Max-Min Fair Energy Beamforming for Wireless Powered Communication With Non-Linear Energy Harvesting

This paper considers a max-min rate optimization problem with practical non-linear energy harvesting (NLEH) in which a multi-antenna hybrid access point transfers power to the devices via energy beamforming (BF), followed by the devices sending their data simultaneously by consuming the harvested energy. Using a sigmoid NLEH model with sensitivity, we tackle the joint energy BF and time allocation problem in two steps by solving the NLEH-aware energy BF problem for given time allocation and then solving the convex time allocation problem formulated with the aforementioned energy BF solution. We propose several iterative methods to solve the non-convex energy BF problem with and without approximation of the NLEH function. In addition, we present an asymptotic energy BF problem for a large-antenna system that can be solved at low complexity. The results show that the algorithms developed with a simple NLEH approximation provide almost the same performance with the algorithms developed with the exact NLEH function. Furthermore, the sensitivity region of the NLEH should be considered more carefully than the saturation region in the max-min rate optimization problem.