CN108712188A - Intelligent anti-interference method based on game theory - Google Patents

Intelligent anti-interference method based on game theory Download PDF

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CN108712188A
CN108712188A CN201810512020.5A CN201810512020A CN108712188A CN 108712188 A CN108712188 A CN 108712188A CN 201810512020 A CN201810512020 A CN 201810512020A CN 108712188 A CN108712188 A CN 108712188A
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strategy
interference
dynamic
communication link
game
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CN108712188B (en
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吴明明
高玉兰
肖悦
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University of Electronic Science and Technology of China
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69—Spread spectrum techniques
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69—Spread spectrum techniques
    • H04B1/707—Spread spectrum techniques using direct sequence modulation
    • H04B1/7097—Interference-related aspects
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69—Spread spectrum techniques
    • H04B1/713—Spread spectrum techniques using frequency hopping
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
    • H04B1/69—Spread spectrum techniques
    • H04B1/713—Spread spectrum techniques using frequency hopping
    • H04B1/715—Interference-related aspects

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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Mobile Radio Communication Systems (AREA)

Abstract

The invention belongs to Communication Anti-Jamming Techniques fields, specifically the intelligent anti-interference method based on game theory.The present invention relates to expand the technologies such as frequency hopping (DS/FH), double-matrix game technology (Bimatrix Games) and Nash Equilibrium (Nash Equilibrium).The present invention is based on games theory, under the partial-band intelligence interference scene that bandwidth is dynamically adapted, the probability distribution of dynamic and intelligent Anti-interference Strategy, that is, spreading gain and the combination of Frequency Hopping Processing Gain allocation strategy is formulated for the communication link of application DS/FH technologies, to solve traditional " static state " DS/FH technologies not good enough deficiency of anti-jamming effectiveness in reply intelligence interference, reach the interference free performance more optimized.

