On parameter estimation of the envelope Gaussian mixture model

In many communication systems, the Gaussian mixture model (GMM) is widely used to characterize non-Gaussian man-made and natural interference. The envelope distribution of such noise model is often expressed as a weighted sum of Rayleigh if in-phase and quadrature components of the noise are dependent. Instead, in this paper, a simple and exact closed form probability density function of the envelope Gaussian mixture model (i.e. the envelope of independent in-phase and quadrature components of complex non-Gaussian noise) is obtained. Further-more, the problem of estimating of the envelope Gaussian mixture parameters is addressed. The proposed estimator of weights and variances is based upon the Expectation-Maximization (EM) algorithm.