A new approach to modeling signal amplitude statistics by the K distributions

In this paper we re-derive the probability density functions (pdfs) of the K distribution, the homodyned K distribution, and the generalizedK distribution in theframework ofscale mixture of Gaussians models. This is done by considering the complex envelope corresponding to a received signal as a double stochastic circular Gaussian variable, in which both the variance and the mean are linearly scaled by a stochastic factor Z. By assuming Z to be F distributed, the three K distributions are shown to be statistical models for the amplitude signals, corresponding to special cases of this generic model. We also present new iterative algo-rithms for estimating the parameters associated with each model. 1