Robust multiple classification of known signals in additive noise-an asymptotic weak signal approach

The problem of extracting one out of a finite number of possible signals of known form given observations in an additive noise model is considered. Two approaches are studied: either the signal with shortest distance to the observed data or the signal having maximal correlation with some transformation of the observed data is chosen. With a weak signal approach, the limiting error probability is a monotone function of the Pitman efficacy and it is the same for both the distance-based and correlation-based detectors. Using the minimax theory of Huber, it is possible to derive robust choices of distance/correlation when the limiting error probability is used as performance criterion. This generalizes previous work in the area, from two signals to an arbitrary number of signals. Considered are M-type and R-type distances and also one-dimensional and two-dimensional signals. Some Monte Carlo simulations are performed to compare the finite sample size error probabilities with the asymptotic error probabilities