Stochastic Geometry of Cylinders: Characterizing Inter-Nodal Distances for 3D UAV Networks

TL;DR

This paper develops an exact analytical framework for coverage probability in finite 3D UAV networks modeled within cylindrical regions, overcoming previous analytical challenges and enabling accurate performance evaluation.

Contribution

It introduces the first exact analytical method for finite 3D networks using a binomial point process, leveraging convolution and Laplace transform properties for efficiency.

Findings

Analytical framework verified by extensive simulations.

Significant accuracy improvements over Poisson-based models.

Framework applicable to aerial, underwater, and robotic networks.

Abstract

The analytical characterization of coverage probability in finite three-dimensional wireless networks has long remained an open problem, hindered by the loss of spatial independence in finite-node settings and the coupling between link distances and interference in bounded geometries. This paper closes this gap by presenting the first exact analytical framework for coverage probability in finite 3D networks modeled by a binomial point process within a cylindrical region. To bypass the intractability that has long hindered such analyses, we leverage the independence structure, convolution geometry, and derivative properties of Laplace transforms, yielding a formulation that is both mathematically exact and computationally efficient. Extensive Monte Carlo simulations verify the analysis and demonstrate significant accuracy gains over conventional Poisson-based models. The results generalize to any confined 3D wireless system, including aerial, underwater, and robotic networks.