Cognitive beamforming exploiting Stiefel manifold for sum-transmit power minimization

Cognitive users need to be capable of utilizing wireless spectrum without causing harmful interference to primary users. In this paper, we consider a multi-antenna cognitive radio system with multiple secondary data streams subject to individual signal-to-noise-ratio (SNR) constraints. With cognitive beamforming, the secondary transmitter attempts to nullify the interference received at the primary receiver while minimizing the secondary sum transmit power. By exploiting the Stiefel manifold, we derive the closed-form solution for the optimal beamforming matrix that minimizes the sum transmit power while satisfying the individual SNR constraints. Numerical results are presented to show the significant power saving brought by the optimal cognitive beamforming solution.