Fine Beam Tracking Using Spatio–Temporal Interpolation in Wireless Power Transfer Systems

The use of transmit beamforming in a radio-frequency wireless power transfer (WPT) system can improve the energy transmission efficiency by concentrating the transmit power in the angle of departure (AoD). Optimal beamforming requires information regarding the AoD or the channel between the transmitter and receiver. A previously proposed WPT system continually estimates the optimal AoD using custom-designed pilot signals, which are known as beam-steered pilot signals and are transmitted periodically at every frame. Herein, we propose a spatio–temporal interpolation technique to improve the accuracy of beam tracking for such a WPT system. Specifically, thin-plate spline interpolation is adopted in the space domain to overcome the limited angular resolution of the beam-steered pilot signals in a three-dimensional channel. In the time domain, polynomial interpolation is performed to track the changing AoD during consecutive frames. Numerical results show that the proposed technique can improve the WPT efficiency as well as the mean square error performance of the beamforming weight vector.