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

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.