  Multi-antenna or multiple-input multiple-output (MIMO) technique can
significantly improve the efficiency of radio frequency (RF) signal enabled
wireless energy transfer (WET). To fully exploit the energy beamforming gain at
the energy transmitter (ET), the knowledge of channel state information (CSI)
is essential, which, however, is difficult to be obtained in practice due to
the hardware limitation of the energy receiver (ER). To overcome this
difficulty, under a point-to-point MIMO WET setup, this paper proposes a
general design framework for a new type of channel learning method based on the
ER's energy measurement and feedback. Specifically, the ER measures and encodes
the harvested energy levels over different training intervals into bits, and
sends them to the ET via a feedback link of limited rate. Based on the
energy-level feedback, the ET adjusts transmit beamforming in subsequent
training intervals and obtains refined estimates of the MIMO channel by
leveraging the technique of analytic center cutting plane method (ACCPM) in
convex optimization. Under this general design framework, we further propose
two specific feedback schemes termed energy quantization and energy comparison,
where the feedback bits at each interval are generated at the ER by quantizing
the measured energy level at the current interval and comparing it with those
in the previous intervals, respectively. Numerical results are provided to
compare the performance of the two feedback schemes. It is shown that energy
quantization performs better when the number of feedback bits per interval is
large, while energy comparison is more effective with small number of feedback
bits.
