Success Probability In Wirelessly Powered Networks With Energy Correlation

In the analysis of large-scale wirelessly powered networks, the energy correlation is often ignored for analytical tractability. Accounting for the energy correlation, this paper introduces and promotes the Poisson disk process (PDP) as a model for the active RF-powered nodes that succeed in harvesting energy. To show that the model leads to tractable results in several cases of interest, we derive the density and second moment density of the PDP and find the key property that the PDP can be fully characterized by its first- and second-order statistics. Tight bounds for its probability generating functional (PGFL) are also provided. To show that the model is relevant for wirelessly powered networks that exhibit positive energy correlation, we fit the PDP to a given energized point process incorporating practical energy harvesting factors and derive the information transmission success probability. It turns out that the resulting PDP can closely model the distribution of actual energized RF-powered nodes in terms of the success probability and other statistics while preserving analytical tractability.