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 generalized K distribution in the framework of scale 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 Y 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 algorithms for estimating the parameters associated with each model