Game-Theoretic Joint Power Allocation and Feedback Rate Control for Cognitive MIMO Systems with Limited Feedback

In this paper, we consider a case with imperfect channel state information (CSI) in practical cognitive MIMO systems. We first analyze interference to the primary users (PUs) and then propose a joint power allocation and feedback rate control algorithm based on game theory. The utility function of each secondary user (SU) is defined as the corresponding throughput by CSI feedback minus the price as a linear function of feedback rate. Besides, the existence of the Nash equilibrium (NE) is proven. We derive the relationship between power allocation and feedback rate, and an iterative algorithm is proposed to reach the NE. Also, with the purpose of reduce interference and increase system capacity, water-filling (WF) power allocation and zero-forcing (ZF) beamforming are proposed. Simulation results shows that the proposed algorithm is better than equally distributed feedback rate scheme, obviously.