  We study RF-enabled wireless energy transfer (WET) via energy beamforming,
from a multi-antenna energy transmitter (ET) to multiple energy receivers (ERs)
in a backscatter communication system, such as RFID, where each ER (or RFID
tag) reflects back a portion of the incident signal to the ET (or RFID reader).
For such a system, the acquisition of the forward-channel (i.e., ET-to-ER)
state information (F-CSI) at the ET is challenging, since the ERs are typically
too energy-and-hardware-constrained to estimate or feed back the F-CSI. The ET
leverages its observed backscatter signals to estimate the backscatter-channel
(i.e., ET-to-ER-to-ET) state information (BS-CSI) directly. We first analyze
the harvested energy obtained by using the estimated BS-CSI. Furthermore, we
optimize the channel-training energy and the energy allocation weights for
different energy beams, for weighted-sum-energy (WSE) maximization and
proportional-fair-energy (PFE) maximization. For WET to single ER, we obtain
the optimal channel-training energy in a semi-closed form. For WET to multiple
ERs, the optimal WET scheme for WSE maximization is shown to use only one
energy beam. For PFE maximization, we show it is a biconvex problem, and
propose a block-coordinate-descent based algorithm to find the close-to-optimal
solution. Numerical results show that with the optimized solutions, the
harvested energy suffers slight reduction of less than 10%, compared to that
obtained by using the perfect F-CSI. Hence, energy beamforming by using the
estimated BS-CSI is promising, as the complexity and energy requirement is
shifted from the ERs to the ET.
