Relay Selection in Cognitive Relay Networks via Potential Game

We study the game theoretic relay selection in cognitive relay networks under the interference power constraint at the primary receivers and the total available power constraint for the secondary relays. Based on the game model proposed in [1], the problem of relay selection is formulated as a noncooperative game where the rate of cognitive relay network is used as the common utility. This game is shown to be a potential game which has at least one pure strategy Nash equilibrium (NE) and the optimal strategy profile which maximizes the rate of the cognitive relay network is a pure strategy NE of our proposed game. We prove that, under mild conditions, our proposed game can guarantee the feasibility of the pure strategy NE without the advance knowledge of the infeasible strategy profiles. In order to achieve the pure strategy NE, an iterative algorithm of relay selection is proposed. The convergence and the complexity of our designed algorithm is studied. It is shown that the proposed algorithm can obtain optimal or near optimal rate performance with low complexity.