Waveform design for fair wireless power transfer with multiple energy harvesting devices

In this paper, we study the waveform design in the wireless power transfer (WPT) system with multiple receivers. In the multi-receiver WPT system, due to the severe power attenuation of RF signals according to the distance and the heterogeneity in the energy harvesting capability, there exists severe unfairness in energy harvesting among receivers at different distances from the transmitter and/or different energy harvesting capabilities. Hence, alleviating unfairness in energy harvesting among receivers is one of the critical challenges in the multi-receiver WPT system. To tackle this challenge in a systematic way, we consider the fairness in our waveform design applying the α-proportional fairness. With the analysis of the rectenna circuit, we derive the output dc voltage and power of the rectifier in closed forms. Thereby, we formulate an optimization problem to design the waveform for fair WPT. The problem is shown to be a non-convex optimization problem, which is hard to solve in general. However, with proper approximations, we convert it into a convex optimization problem that can be solved easily and obtain the waveform for fair WPT. Numerical results show that our designed waveform makes receivers harvest energy fairly and can control the degree of the fairness easily.