Optimum time delay estimation for complex-valued stationary signals

The problem of finding the time delay between complex-valued sequences received at two spatially separated sensors is addressed. Considering white signal and noise processes, three delay estimation algorithms based on the minimum mean square error criterion are devised. Their asymptotic mean and mean square error expressions are derived which show that all are unbiased estimators with performance approaching the Cramér–Rao lower bound. Numerical results are included to validate the theoretical development and contrast the three techniques.