Game Theoretic Joint Beamforming and Power Allocation for Cognitive MIMO Systems with Imperfect Channel State Information

This paper considers a spectrum underlay sharing cognitive radio networks composed of multiple primary users (PUs) and multiple noncooperative secondary users (SUs). With the imperfect channel state information (CSI), our objective is to maximize the total throughput of SUs, while guaranteeing the interference constraints of PUs as well as the peak transmission power constraints of SUs. We formulate the design of the SUs as a non-cooperative game, where the SUs compete with each other over the beamforming weights and transmit power made available by the PUs. Nash equilibrium (NE) is considered as the solution of this game and we analyze the existence and uniqueness of NE. Simulation results show that under the imperfect CSI the proposed algorithm has good performance and can converge to a locally optimal pair of transmission power vector and beamforming vector.