Approximately optimal memoryless detection of random signals in dependent noise (Corresp.)

We consider discrete time memoryless detection of random signals in dependent non-Gaussian noise, where both the signal and noise belong to a large class of strong mixing processes, and where a large amount of dependency may occur between the signal and noise. The problem of approximating the optimal nonlinearity under the criterion of asymptotic relative efficiency is considered, and sufficient conditions are presented to insure that the loss in performance of the approximation can be made arbitrarily small. Particular applications are then made to extensions of existing results where the approximating nonlinearity is a quantizer or a polynomial.