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Comparison of the Ziv-Zakai lower bound on time delay estimation with correlator performance

The Ziv-Zakai Lower Bound (ZZLB) on the mean square error (m.s.e.) of time delay estimators is compared with theoretical and computer simulation results for time delay estimation via cross-correlation. Comparisons are made for both lowpass and narrowband signal spectra. For both signal spectra it is shown that for sufficiently large time-bandwidth product the correlator performance is very close to the ZZLB in both the small and large error regions. This establishes the cross-correlator as an optimal instrumentation (in the m.s.e. sense) while demonstrating that the ZZLB is an extremely tight lower bound. The ZZLB is further used to accurately predict the threshold signal-to-noise ratio (SNR) above which the cross-correlator performance is closely characterized by the Cramer-Rao Lower Bound (CRLB).