Optimal detection in colored non-Gaussian noise with unknown parameters

The problem of detecting a signal known except for amplitude in incompletely characterized non-Gaussian noise is addressed. The use of a generalized likelihood ratio test or its asymptotically equivalent form, the Rao test, is shown to produce a detector that has the identical asymptotic performance as a generalized likelihood ratio test designed with a priori knowledge of the unknown noise parameters. Since the latter clairvoyant detector always produces an upper bound on performance, the generalized likelihood ratio test is optimum. An example is given in which the noise is modeled as an autoregressive process with a mixed-Gaussian noise excitation. Results of a computer simulation are described which verify the theory.