Robust detection of a known signal in nearly Gaussian noise

A detector that is not nonparametric, but that nevertheless performs well over a broad class of noise distributions is termed a robust detector. One possible way to obtain a certain degree of robustness or stability is to look for a min-max solution. For the problem of detecting a signal of known form in additive, nearly Gaussian noise, the solution to the min-max problem is obtained when the signal amplitude is known and the nearly Gaussian noise is specified by a mixture model. The solution takes the form of a correlator-limiter detector. For a constant signal, the correlator-limiter detector reduces to a limiter detector, which is shown to be robust in terms of power and false alarm. By adding a symmetry constraint to the nearly normal noise and formulating the problem as one of local detection, the limiter-correlator is obtained as the local min-max solution. The limiter-correlator is shown to be robust in terms of asymptotic relative efficiency (ARE). For a pulse train of unknown phase, a limiter-envelope sum detector is also shown to be robust in terms of ARE.