Optimal training for wireless energy transfer

Wireless energy transfer (WET) is potentially a promising solution to provide convenient and reliable energy supplies for energy-constrained networks, and has drawn growing interests recently. To overcome the significant propagation loss over distance, employing multi-antennas at the energy transmitter (ET) to more efficiently direct wireless energy to desired energy receivers (ERs), termed energy beamforming, is an essential technique for WET. However, the achievable gain of energy beamforming crucially depends on the available channel state information (CSI) at the ET, which needs to be acquired practically. In this paper, we study the optimal design of one efficient channel-acquisition method for a point-to-point multiple-input multiple-output (MIMO) WET system, by exploiting the channel reciprocity based on which the ET estimates the CSI via dedicated reverse-link training from the ER. Considering the limited energy availability at the ER, the training strategy should be carefully designed so that the channel can be estimated with sufficient accuracy, and yet without consuming excessive energy at the ER. To this end, we propose to maximize the net energy at the ER, which is the total energy harvested offset by that used for channel training. The optimal training design, including the number of receive antennas to be trained, as well as the training time and power allocated, is derived. Our result shows that training helps only when the following conditions are satisfied: (i) the channel coherence time is sufficiently large; (ii) the number of antennas at the ET is large enough; and (iii) the effective signal-to-noise ratio (ESNR) is sufficiently high; otherwise, no training should be applied and isotropic energy transmission is optimal.