The Energy Correlation Coefficient and its Key Role in Wirelessly Powered Networks

Energy correlation critically affects the performance of a wirelessly powered network due to its key effect on the spatial distribution of concurrent RF-powered transmitters. This paper introduces a powerful analytical framework with foundations in stochastic geometry to characterize the energy correlation in a general wirelessly powered network. Unlike the commonly used pair correlation function (pcf)-based method, it is based on the energy correlation coefficient (ECC) and yields the energy correlation distance that gives a sufficiently small ECC. Specifically, we focus on the spatial correlation of the energy harvested from a Poisson field of RF power sources with directional beams under two cases: i) each power source points the beam in a random direction; ii) each power source points the beam to an RF-powered node located in its Voronoi cell. The results demonstrate that the energized RF-powered nodes in both cases exhibit positive correlation that is weaker than in the omni-directional case due to the introduction of energy beamforming. As an application, we provide an ECC-based method using the energy correlation distance to approximate the success probability and area spectral efficiency in the communication phase. It turns out that the ECC-based approximation matches the exact result well, and, more importantly, it can deal with the energy correlation in more general and complicated scenarios (where the pcf analysis is infeasible) due to its superior tractability.