Optimal and Near-Optimal Policies for Wireless Power Transfer Considering Fairness

Radio frequency wireless power transfer (RF- WPT) is an emerging technology that enables transferring energy from a power source to wireless devices over the air. In this paper, we aim at finding {the optimal policy for wireless power transfer (WPT) from an energy access point} (E-AP) to multiple energy receivers (E-Rs) that maximizes the wireless power transfer efficiency. For this purpose, in the first part of the paper, we formulate the problem of maximizing the total average received power of the E-Rs subject to the average and peak power constraints of the E-AP. The formulated problem is a non-convex stochastic optimization problem, and is highly non-trivial. Using some stochastic optimization techniques, we tackle the aforementioned challenges to solve the problem and derive a closed-form expression for the optimal solution, which requires the CSI distribution. In addition, we propose a heuristic algorithm that does not require any explicit information on the CSI distribution. We prove that the proposed algorithm attains a near-optimal solution within a guaranteed gap to the optimal solution. In the second part of the paper, we focus on the problem of considering fairness among the E-Rs and propose two fair policies, namely Max- Min Fair (MMF) policy and Quality-of-service- aware Proportional Fair (QPF) policy. MMF policy maximizes the minimum received power among the E-Rs. Moreover, QPF policy balances the received power levels of different E-Rs as much as possible, while guaranteeing the required minimum QoS for each of them. Various numerical results demonstrate the significant performance of the proposed solutions.