Application of information criteria for the selection of the statistical small scale fading model of the radio mobile channel

Modeling of radio channel behavior is very important for digital communication. It is the reason why several propagation models have been implemented to take into account the electromagnetic phenomena inherent to the radio wave channel. So, among these models is the family of statistical distributions, fast in computation time, to describe channel fast fading. In this study context, our problematic is to find among the different statistical laws the one which best coincides with radio channel behavior. Different research has been realized on this subject over about 20 years. Thus, the Kolmogorov–Smirnov (KS) test using cumulative distribution functions (CDF) is usually employed by the radio mobile community partly for its simplicity. Nevertheless, there exist other approaches like Kulback–Leibler (KL) divergence, which consider distances between probability density functions that may be respresented as histograms. The bins of those histograms are obtained empirically, i.e. the bins are same size and their number is arbitrary. The authors propose approaches allowing optimal histograms in terms of the number and size of bins. These approaches are based on information criteria and we show that the KL discriminative method is more stable with the optimal histograms than with the empirical one. Moreover, our approaches are more reliable than the KS test whatever the number of considered samples. This last point is directly connected to the campaign of measures or of deterministic simulations, the duration of which can be very significant.