Information-Theoretic Analysis of Inverse Gamma Substitution for Lognormal Shadowing Models

Due to its outstanding mathematical tractability, the inverse gamma (InvG) distribution is used as a substitute for the lognormal distribution to characterize the random fluctuations of the wireless signal envelope caused by shadowing. In this paper, we carry out the information-theoretic study of this channel model substitution (CMS) technique in terms of feasibility, approximation accuracy, and optimality by adopting both moment matching and Kullback-Leibler divergence (KLD) minimization criteria for parametric mapping. Specifically, we derive the minimum achievable KLD by the lognormal-to-InvG CMS and the corresponding optimal parametric mapping relation. By comparing to the gamma substitute that has been widely used for approximating the lognormal shadowing model, we demonstrate that the InvG substitute is more mathematically tractable and rigorously prove that the InvG substitute, however, cannot yield a lower KLD than the gamma substitute when applying the same parametric mapping criterion.