A Tractable Model for Wirelessly Powered Networks With Energy Correlation

In the analysis of large-scale wirelessly powered networks, the energy correlation is often ignored. While this leads to remarkably simple results for key performance metrics, it is typically not realistic and accurate. Considering the accuracy, tractability, and practicability tradeoffs, this paper introduces and promotes the Poisson disk process (PDP) as a model for the energized nodes that succeed in harvesting energy. To show that the model leads to analytically tractable results in several cases of interest, we derive its first and second moment densities, which fully characterize the PDP. Besides, we also provide tight bounds for its probability generating functional as well as its contact and nearest-neighbor distance distributions. Then, to show that the model is relevant for wirelessly powered networks-which all have positive energy correlation-we provide two approaches to fit the PDP to a given energized point process incorporating practical energy harvesting factors. Further, we derive the success probability in the information transmission phase, where the distribution of the active transmitters is modeled by a PDP. It turns out that the resulting PDP can closely model the distribution of actual energized nodes in terms of the success probability and other statistics while preserving analytical tractability.