Internodal Distance Distributions for Static and Mobile Nodes in 2D/3D Wireless Networks

TL;DR

This paper develops a comprehensive analytical framework for internodal distance distributions in 2D and 3D wireless networks, considering various static and mobile deployment scenarios with geometric and mobility effects.

Contribution

It introduces a unified approach with closed-form expressions for internodal distances in multiple deployment scenarios, including mobility and geometric constraints.

Findings

Analytical expressions closely match Monte Carlo simulations.

Framework applies to both static and mobile nodes in 2D and 3D.

Beta-distribution approximations validate the analytical models.

Abstract

This letter presents a unified analytical framework for internodal distance distributions in 2D and 3D wireless networks, with nodes confined to concentric circular or spherical regions. Four deployment scenarios are considered, covering all combinations of static (uniform) and mobile (random waypoint-based) nodes. For each scenario, closed-form expressions for the internodal distance probability density functions are derived, incorporating both geometric constraints and spatial effects introduced by mobility. Equal-radius cases are also addressed. Beta-distribution approximations and Monte Carlo simulations demonstrate the accuracy and validity of the analytical results.