  This paper studies the transmit energy beamforming in a multi-antenna
wireless power transfer (WPT) system, in which an access point (AP) equipped
with a uniform linear array (ULA) sends radio signals to wirelessly charge
multiple single-antenna energy receivers (ERs). Different from conventional
energy beamforming designs that require the AP to acquire the channel state
information (CSI) via training and feedback, we propose a new training-free
energy beamforming approach assisted by wireless radar sensing, which is
implemented based on the following two-stage protocol. In the first stage, the
AP performs wireless radar sensing to estimate the path gain and angle
parameters of the ERs for constructing the corresponding CSI. In the second
stage, the AP implements the transmit energy beamforming based on the
constructed CSI to efficiently charge these ERs in a fair manner. Under this
setup, first, we jointly optimize the sensing beamformers and duration in the
first stage to minimize the sensing duration, while ensuring a given accuracy
threshold for parameters estimation subject to the maximum transmit power
constraint at the AP. Next, we optimize the energy beamformers in the second
stage to maximize the minimum harvested energy by all ERs. In this approach,
the estimation accuracy threshold for the first stage is properly designed to
balance the resource allocation between the two stages for optimizing the
ultimate energy harvesting performance. Finally, numerical results show that
the proposed training-free energy beamforming design performs close to the
performance upper bound with perfect CSI, and outperforms the benchmark schemes
without such joint optimization and that with isotropic transmission.
