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

The fundamental limits on estimating the multipath time delay for a single, resolvable multipath are examined. We assume that the received signal is given by r(t) = s(t) + as (t - D0) + n(t) where s and n are uncorrelated Gaussian random processes and a is an attenuation coefficient. The Cramer-Rao Lower Bound (CRLB) and the Ziv-Zakai Lower Bound (ZZLB) are derived and compared with the performance (theoretical and computer simulation) of an autocorrelator. It is shown that for low-pass signals the ZZLB is within 2 dB in input signal-to-noise ratio (SNR) of being a greatest lower bound for this problem. It is further shown that below threshold SNR the autocorrelator is within 2 dB of being an optimal instrumentation. Above threshold SNR the autocorrelator does not reach the CRLB and hence is not optimal.