## Abstract

Existing stochastic Ziv-Zakai bound (ZZB) for compressive time delay estimation from compressed measurement relies on a Gaussian approximation, which makes it inaccurate in the asymptotic region when the stochastic component dominates the received signals. In this letter, we apply different random projections on zero-mean Gaussian received signal to obtain multiple compressed measurements, based on which the log-likelihood ratio test is exactly formulated as the difference of two generalized integer Gamma variables. Accordingly, we further derive the exact expression of the stochastic ZZB for compressive time delay estimation from zero-mean Gaussian signal. Simulation results show that the derived ZZB is globally tight to accurately predict the estimation performance regardless of the number of compressed measurements, and it can also accurately predict the threshold signal-to-noise ratio for the estimator when the number of compressed measurements is large.

Original language | English |
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Pages (from-to) | 1112-1116 |

Number of pages | 5 |

Journal | IEEE Signal Processing Letters |

Volume | 30 |

DOIs | |

State | Published - 2023 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 1994-2012 IEEE.

### Funding

The work of Z. Zhang was supported by China Scholarship Council for his stay at the University of Pisa. The work of Z. Zhang and Z. Shi was supported by the National Natural Science Foundation of China under Grants U21A20456, 61901413, and 62271444.

Funders | Funder number |
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National Natural Science Foundation of China | 62271444, 61901413, U21A20456 |

China Scholarship Council | |

Università di Pisa |

## Keywords

- Bayesian estimation
- compressive sensing
- mean square error
- stochastic Ziv-Zakai bound
- time delay estimation