Optimal Wireless Power Transfer with Distributed Transmit Beamforming
"This paper considers the performance of wireless power
transfer (WPT) with distributed transmit beamforming (DTB) in
a narrowband setting. One or more receive nodes, each equipped
with energy harvesting and storage capabilities, provide periodic
channel state feedback to a cluster of transmit nodes, each with an
independent local oscillator, to facilitate beamforming and passband
signal alignment for efficient WPT. Without channel state
feedback, the transmit cluster can not align the passband signals at
the receivers and the receivers can only harvest incoherent power.
Since feedback improves the beamforming gain but requires the receivers
to expend energy, there is a fundamental tradeoff between
the feedback period and the energy harvesting efficiency. This paper
analyzes the optimal feedback period to maximize the weighted
mean energy harvesting rate as a function of the oscillator parameters.
An optimization problem is formulated and an explicit
method to numerically calculate the globally optimal feedback period
is developed. Numerical results are provided to confirm the
analysis and demonstrate the sensitivity of the weighted mean energy
harvesting rate with respect to the feedback period and the
DTB system parameters."