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 language | English |
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Title of host publication | Information-Theoretic Radar Signal Processing |
Publisher | wiley |
Pages | 87-121 |
Number of pages | 35 |
ISBN (Electronic) | 9781394216956 |
ISBN (Print) | 9781394216925 |
DOIs | |
State | Published - 1 Jan 2024 |
Externally published | Yes |
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