  Wireless energy transfer (WET) has attracted significant attention recently
for providing energy supplies wirelessly to electrical devices without the need
of wires or cables. Among different types of WET techniques, the radio
frequency (RF) signal enabled far-field WET is most practically appealing to
power energy constrained wireless networks in a broadcast manner. To overcome
the significant path loss over wireless channels, multi-antenna or
multiple-input multiple-output (MIMO) techniques have been proposed to enhance
the transmission efficiency and distance for RF-based WET. However, in order to
reap the large energy beamforming gain in MIMO WET, acquiring the channel state
information (CSI) at the energy transmitter (ET) is an essential task. This
task is particularly challenging for WET systems, since existing channel
training and feedback methods used for communication receivers may not be
implementable at the energy receiver (ER) due to its hardware limitation. To
tackle this problem, in this paper we consider a multiuser MIMO system for WET,
where a multiple-antenna ET broadcasts wireless energy to a group of
multiple-antenna ERs concurrently via transmit energy beamforming. By taking
into account the practical energy harvesting circuits at the ER, we propose a
new channel learning method that requires only one feedback bit from each ER to
the ET per feedback interval. The feedback bit indicates the increase or
decrease of the harvested energy by each ER between the present and previous
intervals, which can be measured without changing the existing hardware at the
ER. Based on such feedback information, the ET adjusts transmit beamforming in
different training intervals and at the same time obtains improved estimates of
the MIMO channels to ERs by applying a new approach termed analytic center
cutting plane method (ACCPM).
