Enriched K-Tier Heterogeneous Satellite Networks Model with User Association Policies

In the rapid evolution of the non-terrestrial networks (NTNs), satellite communication has emerged as a focal area of research due to its critical role in enabling seamless global connectivity. In this paper, we investigate two representative user association policies (UAPs) for multi-tier heterogeneous satellite networks (HetSatNets), namely the nearest satellite UAP and the maximum signal-to-interference-plus-noise-ratio (max-SINR) satellite UAP, where each tier is characterized by a distinct constellation configuration and transmission pattern. Employing stochastic geometric, we analyze various intermediate system aspects, including the probability of a typical user accessing each satellite tier, the aggregated interference power, and their corresponding Laplace transforms (LTs) under both UAPs. Subsequently, we derive explicit expressions for coverage probability (CP), non-handover probability (NHP), and time delay outage probability (DOP) of the typical user. Furthermore, we propose a novel weighted metric (WM) that integrates CP, NHP, and DOP to explore their trade-offs in the system design. The robustness of the theoretical framework is verified is verified through Monte Carlo simulations calibrated with the actual Starlink constellation, affirming the precision of our analytical approach. The empirical findings underscore an optimal UAP in various HetSatNet scenarios regarding CP, NHP, and DOP..