Game-Theoretic Joint Power Allocation and Beamforming for Cognitive MIMO Systems with Finite Feedback

In the paper, we consider the imperfect channel state information (CSI) in practical cognitive MIMO systems. We first analyze the feedback of quantified CSI from the primary user (PU) and propose a joint power allocation and beamforming algorithm via game theory. Compared with the game under the condition of perfect CSI, new utility function and cost function are constructed under imperfect CSI. We analyze the error introduced from the uniformly quantified CSI and obtain new constraints. Besides, existence of the Nash equilibrium in case of both perfect CSI and imperfect CSI are proven. We propose a new iterative algorithm to reach the Nash equilibrium (NE). Simulation results show that the proposed algorithm can converge quickly.