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This paper studies a multi-user multiple-input single-output (MISO) downlink system for simultaneous wireless information and power transfer (SWIPT), in which a set of single-antenna mobile stations (MSs) receive information and energy simultaneously via power splitting (PS) from the signal sent by a multi-antenna base station (BS). We aim to minimize the total transmission power at BS by jointly designing transmit beamforming vectors and receive PS ratios for all MSs under their given signal-to-interference-plus-noise ratio (SINR) constraints for information decoding and harvested power constraints for energy harvesting. First, we derive the sufficient and necessary condition for the feasibility of our formulated problem. Next, we solve this non-convex problem by applying the technique of semidefinite relaxation (SDR). We prove that SDR is indeed tight for our problem and thus achieves its global optimum. Finally, we propose two suboptimal solutions of lower complexity than the optimal solution based on the principle of separating the optimization of transmit beamforming and receive PS, where the zero-forcing (ZF) and the SINR-optimal based transmit beamforming schemes are applied, respectively.

Joint Transmit Beamforming and Receive Power Splitting for MISO SWIPT Systems