Stochastic Modelling and Performance Analysis of Large LEO Constellations for Arctic Coverage

Abstract

This paper provides a thorough examination of low Earth orbit (LEO) satellite constellations as a ubiquitous solution for 6G services, particularly focusing on their performance in providing coverage over the timely Arctic region. Utilizing stochastic geometry, the spatiotemporal distributions of both satellites and users are mathematically modeled over all possible network topologies, where satellites are assumed to be uniformly distributed in circular polar orbits and user locations become uniformly distributed along circles of latitude due to Earth's rotation. This approach allows for precise analytical derivation of key performance metrics, including coverage probability and ergodic capacity, as well as tractable performance analysis without simulations. We investigate how various parameters - such as satellite altitude, user altitude, user latitude, the minimum elevation angle, the number of satellites, and service by the nth nearest satellite - impact these metrics. The findings are validated by comparisons to simulations, offering valuable insights into optimizing LEO satellite constellations for effective and reliable Arctic coverage.