  Future wireless networks are expected to provide high spectral efficiency,
low hardware cost, and scalable connectivity. An appealing option to meet these
requirements is the intelligent reflective surface (IRS), which guarantees a
smart propagation environment by adjusting the phase shift and direction of
received signals. However, the composite channel of IRS-assisted wireless
networks, which is composed of a direct link and cascaded link aided by the
IRS, has made it challenging to carry out system design and analysis. This
motivates us to find tractable and accurate channel modeling methods to model
multiple types of channels. To this end, we adopt mixture Gamma distributions
to model the direct link, the cascaded link, and the mixture channel. Moreover,
this channel modeling method can be applied to various transmission
environments with an arbitrary type of fading as the underlying fading of each
link. Additionally, a unified stochastic geometric framework is introduced
based on this tractable channel model. First, we derived distributions of the
cascaded link and the mixture channel by proving multipliability and quadratic
form of mixture Gamma distributed channels. Then, we carried out a stochastic
geometric analysis of the system performance of the IRS-assisted wireless
network with the proposed channel modeling method. Our simulation shows that
the mixture Gamma distributed approximation method guarantees high accuracy and
promotes the feasibility of system performance analysis of IRS-assisted
networks with complicated propagation environments, especially with a
generalized fading model. Furthermore, the proposed analytical framework
provides positive insights into the system design regarding reliability and
efficiency.
