Energy Beamforming With One-Bit Feedback

Multi-antenna or multiple-input multiple-output (MIMO) techniques are appealing to enhance the transmission efficiency and range for radio frequency (RF) signal enabled wireless energy transfer (WET). In order to reap the energy beamforming gain in MIMO WET, acquiring the channel state information (CSI) at the energy transmitter (ET) is an essential task. This task is particularly challenging, since existing channel training and feedback methods used for communication receivers may not be implementable at the energy receiver (ER) due to its hardware limitation. To tackle this problem, we consider in this paper a multiuser MIMO WET system, and propose a new channel learning method that requires only one feedback bit from each ER to the ET per feedback interval. Specifically, each feedback bit indicates the increase or decrease of the harvested energy by each ER in the present as compared to the previous intervals, which can be measured without changing the existing structure of the ER. Based on such feedback information, the ET adjusts transmit beamforming in subsequent training intervals and at the same time obtains improved estimates of the MIMO channels to different ERs by applying an optimization technique called analytic center cutting plane method (ACCPM). For the proposed ACCPM based channel learning algorithm, we analyze its worst-case convergence, from which it is revealed that the algorithm is able to estimate multiuser MIMO channels simultaneously without reducing the analytic convergence speed. Also, we provide extensive simulations to show its performances in terms of both convergence speed and energy transfer efficiency.