Robust beamforming and power splitting ratio optimization in cognitive downlink multiuser MISO networks

Abstract

In this paper, we investigate a robust beamforming and power splitting ratio (RBFPS) optimization problem with simultaneous wireless information and power transfer (SWIP-T) for the downlink multiuser multi-input-single-out (MISO) cognitive networks. Since the perfect channel state information (CSI) is difficult to obtain in practice, we consider the CSI errors follow a complex Gaussian distribution in this paper. We aim to minimize the average total transmit power at the cognitive base station (CBS) subject to the probabilistic signal-to-interference-plus-noise ratio (SINR) and energy harvesting (EH) constraints at each secondary user (SU) and probabilistic interference temperature constraint at primary receiver (PR), respectively. As the probabilistic constraints have no closed-form expression, the original optimization problem is difficult to be solved. As a solution, the probabilistic approach based on two kinds of Bernstein-type inequalities is proposed to reformulate the original non-convex problem to the form of semi-definite programming (SDP) after rank-one relaxation. We also propose the worst-case approach based on S-Procedure to solve the original problem. Simulation results are performed to demonstrate that the proposed RBFPS based on both probabilistic approach and the worst-case approach are robust to the CSI errors. In addition, the probabilistic approach is less conservative and more energy-saving.