Stochastic Coverage Analysis for Multi-Altitude LEO Satellite Networks

While leading companies will soon have launched their low Earth orbit (LEO) constellations with different orbital characteristics, e.g., altitude and inclination, the analytical understanding of these networks with satellites flying on varying altitudes is only limited to specific network setups, e.g., polar orbits. In this letter, we derive the coverage probability of a generic multi-altitude LEO network with the satellites being distributed uniformly on inclined circular orbits at varying altitudes. To maintain tractability of our derivations, we firstly model the satellites as a binomial point process assuming their altitude to be an arbitrarily distributed random variable. Secondly, we take into account the latitude-dependent distribution of satellites over the orbits through finding the effective number of satellites. The coverage probabilities of four multi-altitude benchmark constellations are evaluated in terms of different constellation parameters as well as the user's latitude. The numerical results reveal that after a certain limit, the coverage probability improves only slightly with increasing the constellation size; therefore, the costly over-sizing of LEO networks is not always recommendable.