Time-Division Energy Beamforming for Multiuser Wireless Power Transfer with Non-Linear Energy Harvesting

Energy beamforming has emerged as a promising technique for enhancing the energy transfer efficiency of radiofrequency (RF) enabled wireless power transfer (WPT). However, the performance of conventional energy beamforming may seriously degrade due to the non-linear RF to direct current (DC) conversion at energy receivers (ERs). To tackle this issue, this letter proposes a new time-division energy beamforming scheme, in which different energy beamforming matrices (of high ranks in general) are time shared to exploit the “convex-concave” shape of the RF-DC power relation at ERs. In particular, we maximize the minimum harvested DC energy among all ERs, by jointly optimizing the energy beamforming matrices and the corresponding time allocation subject to a given charging time duration (e.g., a second). To solve the formulated non-convex min-DC-energy maximization problem, we propose an efficient solution by using the techniques of alternating optimization and successive convex approximation (SCA). Numerical results show that the proposed time-division energy beamforming design indeed outperforms the conventional multi-beam and time-divisionmultiple-access (TDMA)-based energy transmissions.