Game theoretic approach for joint transmit beamforming and power control in cognitive radio MIMO broadcast channels

In this paper, we present a game-theoretic approach to the problem of joint transmit beamforming and power control in cognitive radio (CR) multiple-input multiple-output broadcast channels (MIMO-BCs), where the primary users (PUs) coexist with the secondary users (SUs) and share the same spectrum. The cognitive base station (CBS) is equipped with multiantenna and transmits independent data streams to several decentralized single-antenna terminals. Our design goal is to jointly adjust the beamformers and transmission powers according to individual SINR (signal-to-interference-plus-noise ratio) requirements in order to meet SINR balancing for CR MIMO-BCs. In this context, two problems need to be solved: (1) the design beamforming must enable a balancing of the SINR among all SUs for a fixed total power of CBS and (2) the total transmission power must be minimized while satisfying a set of SINR constraints for fixed beamformers. The proposed approach is an application of separable games, where beamforming vectors are modeled as beamforming subgame and power control is modeled as power control subgame. We then use the convex theory of noncooperative game to solve the optimalization problem. Finally, we propose an iterative algorithm to reach Nash equilibrium (NE) of the joint beamforming subgame and power control subgame. Numerical results are provided to validate the optimality and the convergence of the proposed algorithm.