Distributed energy beamforming with one-bit feedback

Energy beamforming (EB) is a key technique for achieving efficient radio-frequency (RF) transmission enabled wireless energy transfer (WET). By optimally designing the waveforms from multiple energy transmitters (ETs) over the wireless channels, they are constructively combined at the energy receiver (ER) to achieve an EB gain that scales with the number of ETs. However, the optimal design of transmit waveforms requires accurate channel state information (CSI) at the ETs, which is challenging to obtain in practical WET systems. In this paper, we propose a new channel training scheme to achieve optimal EB gain in a distributed WET system, where multiple separated ETs adjust their transmit phases to collaboratively send power to a single ER in an iterative manner, based on one-bit feedback from the ER per training interval which indicates the increase/decrease of the received power level from one particular ET over two preassigned transmit phases. The proposed EB algorithm can be efficiently implemented in practical WET systems even with a large number of distributed ETs, and is analytically shown to converge quickly to the optimal EB design as the number of feedback intervals per ET increases. Numerical results are provided to evaluate the performance of the proposed algorithm as compared to other distributed EB designs.