Ziv-Zakai Bound for Compressive Time Delay Estimation

Zongyu Zhang, Zhiguo Shi, Chengwei Zhou, Chenggang Yan, Yujie Gu

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Compressive radar receiver can keep a good balance between sub-Nyquist sampling and high resolution. To evaluate the performance of compressive time delay estimators, Cramér-Rao bound (CRB) has been derived for lower bounding the mean square error (MSE), which, unfortunately, is a local bound being tight in the asymptotic region only. In this paper, we use the Ziv-Zakai bound (ZZB) methodology to develop a Bayesian MSE bound on compressive time delay estimation by incorporating the a priori information of the unknown time delay. Specifically, we respectively derive deterministic ZZB and stochastic ZZB as functions of compressive sensing (CS) kernel, where there is no restriction on CS kernels and Gaussian noise colors. Simulation results demonstrate that compared with Bayesian CRB, ZZB provides a better performance prediction for minimum MSE estimator of compressive time delay estimation over a wide range of signal-to-noise ratios, where different CS kernels, compression ratios, a priori distributions and Gaussian noise colors are tested.

Original languageEnglish
Pages (from-to)4006-4019
Number of pages14
JournalIEEE Transactions on Signal Processing
StatePublished - 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 1991-2012 IEEE.


  • Bayesian estimation
  • Ziv-Zakai bound
  • compressive sensing
  • mean square error
  • minimum probability of error
  • time delay estimation


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