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

2025-10-30

AI Summary

In finite three-dimensional wireless networks, the coverage probability lacks accurate closed-form analytical solutions due to enhanced spatial dependence among nodes within bounded domains and strong coupling between link distances and interference. Method: This paper proposes the first rigorous analytical framework based on a cylindrical-domain binomial point process (BPP), innovatively decoupling the inter-node distance distribution from the interference term—overcoming inherent limitations of Poisson point process (PPP) modeling in bounded spaces. Leveraging stochastic geometry, along with convolution and derivative properties of Laplace transforms, we derive a computationally efficient and mathematically rigorous closed-form expression for the coverage probability. Results: Monte Carlo simulations validate that the proposed model achieves significantly higher accuracy than conventional PPP-based approaches in constrained 3D scenarios—including UAV, underwater, and robotic networks—with error reductions of 30%–50%. The framework thus bridges theoretical rigor and practical engineering applicability.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• Analytical characterization of coverage probability in finite 3D networks
• Modeling wireless networks using binomial point process in cylinders
• Overcoming spatial dependence and interference coupling in bounded geometries

Innovation

• Exact analytical framework for finite 3D networks
• Leveraging Laplace transforms for computational efficiency
• Generalizing to confined aerial underwater robotic networks