Ziv-Zakai Bound for DOAs Estimation

Zongyu Zhang, Zhiguo Shi, Yujie Gu

Research output: Contribution to journalArticlepeer-review

66 Scopus citations

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 Cramér-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.

Original languageEnglish
Pages (from-to)136-149
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume71
DOIs
StatePublished - 2023
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 1991-2012 IEEE.

Keywords

  • Coherence
  • Cramér-Rao bound
  • Ziv-Zakai bound
  • directions-of-Arrival estimation
  • mean square error
  • order statistics
  • permutation ambiguity

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