Uplink performance analysis of heterogeneous non-terrestrial networks in harsh environments: a novel stochastic geometry model

Abstract

In harsh environments, such as mountainous terrain, dense vegetation and 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 to collaborate along with satellite assistance, 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 Matérn hard-core cluster process (MHCCP) which possesses both properties of exclusivity and clustering. Through simulations, MHCCP has been validated as a more suitable model for UAV groups composed of multiple clusters, compared with traditional point processes such as Poisson point process, binomial point process, and Poisson cluster process. This is because MHCCP ensures inter-cluster repulsion while effectively capturing the clustered distribution observed in practical scenarios. Then, taking into account the influence of terrain shadows on the aerial-satellite links in low-altitude harsh environments, we derive closed-form expressions of the outage probability and average ergodic rate for the aerial-to-satellite uplink of heterogeneous NTNs. Unlike existing studies, our analysis adopts an advanced system configuration that combines beamforming with frequency division multiple access and incorporates a shadowed-Rician fading model to accurately capture signal fading under complex environmental conditions. Furthermore, we investigate link performance in the presence of co-channel interference. Monte Carlo simulations validate that the derived closed-form solutions of the outage probability and the average ergodic rate provide a precise quantitative tool for evaluating the reliability and transmission efficiency of the aerial-satellite links, offering deeper insights into system performance in complex environments.

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