Figure BDA0002782048100000021
wherein p isnRepresenting the transmission power, p, of user nj' denotes the transmit power of the jammer j,
Figure BDA0002782048100000031
for the desired weighting and interference experienced by user n in the z segment, dj，n，zFor the distance between user n and jammer j for the z-th drone communication pair,
Figure BDA0002782048100000032
dk，n，zfor the distance between drone communication pair user n and drone communication pair user k,
Figure BDA0002782048100000033
Figure BDA0002782048100000034
as an indicative function, an，zSelecting the channel selected in the z-th segment for user n, cj，zSelecting the channel selected in the z-th segment for the jammer, dn，z，z-1＝((xn，z-xn，z-1)2+(yn，z-yn，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:
Figure BDA0002782048100000035
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 segment.
Further, in step S2, the process of planning the trajectory of the drone user by using the convex optimization solution method includes the following steps:
s211, modeling and transforming the loss of user n into:
Figure BDA0002782048100000036
wherein Hn、HkIs the flight height, x, of the user n, ki，zFor user i on the abscissa, y, of segment zi，zFor user i in the z-th segment, xjAnd yjRespectively 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:
Figure BDA0002782048100000041
wherein d iszFor the distance of the unmanned plane from the target position in the z-th segment, dmax＝Vmax*T0For maximum flight distance, V, of each segment of the dronemaxFor 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:
Figure BDA0002782048100000042
s213, describing the trajectory planning problem of the unmanned aerial vehicle as follows:
Figure BDA0002782048100000043
s214, the problem P1 is solved by using the continuous convex approximation method.
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
Figure BDA0002782048100000045
Sn，z＝((xn，z-xn，z-1)2+(yn，z-yn，z-1)2)1/2
problem P1 was converted into:
Figure BDA0002782048100000044
s2142, to Sn，z、Sn，j，z、Sk，n，zThe following scaling was performed:
Sn，z≥((xn，z-xn，z-1)2+(yn，z-yn，z-1)2)1/2
Figure BDA00027820481000000513
Sk，n，z≥((xk，z-xn，z)2+(yk，z-yn，z)2+(Hn-Hk)2)-1；
converting P2 to:
Figure BDA0002782048100000051
s2143, approximation is performed by using continuous convex approximation, and the following is obtained:
Figure BDA0002782048100000052
Figure BDA0002782048100000053
Figure BDA0002782048100000054
wherein
Figure BDA0002782048100000055
And
Figure BDA0002782048100000056
are respectively xk，z、xn，z、yk，z、yn，zAnd Sn，zThe corresponding first order taylor expansion point, N, k is 1,2, …, N; 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.
Further, in step S2, the process of modeling the spectrum decision problem as a Stackelberg game, performing equilibrium solution through layered learning, and finally implementing joint optimization of the trajectory and the spectrum includes the following steps:
s221, modeling the spectrum decision problem in the step S1 into a Stackelberg game, which is expressed as
Figure BDA0002782048100000057
Wherein,
Figure BDA00027820481000000514
representing a set of pairs of drone users,
Figure BDA0002782048100000058
indicating an external malicious disturbance that may be present,
Figure BDA0002782048100000059
and
Figure BDA00027820481000000510
respectively representing the set of policies for in-network users and interference,
Figure BDA00027820481000000511
the strategy adopted for the trajectory abscissa of the drone user pair,
Figure BDA00027820481000000512
strategy adopted for the trajectory ordinate of the unmanned aerial vehicle user pair, unAnd ujRespectively 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:
un，z(an，z，a-n，z，cj，z，X，Y)＝W-En，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:
Figure BDA0002782048100000061
the lower level user sub-game is defined as:
Figure BDA0002782048100000062
for interference, its goal is to achieve a maximization of the interference utility function, which is defined as:
Figure BDA0002782048100000063
the optimization problem of the interference is denoted cj＝arg max uj(a，cj)；
The upper level disturbing sub-game is defined as:
Figure BDA0002782048100000064
wherein, the strategy set is an interference channel set c;
s223, lower layer game
Figure BDA0002782048100000065
The strategy space of (A) is composed of discrete frequency strategy and continuous track, and the lower layer is
Figure BDA0002782048100000066
The sub-game is divided into two sub-problems to solve to give hierarchical equilibrium.
