On adaptive detectors for two-input systems

This paper considers a two-input detection problem which is frequently encountered - that of deciding if a random signal is common to two channels each containing independent noise processes with identical statistical properties. It has been demonstrated that both the Neyman-Pearson and the correlation detectors can be made adaptive to processes with finite fourth moments that are wide-sense stationary during any test interval. The adaptive Neyman - Pearson detector is asymptotically one half as efficient as the original on the assumption of stationary gaussian noise processes. The adaptive correlation detector is asymptotically as efficient as the original and is essentially equivalent to the adaptive Neyman-Pearson detector. The PCC can be made adaptive with respect to the class of processes with quasi-stationary medians. This adaptive PeC is at least as efficient as the original and under certain conditions is more efficient. In addition, this detector performs well in the presence of impulse noise. These results together with its simplicity indicate that the adaptive PCC is a useful device for the two-input detection problem.