Relay selection and discrete power control in cognitive relay networks using learning automata

This paper investigates the joint relay selection and discrete power control in cognitive relay networks through a game theoretic approach. Using the rate of cognitive relay network as the common utility, we firstly formulate the problem of the joint relay selection and discrete power control as a noncooperative game. Then, we prove that the proposed game is a potential game which possess at least one pure strategy Nash equilibrium (NE) and the optimal strategy profile which maximizes the rate of the cognitive relay network constitutes 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. Then we design a decentralized stochastic learning algorithm based on learning automata and prove that the proposed algorithm can converge to a pure strategy NE. Numerical results show that our proposed algorithm has good convergence and promising performance.