EM algorithm on the approximation of arbitrary PDFs by Gaussian, gamma and lognormal mixture distributions

Abstract

In wireless communication systems, finding a model to describe shadow fading that is easy-to-work and has a good fidelity with the observed phenomena is a topic that is receiving the attention of several studies. This is because the well-known lognormal model, discussed in the literature, does not describe accurately what is experienced in the real world. Because gamma distribution has closed form expressions a few authors have proposed the use of the gamma PDF in order to model shadowing effect, since it facilitates the mathematical analysis of the system being designed. Other authors have proposed the use of lognormal mixture model to approximate the probability distribution of the local mean received power. This last approach yielded good results when compared to the distribution of actual measurements. Motivated by these facts, we present in this paper a study on the approximation of arbitrary PDFs by Gaussian, gamma, and lognormal mixture models using Expectation Maximization (EM) algorithm to estimate the necessary parameters. We show the results of our implementation of the algorithms and discuss important insights about them.