Wireless Power Transfer With Hybrid Beamforming: How Many RF Chains Do We Need?

Wireless power transfer (WPT) via dedicated radio frequency (RF) transmission is an appealing technology to provide cost-effective energy supply to low-power devices in the future era of Internet of Things. To achieve efficient power delivery over moderate distance, WPT usually relies on highly directional power transmission from the energy transmitter (ET) to the energy receiver (ER). To this end, the ET needs to be equipped with a large number of antennas and employ adaptive energy beamforming to flexibly control the energy focusing directions to the ER based on the multipath channels between them. However, this renders the conventional fully digital beamforming with one dedicated RF chain for each transmit antenna too costly, in terms of both hardware implementation and energy consumption. To overcome this issue, we study in this paper, a new WPT system based on the hybrid analog or digital beamforming technique, where the number of RF chains is in general significantly less than that of transmit antennas. We first show that for a general point-to-point multiple-input multiple-output WPT system over frequency-selective channels, hybrid beamforming is able to achieve the optimal performance as the fully digital beamforming, as long as the number of RF chains at the ET is no less than twice the number of sub-bands used or twice the number of channel paths. Furthermore, for the special cases of line-of-sight channel or multiple-input single-output WPT, the required number of RF chains can be further reduced to equal the number of channel paths only. Finally, for the scenarios when the given number of RF chains is insufficient to achieve the fully digital beamforming performance, we propose efficient algorithms for the hybrid beamforming design to maximize its efficiency. Numerical results are provided to validate our analytical results and demonstrate the effectiveness of the proposed hybrid beamforming design.