Non-convex power allocation games in MIMO cognitive radio networks

We consider a sensing-based spectrum sharing scenario in a MIMO cognitive radio network where the overall objective is to maximize the total throughput of each cognitive radio user by jointly optimizing both the detection operation and the power allocation over all the channels, under a interference constraint bound to primary users. The resulting optimization problems lead to a non-convex game, which presents a new challenge when analyzing the equilibria of this game. In order to deal with the non-convexity of the game, we use a new relaxed equilibria concept, namely, quasi-Nash equilibrium (QNE). We show the sufficient conditions for the existence and the uniqueness of a QNE. A primal-dual interior point optimization method that converges to a QNE is also discussed in this paper. Simulation results show that the proposed game can achieve a considerable performance improvement with respect to a deterministic game.