Joint Waveform and Beamforming Optimization for MIMO Wireless Power Transfer

In this paper, we study a multi-sine multiple-input multiple-output (MIMO) wireless power transfer (WPT) system with the objective to increase the output DC power. We jointly optimize the multi-sine waveform and beamforming accounting for the rectenna nonlinearity, and consider two combining schemes for the rectennas at the receiver, namely DC and RF combinings. For DC combining, the waveform and transmit beamforming are optimized, as a function of the channel state information (CSI). For RF combining, the optimal transmit and receive beamformings are provided in closed form and the waveform is optimized. We also consider a practical RF combining circuit using phase shifter and RF power combiner and optimize the waveform, transmit beamforming, and analog receive beamforming adaptive to the CSI. Two types of performance evaluations, based on the nonlinear rectenna model and accurate and realistic circuit simulations, are provided. The evaluations demonstrate that the joint waveform and beamforming design can increase the output DC power by leveraging the beamforming gain, the frequency diversity gain, and the rectenna nonlinearity. It also shows that the joint waveform and beamforming design provides a higher output DC power than the beamforming-only design with a relative gain of 180% in a two-transmit antenna sixteen-sinewave two-receive antenna setup.