On Shadowing the $\kappa$-$\mu$ Fading Model.

In this paper, we extensively investigate the way in which $\kappa$-$\mu$ fading channels can be impacted by shadowing. Following from this, a family of shadowed $\kappa$-$\mu$ fading models are introduced, classified according to whether the underlying $\kappa$-$\mu$ fading undergoes single or double shadowing. In total six types of single shadowed $\kappa$-$\mu$ model and six types of double shadowed $\kappa$-$\mu$ model are discussed. Most importantly, the single shadowed $\kappa$-$\mu$ Type II, Type III, Type IV, and all of the double shadowed models are novel. For the single shadowed models, the taxonomy is dependent upon whether a) the fading model assumes that the dominant component, the scattered waves, or both experience shadowing and b) whether this shadowing is shaped by a Nakagami-$m$ or an inverse Nakagami-$m$ random variable (RV). The categorization of the double shadowed models is dependent upon whether a) the envelope experiences shadowing of the dominant component, which is preceded (or succeeded) by a secondary round of multiplicative shadowing, b) the dominant and scattered contributions are fluctuated by two independent shadowing processes, or c) the scattered waves of the envelope are subject to shadowing, which is also preceded (or succeeded) by a secondary round of multiplicative shadowing. In all of these models the shadowing phenomena are shaped by either a Nakagami-$m$ RV, an inverse Nakagami-$m$ RV or their mixture. It is worth highlighting that the double shadowed $\kappa$-$\mu$ models offer remarkable flexibility as they include the $\kappa$-$\mu$, $\eta$-$\mu$, and the various types of single shadowed $\kappa$-$\mu$ distribution as special cases. Lastly, we demonstrate a practical application of the double shadowed $\kappa$-$\mu$ Type I model by applying it to some field measurements obtained for device-to-device communications channels.