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Energy beamforming has emerged as a promising technique for enhancing theenergy transfer efficiency of wireless power transfer (WPT). However, theperformance of conventional energy beamforming may seriously degrade due to thenon-linear radio frequency (RF) to direct current (DC) conversion at energyreceivers (ERs). To tackle this issue, this letter proposes a new time-divisionenergy beamforming, in which different energy beamforming matrices (of highranks in general) are time shared to exploit the "convex-concave" shape of theRF-DC power relation at ERs. By considering a particular time duration for WPT,we maximize the minimum harvested DC energy among all ERs, by jointlyoptimizing the energy beamforming matrices and the corresponding timeallocation. In order to solve the non-convex min-DC-energy maximizationproblem, we propose an efficient solution by using the techniques ofalternating optimization and successive convex approximation (SCA). Numericalresults show that the proposed time-division energy beamforming design indeedoutperforms the conventional multi-beam and time-division-multiple-access(TDMA)-based energy transmissions.

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