Joint probabilistic constrained robust beamforming and antenna selection

We propose a novel method for joint probabilistic constrained robust beamforming and antenna selection used in cognitive radio (CR) networks. Assuming complex Gaussian distributed channel state information (CSI) errors, the Bernstein-type inequalities are used to transform the no closed-form probabilistic constrained into the deterministic forms. Moreover, l1-norm is introduced as the closest convex approximation of ℓ0-norm. So, the original NP-hard optimal problem can be relaxed to as a tractable convex optimization problem. A computationally efficient and near-optimal solution is obtained by a iteratively re-weighted algorithm. Simulations show that the proposed algorithm meet prescribed service levels at a relatively small excess transmission power in a number of transmitter reduction scenarios.