  Emerging cellular technologies such as those proposed for use in 5G
communications will accommodate a wide range of usage scenarios with diverse
link requirements. This will include the necessity to operate over a versatile
set of wireless channels ranging from indoor to outdoor, from line-of-sight
(LOS) to non-LOS, and from circularly symmetric scattering to environments
which promote the clustering of scattered multipath waves. Unfortunately, many
of the conventional fading models adopted in the literature to develop network
models lack the flexibility to account for such disparate signal propagation
mechanisms. To bridge the gap between theory and practical channels, we
consider $\kappa$-$\mu$ shadowed fading, which contains as special cases, the
majority of the linear fading models proposed in the open literature, including
Rayleigh, Rician, Nakagami-m, Nakagami-q, One-sided Gaussian, $\kappa$-$\mu$,
$\eta$-$\mu$, and Rician shadowed to name but a few. In particular, we apply an
orthogonal expansion to represent the $\kappa$-$\mu$ shadowed fading
distribution as a simplified series expression. Then using the series
expressions with stochastic geometry, we propose an analytic framework to
evaluate the average of an arbitrary function of the SINR over $\kappa$-$\mu$
shadowed fading channels. Using the proposed method, we evaluate the spectral
efficiency, moments of the SINR, bit error probability and outage probability
of a $K$-tier HetNet with $K$ classes of BSs, differing in terms of the
transmit power, BS density, shadowing characteristics and small-scale fading.
Building upon these results, we provide important new insights into the network
performance of these emerging wireless applications while considering a diverse
range of fading conditions and link qualities.
