Energy beamforming with one-bit feedback

Wireless energy transfer (WET) via far-field radio signal has emerged as a new solution for powering wireless networks. To overcome the significant path loss in wireless channels, multi-antenna or multiple-input multiple-output (MIMO) techniques have been proposed to enhance the transmission efficiency and distance for WET. However, in order to reap the large energy beamforming gain in WET, acquiring channel state information (CSI) at the energy transmitter (ET) is an essential task. This task is particularly challenging for WET systems, since existing channel training and feedback methods used for communication receivers cannot be implemented at the energy receiver (ER) due to the hardware limitation. To tackle this problem, in this paper we consider a point-to-point MIMO WET system with transmit energy beamforming, and propose a new channel learning method that requires only one feedback bit from the ER to ET per feedback interval. Each feedback bit indicates the increase or decrease of the harvested energy by the ER between the present and previous intervals, which can be measured without changing the existing hardware at the ER. Based on such feedback information, the ET adjusts transmit energy beamforming in different intervals and at the same time obtains an improved estimate of the MIMO channel by applying the analytic center cutting plane method (AC-CPM). By numerical examples, we show the performance of our proposed new channel learning algorithm for MIMO WET systems in terms of convergence speed and energy transfer efficiency, as compared to existing algorithms.