A Repeated Coalition Formation Game for Physical Layer Security Aware Wireless Communications With Third-Party Intelligent Reflecting Surfaces

In this paper, we introduce third-party intelligent reflecting surfaces (TIRSs) into the physical layer security aware wireless communication system, where a central legitimate transmitter is designed to transmit secret signals to a group of legitimate receivers in the presence of the threat from an active eavesdropper (EV). Due to the channel reshaping ability of TIRSs, they are able to not only help legitimate pairs (LPs) enhance the secure transmission rate but also assist EV in improving the eavesdropping performance. Furthermore, with the potential selfishness, TIRSs may dynamically choose to ally with LPs or EV in exchange for potential benefits (e.g., payoffs). This leads to complex dynamic ally-adversary relationships among LPs, EV, and TIRSs under unpredictable wireless channel conditions. To address this issue, we formulate a repeated coalition formation game (RCFG) with dynamic decision-making to model the long-term strategic interactions among LPs, EV, and TIRSs. In particular, we theoretically analyze the existence of Nash equilibrium in the formulated RCFG, and then propose a switch operations-based coalition selection along with a deep reinforcement learning (DRL)-based approach for obtaining such an equilibrium. Simulations examine the feasibility of the proposed approach and show its superiority over counterparts.