Performance Analysis of Space-Air-Ground Integrated Networks: Stochastic Geometry Approaches

In the vision of 6th generation (6G) communication systems, the space-air-ground integrated network (SAGIN) leverages space/aerial platforms at various altitudes, such as satellites (S), high altitude platforms (HAPs), unmanned aerial vehicles (UAVs), and tethered balloons, to provide large-capacity and ubiquitous global connectivity. In this dissertation, by using stochastic geometry, we analyze the performance of SAGIN from three aspects: satellite-UAV down-link network, the space-aerial up-link and the aerial-ground up-link networks. Firstly, we investigate the down-link performance of a dual-hop cooperative satellite-UAVs communication system in which S sends information to a group of UAV cluster headers (CHs) and the CHs decode-and-forward the received signals to the UAVs uniformly distributed around them within a specific distance. The positions of the CHs follow the three-dimensional (3D) Matérn hard-core point processes type-II. We study the coverage probabilities (CPs) of the S-CH, the CH-UAV, and the end-to-end links of this network. Secondly, we analyze the up-link performance of a satellite-aerial communication system including a geostationary S, a target aircraft (TA), and a set of interference aircraft (IA). Specifically, TA sends signals to S and IA generate interference. Considering the trajectory, hierarchy, and safety distance of the aircraft's flight routes, we propose a 3D stacked Poisson line hardcore point process (PLHCP) to describe the aerial locations of IA. We also propose two approximations, namely, equi-dense model and discretization model, to overcome the intractability of the stacked PLHCP and study the up-link CP of this system. Moreover, we investigate the CP of the aviation use case with predefined flight altitudes. At last, we utilize PLHCP to model the locations of vehicles on the roads and study the performance of vehicular ad-hoc networks (VANETs) by equi-dense and discretization models. To this end, the cellular vehicle-to-infrastructure network is characterized in terms of distances distribution, association probabilities, and CP. We further extend the system to 3D cellular vehicle-to-UAV communications where the receiver is a UAV heaving in the sky and investigate its CP. Numerical results and Monte Carlo simulations are presented to validate the correctness and accuracy of our derived mathematical models for these aforementioned communication systems.