  Small cells deployment is one of the most significant long-term strategic
policies of the mobile network operators. In heterogeneous networks (HetNets),
small cells serve as offloading spots in the radio access network to offload
macro users (MUs) and their associated traffic from congested macrocells. In
this paper, we perform analytical analysis and investigate how the radio
propagation effects such as multipath and shadowing and small cell base station
density affect MUs' offloading to small cell network (SCN). In particular, we
exploit composite fading channels in our evaluation when an MU is offloaded to
SCN with varying small and macro cell densities in the stochastic HetNets
framework. We derive the expressions for outage probability (equivalently
success probability) of the MU in macro network and SCN for two different
cases, viz.: i) Nakagami-lognormal channel fading; ii) time-shared (combined)
shadowed/unshadowed channel fading. We propose efficient approximations for the
probability density functions of the channel fading (power) for the
above-mentioned fading distributions that do not have closed-form expressions
employing Gauss-Hermite integration and finite exponential series,
respectively. Finally, the outage probability performance of MU with and
without offloading options/services is analyzed for various settings of fading
channels.