Further, in step S223, the lower layer is formed
Figure BDA0002782048100000067
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 cjLower, lower-layer unmanned aerial vehicle user pair composition game
Figure BDA0002782048100000068
Figure BDA0002782048100000069
Is an accurate potential energy game and the game has at least one nash equilibrium; at the same time obtain
Figure BDA00027820481000000610
Under the condition of equilibrium solution of (2), the trajectory planning is converted intoSolving the convex problem 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
Figure BDA00027820481000000611
After the strategy of the user is solved, the interference determines the own interference strategy so as to form layered balance.
Further, the game model
Figure BDA00027820481000000612
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
Figure BDA00027820481000000613
Accurate potential energy game converted into game with at least one pure strategy Nash equilibrium after track adjustment is completed
Figure BDA00027820481000000614
On game
Figure BDA00027820481000000615
In the presence of NE (theta)0) Calculating a stationary strategy for interference
Figure BDA00027820481000000616
Figure BDA0002782048100000071
Will be provided with
Figure BDA0002782048100000072
A hierarchical equalization in the sense of stationarity is formed.
The invention has the beneficial effects that:
according to the invention, by jointly optimizing the track and the frequency of the unmanned aerial vehicle user, the purpose of interference resistance of the unmanned aerial vehicle can be realized by adaptively adjusting the track to avoid an interference machine and changing the frequency to avoid an interference frequency band, and compared with the previous single frequency optimization, the joint optimization can further improve the communication benefit of the unmanned aerial vehicle user and reduce the loss caused by external malicious interference.
Drawings
Fig. 1 is a schematic diagram of a communication countermeasure scene of an unmanned aerial vehicle and an jammer designed by the invention.
Fig. 2 is a schematic diagram of the flight path of the unmanned aerial vehicle divided into 4 segments.
Fig. 3 is a schematic view of the flight trajectory of the drone when the jammer is not in position.
Fig. 4 is a schematic diagram corresponding to the frequency situation of the unmanned aerial vehicle in the case of fig. 2.
Fig. 5 is a schematic diagram of the frequencies and trajectories of the unmanned aerial vehicle, which are obtained by selecting the sections 47-48 in fig. 2 and 3, respectively.
Fig. 6 is a schematic diagram of the flight trajectory of the drone when the jammer powers are different.
Figure 7 is a comparison of drone consumption per segment averaged for different jammer locations.
Fig. 8 is a comparison of average consumption of drones in different segments.
Fig. 9 is a consumption comparison of drones at different maximum flight speeds.
Fig. 10 is a convergence curve of the proposed optimization problem.
Fig. 11 is a flowchart of the unmanned aerial vehicle anti-interference method combining trajectory planning and spectrum decision according to the present invention.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings.
It should be noted that the terms "upper", "lower", "left", "right", "front", "back", etc. used in the present invention are for clarity of description only, and are not intended to limit the scope of the present invention, and the relative relationship between the terms and the terms is not limited by the technical contents of the essential changes.
In order to clearly illustrate the anti-interference method for the unmanned aerial vehicle, a part of symbols and corresponding value examples thereof involved in the following embodiments are first described. Table 1 is a summary table of the meanings of all symbols of the present invention, and table 2 is an exemplary table of values of some symbols.
TABLE 1 symbol table
Figure BDA0002782048100000073
Figure BDA0002782048100000081
TABLE 2 partial character value-taking table
Figure BDA0002782048100000082
Figure BDA0002782048100000091
With reference to fig. 11, the present invention provides an unmanned aerial vehicle anti-interference method combining trajectory planning and spectrum decision, where the unmanned aerial vehicle anti-interference method is used in an intelligent interference environment, where multiple unmanned aerial vehicle communication pairs start from an origin and go to a destination at different flight heights to perform a task, jointly optimize frequency-usage strategies and flight trajectories of all unmanned aerial vehicle communication pairs, and pursue 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 according to 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.
A plurality of unmanned aerial vehicle communication pairs are started from the starting place to carry out tasks with different flying heights to the destination under the intelligent interference environment. The aim is to jointly optimize the frequency utilization strategy and flight trajectory of all unmanned aerial vehicle communication pairs, and strive to maximize the communication rate of the unmanned aerial vehicle communication pairs.
