Multi-Dimensional Modeling and Connectivity Analysis for THz Space-Air-Ground Integrated Network

Non-terrestrial networks (NTNs) are integrated with terrestrial networks to form space-air-ground integrated networks (SAGINs), providing seamless global coverage and supporting the development of the digital economy. However, when it comes to the actual design and deployment of SAGINs, the heterogeneity, self-organization, and flexibility of SAGIN pose challenges for precise modeling and quantitative analysis. In this regard, this paper proposes a multi-dimensional analysis model based on stochastic geometry for SAGIN, which considers the randomness of ground users’ (GUs) distribution and the multi-dimensional coverage characteristics of NTN nodes. The model determines the policies for GUs to access NTNs by adopting the maximum received average signal-to-interference-plus-noise ratio (SINR) association policy (AP) and the balanced satellite load AP. Specifically, we analyze the interference distribution of different links in the terahertz (THz) band and their Laplace transforms, then derive the uplink connectivity expressions of ground-to-space links with/without aerial relays under the two APs. Numerical results validate the accuracy of the theoretical model and explore the impact of APs, SINR thresholds, THz channel propagation coefficients, and aerial relay numbers on SAGIN connectivity, providing theoretical guidance for the deployment of THz SAGINs.