Description

Intelligent anti-interference method based on game theory
Technical field
The invention belongs to Communication Anti-Jamming Techniques fields, specifically the intelligent anti-interference method based on game theory.This Invention is related to expanding frequency hopping (DS/FH), double-matrix game technology (Bimatrix Games Theory) and Nash Equilibrium (Nash Equilibrium) scheduling theory frame.
Background technology
Expand frequency hopping (Direct Sequence&Frequency Hopping, DS/FH) with its excellent anti-interference One of the mainstream technology for communicating anti-interference field can be become.Compared to single direct expansion, frequency-hopping mode, although expanding frequency hopping in technology reality It is now upper increasingly complex, but have greater advantages in the performances such as anti-interference ability, message capacity, transmission rate.DS/FH mixing is expanded The advantages of frequency technological synthesis DS mode signal anti-multipath jammings, good confidentiality and FH modes are difficult to track is a kind of great grinds Study carefully the hybrid spread spectrum mode of value and application value.However, traditional DS/FH technical research often assumes that enemy has " static state " Jamming exposure area and formulate corresponding counterplot and carry out correlated performance analysis.Since such Anti-Jamming Technique only considers one's own side The interference protection measure that can take and ignore " dynamic " intelligent jamming exposure area that enemy may take, the practical interference free performance of system compared with It estimates performance to be declined, to influence system communication effect.Under intelligent interference scene, hostile jammer can be according to other side's " static state " Anti-interference Strategy " dynamic " adjusts jamming exposure area, to reach optimum jamming effect.Due to pair intrinsic in communication countermeasure The incomprehensiveness of enemy's strategy, one's own side are difficult the precognition specific jamming exposure area of enemy.Therefore, traditional under intelligent interference scene to answer It is extremely difficult to good interference free performance with the DS/FH technologies of " static state " strategy.
Game theory mainly studies the interindividual interaction process with competition property, considers a in competition process Corresponding optimisation strategy is formulated in predictive behavior between body and practical action.In view of the competitiveness of communication countermeasure both sides, game theory at To analyze effective mathematical tool of dynamic Anti-interference Strategy problem under intelligent interference scene.Whether have about according to game both sides The cooperation agreement of beam force, game theoretical model can be divided into cooperative game and non-cooperative game, it is contemplated that communication countermeasure both sides' is hostile Property is competed, the present invention selects non-cooperative game model to analyze improved DS/FH Technique dynamics policy selection problem naturally. Whether have whether the impaired of the complete opposite i.e. side's income of target is equal to another party according to game both sides in non-cooperative game Acquisition income, zero-sum game and double-matrix game (nonzero sum game) can be divided into.In view of communication countermeasure both sides are with endless Complete opposite target, such as a square mesh are designated as minimizing the bit error rate, and another party's target is to minimize traffic rate, uses double-matrix Intelligent Anti-interference Strategy is analyzed in game, this so that the method for the present invention is more realistic and extend its application range.Gambling process Reach stable state at Nash Equilibrium, Nash Equilibrium is a kind of probabilistic combination of strategy so that the dynamic strategy of a side is pair The peak optimization reaction of another party's dynamic strategy, either party can not more preferably be received by unilaterally changing itself strategy with reaching Benefit.
Invention content
The present invention is based on games theory, under the partial-band intelligence interference scene that bandwidth is dynamically adapted, to apply DS/FH The communication link of technology formulates dynamic and intelligent Anti-interference Strategy, the i.e. probability point of spreading gain and the combination of Frequency Hopping Processing Gain allocation strategy Cloth, it is more excellent to reach to solve the problems, such as that traditional " static state " DS/FH technologies anti-jamming effectiveness in reply intelligence interference is not good enough Interference free performance.
Improved DS/FH intelligence anti-interference method by adjusting spreading gain and Frequency Hopping Processing Gain allocation strategy probability distribution To cope with the partial-band intelligence jamming exposure area of enemy.Specifically, it is assumed that the total bandwidth of communication link is fixed as W, and a certain kind expands Frequency gain and Frequency Hopping Processing Gain allocation strategy are represented by k*BsIt is B that=W/i, wherein i, which correspond to original signal bandwidth,s, spreading gain is Frequency hopping channel quantity when k.Partial-band intelligence jamming exposure area is represented by j*Bn=W, wherein j correspond to partial-band jamming Bandwidth is BnWhen interference band quantity.Then the purpose of jammer is to adjust j values by dynamic to maximize average interference success Rate, and intelligent Anti-interference Strategy by dynamic select i values, that is, can formulate the probability distribution of different i values to maximize average channel Capacity, with the anti-jamming effectiveness being optimal.
The anti-interference dynamic strategy select permeability of intelligence is solved based on double-matrix game, it is ensured that the dynamic strategy formulated It is the peak optimization reaction to dynamic disturbance strategy.Specifically, game both sides are respectively the communication link using DS/FH technologies and application The hostile jammer that partial-band intelligently interferes.The pure strategy collection of communication link intelligence Anti-interference Strategy is denoted as I={ i1, i2,...,in},i1<i2...<in, kth kind pure strategy ikBelong to positive integer collectionIts dynamic select strategy combination Probability distribution, i.e. mixed strategy can be denoted as xT=&#91;x1,x2,...xn]1×n,xk≥0,xT1=1；The part frequency of hostile jammer Pure strategy collection with intelligent jamming exposure area is denoted as J={ j1,j2,...jm},j1<j2...<jm, kth kind pure strategy jkBelong to In positive integer collectionThe probability distribution of its dynamic select strategy combination is denoted as yT=&#91;y1,y2,...ym]1×m, yk≥0,yT1= 1.When part interference band and frequency hopping channel frequency range used in communication link be not completely be overlapped, i.e., communication link is only by white Gaussian Influence of noise, then channel SNRs beWherein PsFor signal transmitting power fixed value, NwIndicate Gauss white noise Power sound spectrum density；When part interference band has overlapping with frequency hopping channel frequency range used in communication link, lap is remembered Bandwidth is Br, then channel SNRs beWherein NjIndicate that partial-band interfering signal power spectrum is close Degree.It is in interference pure strategyIt is with anti-interference pure strategyWhen, corresponding average interference success rate interferes gain matrix kth1 Row kth2Column elementFor
