Relay Selection and Discrete Power Control for Cognitive Relay Networks via Potential Game

In this paper, we study the joint relay selection and discrete power control problem for cognitive relay networks via a game-theoretic approach subject to the interference power constraint at the primary receivers and the total available power constraint for the secondary relays. The problem is formulated as a noncooperative game where the achievable rate of the cognitive relay network is used to design a common utility. This game is shown to be a potential game which possesses at least one pure strategy Nash equilibrium (NE) and an optimal strategy profile that maximizes the rate of cognitive relay network constitutes a pure strategy NE of our proposed game. We prove that under some mild conditions, our proposed game can guarantee the feasibility of a pure strategy NE without advance knowledge of infeasible strategy profiles. Moreover, we find that the price of anarchy (PoA) of our proposed game is equal to 1 under some conditions. In order to achieve the pure strategy NE, we design a centralized iterative algorithm and a decentralized stochastic learning algorithm based on learning automata. The convergence and the complexity of our designed algorithms are discussed. It is shown that our designed algorithms can achieve optimal or near-optimal rate performance with low complexity.