Placing Wireless Chargers with Multiple Antennas

Abstract

This paper studies the problem of Wireless ChArger PlacemeNt with Multiple (Directional) Antennas (WANDA). Given a set of wireless chargers wherein each charger is equipped with multiple directional antennas and a set of wireless rechargeable sensors, determining the chargers' positions and the antennas' orientations, such that the overall charging utility is maximized. To address WANDA, we first present a piecewise constant function to approximate the nonlinear relationship between charging power and charging distance. Then, we propose an area discretization technique to reduce the infinite solution space to a limited one without performance loss. Next, we present approximation algorithms for both Relative Orientation Fixed (WANDA-ROF) and Relative Orientation Unfixed (WANDA-ROU) situations. For WANDA-ROF, we propose a Maximum Coverage Set extraction method that transforms WANDA-ROF into the problem of maximizing a monotone submodular function subject to a partition matroid constraint and then present a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1/2 -\epsilon$</tex> approximation algorithm. For WANDA-ROU, we construct a candidate position set for each charger to limit the searching space. Then, we propose a novel two-level submodular optimization scheme to address it, which achieves an approx-imation ratio of 1/6 - ∊. Simulation and experimental results show that our algorithms outperform comparison algorithms by at least 22%.