Estimation of the relative delay of two similar signals of unknown phases in white Gaussian noise

In this paper we consider the estimation of the delay of a signal of unknown phase obscured by white noise and by another signal of unknown phase and known delay. We also consider the situation where both delays are unknown. Use is made of Shannon\´s sampling analysis as developed by Woodward. We conclude that the relative carrier phase of the two signals must be first estimated in order to maximize the {em a posteriori} probability of the estimate, but that knowledge of the absolute phase is only of secondary value.