Wireless energy transfer to a pair of energy receivers using signal strength feedback

This paper focuses on wireless energy transfer (WET) to a pair of low complex energy receivers (ER), by only utilizing received signal strength indicator (RSSI) values that are fed back from the ERs to the energy transmitter (ET). Selecting the beamformer that maximizes the total average energy transfer between the ET and the ERs, while satisfying a minimum harvested energy criterion at each ER, is studied. This is a non-convex constrained optimization problem which is difficult to solve analytically. Also, any analytical solution to the problem should only consists of parameters that the ET knows, or the ET can estimate, as utilizing only RSSI feedback values for channel estimation prohibits estimating some channel parameters. Thus, the paper focuses on obtaining a suboptimal solution analytically. It is proven that if the channels between the ET and the ERs satisfy a certain sufficient condition, this solution is in fact optimal. Simulations show that the optimality gap is negligibly small as well. Insights into a system with more than two ERs are also presented. To this end, it is highlighted that if the number of ERs is large enough, it is possible to always find a pair of ERs satisfying the sufficient condition, and hence, a pairwise scheduling policy that does not violate optimality can be used for the WET.