Minimizing Charging Delay for Directional Charging

As a more energy-efficient WPT technology, directional WPT is applied to supply energy for wireless rechargeable sensor networks (WRSNs). Conventional methods that ignore anisotropic energy receiving property of rechargeable sensors cause a waste of energy. To address this issue, in this paper, we focus on minimizing the charging delay with a directional charging scheme. At first, we introduce linear constraints to improve an energy transfer model, which is verified to be practical by experiments. Then, we concern a Minimal chArging Delay with Single charger (S-MAD) problem to promote efficiency, followed by an Optimal Direction Charge with Single charger (S-ODC) solution. Through discretizing charging power and angle, we bound the performance gap of the solution to the optimal one with $\text{a}^{^{^{^{}}}}\,\,\frac {1}{1-\epsilon ^{2}}$ approximation ratio, where $\epsilon $ is the error threshold of discretization. After that, we extend the original S-MAD problem into the large scale WRSN with multiple chargers (i.e., M-MAD) and solve it by proposing M-ODC (i.e., Optimal Direction Charge with Multiple chargers (M-ODC)). Theoretical analyses are presented to exploit the feature of the proposed schemes. Finally, we demonstrate that our methods outperform the baseline methods by an average of 34.2% through simulations and test-bed experiments.