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A unifying maximum-likelihood view of cumulant and polyspectral measures for non-Gaussian signal classification and estimation

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2 Author(s)
G. B. Giannakis ; Dept. of Electr. Eng., Virginia Univ., Charlottesville, VA, USA ; M. K. Tsatsanis

Classification and estimation of non-Gaussian signals observed in additive Gaussian noise of unknown covariance are addressed using cumulants or polyspectra. By integrating ideas from pattern recognition and model identification, asymptotically optimum maximum-likelihood classifiers and ARMA (autoregressive moving average) parameter estimators are derived without knowledge of the data distribution. Identifiability of noncausal and nonminimum phase ARMA models is established using a finite number of cumulant or polyspectral lags of any order greater than two. A unifying view of cumulant and polyspectral discriminant measures utilizes these lags and provides a common framework for development and performance analysis of novel and existing estimation and classification algorithms. Tentative order determination and model validation tests for non-Gaussian ARMA processes are described briefly. Illustrative simulations are also presented.<>

Published in:

IEEE Transactions on Information Theory  (Volume:38 ,  Issue: 2 )