Ziv-Zakai Bound for DOAs Estimation

TL;DR

This paper derives a new global tight Ziv-Zakai bound for multiple sources DOA estimation, accounting for source coherence and outperforming the traditional CRB in performance evaluation.

Contribution

It introduces an explicit ZZB for multiple sources that incorporates source coherence and extends applicability to overdetermined and underdetermined scenarios.

Findings

The derived ZZB is tighter than the CRB for multiple sources.

The ZZB accounts for source coherence and ordering effects.

Simulation confirms the ZZB's effectiveness in performance prediction.

Abstract

Lower bounds on the mean square error (MSE) play an important role in evaluating the direction-of-arrival (DOA) estimation performance. Among numerous bounds for DOA estimation, the local Cramer-Rao bound (CRB) is only tight asymptotically. By contrast, the existing global tight Ziv-Zakai bound (ZZB) is appropriate for evaluating the single source estimation only. In this paper, we derive an explicit ZZB applicable for evaluating hybrid coherent/incoherent multiple sources DOA estimation. It is first shown that, a straightforward generalization of ZZB from single source estimation to multiple sources estimation cannot keep the bound valid in the a priori performance region. To derive a global tight ZZB, we then introduce order statistics to describe the change of the a priori distribution of DOAs caused by ordering process during the MSE calculation. The derived ZZB is for the first time formulated as a function of coherent coefficients between coherent sources, and reveals the relationship between the MSE convergency in the a priori performance region and the number of sources. Moreover, the derived ZZB also provides a unified tight bound for both overdetermined and underdetermined DOA estimation. Simulation results demonstrate the obvious advantages of the derived ZZB over the CRB on evaluating and predicting the estimation performance for multiple sources DOA.