Joint beamforming and power allocation for cognitive MIMO systems under imperfect CSI based on game theory

The problem of joint beamforming and power allocation for cognitive multi-input multi-output systems is studied via game theory. The objective is to maximize the sum utility of secondary users (SUs) subject to the primary user (PU) interference constraint, the transmission power constraint of SUs, and the signal-to-interference-plus-noise ratio (SINR) constraint of each SU. In our earlier work, the problem was formulated as a non-cooperative game under the assumption of perfect channel state information (CSI). Nash equilibrium (NE) is considered as the solution of this game. A distributed algorithm is proposed which can converge to the NE. Due to the limited cooperation between the secondary base station (SBS) and the PU, imperfect CSI between the SBS and the PU is further considered in this work. The problem is formulated as a robust game. As it is difficult to solve the optimization problem in this case, existence of the NE cannot be analyzed. Therefore, convergence property of the sum utility of SUs will be illustrated numerically. Simulation results show that under perfect CSI the proposed algorithm can converge to a locally optimal pair of transmission power vector and beamforming vector, while under imperfect CSI the sum utility of SUs converges with the increase of the transmission power constraint of SUs.