  Modeling the locations of nodes as a uniform binomial point process (BPP), we
present a generic mathematical framework to characterize the performance of an
arbitrarily-located reference receiver in a finite wireless network. Different
from most of the prior works where the serving transmitter (TX) node is located
at the fixed distance from the reference receiver, we consider two general
TX-selection policies: i) uniform TX-selection: the serving node is chosen
uniformly at random amongst transmitting nodes, and ii) k-closest TX-selection:
the serving node is the k-th closest node out of transmitting nodes to the
reference receiver. The key intermediate step in our analysis is the derivation
of a new set of distance distributions that lead not only to the tractable
analysis of coverage probability but also enable the analyses of wide range of
classical and currently trending problems in wireless networks. Using this new
set of distance distributions, we first investigate the diversity loss due to
SIR correlation in a finite network. We then obtain the optimal number of links
that can be simultaneously activated to maximize network spectral efficiency.
Finally, we evaluate optimal caching probability to maximize the total hit
probability in cache-enabled finite networks.
