Robust downlink beamforming design for multiuser MISO communication system with SWIPT

In this paper, a robust downlink beamforming design for simultaneous wireless information and power transfer (SWIPT) in a multiuser MISO communication system is proposed. Our design is to maximize the minimum harvested energy among the multi-antenna energy receivers (ERs) while guaranteeing the secure communication requirement at the information receiver (IR) by optimizing the transmit beamforming vectors and power splitting ratio jointly. The considered max-min fair problem is non-convex and hard to tackle. Using the semi-definite relaxation (SDR) technique, we solve this problem by carrying out a one-dimensional search which refer to the solution of a series of semi-definite programs (SDPs). Also, we provide the closed-form solution based on Lagrange duality and prove that the utilized SDR is tight. Simulation results show our proposed robust scheme is more efficient than the conventional isotropic scheme in terms of energy harvesting.