Wherein, Pu,vIndicate combination when communication link selects u-th of frequency hopping channel jammer to select v-th of interference band Probability, it is assumed that it obeys non-uniform probability distribution；Iu,vFor an integer variable, represent whether interference succeeds, such as corresponding signal-to-noise ratioLess than given thresholdIt then represents and interferes successfully, value sets 1, otherwise, is set to 0.Corresponding communication link gain matrix ElementFor
Wherein, it is contemplated that the requirement to communication quality, communication link should ensure that signal-to-noise ratio is not less than a certain threshold value.Therefore, Consider when communication link signal-to-noise ratio be less than threshold value when, receiving terminal can not correct decoding, channel capacity zero.
The object function of communication link isThe object function of hostile jammer is Intelligent Anti-interference Strategy is represented by Indicate m dimensional vector spaces.In conjunction with actual scene, Increase jamming power constraint for hostile jammer, considers hard constraints respectivelyWith loose constraint jT·y≥jave, jave Indicate the policy constraints threshold value corresponding to power constraint.Wherein hard constraints are the limitations to interfering pure strategy collection, it is desirable that are made The corresponding interference power values of pure strategy are no more than setting jamming power threshold value；Loose constraint is the pact to interfering mixed strategy Beam, it is desirable that the corresponding average interference power of mixed strategy is no more than setting average interference power threshold value.
The technical scheme is that：
S1, the communication link pure strategy collection I={ i for applying DS/FH are determined1,i2,...,in},i1<i2...<inWith The pure strategy collection J={ j of hostile jammer1,j2,...jm},j1<j2...<jm, and corresponding jamming power constraint Threshold value jave。
The gain matrix A of S2, the gain matrix B for calculating communication link and hostile jammer, foundation confrontation both sides receive assorted Mixed strategy equation group at equilibrium
The anti-interference dynamic strategy of intelligence is while meeting the optimal solution x of above-mentioned equation group*。
S3, it is derived under given Linear Constraints existing for this double-matrix game Nash Equilibrium Solution according to S2 equation groups Necessary and sufficient condition can obtain necessary and sufficient condition such as following table using KKT conditions
TABLE I
Wherein, α, v, β are the Lagrangian multipliers corresponding to various boundary conditions, and R indicates set of real numbers.Meet TABLE The mixed strategy x of I*Intelligent Anti-interference Strategy as under communication link reply dynamic disturbance.If there is no meet necessary and sufficient condition Feasible solution then return to S1, adjust pure strategy collection or constraints；Otherwise, it carries out in next step.
S4, for double-matrix gambling processEstablish corresponding quadratic programming equation
Wherein, (x*,y*) beNash Equilibrium Solution, and if only if there are parameter v*>=0, α*,β*∈ R make (x*,y*,v*, α*,β*) be quadratic programming equation globally optimal solution when set up.
S5, the quadratic programming tool box (Quadprog Toolbox) based on MATLAB, the quadratic programming that input S4 is established Equation exports intelligent Anti-interference Strategy.Transmitting terminal designs dynamic strategy DS/FH transmission schemes accordingly.
Technical scheme of the present invention is answered by the dynamically allocation strategy of the spreading gain of adjustment DS/FH and Frequency Hopping Processing Gain To implementing the intelligence band interference of dynamic disturbance strategy, the correspondence between double-matrix game and quadratic programming equation is established To solve corresponding intelligent Anti-interference Strategy.The beneficial effects of the invention are as follows：Based on game theory, analysis establishes communication countermeasure both sides' Double-matrix betting model designs dynamic strategy DS/FH transmission schemes, solves traditional approach performance when coping with dynamic disturbance strategy Not good enough problem so that system rejection to disturbance performance reaches.
Description of the drawings
Fig. 1 is communication link ergodic capacity and snr threshold relationship analogous diagram, wherein J under various boundary conditionss Indicate hard constraints jamming power threshold value, JrIndicate loose constraint jamming power threshold value；Fig. 2 is disturbance type algorithms of different Lower communication link performance comparison, " MDP " indicate that communication link uses non intelligent strategy, " BGT " to indicate that communication link uses intelligence Strategy, " Random attack " indicate that jammer uses non intelligent jamming exposure area, " Intelligent attack " to indicate interference Machine uses intelligent jamming exposure area.
Specific implementation mode
Below in conjunction with the accompanying drawings and example, detailed description of the present invention technical solution：
In this example, if available total bandwidth W=200M；Communication link fixed transmission signal power value Ps=0.1W；Enemy Interfering signal power spectrum density N is fixed to jammerj=10-8W/HZ；The power spectral density N of channel white Gaussian noisew=10- 10W/HZ, communication link pure strategy collection I={ 2,4,6,8,10,12 }；Jammer pure strategy collection J={ 2,4,6,8,10,12 }.
It is as follows：
Step 1：Given parameters are inputted, in snr thresholdUnder calculate separately the lower communication link of Different Strategies combination and receive Beneficial matrix elementAnd hostile jammer gain matrix elementBoth sides gain matrix A and B are obtained, foundation is received assorted equal The equation group of Heng Chu；
Step 2：Necessary and sufficient condition existing for Nash Equilibrium Solution is derived according to TABLE I, verification institute meets condition then to parameter It carries out in next step；
Step 3：According to the double-matrix gambling process of given parameters, corresponding quadratic programming equation group is established, and change For canonical form；
Step 4：The quadratic programming problem for the canonical form that step 3 obtains is input to the quadratic programming tool box of MATLAB In, solution obtains intelligent Anti-interference Strategy；
Step 5：Transmitting terminal designs dynamic strategy DS/FH transmission schemes according to step 4 solving result.
By analogous diagram as can be seen that under disturbance power constraint and different snr threshold constraintss, it is based on No matter the ergodic capacity under the interference of reply intelligence or non intelligent interference is than tradition for the intelligent anti-interference method of game theory Non intelligent anti-interference method want high, illustrate that the present invention improves the anti-jamming effectiveness of DS/FH systems.

