Outage Probability Analysis of Uplink Heterogeneous Non-terrestrial Networks: A Novel Stochastic Geometry Model

In harsh environments such as mountainous terrain, dense vegetation areas, or urban landscapes, a single type of unmanned aerial vehicles (UAVs) may encounter challenges like flight restrictions, difficulty in task execution, or increased risk. Therefore, employing multiple types of UAVs, along with satellite assistance, to collaborate becomes essential in such scenarios. In this context, we present a stochastic geometry based approach for modeling the heterogeneous non-terrestrial networks (NTNs) by using the classical binomial point process and introducing a novel point process, called Mat{\'e}rn hard-core cluster process (MHCCP). Our MHCCP possesses both the exclusivity and the clustering properties, thus it can better model the aircraft group composed of multiple clusters. Then, we derive closed-form expressions of the outage probability (OP) for the uplink (aerial-to-satellite) of heterogeneous NTNs. Unlike existing studies, our analysis relies on a more advanced system configuration, where the integration of beamforming and frequency division multiple access, and the shadowed-Rician (SR) fading model for interference power, are considered. The accuracy of our theoretical derivation is confirmed by Monte Carlo simulations. Our research offers fundamental insights into the system-level performance optimization of NTNs.