Large and small error performance limits for multipath time delay estimation

The Cramer-Rao lower bound (CRLB) and a lower bound on the probability of large errors for multipath time delay estimation, for a single resolvable multipath, are developed. These theoretical results are compared to the performance of the maximum likelihood estimator (MLE) and an autocorrelator, via computer simulation. For small errors and large SNR, the MLE reaches the CRLB; the variance of the time delay estimate for the autocorrelator is much larger than the CRLB if the reflection coefficient for the delayed path is near unity. For small errors and small SNR, the MLE reduces to an autocorrelator, hence, their performance is identical. For large errors and bandwidth time products greater than 500, the error probability for the autocorrelator is within 1 dB in input SNR of the lower bound on large error probability. Thus, the autocorrelator is nearly an optimal instrumentation from the point of view of large errors, at least for large bandwidth time products and the flat, low-pass spectrum considered here.