The system comprises N unmanned aerial vehicle communication pairs for users and an external malicious interference. The unmanned aerial vehicle communication needs to transmit data in real time to complete a target communication task when a user flies from a starting point to an end point. Unmanned aerial vehicle user pair set is defined as UnN, the available channel set is defined as M { c ═ 1,21，c2，…，cM}，cMRepresenting the available channels of a drone user pair, M drone communication pairs the number of available channels, the set of interference channels being defined as, c ═ c1，c2，…，cJ)，cJTo interfere with the available channels, J is the number of interfering available channels. In the system, interference can sense the channel of a user, and the interference strategy can be adjusted according to the strategy and environment information of the user, and the interference utility is sought to be maximized. On the other hand, users also have intelligence, and they adopt flexible channel selection strategies to reduce the influence caused by mutual interference among users and external malicious interference. Simultaneously, the unmanned aerial vehicle user is to the change flight path that can be nimble to reduce the influence that mutual interference and external disturbance caused between the user. Fig. 1 is a system model diagram of the present invention, which includes N drone communication to a user and an external malicious disturbance, and embodies a process of the drone communication to the user from a starting point to an ending point.
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 sectionn，z，yk，z)，xn，zDenotes the abscissa, y, of drone n in the z-th segmentn，zIndicating the 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，yn，0)，(xn，1，yn，1)，(xn，2，yn，2)，...，(xn，z，yn，z)，...，(xn，Z，yn，Z) (Z ═ 1, 2.., Z), where (x) isn，0，yn，0)，(xn，z，yn，z)，(xn，Z，yn，Z) The coordinates of the beginning, the z-th segment and the end point of the unmanned aerial vehicle communication pair are respectively represented. Note that the vector formed by the abscissa of all users in the z segment is X, and X ═ X1，z，x1，z，...xn，z]If the vector formed by the vertical coordinates of all users in the z segment is Y, Y ═ Y1，z，y1，z，…yn，z]。
Assume that the channel selection policy combination for all users is a ═ a1，a2，…，aN}。a-n＝{a0，a1，…，an-1，an+1，...，aNDenotes the channel selection policy combination of all users except user n. If two or more users select the same channel, mutual interference will occur to the users. For interference, it selects 1 channel cjInterference is performed. Assuming that the available channels experience free space fading, the interfering available channels are the same as the set of user available channels, and each user selects one channel for information transmission in one time slot.
At each stage z, assume that user n and the selected channel of interference are a respectivelynE.g. M and cjE.g. c. The user-achievable rate for n can be expressed as
Figure BDA0002782048100000101
Wherein p isnWhich represents the transmit power of the user n,
Figure BDA0002782048100000102
indicating the inter-user interference in the z-th segment (segment numbers from z-1 to z),
Figure BDA0002782048100000103
representing external interference, B representing channel bandwidth, N0The power spectral density of the noise is represented,
Figure BDA0002782048100000104
represent user pairsn free space attenuation.
In this scenario, achieving efficient anti-interference faces the following challenges: (1) the problem of co-channel interference caused by frequency conflict is considered; (2) considering the problem of external malicious interference; (3) flight paths are considered to mitigate co-channel interference and malicious interference.
The desired weighting and interference experienced by user n in segment z can be expressed as:
Figure BDA0002782048100000105
wherein,
Figure BDA0002782048100000106
dj，n，zand the distance between the user n and the jammer j is the z-th segment of unmanned aerial vehicle communication pair.
Figure BDA0002782048100000107
dk，n，zThe distance between user n for drone communication and user k for drone communication.
Figure BDA0002782048100000108
f (x, y) is an indicative function, an，zSelecting the channel selected in the z-th segment for user n, cj，zThe channel selected in the z-th segment is selected for the jammer.
Because the flight energy of the unmanned aerial vehicle user is certain, the flight distance of the unmanned aerial vehicle user is very limited, so the influence of the flight energy consumption on the unmanned aerial vehicle user cannot be ignored, and the influence needs to be counted in the calculation of user loss.
On the basis of the expected weighting and interference and considering the flight cost, the loss of the unmanned aerial vehicle user in the z-th segment is described as follows:
Figure BDA0002782048100000111
dn，z，z-1＝((xn，z-xn，z-1)2+(yn，z-yn，z-1)2)1/2 (7)
wherein d isn，z，z-1For the flight distance of the nth segment of the user, C0Energy consumption per unit distance, C1Is a balance factor of interference level and flight energy consumption.
