Lognormal Mixture Shadowing

Modeling the variations in the local mean received power, the shadow fading is a relatively understudied effect in the literature. The inaccuracy of the universally accepted lognormal model is shown in many works. However, proposing other statistical distributions, such as gamma, which are not stemmed from the natural underlying physical process, cannot provide sufficient insights. Conceding the physical process of multiple reflections generating the lognormal distribution, in this paper, we propose a generalized mixture model that can address the modeling inaccuracies observed with a single lognormal distribution that may not correctly represent empirical data sets. To show that lognormal mixture model can be used under any shadow fading condition, we prove that an arbitrary probability density function can accurately be represented by a mixture of lognormal random variables (RVs). One of the main issues associated with mixture models is the determination of the mixture components. Here, we propose two solutions. Our first solution is a Dirichlet-process-mixture-based estimation technique that can provide the optimum number of components. Our second solution is an expectation-maximization (EM) algorithm-based technique for a more practical implementation. The proposed model and solution approaches are applied to our empirical data set, where the accuracy of the mixture model is verified by using both confidence-based and error-vector-norm-based techniques. Concluding this paper, we provide outage and cellular coverage probability expressions, where we show that more accurate shadow fading models yield more realistic performance estimates.