  Assuming a network of infinite extent, several researchers have analyzed
small-cell networks using a Poisson point process (PPP) location model, leading
to simple analytic expressions. The general assumption has been that these
results apply to finite-area networks as well. However, do the results of
infinite-area networks apply to finite-area networks? In this paper, we answer
this question by obtaining an accurate approximation for the achievable
signal-to-interference-plus-noise ratio (SINR) and user capacity in the
downlink of a \textit{finite-area} network with \textit{a fixed number of}
access points (APs). The APs are uniformly distributed within the area of
interest. Our analysis shows that, crucially, the results of infinite-area
networks are very different from those for finite-area networks of
low-to-medium AP density. Comprehensive simulations are used to illustrate the
accuracy of our analysis. For practical values of signal transmit powers and AP
densities, the analytic expressions capture the behavior of the system well. As
an added benefit, the formulations developed here can be used in parametric
studies for network design. Here, the analysis is used to obtain the required
number of APs to guarantee a desired target capacity in a finite-area network.
