The Energized Point Process as a Model for Wirelessly Powered Communication Networks

The spatial correlation of the RF-powered nodes that harvest enough energy plays a critical role in the performance evaluation of large-scale wirelessly powered communication networks (WPCNs). However, such correlation is mostly ignored in the literature for analytical tractability. In this paper, we explore the correlation and propose a new point process, named energized point process (EPP), as a model for the RF-powered nodes that succeed in harvesting energy. Specifically, we focus on the spatial correlation of the energy harvested from a Poisson field of RF power sources. Two energy harvesting models with different degrees of practicality are introduced to concretize the EPP with the aim of visualizing the point process of the energized nodes and characterizing its density and pair correlation function theoretically. It turns out that for both models the resulting process exhibits positive correlation. With the first-and second-order statistics of the EPP, we use a fitted Poisson cluster process to provide good approximations of the success probability and area spectral efficiency in the information transmission phase. Numerical results investigate the impacts of the key parameters related to the energy transfer on the spatial correlation of the EPP and the communication performance. An important conclusion is that although the Poisson point process has been so far the most widely used model for wirelessly powered networks, it is inadequate due to the positive energy correlation.