Connectivity of Soft Random Geometric Graphs Over Annuli

TL;DR

This paper derives analytical formulas for the probability of connectivity in soft random geometric graphs formed by randomly distributed nodes in annular regions, accounting for Rayleigh fading effects, thus extending models of ad hoc networks in complex domains.

Contribution

It provides new analytical expressions for connection probability in non-convex domains with Rayleigh fading, advancing the understanding of network connectivity in such environments.

Findings

Derived formulas for connection probability in annular regions.

Extended existing models to non-convex domains.

Analyzed connectivity behavior as network density increases.

Abstract

Nodes are randomly distributed within an annulus (and then a shell) to form a point pattern of communication terminals which are linked stochastically according to the Rayleigh fading of radio-frequency data signals. We then present analytic formulas for the connection probability of these spatially embedded graphs, describing the connectivity behaviour as a dense-network limit is approached. This extends recent work modelling ad hoc networks in non-convex domains.