Optimized training design for multi-antenna wireless energy transfer in frequency-selective channel

This paper studies the optimized training design for multiple-input single-output (MISO) wireless energy transfer (WET) systems in frequency-selective channels, where the frequency-diversity and energy-beamforming gains can be both reaped by properly learning the channel state information (CSI) at the energy transmitter (ET). By exploiting channel reciprocity, a two-phase channel training scheme is proposed to achieve the diversity and beamforming gains, respectively. In the first phase, pilot signals are sent from the energy receiver (ER) over a selected subset of the available frequency sub-bands, through which the sub-band that exhibits the largest sum-power over all the antennas at the ET is determined and its index is sent back to the ER. In the second phase, the selected sub-band is further trained by the ER, so that the ET obtains an estimation for the MISO channel and implement energy beamforming. We propose to maximize the net energy harvested at the ER, which is the total harvested energy offset by that used for the two-phase channel training. The optimal training design, including the number of sub-bands trained and the energy allocated for each of the two training phases, is derived.