Claims (1)

1. the intelligent anti-interference method based on game theory, which is characterized in that include the following steps：
S1, the communication link pure strategy collection I={ i for applying DS/FH technologies are determined1,i2,...,in}, 1<i2...<in, the K kind pure strategies ikBelong to positive integer collectionThe probability distribution of its dynamic select strategy combination, i.e. mixed strategy are denoted as xT=&#91;x1, x2,...xn]1×n,xk≥0,xT1=1；
The pure strategy collection J={ j of hostile jammer1,j2,...jm},j1<j2...<jm, kth kind pure strategy jkBelong to just Set of integersThe probability distribution of its dynamic select strategy combination is denoted as yT=&#91;y1,y2,...ym]1×m, yk≥0,yT1=1；
And corresponding jamming power constraint threshold value jave；
The gain matrix A of S2, the gain matrix B for calculating communication link and hostile jammer establish confrontation both sides' Nash Equilibrium The mixed strategy equation group at place
The anti-interference dynamic strategy of intelligence is while meeting the optimal solution x of above-mentioned equation group*；
S3, it derives to fill existing for this double-matrix game Nash Equilibrium Solution under given Linear Constraints according to S2 equation groups and want It is as follows can to obtain necessary and sufficient condition using KKT conditions for condition：
Wherein, α, v, β are the KKT multipliers corresponding to various boundary conditions, and R indicates set of real numbers；Meet the mixed of above-mentioned necessary and sufficient condition Close strategy x*Intelligent Anti-interference Strategy as under communication link reply dynamic disturbance；If there is no meet the feasible of necessary and sufficient condition Xie Ze returns to S1, adjusts pure strategy collection or constraints；Otherwise, it carries out in next step；
S4, for double-matrix gambling processEstablish corresponding quadratic programming equation
Wherein, (x*,y*) beNash Equilibrium Solution, and if only if there are parameter v*>=0, α*,β*∈ R make (x*,y*,v*,α*,β*) For quadratic programming equation globally optimal solution when set up；
S5, the quadratic programming tool box based on MATLAB, the quadratic programming equation that input S4 is established, the anti-interference plan of output intelligence Slightly, transmitting terminal designs dynamic strategy DS/FH transmission schemes accordingly.
CN201810512020.5A 2018-05-25 2018-05-25 Intelligent anti-interference method based on game theory Expired - Fee Related CN108712188B (en)

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CN115022952A (en) * 2022-08-09 2022-09-06 中国人民解放军国防科技大学 Satellite communication power resource allocation method under confrontation condition

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CN115022952A (en) * 2022-08-09 2022-09-06 中国人民解放军国防科技大学 Satellite communication power resource allocation method under confrontation condition

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