Signal detection in incompletely characterized impulsive noise modeled as a stable process

We address the problem of detection of signals of known shape but unknown level in incompletely characterized impulsive noise using lower-order moments and order statistics. We form a generalized likelihood ratio test which is based on fractional moment and order statistics, rather than maximum likelihood, estimates of the unknown parameters of the detection problem. We show theoretically, that the estimates we propose are consistent and that the proposed generalized likelihood ratio test is asymptotically equivalent to the optimum likelihood ratio test corresponding to completely known signal and noise parameters (clairvoyant test)