  This work develops an analytical framework for downlink low Earth orbit (LEO)
or medium Earth orbit (MEO) satellite communications, leveraging tools from
stochastic geometry. We propose a tractable approach to the analysis of such
satellite communication systems, accounting for the fact that satellites are
located on circular orbits. We accurately incorporate this geometric property
of LEO or MEO satellite constellations by developing a Cox point process model
that jointly produces orbits and satellites on these orbits. Our work contrasts
with previous modeling studies that presumed satellite locations to be entirely
random, thereby overlooking the fundamental fact that satellites are jointly
positioned on orbits. Employing this Cox model, we analyze the network
performance experienced by users located on Earth. Specifically, we evaluate
the no-satellite probability of the proposed network and the Laplace transform
of the interference created by such a network. Using it, we compute its SIR
(signal-to-interference) distribution, namely its coverage probability. By
presenting fundamental network performance as functions of key parameters, this
model allows one to assess the statistical properties of downlink LEO or MEO
satellite communications and can thus be used as a system-level design tool to
operate and optimize forthcoming complex LEO or MEO satellite networks.
