User-Centric Energy Efficiency Optimization for MISO Wireless Powered Communications

We consider a multiple-input single-output wireless powered communication network (WPCN), where the single-antenna users harvest energy from a multi-antenna access point (AP) and then transmit information back to the AP. With multiple antennas, the AP can perform energy beamforming in the downlink and exploit multiplexing- or (receive) beamforming-gain in the uplink. We consider maximizing the sum of the users' energy efficiencies (EEs) by jointly optimizing the energy beamforming of the AP, transmit powers of the users, and time allocation. We formulate EE maximization problems for both TDMA-based WPCN (T-WPCN) and SDMA-based WPCN (S-WPCN), which are non-convex because they have the sum-of-ratios objective functions. We optimally solve the former by reformulating it into an equivalent parametric problem, whose solution can be obtained by iteratively solving convex problems, while the latter is optimally solved by convexifying it using the so-called feasible set reduction scheme. We show that the T-WPCN outperforms S-WPCN when there is no minimum throughput requirement, while we can observe that the S-WPCN outperforms T-WPCN when minimum throughput requirement is high. The simulation results verify our theoretical findings and demonstrate the effectiveness of our proposed schemes.