  Providing truly ubiquitous connectivity requires development of low Earth
orbit (LEO) satellite Internet, whose theoretical study is lagging behind
network-specific simulations. In this paper, we derive analytical expressions
for the downlink coverage probability and average data rate of a massive
inclined LEO constellation in terms of total interference power's Laplace
transform in the presence of fading and shadowing, ergo presenting a stochastic
geometry based analysis. We assume the desired link to experience Nakagami m
fading, which serves to represent different fading scenarios by varying integer
m, while the interfering channels can follow any fading model without an effect
on analytical tractability. To take into account the inherent nonuniform
distribution of satellites across different latitudes, we model the LEO network
as a nonhomogeneous Poisson point process with its intensity being a function
of satellites' actual distribution in terms of constellation size, the altitude
of the constellation, and the inclination of orbital planes. From the numerical
results, we observe optimum points for both the constellation altitude and the
number of orthogonal frequency channels; interestingly, the optimum user's
latitude is greater than the inclination angle due to the presence of fewer
interfering satellites. Overall, the presented study facilitates general
stochastic evaluation and planning of satellite Internet constellations without
specific orbital simulations or tracking data on satellites' exact positions in
space.
