Modeling and Analysis of Non-Terrestrial Networks by Spherical Stochastic Geometry

TL;DR

This paper tackles NTN performance analysis by leveraging spherical SG to model three-dimensional, dynamic topologies with tractable interference analysis. It develops a taxonomy of spatial models (non-orbital, stochastic-orbital, fixed-orbital) and provides methodological advances (e.g., Dual Stochastic Binomial Point Process) along with mapping rules to evaluate the necessity of spherical modeling. It elaborates topology metrics (central/zenith angles, contact distances, availability) and channel models across space, air, ground, and sea links, including beamforming and fading models, while discussing routing, security, clusters, energy harvesting, and satellite-enabled positioning as advanced topics. The work demonstrates that spherical SG can yield accurate, low-complexity performance insights for NTNs, enabling informed NTN design and planning in the face of growing mega-constellations and SAGIN architectures.

Abstract

Non-terrestrial networks (NTNs) are anticipated to be indispensable in extending coverage and enabling global communication access in next-generation wireless networks. With the extensive deployment of non-terrestrial platforms, evaluating the performance of NTN-enabled communication systems becomes a challenging task. Spherical stochastic geometry (SG) is a recently proposed analytical framework that has garnered increasing attention. Due to its suitability for modeling large-scale dynamic topologies and its ability to provide an analytical framework for interference analysis and low-complexity performance evaluation, spherical SG has been widely applied in NTN performance analysis. This paper surveys the modeling and analysis of NTN networks based on spherical SG. We begin by introducing the spherical SG framework, detailing its history and development. Next, we categorize existing spherical SG models into three types based on orbital modeling methods and provide algorithm implementations for common models. Furthermore, we investigate the accuracy and necessity of spherical modeling through case studies. On the topology level, concepts such as association strategy, central angle, zenith angle, contact angle, and availability probability are introduced, with simple derivations provided. On the channel level, we detail the modeling of large-scale fading, small-scale fading, and beam gain for different channel links. Finally, we discuss several advanced topics that have not been fully explored but have strong motivation and research potential, and we predict future research directions.

Figures (10)

• Figure 1: Illustration of a space-air-ground-sea integrated network.
• Figure 2: Development of spherical SG.
• Figure 3: Structure of the survey.
• Figure 4: Schematic diagrams for constellation configurations.
• Figure 5: Diagram for the orbital-based model.