On the Optimality of Inverse Gaussian Approximation for Lognormal Channel Models

Because of the equilibrium between mathematical tractability and approximation accuracy maintained by the inverse Gaussian (IG) distributional model, it has been regarded as the most appropriate approximation substitute for the lognormal distributional model for shadowed and atmospheric turbulence induced (ATI) fading in the past decades. In this paper, we conduct an in-depth information-theoretic analysis for the lognormal-to-IG channel model substitution (CMS) technique and study its parametric mapping optimality achieved by minimizing the Kullback-Leibler (K-L) divergence between the two distributional models. In this way, we rigorously prove that the moment matching criterion produces the optimal IG substitute for lognormal reference distributions, which has never been observed in other CMS techniques. In addition, we clarify a myth in the realm of CMS that the IG substitute outperforms the gamma substitute for approximating lognormal reference distributions; instead, the substitution superiority shall depend on the parametric mapping criterion and the scale parameter of the lognormal reference distribution. All analytical insights presented in this paper are validated by simulation results.