Joint Beamforming and Power Allocation Cognitive Radio Networks under Imperfect CSI

Traditional beamforming and power control algo-rithms in cognitive radio (CR) are based on the assumption of perfect channel state information (CSI) however; this may lead to performance degradation in realistic systems. In this paper, the problem of joint beamforming and power control is investigated in underlay CR networks with imperfect CSI. Our objective is to maximize the sum utility of secondary users (SUs) under the primary users (PUs) interference power constraints and the transmission power constraint of SUs. First, the joint beamforming and power control problem is formulated under game theory framework, where the SUs compete with each other over the beamforming vectors and transmission power level made available by the PUs. Moreover, the channel uncertainty is described using ellipsoid sets and the interference power constraints can be converted into robust interference power constraints. Besides, Nash equilibrium (NE) is considered as the solution of this game. Finally, simulation results show that the proposed scheme can converge to a locally optimal pair of beamforming vector and transmission power level in the presence of channel uncertainty.