Time Delay Estimation Bounds in Wideband Random Channels

Improved Ziv-Zakai bounds (ZZBs) on time delay estimation (TDE) in wideband random channels are developed. The mean-square error (MSE) bounds are independent of estimator bias and do not require regularity conditions. They assume a known transmitted signal with uniform prior on the delay in [0, T], and a tapped delay line random channel model. The taps are modeled as Gaussian, including non-zero mean and possible correlation between taps. The channel model may be tuned to a variety of environments through the choice of mean and covariance, and models wideband and ultra-wideband line of sight (LOS) and non-LOS (NLOS) cases. The bounds are derived for a given channel realization first, and then averaged over the random channel model. They reflect the impact of the random channel, bounding average MSE performance assuming perfect channel estimates are available to the receiver. Examples illustrate the impact of the key system, channel, and signal parameters.