Phase Aligned Time-Reversal for Multi-User Wireless Power Transfer Systems With Non-Linear Energy Harvesting

In this paper, we study a waveform design based on time-reversal (TR) for multi-user wireless power transfer (WPT) systems in multipath channels. The existing waveforms for WPT using the non-linear energy harvesting (EH) model have been designed in the frequency domain, whereas we design the waveform directly in the time domain by modifying TR to be suitable for WPT. In the non-linear EH model, the peak signal with the largest magnitude among the received signals is responsible for most of the harvested energy at the energy receiver (ER). Since the peak signal of TR for multi-user consists of the sum of the inter-user interference (IUI) signal and the desired signal, the phase difference between these signals can reduce the magnitude of the peak signal. Thus, we propose a novel waveform based on TR, called a phase aligned TR (PATR). The objective of the proposed PATR is to increase the harvested energy by aligning the phase between the desired signal and IUI signal as in-phase. We derive the optimal phase set to be pre-rotated for maximizing the peak signal, and design the PATR waveform by combining the modified TR and the derived optimal phase set. We prove the superior performance of the proposed PATR compared to the existing schemes in the multi-user WPT systems with the non-linear EH model by simulation. Moreover, we show that the gain for the harvested energy of the proposed PATR increases as the number of transmit antennas and the number of ERs increase.