  This paper derives Gaussian approximation bounds for the standardized
aggregate wireless interference (AWI) in the downlink of K-tier heterogeneous
cellular networks when base stations in each tier are distributed over the
plane according to a (possibly non-homogeneous) Poisson process. The proposed
methodology is general enough to account for general bounded path-loss models
and fading statistics. The deviations of the distribution of the standardized
AWI from the standard normal distribution are measured in terms of the
Kolmogorov-Smirnov distance. An explicit expression bounding the
Kolmogorov-Smirnov distance between these two distributions is obtained as a
function of a broad range of network parameters such as per-tier transmission
power levels, base station locations, fading statistics and the path-loss
model. A simulation study is performed to corroborate the analytical results.
In particular, a good statistical match between the standardized AWI
distribution and its normal approximation occurs even for moderately dense
heterogeneous cellular networks. These results are expected to have important
ramifications on the characterization of performance upper and lower bounds for
emerging 5G network architectures.
