  Wirelessly-powered sensor networks (WPSNs) are becoming increasingly
important in different monitoring applications. We consider a WPSN where a
multiple-antenna base station, which is dedicated for energy transmission,
sends pilot signals to estimate the channel state information and consequently
shapes the energy beams toward the sensor nodes. Given a fixed energy budget at
the base station, in this paper, we investigate the novel problem of optimally
allocating the power for the channel estimation and for the energy
transmission. We formulate this non-convex optimization problem for general
channel estimation and beamforming schemes that satisfy some qualification
conditions. We provide a new solution approach and a performance analysis in
terms of optimality and complexity. We also present a closed-form solution for
the case where the channels are estimated based on a least square channel
estimation and a maximum ratio transmit beamforming scheme. The analysis and
simulations indicate a significant gain in terms of the network sensing rate,
compared to the fixed power allocation, and the importance of improving the
channel estimation efficiency.
