Beamforming for MIMO cognitive radio with single primary and multiple secondary users

Beamforming for a cognitive radio system with a primary user and multiple secondary users is presented. It strives to create an interference-free environment for the primary user by cancelation of the secondary users' signals. The optimization objective is to maximize the signal-to-interference-plus-noise ratio (SINR) for the primary user through the transmit beamformers of all users and the receive beamformer of the primary user. Finding the maximum achievable SINR corresponds to maximization of the largest eigenvalue of a constrained Hermitian positive semidefinite matrix. This problem is not a convex optimization, however the upper bound, derived from the interference-free case, is known. Evolutionary algorithms are deployed for finding the beamformer solutions. In the maximum achievable SINR, the secondary users do not have beamformers at their multi-antenna receivers but instead use quasi-maximum-likelihood detection based on semidefinite relaxation (SDR). The prioritized weighted mean-square-error (PWMSE) formulation is also presented. The maximum achievable SINR solution outperforms the PWMSE in the error rate, and its feedback rate is lower because it requires only partial channel knowledge.