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We consider a point-to-point multiple-input-single-output (MISO) system where a receiver harvests energy from a transmitter. To achieve high-efficiency wireless power transfer (WPT), the transmitter performs energy beamforming by using an instantaneous channel state information (CSI). The CSI is estimated at the receiver by training via a preamble and fed back to the transmitter. In this paper, we address the key challenge of balancing the time resource used for channel estimation and WPT to maximize the harvested energy and also investigate the allocation of energy resource used for WPT. First, we consider the general scenario where the preamble length is allowed to vary dynamically depending on channel conditions. The optimal preamble length is obtained online by solving a dynamic programming (DP) problem. The DP problem is proved to reduce to an optimal stopping problem. The optimal policy is then shown to depend only on the channel estimate power. Next, we consider the scenario in which the preamble length is fixed by an offline optimization. Furthermore, we derive the optimal power allocation schemes. For the dynamic-length-preamble scenario, the power is allocated according to both the optimal preamble length and the channel estimate power, while for the fixed-length-preamble scenario, the power is allocated according to only the channel estimate power. By numerical simulations, our results show that with optimal power allocation, the energy harvested by using the optimized fixed-length preamble is close to that harvested by using a dynamic-length preamble, hence allowing a low-complexity yet close-to-optimal WPT system to be implemented in practice.
Yang et al. (Wed,) studied this question.