Game Modeling And Analysis In Cognitive Radar Anti-jamming

As a new radar system,cognitive radar system is endowed with the ability to perceive and learn the external complex environment,which uses artificial intelligence technologies to analyze and infer the changing rules of the external environment.It has been gradually developed from theoretical research to practical development.In order to improve the survival and operational capabilities of radar system in the complex environments,cognitive radar can adjust its operational strategies based on the dynamic change rules of external complex environment.The multistatic form of cognitive radar system will be also the focus of the next generation radar system.Based on joint multistatic technology and cognitive learning ability,the radar system can have the advantages of wide coverage,strong abilities of target detection and interference suppression,and high intelligence.However,there are not only cooperation but also mutual interference between the multistatic cognitive radars.The reasonable resource allocation strategies can help to solve the interference problem between radars.As an effective cooperative and non-cooperative decision theory,game theory can be applied to the resource allocation of the multistatic radar system.The main work of this article is to apply different game theory schemes to the theoretical model of suppressing different interferences.The main contents of this article are as follows:1.Aiming at the power allocation problem of multiple-input multiple-output(MIMO)radar for multi-target detection,two joint power allocation and beamforming game algorithms under the optimal criterion are proposed,which one is the joint power allocation and beamforming game algorithm based on minimum variance distortionless response(MVDR)and another is the joint power allocation and beamforming game algorithm based on linearly constrained minimum variance(LCMV).These two algorithms are based on the framework of strategic non-cooperative game(SNG)between the multistatic MIMO radars.According to the selfishness of each radar in the game framework,an optimization model of minimizing the norm of transmit beamforming weight vector constrained by signal-to-interference noise ratio(SINR)is established.And the variables of the model are replaced to obtain the optimal model of minimizing the radar transmitting power.Based on the SINR constraint of the optimal power allocation model,the best radar response strategy is obtained.Furthermore,the existence and uniqueness of the Nash equilibrium(NE)of the SNG are proved,which can ensure the convergence of the two proposed game algorithms.Numerical simulation results show that the two proposed game algorithms have better interference suppression abilities and need less transmitting power than the related game algorithm,which can improve the detection abilities of the radars.2.For the game problem between multistatic MIMO radars and multiple jammers in the presence of multi-target,two supermodular game algorithms are proposed,which one is a supermodular power allocation game algorithm with fixed weight vector,and another is a joint beamforming and power allocation supermodular game algorithm.In the first algorithm,the interferences are diffi cult to be suppressed by the fixed beamforming weight vectors,so the desired utility values of the radars can only be obtained by controlling the transmitting power.In the second algorithm,the receive beamforming weight vectors are obtained by the three optimal criteria,which can suppress the cross-channel interference,radar direct wave interference and jammer interference.Finally,numerical results show the effectiveness and convergence of the two algorithms,and the interference suppression abilities of the second algorithm are more significant than that of the first algorithm.3.Aiming at the countermeasure game problem between a multistatic radar system and multiple jammers with a single target,a game algorithm of joint power allocation and beamforming is proposed.The algorithm is based on the cooperative operation mode between radars,so it does not consider the interferences between radars.In addition,it only focuses on the game relationship between radars and jammers.The strategies of both sides are the their transmit power,and the utility functions of both sides are considered.The best power response functions of both sides are obtained by theoretical deduction,and the existence and uniqueness of the game are proved,which can ensure the convergence of the proposed algorithm.Then,the minimum variance distortionless response(MVDR)criterion is used to obtain the radar receiving beamforming weight vector,which proposes the game algorithm of joint power allocation and beamforming.Simulation results verify the convergence and the interference suppression abilities of the proposed algorithm.4.Aiming at the coexistence interference problem between a multistatic MIMO radar system and a multi-user communication system,three power allocation game schemes are proposed.These three schemes use effective resource allocation strategies to reasonably schedule the working resources of the two systems,which make the two systems reach a balanced and stable state to reduce the interference effects of both sides.Firstly,the situation that the radar system is affected by signals from the base station,which constructs a supermodular power allocation game framework.According to the existence and uniqueness of pure strategic NE in the supermodular game,a supermodular power allocation game algorithm is proposed.Besides,the situation that the radar system interferes with communication system.We consider the downlink communication mode from base station to multi-user.And then,two kinds of Stackelberg game framework are established:the first is to take the radar system as the leader,the base station as the follower;the second is to take the base station as the leader,the radar system as the follower.In the frameworks of the Stackelberg games,the utility functions of the two systems are considered,respectively.Furthermore,the existence and uniqueness of the NE are verified,which can ensure the convergence of the proposed Stackelberg game algorithms.Finally,the performances of three power allocation game algorithms are compared by numerical simulation,and the results show that the performance of the first Stackelberg power allocation game algorithm is more superior than the other two algorithms.