A Game Theoretical Anti-Jamming Beamforming Approach for Integrated Sensing and Communications Systems
Yuan Liu, Bangning Zhang, Daoxing Guo, Haichao Wang, Guoru Ding, Ning Yang, Jiangchun Gu
Abstract
In this paper, an optimal anti-jamming beamforming approach is investigated for the integrated sensing and communications (ISAC) systems in the presence of malicious jamming from the game theory perspective. 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 subgame of the follower, a closed-form solution is derived for the optimal jamming power. In the subgame of the leader, the optimal transmit precoder is obtained by leveraging semidefinite relaxation and Gaussian randomization method. Furthermore, the proposed Stackelberg equilibrium (SE) has been proven 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.