Dynamic channel estimation and power allocation for wireless power beamforming

We consider a multi-input-single-output (MISO) system where a wireless power transmitter sends wireless power to a receiver via beamforming, taking into account the effects of channel estimation. In this paper, we address the problem of dynamically balancing the amount of time resource used for training, as well as the energy resource used for wireless power transfer, so as to maximize the amount of energy harvested at the receiver. First, the optimal length of preamble is obtained under the case when the length is optimized offline, or dynamically optimized online, depending on the channel estimate. For the latter case, the solution is obtained by solving a dynamic programming (DP) problem, which is shown to be a threshold-type policy that depends only on the channel estimate power. We further derive the optimal dynamic power allocation scheme for DP-based wireless power delivery. The analysis results are validated by numerical simulations. The scheme based on dynamic-length preamble with power allocation is shown to significantly outperform the fixed-length preamble scheme.