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

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 ?-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.