Distance Distributions Between Nodes in Concentric Disk-Annulus or Sphere-Shell Regions

TL;DR

This paper derives analytical formulas for the probability density of distances between nodes in concentric disk or sphere regions, aiding performance analysis in wireless systems.

Contribution

It provides the first closed-form expressions for node distance distributions in heterogeneous concentric geometries, considering various node placement scenarios.

Findings

Closed-form expressions for distance PDFs in concentric regions.

Analytical tools for performance evaluation in wireless networks.

Applicable to scenarios with static or mobile nodes.

Abstract

This letter derives closed-form expressions for the probability density function of the distance between two nodes located in heterogeneous concentric geometries, namely a disk or sphere and a surrounding annulus or spherical shell. Two scenarios are considered: (i) both nodes are independently distributed in different regions, disk or sphere and annulus or shell, and (ii) one node is static in the outer region while the other follows the stationary distribution of the random waypoint model in the inner region. The resulting expressions provide a tractable analytical tool for performance evaluation in concentric wireless regions.