Fast Charging Scheduling under the Nonlinear Superposition Model with Adjustable Phases

Wireless energy transfer has been widely studied in recent decades, with existing works mainly focused on maximizing network lifetime, optimizing charging efficiency, and optimizing charging quality. All these works use a charging model with the linear superposition, which may not be the most accurate. We apply a nonlinear superposition model, and we consider the Fast Charging Scheduling problem (FCS): Given multiple chargers and a group of sensors, how can the chargers be optimally scheduled over the time dimension so that the total charging time is minimized and each sensor has at least energy E? We prove that FCS is NP-complete and propose a 2-approximation algorithm to solve it in one-dimensional (1D) line. In a 2D plane, we first consider a special case of FCS, where the initial phases of all chargers are the same, and propose an algorithm to solve it, which has a bound. Then we propose an algorithm to solve FCS in a general 2D plane. Unlike other algorithms, our algorithm does not need to calculate the combined energy of every possible combination of chargers in advance, which greatly reduces the complexity. Extensive simulations demonstrate that the performance of our algorithm performs almost as good as the optimal algorithm.