The Impact of Beamforming on Energy Correlation in mm-Wave Wirelessly Powered Networks

This paper studies the spatial correlation of the energy harvested from a Poisson field of millimeter-wave (mm-wave) RF power sources which employ beamforming techniques to transfer energy directionally. In particular, each node harvests and stores energy from its nearest RF transmitter and uses it to power the information transmission. Under this setup, we show how the actual point process of nodes that successfully harvest energy looks visually and provide an accurate characterization of its density and pair correlation function theoretically. Surprisingly, it turns out that the process of the energized nodes exhibits repulsive correlations for small distances which wears off as the distance increases. Therefore, we further approximate the energized point process with a fitted beta-Ginibre point process, which is shown to provide a good approximation of the success probability in the information transmission. A useful insight is that there are energy correlations caused by the directional energy transfer, which should be reflected accurately in modeling the active mm-wave RF-powered nodes.