On some detection and estimation problems in heavy-tailed noise
Signal Processing - Signal processing with heavy-tailed models
Finite mixture of α-stable distributions
Digital Signal Processing
Robust initial LLRs for iterative decoders in presence of non-Gaussian noise
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
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Scale mixtures of the Gaussian have been used to approximate the PDF of symmetric alpha stable processes. Such mixtures, however, cannot easily capture the heavy-tails. We propose to use Cauchy-Gaussian mixtures which are natural in this setting. Variations of standard EM algorithms can be used to estimate the parameters of the noise PDFs under various scenarios (noise-only data, weak-signal assumption, partially known-signal case). The fitted mixture models can be used for detection and estimation. In the multivariate case, we present several results on Gaussian mixture approximations of sub-Gaussian PDFs, including robust estimation of the underlying correlation matrix.