Information-Theoretic Compressive Sensing for Time Delay Estimation

Yujie Gu, Nathan A. Goodman, Yimin D. Zhang

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

In this chapter, we adopt an information-theoretic approach to optimize compressive sensing (CS) kernels for the purpose of supporting higher signal bandwidth for enhanced time delay estimation without increasing the sampling rate. By the discretization of the prior probability distribution of the time delay, we utilize a Gaussian mixture model to characterize measurements. Subsequently, we optimize CS kernels to maximize the mutual information between the compressive measurement and the time delay. The optimization process unfolds over the Stiefel manifold, employing a gradient ascent search method. To evaluate the estimation performance, we derive the well-established Bayesian Cramér-Rao bound and the globally tight Ziv-Zakai bound. Through numerical simulations, we validate that the proposed information-theoretic sensing kernel yields substantial performance enhancement compared to random projections, with the estimation performance aligning consistently with theoretical bounds.

Original languageEnglish
Title of host publicationInformation-Theoretic Radar Signal Processing
Publisherwiley
Pages87-121
Number of pages35
ISBN (Electronic)9781394216956
ISBN (Print)9781394216925
DOIs
StatePublished - 1 Jan 2024
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2025 by The Institute of Electrical and Electronics Engineers, Inc.

Keywords

  • Bayesian Cramér-Rao bound (BCRB)
  • Gaussian mixture
  • Ziv-Zakai bound (ZZB)
  • compressive sensing (CS)
  • mutual information
  • sensing kernel optimization
  • time delay estimation

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