  The low-earth-orbit (LEO) satellite network with mega-constellations can
provide global coverage while supporting the high-data rates. The coverage
performance of such a network is highly dependent on orbit geometry parameters,
including satellite altitude and inclination angle. Traditionally,
simulation-based coverage analysis dominates because of the lack of analytical
approaches. This paper presents a novel systematic analysis framework for the
LEO satellite network by highlighting orbit geometric parameters. Specifically,
we assume that satellite locations are placed on a circular orbit according to
a one-dimensional Poisson point process. Then, we derive the distribution of
the nearest distance between the satellite and a fixed user's location on the
Earth in terms of the orbit-geometry parameters. Leveraging this distribution,
we characterize the coverage probability of the single-orbit LEO network as a
function of the network geometric parameters in conjunction with small and
large-scale fading effects. Finally, we extend our coverage analysis to
multi-orbit networks and verify the synergistic gain of harnessing multi-orbit
satellite networks in terms of the coverage probability. Simulation results are
provided to validate the mathematical derivations and the accuracy of the
proposed model.
