A Game Theoretical Anti-Jamming Beamforming Approach for Integrated Sensing and Communications Systems

In this paper, a game theoretical anti-jamming beamforming approach is investigated for the integrated sensing and communications (ISAC) systems in the presence of malicious jamming. The base station (BS) can transmit the communication signal and sense the echo of the target simultaneously. Meanwhile, the malicious jammer uses its sensing ability to adjust jamming power to implement precise jamming attack to the ISAC systems. Considering the impact of incomplete information on the anti-jamming strategy, we have developed a Bayesian Stackelberg game model, where BS acts as the leader and jammer assumes the role of the follower. In the follower sub-game, a closed-form solution is derived for the optimal jamming power. In the leader sub-game, the optimal transmit precoder is obtained by leveraging semidefinite relaxation and Gaussian randomization method. Furthermore, the proposed Stackelberg equilibrium (SE) has been proved to exist and be unique. Simulation results analyze the effect of channel uncertainty, observation error and beam pattern gain threshold on the system effectiveness, which demonstrates that the utility value of the proposed SE is significantly higher than that of the Nash equilibrium.