On Shadowing the κ-μ Fading Model

In this paper, we extensively investigate the way in which κ-μ fading channels can be impacted by shadowing. Following from this, a family of shadowed κ-μ fading models are introduced and classified according to whether the underlying κ-μ fading undergoes single or double shadowing. In total, we discuss three types of single shadowed κ-μ model (denoted Type Ito Type III) and three types of double shadowed κ-μ model (denoted Type I to Type III). The taxonomy of the single shadowed Type I - III models is dependent upon whether the fading model assumes that the dominant component, the scattered waves, or both experience shadowing. Although the physical definition of the examined models make no predetermination of the statistics of the shadowing process, for illustrative purposes, two example cases are provided for each type of single shadowed model by assuming that the shadowing is influenced by either a Nakagami-m random variable (RV) or an inverse Nakagami-m RV. It is worth noting that these RVs have been shown to provide an adequate characterization of shadowing in numerous communication scenarios of practical interest. The categorization of the double shadowed Type I - III 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, or 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. Similar to the single shadowed models, we provide two example cases for each type of double shadowed model by assuming that the shadowing phenomena are shaped by a Nakagami-m RV, an inverse Nakagami-m RV or their mixture. It is worth highlighting that the double shadowed κ-μ models offer remarkable flexibility as they include the κ-μ, η-μ, and the various types of single shadowed κ-μ distribution as special cases. This property renders them particularly useful for the effective characterization and modeling of the diverse composite fading conditions encountered in communication scenarios in many emerging wireless applications.