Time-frequency-based detection in impulsive noise environments using α-stable noise models

Authors:
M. J. Coates;E. E. Kuruoglu
Affiliations:
Department of Electrical and Computer Engineering, McGill University, 3480 University St, Montreal, Que., Canada H3A 2A7;Istituto di Elaborazione della Informazione, CNR, Area della Ricerca di Pisa, via G. Moruzzi 1, I-56124, Pisa, Italy
Venue:
Signal Processing - Signal processing with heavy-tailed models
Year:
2002

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Abstract

We develop near-optimal test statistics for the detection of arbitrary non-stationary second-order random signals in impulsive noise, modelled using a bivariate, isotropic α-stable distribution. The test statistics are derived by approximating the noise model using a mixture of Gaussians, trained using an expectation-maximisation algorithm. We consider the extension to the case when the signal to be detected is subjected to an unknown time-frequency or time-scale shift, and show that approximations to locally optimal test statistics can be implemented using bilinear time-frequency or time-scale representations. We demonstrate that the performance of the locally optimal linear receiver is poor in even mildly impulsive noise; the alternative detection statistics proposed in this paper offer considerably enhanced performance.