Coordinated Multiple-Relays Based Physical-Layer Security Improvement: A Single-Leader Multiple-Followers Stackelberg Game Scheme

In this paper, a coordinated multiple-relays-based cooperative communication scheme is proposed to improve the physical-layer security. In order to benefit the relays in forwarding the signals for defending against the eavesdropping attacks, the interactions between the source and the multiple relays are modeled as a single-leader multiple-followers Stackelberg game. The source plays as the leader to coordinate the relays, including the phase of signals forwarded by the relays and the transmit power of the relays, for maximizing the secrecy capacity of the system. An algorithm is developed for the relays to find an optimal price allocation to achieve the fairness among the multiple relays based on the egalitarian welfare solution, and an approximate optimal strategy of source (i.e., phase coordinated vector and power allocation) is studied. The closed-form intercept probability of the proposed scheme is derived. Numerical studies demonstrate that the proposed scheme can greatly improve the utilities of both the source and multiple relays over that resulted from the Nash equilibrium scheme and rand scheme, which means that the relays are more willing to participate in the cooperative communication, and the source can achieve better secure transmission based on the proposed scheme. It is also shown that the proposed scheme performs much better in defending against the eavesdropping attacks than those existing schemes, for example, the single relay selection scheme, the opportunistic relay selection scheme, the optimal relay scheme, and cooperative jamming scheme.