  In this paper, we consider a finite network of unmanned aerial vehicles
(UAVs) serving a given region. Modeling this network as a uniform binomial
point process (BPP), we derive the downlink coverage probability of a reference
receiver located at an arbitrary position on the ground assuming Nakagami-$m$
fading for all wireless links. The reference receiver is assumed to connect to
its closest transmitting node as is usually the case in cellular systems. After
deriving the distribution of distances from the reference receiver to the
serving and interfering nodes, we derive an exact expression for downlink
coverage probability in terms of the derivative of Laplace transform of
interference power distribution. In the downlink of this system, it is not
unusual to encounter scenarios in which the line-of-sight (LOS) component is
significantly stronger than the reflected multipath components. To emulate such
scenarios, we also derive the coverage probability in the absence of fading
from the results of Nakagami-$m$ fading by taking the limit $m \to \infty$.
Using asymptotic expansion of incomplete gamma function, we concretely show
that this limit reduces to a redundant condition. Consequently, we derive an
accurate coverage probability approximation for this case using dominant
interferer-based approach in which the effect of dominant interferer is exactly
captured and the residual interference from other interferers is carefully
approximated. We then derive the bounds of the approximate coverage probability
using Berry-Esseen theorem. Our analyses reveal several useful trends in
coverage probability as a function of height of the transmitting nodes and the
location of reference receiver on the ground.
