Asymptotics of performance of estimators of arrival time

In the estimation of the time of arrival of a signal, the mean square error of the estimate has a Cramer-Rao lower bound which is inversely proportional to the signal-to-noise ratio whenever the signal pulse is continuous in time. In contrast, other bounding techniques applied to discontinuous rectangular signals yield a lower bound on the mean square estimation error which is inversely proportional to the square of signal-to-noise ratio. We show that the contradiction is more apparent than real