Optimal Relay Placement in Two-Hop RF Energy Transfer

Recently, wireless radio frequency energy transfer (RFET) has emerged as an effective technology for prolonging lifetime of the energy-limited wireless sensor networks. However, low RFET efficiency is still a fundamental bottleneck in its widespread usage. Multi-hop RF energy transfer (MHET) can improve the RFET efficiency by deploying relay nodes that scavenge the dispersed energy and transfer it to the nearby sensor node. The efficiency of MHET is strongly influenced by the relay node's placement. To maximize the RFET efficiency for a two-hop scenario, in this paper a novel optimization model is proposed to determine the optimal relay placement (ORP) on an Euclidean x-y plane. Nontrivial tradeoff between the energy scavenged at the relay versus the effective energy delivered by the relay to the target node is investigated. Due to the nonconvex and highly nonlinear nature of the optimization problem, an α-based branch and bound algorithm has been used. The proposed optimization model is further extended by incorporating distributed beamforming to enhance the RFET efficiency. Numerical results illustrate that the proposed algorithm provides convergence to the ϵ-global optimal solution in a few iterations, and ORP provides significant energy saving over arbitrary relay positions for commercial RF energy harvesting systems.