Minimax Signal Detection in the Presence of Noise with an Incompletely Specified Spectral Density

We consider signal detection in the presence of Gaussian noise, which is an additive mixture of two components; the spectral density of one of the components is known and the spectral density of the other component is unknown but satisfies a given system of moment inequalities. It is shown that a decision rule having a maximum guaranteed probability of correct detection for a given guaranteed probability of false alarms is the Neyman–Pearson rule in which the noise spectral density and the compatible linear filter are a saddle point of the signal/noise functional. An example is considered.