## 1 Introduction  
In the past decades, how to model wireless fading channels accurately has been an important and inevitable topic in the research of conventional and emerging wireless communication systems, such as cellular networks, wearable communications, and vehicular wireless networks. Generally, the received signals of wireless transmission undergo either small-scale (multipath) fading or large-scale (shadowing) fading, or even the composite effects of both. For small-scale fading, some classical fading models have been reported in [1], namely the Rayleigh, the Rice, the Nakagami-m, the Weibull, and so on. To accurately characterize the envelope fluctuation of the received signals and better fit empirical data encountered in some emerging wireless applications, some more general and sophisticated versions of the above multipath fading models have also been proposed, such as \(\eta\)-\(\mu\), \(\kappa\)-\(\mu\), \(\alpha\)-\(\mu\), \(\alpha\)-\(\eta\)-\(\mu\), \(\kappa\)-\(\mu\) and \(\alpha\)-\(\eta\)-\(\kappa\)-\(\mu\) in [2] and references therein. For large-scale fading, the lognormal (LN) model is a typical shadowing fading example [1]. Unfortunately, the main disadvantage of this model is that its probability density function (PDF) contains an integral form which limits its applications for performance analysis purposes. For this reason, two substituted versions of the LN model have been proposed to approximate it, namely the Gamma (GA) model [3] and the inverse Gaussian (IG) model [4]. However, in some practical wireless communication scenarios, the composite effects of both multipath andshadowing fading become a dominating fading phenomenon. To this end, the composite fading models have been extensively explored by combining multipath fading with shadowing, which comprise the LN-based composite model (such as Rayleigh/LN, Rice/LN, Nakagami/LN, Weibull/LN, \(\alpha\)-\(\eta\)-\(\mu\)/LN, and \(\alpha\)-\(\kappa\)-\(\mu\)/LN [5]), the GA-based composite model (such as [PERSON]/GA, Nakagami/GA, Weibull/GA, \(\eta\)-\(\mu\)/GA, \(\kappa\)-\(\mu\)/GA, and \(\alpha\)-\(\mu\)/GA [6]), the IG-based model (such as [PERSON]/IG, [PERSON]/IG, \(\eta\)-\(\mu\)/IG, \(\kappa\)-\(\mu\)/IG, and \(\alpha\)-\(\mu\)/IG [7]), the line-of-sight (LOS) shadowing composite model (such as Rician shadowed [1] and \(\kappa\)-\(\mu\) shadowed [8]), and the double shadowing composite model [9; 10]. Furthermore, a double \(\alpha\)-\(\mu\) model in [11; 12] has also been proposed to describe the composite multipath-shadowing models, where the first \(\alpha\)-\(\mu\) model denotes the multipath fading and the second one is the shadowing fading. More recently, an inverse Gamma (IGA) model to characterize shadowing has been widely studied to achieve an appropriate balance between modeling accuracy and calculation complexity. For the empirical field measurements of the IGA model, the authors in [13] provided the experimental studies through wearable communication channels tests to prove that the underlying IGA model shadowing is very available compared with the LN and the GA models. At the same time, the authors in [14; 15] also confirmed that describing light and moderate shadowing with the IGA model is a reasonable alternative for the LN and the GA models by considering more testing scenarios, including both indoor and outdoor with many different frequency bands. More importantly, [14; 15] showed some mathematical expressions based on the IGA model are more tractable and simpler than those by using the LN or the IG model. By employing the IGA shadowing model, an unmanned aerial vehicle-to-ground communications channel model was presented in [16] which can provide a notable fit for empirical data. For the application of the underlying IGA model, [17; 18] first obtained the average symbol error rate of multiple amplitude modulation and the ergodic capacity over \(\kappa\)-\(\mu\)/IGA and \(\eta\)-\(\mu\)/IGA composite fading channels, respectively.