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In this paper, a multi-antenna base station (BS) concurrently serves uplink users with harvested energy in wireless-powered communication networks (WPCNs). We minimize the average power consumption of the BS due to wirelessly charging under the quality-of-service (QoS) requirements for uplink users. Based on this, the downlink/uplink beamforming, downlink/uplink time allocation, and uplink multiuser power control are jointly designed. The non-convex problem is first solved with fixed time allocation and uplink receive beamforming via a semi-definite relaxation (SDR) approach, based on which an iterative algorithm is proposed for updating the optimal time allocation and the receive beamforming. The feasibility condition and the equivalence condition between the original and relaxed problems are analyzed. Simulation results show that the average charging power consumption of the BS is significantly reduced compared with a heuristic scheme that adopts the average user channel gain as energy beamforming in the downlink and exhausts the harvested energy for multiuser power control with zero-forcing (ZF) receive beamforming in the uplink.

Beamforming and Resource Allocation for Charging Power Minimization in Multiuser Wireless-Powered Networks