KKT-based iterative algorithm for beamforming in cognitive radio system

In this paper, we consider the downlink channel of multi-user multi-input single-output (MU-MISO) system in cognitive radio network, where the cognitive base station (CBS) resort to beamforming scheme to relief co-channel interference. The design criterion is to minimize the transmit power at CBS, subject to the signal-to-interference-plus-noise-ratio (SINR) constraints of cognitive users (CUs) and the interference constraints at primary users (PUs). Standard conic optimization packages can handle the problem, however, the complexity is very high and optimization packages are not always available. Basing on the karush–kuhn–tucker (KKT) conditions of the converted optimization problem, we proposed an iteration algorithm. Simulation results reveal that the proposed algorithm can converge to the optimal beamforming vectors that lead to minimum transmit power with all constraints satisfied.