Omnidirectional chargability with directional antennas

Wireless Power Transfer (WPT) has received more and more attentions because of its convenience and reliability. In this paper, we first propose the notion of omnidirectional charging by which an area is omnidirectionally charged if a device with directional antennas at any position in the area with any orientation can be charged by directional chargers with power being no smaller than a given threshold. We present our empirical charging model based on field experimental results using off-the-shelf WPT products. Next, we consider the problem of detecting whether the target area achieves omnidirectional charging given a deterministic deployment of chargers. We develop piecewise constant approximation and area discretization techniques to partition the target area into subareas and approximate powers from chargers as constants. Then we propose the Minimum Coverage Set extraction technique which reduces the continuous search space to a discrete one and thereby allows a fast detection algorithm. Moreover, we consider the problem of determining the probability that the target area achieves omnidirectional charging given a random deployment of chargers. We first replace the target area by grid points on triangular lattices to reduce the search space from infinite to finite, then approximate chargers' power with reasonable relaxation, and derive an upper bound of the omnidirectional charging probability. Finally, we conduct both simulation and field experiments, and the results show that our algorithm outperforms comparison algorithms by at least 120%, and the consistency degree of our theoretical results and field experimental results is larger than 93.6%.