Cramer-Rao lower bounds on estimating the parameters of a filtered burst of sinusoid

Using Cramer-Rao lower bounds (CRLBs) for estimating time of arrival and frequency of a burst of sinusoid, we investigate the effect of the location and extent of the observation interval, relative to the support of the received signal pulse, and the effect of not knowing the time duration of the pulse. The effect of filtering the received waveform using a known bandpass filter is also studied and is found to be small. The tail portion of the filter response after the signal pulse ends provides almost no information about the signal parameters. The initial transient build-up portion of the signal pulse response provides specially important information about time of arrival. For observation intervals which include the whole pulse duration, there are significant potential performance differences between the cases of known and unknown pulse duration.