Asymptotically robust detection of known signals in nonadditive noise

Robust detection of known weak signals of unknown amplitude is considered for a class of combined additive and nonadditive noise models and an asymptotically large set of independent observations. This class includes observation models that may have combinations of multiplicative and signal-dependent noise terms. Sufficient conditions are given for robust detection schemes for cases where the general form of the observation model is known but the additive noise distribution is known only to be a member of a general convex uncertainty class. Robust schemes satisfying these conditions are found for some example cases where additive signals and noise have been processed by memoryless nonlinearities. Some interesting example cases of combined multiplicative and signal-dependent noise are shown to use redescending nonlinearities, instead of the limiter nonlinearities typically found for similar additive noise cases