By optimizing the horizontal and vertical coordinates of the user and the frequency strategy to minimize the loss on each segment, the loss of the whole process is reduced, and the problem can be described as follows:
Figure BDA0002782048100000112
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 segment.
Carrying out problem solving on the unmanned aerial vehicle user of the owner by the following steps:
the method comprises the following steps: the problem can be modeled as a Stackelberg game. Mathematically, it can be expressed as
Figure BDA0002782048100000113
Wherein,
Figure BDA0002782048100000114
representing a set of pairs of drone users,
Figure BDA0002782048100000115
indicating an external malicious disturbance that may be present,
Figure BDA0002782048100000116
and
Figure BDA0002782048100000117
policy sets representing in-network users and interference, respectively，
Figure BDA0002782048100000118
The strategy adopted for the trajectory abscissa of the drone user pair,
Figure BDA0002782048100000119
strategy adopted for the trajectory ordinate of the unmanned aerial vehicle user pair, unAnd ujRespectively representing utility functions of drone users for n and interference. In the model, the unmanned aerial vehicle user pair needs to carry out interference detection for effectively coping with interference resistance, and the unmanned aerial vehicle user pair is a follower assuming that interference is a leader. And modeling users and interference in the network as game participants, and constructing a game model. For drone user pair n, it is desirable to achieve loss minimization. Thus, in the z-th segment, the utility function can be defined as:
un，z(an，z，a-n，z，cj，z，X，Y)＝W-En，z (9)
wherein, W is a predefined normal number, the value of which is determined by the user power in the environment and can be freely adjusted. The user optimization problem for n can be expressed as:
Figure BDA00027820481000001110
the lower level user sub-game is defined as:
Figure BDA00027820481000001111
for interference, its goal is to maximize the interference utility function, which can be defined as:
Figure BDA0002782048100000121
the optimization problem of interference can be expressed as:
cj＝arg max uj(a，cj)。 (13)
the upper level of the interference sub-game can be defined as
Figure BDA0002782048100000122
Wherein the strategy set is an interference channel set
Figure BDA0002782048100000123
Lower level gaming
Figure BDA0002782048100000124
The strategy space of (2) is composed of a discrete frequency strategy and a continuous track, and the tracks of the users have strong coupling with other users according to the formulas (6) and (7), and the lower layer is
Figure BDA0002782048100000125
The sub-game is divided into two sub-problems to solve to give hierarchical equilibrium.
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 cjLower, lower-layer unmanned aerial vehicle user pair composition game
Figure BDA0002782048100000126
Figure BDA0002782048100000127
Is an accurate potential energy game and there is at least one nash equilibrium for the game. At the same time obtain
Figure BDA0002782048100000128
Under the condition of the equilibrium solution, the trajectory planning is converted into a convex problem, and a continuous convex approximation method is used for solving. And finally, giving a strategy of the lower-layer sub game by using frequency balance points and track optimization and continuous iteration. Game playing model
Figure BDA0002782048100000129
After the strategy of the user is solved, the interference determines the own interference strategy so as to form layered balance.
Step two:
as previously described, the loss for user n is modeled as:
Figure BDA00027820481000001210
wherein Hn、HkIs the flight height, x, of the user n, ki，zFor user i on the abscissa, y, of segment zi，zFor user i in the z-th segment, xjAnd yjRespectively the abscissa and ordinate of the jammer.
The constraints are 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:
Figure BDA0002782048100000131
wherein d iszFor the distance of the unmanned plane from the target position in the z-th segment, dmax＝Vmax*T0For maximum flight distance, V, of each segment of the dronemaxFor maximum flight speed, T, of the unmanned aerial vehicle0Is the time of flight of each segment. FIG. 2 is a schematic view of the flight path of the UAV divided into 4 segments, where the flight path of the UAV is divided into 4 segments of 0. T0Start flying at 0 seconds to 1. T0＝T0At second (i.e. the end of the first flight interval), the distance between the unmanned plane and the end point should be less than 3 x dmaxSo as to be at the rest 3T0Flying to the destination in time; 1. T0＝T0Start flying second to 2.T0＝2T0At the second (i.e. the end of the second flight interval), the position of the drone from the end point should be less than 2 x dmax。
(2) Speed constraint
Since the flight speed of the unmanned aerial vehicle cannot be infinite, the maximum distance of each flight of the unmanned aerial vehicle is constrained:
Figure BDA0002782048100000132
thus, the trajectory planning problem for a drone may be described as:
Figure BDA0002782048100000133
the problem P1 is a non-convex problem as can be found by performing a second derivative on P1 and analyzing the derivative.
