Nearest Neighbor and Contact Distance Distribution for Binomial Point Process on Spherical Surfaces

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25 August 2020

journal article
research article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Communications Letters

Vol. 24 (12) , 2659-2663
DOI:10.1109/lcomm.2020.3019436

Abstract

This letter characterizes the statistics of the contact distance and the nearest neighbor (NN) distance for binomial point processes (BPP) spatially-distributed on spherical surfaces. We consider a setup of n concentric spheres, with each sphere Sk has a radius rk and Nk points that are uniformly distributed on its surface. For that setup, we obtain the cumulative distribution function (CDF) of the distance to the nearest point from two types of observation points: (i) the observation point is not a part of the point process and located on a concentric sphere with a radius re<rk∀k, which corresponds to the contact distance distribution, and (ii) the observation point belongs to the point process, which corresponds to the nearest-neighbor (NN) distance distribution.

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King Abdullah University of Science and Technology

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