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.
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