Detection in incompletely characterized colored non-Gaussian noise via parametric modeling

The problem of detecting a weak signal known except for amplitude in incompletely characterized colored non-Gaussian noise is addressed. The problem is formulated as a test of composite hypotheses, using parameteric models for the statistical behavior of the noise. A generalized likelihood ratio test (GLRT) is employed. It is shown that for a symmetric noise probability density function the detection performance is asymptotically equivalent to that obtained for a similar detector designed with a priori knowledge of the noise parameters. Non-Gaussian distributions are found to be more favorable for the purpose of detection than the Gaussian distribution. The computational burden of the GLRT may be partially reduced by employing a Rao efficient score test which shares all the nice asymptotic properties of the GLRT for small signal amplitudes. Computer simulations of the performance of the Rao detector support the theoretical results