Recording: sk，n，z＝((xk，z-xn，z)2+(yk，z-yn，z)2+(Hn-Hk)2)-1 (19)
Figure BDA0002782048100000134
Sn，z＝((xn，z-xn，z-1)2+(yn，z-yn，z-1)2)1/2 (21)
Then there are:
Figure BDA0002782048100000135
to Sn，z、Sn，j，z、Sk，n，zThe following scaling was performed:
Sn，z≥((xn，z-xn，z-1)2+(yn，z-yn，z-1)2)1/2 (23)
Figure BDA0002782048100000141
Sk，n，z≥((xk，z-xn，z)2+(yk，z-yn，z)2+(Hn-Hk)2)-1 (25)
from (19), (20) and (21), when (23), (24) and (25) take equal signs, the scaling is equivalent relaxation, i.e. P2 approaches the target minimum value. Then P2 would transition to:
Figure BDA0002782048100000142
analysis (23), (24) and (25) shows that the inequalities are non-convex inequalities, so that P3 is still a non-convex problem and cannot be directly solved. Thus, using successive convex approximations to perform the approximation, one can obtain:
Figure BDA0002782048100000143
Figure BDA0002782048100000144
Figure BDA0002782048100000145
Figure BDA0002782048100000146
wherein
Figure BDA0002782048100000147
Are respectively xk，z，xn，z，yk，z，yn，z，Sn，zThe corresponding first order taylor expansion point.
And finally, carrying out iterative solution on the P4 by giving an initial Taylor expansion point, taking the solution obtained by each iteration as a new Taylor expansion point, and obtaining the solution of the original problem P1 through multiple iterations.
Step three:
given an interference strategy cjLower level sub game
Figure BDA0002782048100000148
Is an accurate potential energy game and the game
Figure BDA0002782048100000149
There is at least one nash equilibrium. Thus, an interference strategy c is specifiedjThe potential energy function of the lower level sub-game may be configured as:
Figure BDA0002782048100000151
wherein,
Figure BDA0002782048100000152
consider the symmetry of interference between pairs of users. Using symmetry
Figure BDA0002782048100000153
And
Figure BDA0002782048100000154
the following can be obtained:
Figure BDA0002782048100000155
to sum up, phi1(an，a-n，cj) Restated as:
Figure BDA0002782048100000156
wherein,
Figure BDA0002782048100000157
and an，zIs irrelevant.
In addition to this, the present invention is,
Figure BDA0002782048100000158
wherein,
Figure BDA0002782048100000159
and an，zIs irrelevant.
Note that phi3(dn，z，z-1) Is a function of distance, withnIs irrelevant. Thus, can obtain
Figure BDA0002782048100000161
The analysis shows that the change of the utility function of the user and the change of the potential energy function caused by the fact that any user changes the strategy in a unilateral way are the same, and the sub-game of the lower layer
Figure BDA0002782048100000162
Is an accurate potential energy game.
In the anti-interference game, an interference smooth strategy and a NE strategy of a user exist to form hierarchical balance.
Gaming due to given interference policy
Figure BDA0002782048100000163
Game converted into accurate potential energy after track adjustment is completed
Figure BDA0002782048100000164
At least one pure strategy Nash equilibrium exists for accurate potential energy gaming. Thus, at a given interference strategy θ0In the game of
Figure BDA0002782048100000165
Total NE (theta)0). The smoothing strategy for interference may be expressed as
Figure BDA0002782048100000166
There is a mix of policy balance for each limited policy game, therefore
Figure BDA0002782048100000167
A hierarchical equalization in the sense of stationarity is formed.
Fig. 3 shows the trajectory of the drone user for 6 users with 3 available frequency bands having the same interference power, and it can be clearly found that all drone users are far from the interference in order to keep smooth communication when the drone user flies near the interference. Meanwhile, as the unmanned aerial vehicles interfere with each other, the positions of the unmanned aerial vehicles are also continuously adjusted. For example, in the section of X-axis coordinate 80-400m in sub-diagram a in fig. 3, drone user 2 and drone user 3 are very close to each other at 80-200m, and are very far from each other after 400 m. This occurs primarily to reduce cross-talk between users.
