A Generalized Framework for Downlink Coverage Analysis in Polar-Orbit LEO Satellite

Recent advancements in stochastic geometry have enabled tractable performance analysis of Low Earth Orbit (LEO) satellite constellations by modeling satellite locations as random point processes. These approaches offer valuable insights into average coverage behavior in large-scale networks. However, most prior studies impose restrictive assumptions such as fixed user locations at the poles or homogeneous satellite distributions, thereby limiting their applicability to realistic orbital configurations. In particular, for systems such as OneWeb, where multiple polar orbits intersect at the North Pole, the impact of user latitude becomes non-negligible and necessitates a more generalized modeling approach. This paper presents an analytical framework that captures the effect of arbitrary user locations on the coverage performance of polar-intersecting multi-orbit LEO satellite networks. Leveraging a OneWeb-inspired orbital structure, we derive a closed-form expression for the visible satellite trajectory length as a function of user latitude. This expression is then used to evaluate the coverage probability under an opportunistic communication scheme that selects the best visible satellite based on instantaneous geometry. Our analysis reveals that the visible satellite trajectory length increases with user latitude, which in turn improves the likelihood of finding a viable communication link. Moreover, we demonstrate that orbit selection diversity consistently enhances coverage probability across all latitudes, even under spatial randomness. These findings provide a more flexible and location-aware analytical basis for the design and optimization of next-generation LEO networks using stochastic geometry techniques.