Feedback rate optimization in receiver-coordinated distributed transmit beamforming for wireless power transfer

This paper considers the combination of receiver-coordinated distributed transmit beamforming with wireless power transfer in a narrowband wireless communication system. A single receiver measures the channel states of two or more independent transmit nodes and provides feedback to the transmitters to facilitate beamforming and passband signal alignment at the receiver. The receive node is equipped with energy harvesting and storage devices which can harvest and store the beamforming energy for future utilization. Since feedback improves the beamforming gain but requires the receiver to expend energy, there is an inherent tradeoff between the feedback rate and the efficiency of the energy harvesting at the receiver. This paper analyzes the optimal feedback rate to maximize the amount of energy harvested by the receive node per unit of time. Analysis shows that there always exists a unique optimal feedback rate for the system. Numerical results are also provided to confirm the analysis and demonstrate the effect of the feedback rate on the mean energy harvesting rate.