Fig. 4 shows the frequency usage on each segment, and it can be seen that the jammer can interfere with more users when the drone and the jammer are located closer. Sub-graph a corresponds to interference locations (800, 130), and for segments 10-18, the jammer can interfere with the most users at a time and there are available channels unused. Sub-graph b corresponds to interference locations (200, 30), with 2-7 segments each time the jammer can interfere with the most users and there are available channels unused. Sub-graph c corresponds to interference locations (1600, 275), segments 22-29, where the jammer can interfere with the most users at a time and there are channels available that are unused. This is because the user is closer to the jammer, and the user decides first after the jammer. The interference is close to the user and in order to avoid strong interference from the interference, the user gives up the interfered channel. The interference is intelligent, and after the user decides, the interference is carried out on the channels with the most users in order to maximize the utility of the interference.
Fig. 5 selects the frequencies and tracks of the users with numbers 47-48 in fig. 3 and fig. 4, so as to specifically analyze the effect of the proposed algorithm in reducing the mutual interference between users. Observing sub-graph a.1 and sub-graph a.2, it can be seen that at segment number 47, user 1 and user 5 are close in distance, but the channels they use are different. User 2, user 5 and user 6 share the same frequency and are therefore far apart. This phenomenon also exists in sub-diagrams b.1 and b.2 and sub-diagrams c.1 and c.2. This phenomenon is caused by the fact that, when channels are used, the farther the distance is, the smaller the mutual interference is, and the closer the distance is, the larger the mutual interference is.
Fig. 6 shows the user trajectory under different interference powers, sub-graphs a and b and corresponding interference powers 100w, 50w and 25w, respectively. It can be seen that the larger the interference, the further away the user is from the interference.
In fig. 7, locl, loc2, loc3 and loc4 correspond to interference positions (800, 130), (200, 30), (1600, 275) and (1000, 130), respectively. It can be seen that wherever the interference is located, the higher the interference power the greater the tie consumption, since the drone will fly further in order to contrast the interference.
As can be seen from fig. 8, the higher the maximum flying speed is, the lower the loss of the drone is, because the greater the maximum flying speed is, the greater the freedom of the drone trajectory to be adjusted is. In other words, the same-frequency mutual interference between the unmanned aerial vehicles can be reduced.
Fig. 9 is a comparison of algorithms designed for different interference powers with other algorithms. The ratio of frequency random trajectory uniformity to frequency optimization trajectory uniformity can be found, and the loss of frequency optimization is less; compared with joint solution, the joint solution has smaller loss by using frequency optimization trajectory uniformity. In summary, the proposed algorithm suffers the least loss, i.e. its best performance.
The convergence curve of the proposed optimization problem is provided in fig. 10. If the preset objective function tolerance is met or the number of iterations reaches a maximum value, the iteration is stopped. Specifically, the frequency probability is required to be more than 1-0.001 when the frequency is used for solving, the maximum iteration number is 1000, and the relative change of the two times before and after is required to be less than 10-4And the maximum number of iterations is 100. As can be seen from the figure, the convergence time of the calculation method set by the patent is less than 200 times, which shows the effectiveness of the calculation method set by the patent.
