Geometric Analysis of Energy Saving for Directional Charging in WRSNs

Abstract

Wireless power transfer (WPT) enables a reliable and convenient charging paradigm. This article concerns the fundamental issue of energy saving in wireless rechargeable sensor networks (WRSNs), i.e., given a fixed number of rechargeable sensors (RSs) with their locations and charging demands, we focus on a minimal charging expenditure (MAP) problem with directional WPT to decrease the energy expenditure of the charger, on condition that the charging demands of all sensors are satisfied. In particular, we consider the anisotropic energy receiving property of RSs, which is closely related to the distance and the angle between the sensor and the charger antenna's orientation in directional WPT. We transform the MAP problem into an optimal function placement (OFA) problem, which can be geometrically analyzed in a rectangular coordinate system and is NP-hard. First, we study the OFA problem in the case of uniformly distributed sensors with identical charging demands, we develop the uniform charging strategy (UCS) to bound the total charging expenditure as Θ(1) for any number of sensors N. Based on the acquired insights, we further studied the OFA problem when the distribution of charging demands is Gaussian. We bound the total charging expenditure as Θ(1) for any number of sensors N, by developing the layered charging strategy (LCS). Extensive simulation results confirmed the performance of our design compared with two baseline algorithms. Both of the theoretical and simulations results reveal that the total energy expenditure of the charger is strongly related to the sensors' charging demands, however, is less affected by the number of sensors in the network.