  Performances of cellular networks over {\kappa}-{\mu} shadowed fading with
long-term shadowing has been studied in the existing literature. However, the
impact of {\kappa}-{\mu} shadowed fading with instantaneous shadowing on
performances of cellular networks is unknown. Therefore, this letter analyzes
the downlink coverage probability of a Poisson network with double shadowed
fading which is composed of a large-scale fading of lognormal distribution and
{\kappa}-{\mu} shadowed fading with integer fading parameters. The closest base
station association rule without shadowing is considered. For analytical
tractability, the double shadowed fading is approximated as a weighted sum of
{\kappa}-{\mu} shadowed distributions based on the Gaussian-Hermit quadrature.
As a main theoretical result, a closed-form expression for the downlink
coverage probability of a Poisson network under double shadowed fading for the
desired signal and arbitrary fading for the interfering signals is successfully
derived. Numerical simulations reveal that the double shadowed fading provides
a pessimistic coverage on a Poisson network compared with the long-term
shadowing which is incorporated into cell selection.
