Combating Full-Duplex Active Eavesdropper: A Hierarchical Game Perspective

Security is an issue of paramount importance, yet is it a significant challenge for wireless communications, which becomes more intricate when facing a full duplex (FD) active eavesdropper capable of performing eavesdropping and jamming simultaneously. In this paper, we investigate the physical layer security issue in the presence of an FD active eavesdropper, who launches jamming attacks to further improve the eavesdropping. The jamming, however, also results in self-interference at the eavesdropper itself. This security problem is formulated within a hierarchical game framework where the eavesdropper acts as the leader and the legitimate user is the follower. In particular, we first investigate the follower's secrecy rate maximization problem and derive the optimal legitimate transmission strategy. Then, the leader's wiretap rate maximization is expressed as a mathematical program with equilibrium constraints (MPEC). Leveraging the concavity of the follower's problem, we transform the MPEC problem into a single-level optimization and obtain the jamming power allocation strategy by applying the primal-dual interior-point method. Moreover, we analyze the situations where only partial channel state information is available at the legitimate user and the corresponding impacts on the game. Finally, we present extensive simulation results to validate our theoretical analysis.