  In this paper, we consider a downlink satellite communication system where
multiple satellites are uniformly distributed over a sphere at a certain
altitude. We analytically derive three things: 1) the satellite-visible
probability for a given location, which is defined as the probability that a
terminal sees at least one satellite above the minimum elevation angle, i.e., a
pre-defined elevation angle above which the terminal can be served by a
satellite, 2) the distribution of distance between the terminal and serving
satellite when the terminal is associated with the nearest satellite, and 3)
the exact expressions for the outage probability and throughput of the system.
With the derived expressions, the system throughput maximization problem is
formulated under the satellite-visibility and outage constraints. To solve the
problem, we reformulate the problem with bounded feasible sets and obtain the
optimal solution by using an exhaustive search. Using the Poisson limit
theorem, we derive approximated expressions for the satellite-visible
probability, outage probability, and system throughput, which reduce
computational complexity of performance evaluation and search time for the
optimal solution of the throughput maximization problem. Simulation results
perfectly match the derived exact expressions for the outage probability and
system throughput. It is also shown that the analytical results of the
approximated expressions are fairly close to those of the exact expressions.
