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

In various signal processing scenarios, the signal exhibits a nonstationary behaviour and is observed under non-Gaussian noise. Although one can find several work in the literature on dealing with nonstationary signals using time-frequency analysis and with non-Gaussian noise, these two problems have not been studied together. In this paper, we aim to address both nonstationarity and non-Gaussiannity in a unified manner. In particular, we develop test statistics for the detection of arbitrary nonstationary second order signals observed under impulsive noise. We model the impulsive noise with symmetric alpha-stable distributions which recently received interest in the signal processing community. We consider the problem of detecting such signals in the presence of unknown time-frequency and time-scale offsets and demonstrate that approximations to locally-optimal test statistics can be expressed in a manner conducive to efficient implementation using time-frequency or time-scale representations.