Ziv-Zakai Bound for Wideband Single-Source Direction-of-Arrival Estimation

The Ziv-Zakai bound (ZZB) for wideband Direction- of-Arrival (DOA) estimation of a single source within the subband model is examined. The study involves deriving the regularity condition and determining the minimum error probability, ultimately leading to a closed-form expression of the ZZB. This expression is dependent on several factors: the prior DOA distribution, the number of snapshots, signal wavelength, the quantity of involved subbands, and the signal-to-noise ratio (SNR). In scenarios with high SNR or a large number of snapshots, the estimation error decreases, causing the ZZB to approach the well- known Cramér-Rao bound (CRB). Conversely, in the a priori performance region, where the number of snapshots or SNR is low, the estimation error tends to be distributed across the entire prior parameter space, with its boundary approaching the prior covariance. The ZZB theoretically analyzes and derives a tighter bound, providing a more effective reference for the analysis of estimation errors.Simulation results indicate that the ZZB effectively predicts performance across all regions of interest.