The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the 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 Un(N ═ 1, 2.. N), and the available channel set is defined as
Figure FDA0002782048090000011
cMRepresenting 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
Figure FDA0002782048090000012
cJJ 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 sectionn,z,yn,z)，xn,zDenotes the abscissa, y, of drone n in the z-th segmentn,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,yn,0),(xn,1,yn,1),(xn,2,yn,2),...,(xn,z,yn,z),...,(xn,Z,yn,Z) 1,2, Z, wherein (x)n,0,yn,0),(xn,z,yn,z),(xn,Z,yn,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 ═ X1,z,x1,z,...xn,z]If the vector formed by the vertical coordinates of all users in the z segment is Y, Y ═ Y1,z,y1,z,...yn,z]；
S13, assuming that the combination of the channel selection policies of all users is a ═ a1,a2,…,aN}，a-n＝{a0,a1,…,an-1,an+1,…,aNRepresents 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:
Figure FDA0002782048090000013
wherein p isnRepresenting the transmission power, p, of user nj' denotes the transmit power of the jammer j,
Figure FDA0002782048090000014
for the expectation that user n suffers in section zWeight and interference, dj,n,zFor the distance between user n and jammer j for the z-th drone communication pair,
Figure FDA0002782048090000021
dk,n,zfor the distance between drone communication pair user n and drone communication pair user k,
Figure FDA0002782048090000022
Figure FDA0002782048090000023
as an indicative function, an,zSelecting the channel selected in the z-th segment for user n, cj,zSelecting the channel selected in the z-th segment for the jammer, dn,z,z-1＝((xn,z-xn,z-1)2+(yn,z-yn,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:
Figure FDA0002782048090000024
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:
Figure FDA0002782048090000025
wherein Hn、HkIs the flight height, x, of the user n, ki,zFor user i on the abscissa, y, of segment zi,zFor user i in the z-th segment, xjAnd yjRespectively 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:
Figure FDA0002782048090000026
wherein d iszFor the distance of the unmanned plane from the target position in the z-th segment, dmax＝Vmax*T0For maximum flight distance, V, of each segment of the dronemaxFor 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:
Figure FDA0002782048090000031
s213, describing the trajectory planning problem of the unmanned aerial vehicle as follows:
Figure FDA0002782048090000032
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:
Sk,n,z＝((xk,z-xn,z)2+(yk,z-yn,z)2+(Hn-Hk)2)-1
Figure FDA0002782048090000033
Sn,z＝((xn,z-xn,z-1)2+(yn,z-yn,z-1)2)1/2
problem P1 was converted into:
Figure FDA0002782048090000034
s2142, to Sn,z、Sn,j,z、Sk,n,zThe following scaling was performed:
Sn,z≥((xn,z-xn,z-1)2+(yn,z-yn,z-1)2)1/2
Figure FDA0002782048090000035
Sk,n,z≥((xk,z-xn,z)2+(yk,z-yn,z)2+(Hn-Hk)2)-1；
converting P2 to:
Figure FDA0002782048090000041
s2143, approximation is performed by using continuous convex approximation, and the following is obtained:
Figure FDA0002782048090000042
Figure FDA0002782048090000043
Figure FDA0002782048090000044
Figure FDA0002782048090000045
wherein
Figure FDA0002782048090000046
And
Figure FDA0002782048090000047
are respectively xk,z、xn,z、yk,z、yn,zAnd Sn,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
Figure FDA0002782048090000048
Wherein,
Figure FDA0002782048090000049
representing a set of pairs of drone users,
Figure FDA00027820480900000410
indicating an external malicious disturbance that may be present,
Figure FDA00027820480900000411
and
Figure FDA00027820480900000412
respectively representing the set of policies for in-network users and interference,
Figure FDA00027820480900000413
the strategy adopted for the trajectory abscissa of the drone user pair,
Figure FDA00027820480900000414
strategy adopted for the trajectory ordinate of the unmanned aerial vehicle user pair, unAnd ujRespectively 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:
un,z(an,z,a-n,z,cj,z,X,Y)＝W-En,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:
Figure FDA0002782048090000051
the lower level user sub-game is defined as:
Figure FDA0002782048090000052
for interference, its goal is to achieve a maximization of the interference utility function, which is defined as:
Figure FDA0002782048090000053
the optimization problem of the interference is denoted cj＝argmaxuj(a,cj)；
The upper level disturbing sub-game is defined as:
Figure FDA0002782048090000054
wherein the strategy set is an interference channel set
Figure FDA0002782048090000055
S223, lower layer game
Figure FDA0002782048090000056
The strategy space of (A) is composed of discrete frequency strategy and continuous track, and the lower layer is
Figure FDA0002782048090000057
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
Figure FDA0002782048090000058
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 cjLower, lower-layer unmanned aerial vehicle user pair composition game
Figure FDA0002782048090000059
Figure FDA00027820480900000510
Is an accurate potential energy game and the game has at least one nash equilibrium; at the same time obtain
Figure FDA00027820480900000511
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
Figure FDA00027820480900000512
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
Figure FDA00027820480900000513
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
Figure FDA00027820480900000514
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
Figure FDA00027820480900000515
On game
Figure FDA00027820480900000516
In the presence of NE (theta)0) Calculating a stationary strategy for interference
Figure FDA00027820480900000517
Figure FDA0002782048090000061
Will be provided with
Figure FDA0002782048090000062
A hierarchical equalization in the sense of stationarity is formed.
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