  This paper investigates a multi-input single-output (MISO) wireless powered
communication network (WPCN) under the protocol of harvest-then-transmit. The
power station (PS) with reliable power supply can replenish the passive user
nodes by wireless power transfer (WPT) in the downlink (DL), then each user
node transmits independent information to the sink by a time division multiple
access (TDMA) scheme in the uplink (UL). We consider the joint time allocation
and beamforming design to maximize the system sum-throughput. The semidefinite
relaxation (SDR) technique is applied to solve the nonconvex design problem.
The tightness of SDR approximation, thus the global optimality, is proved. This
implies that only one single energy beamformer is required at the PS. Then a
fast semiclosed form solution is proposed by exploiting the inherent structure.
Simulation results demonstrate the efficiency of the proposed algorithms from
the perspectives of time complexity and information throughput.
