  Energy beamforming has emerged as a promising technique for enhancing the
energy transfer efficiency of wireless power transfer (WPT). However, the
performance of conventional energy beamforming may seriously degrade due to the
non-linear radio frequency (RF) to direct current (DC) conversion at energy
receivers (ERs). To tackle this issue, this letter proposes a new time-division
energy beamforming, 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. By considering a particular time duration for WPT,
we maximize the minimum harvested DC energy among all ERs, by jointly
optimizing the energy beamforming matrices and the corresponding time
allocation. In order to solve the 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-division-multiple-access
(TDMA)-based energy transmissions.
