Representation of Composite Fading and Shadowing Distributions by Using Mixtures of Gamma Distributions

The Nakagami-lognormal distribution is the commonly used composite distribution for modeling multipath fading and shadowing. In this paper, simple and new form of distribution which can accurately represent both the mutlipath fading and shadowing effects is introduced. The signal-to-noise ratio (SNR) of the Nakagami-lognormal distribution follows the gamma-lognormal distribution, which is accurately approximated by a weighted mixture of gamma distributions. We show how the weights and other parameters of the summands are obtained. Further, accuracy of the mixture distribution is compared with the $K_G$ distribution -- a popular approximation of the Nakagami-lognormal distribution.