Efficacy of Hybrid Energy Beamforming With Phase Shifter Impairments and Channel Estimation Errors

Hybrid energy beamforming (HEB) can reduce the hardware cost, energy consumption, and space constraints associated with massive antenna array transmitter (TX). With a single radio frequency chain having N digitally controlled phase shifter pairs, one per antenna element, theoretically achieving the same performance as a fully digital beamforming architecture with N RF chains, this letter investigates the practical efficacy of the HEB. First adopting the proposed analog phase shifter impairments model and exploiting the channel reciprocity along with the available statistical information, we present a novel approach to obtain an accurate minimum mean-square error estimate for the wireless channel between TX and energy receiver (RX). Then, tight analytical approximation for the global optimal time allocation between uplink channel estimation and downlink energy transfer operations is derived to maximize the mean net harvested energy at RX. Numerical results, validating the analysis and presenting key design insights, show that with an average improvement of 58% over the benchmark scheme, the optimized HEB can help in practically realizing the fully digital array gains.