In this paper, we present a game-theoretic approach for the purpose of deriving the problem of joint beamforming\nand power control in cognitive radio (CR) multiple-input multiple-output (MIMO) broadcast channels (CR MIMO-BCs),\nwhere the primary users (PUs) coexist with the secondary users (SUs) and they share the same spectrum. The\ncognitive base station (CBS), which is equipped with multiple antennas, is capable of transmitting data to the SU�s\nmultiple-antenna receiver by employing the technology of beamforming. The proposed approach is an application of\nseparable games, which are formally stated by the subgames of beamforming and power control. Furthermore, based\non the model of noncooperative separate games, separable cost functions for the parameters of beamforming and\npower control are also proposed, showing that these cost functions are convex. Therefore, the convex theory of a\nnoncooperative game can be employed to investigate the best response strategies as well as existence of Nash\nequilibrium solutions. Finally, we propose an iterative algorithm to achieve the optimal Nash equilibrium of the\nproposed joint beamforming subgame and power control subgame. Numerical results verify both the convergence\nand the tracking properties of the proposed algorithm for variant scenarios.
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