  We here introduce an extension and natural generalization of both the
\kappa-\mu$\,$shadowed and the classical Beckmann fading models: the
Fluctuating Beckmann (FB) fading model. This new model considers the clustering
of multipath waves on which the line-of-sight (LoS) components randomly
fluctuate, together with the effect of in-phase/quadrature power imbalance in
the LoS and non-LoS components. Thus, it unifies a variety of important fading
distributions as the one-sided Gaussian, Rayleigh, Nakagami-m, Rician,
\kappa-\mu, \eta-\mu, \eta-\kappa, Beckmann, Rician shadowed and the
\kappa-\mu$\,$shadowed distribution. The chief probability functions of the FB
fading model, namely probability density function, cumulative distribution
function and moment generating function are derived. The second-order
statistics such as the level crossing rate and the average fade duration are
also analyzed. These results can be used to derive some performance metrics of
interest of wireless communication systems operating over FB fading channels.
