Ziv-Zakai Time Delay Estimation Bound for Ultra-Wideband Signals

The Ziv-Zakai bound (ZZB) provides a general mean-square error analytical baseline to evaluate time delay estimation (TDE) techniques for a wide range of time-bandwidth products and signal-to-noise ratios, but generally can only be numerically evaluated. The Weiss-Weinstein bound (WWB) further improves characterization of the attainable system performance, for narrowband and wide-band signals with small to moderate fractional bandwidth. Similar to the WWB, here we find a simplified closed-form ZZB for TDE with ultra-wideband (UWB) signals. The resulting simplified bound is found over disjoint segments, separated by thresholds that characterize different regions of ambiguity. The closed-form simplified bound can be analytically studied, and approaches both the ZZB and the TDE performance of a maximum likelihood estimator.