Optimal detection of non-Gaussian random signals in Gaussian noise

A method of detecting arbitrary random signals in the presence of additive Gaussian noise is discussed. The method is based on eigendecomposition of the noise probability subspace. This decomposition leads to unique detector structure, invariant with respect to the signal distribution. The resulting detection scheme uses a variable number of terms per decision, but any decision made is exactly the same as the one produced by the optimal detector. The scheme is found to be computationally efficient, and well suited for generalization to the case of unknown (or only partially known) statistics. The efficiency of the algorithm is demonstrated in a typical example, with the aid of computer simulations