Low-Complexity Beamforming Design for Multi-User MIMO Cognitive Radio Systems

In this paper, we study beamforming design for multi-user MIMO cognitive radio systems, where a secondary base station transmits multiple data streams to multiple secondary users while imposing interference on primary users. We focus on the weighted sum rate (WSR) maximization problem with the sum power constraint (SPC) and the interference constraints (ICs) by optimizing the beamforming matrices. Firstly, through an analysis of the generalized utility optimization problem, we prove that the WSR maximization problem with a single quadratic constraint can be simplified to an unconstrained WSR maximization problem with adaptive covariance matrices, which can be further solved by the weighted minimal mean square error (WMMSE) method with much lower complexity. Then, we propose the modified subgradient method (MSM)-reduced (R)-WMMSE algorithm for the general scenario and the null-space projection (NSP)-R-WMMSE algorithm for the special scenario with zero ICs. Finally, theoretical and numerical results show superior performances of the proposed algorithms compared to benchmark schemes in terms of computational complexity.