Sub-Nyquist USF spectral estimation: K frequencies with 6K+4 modulo samples
File(s)
Accepted version
Author(s)
Guo, Ruiming
Zhu, Yuliang
Bhandari, Ayush
Type
Journal Article
Abstract
Digital acquisition of high bandwidth signxals is particularly challenging when Nyquist rate sampling is impractical. This has led to extensive research in sub-Nyquist sampling methods, primarily for spectral and sinusoidal frequency estimation. However, these methods struggle with high-dynamic-range (HDR) signals that can saturate analog-to-digital converters (ADCs). Addressing this, we introduce a novel sub-Nyquist spectral estimation method, driven by the Unlimited Sensing Framework (USF), utilizing a multi-channel system. The sub-Nyquist USF method aliases samples in both amplitude and frequency domains, rendering the inverse problem particularly challenging. Towards this goal, our exact recovery theorem establishes that K sinusoids of arbitrary amplitudes and frequencies can be recovered from 6K+4 modulo samples, remarkably, independent of the sampling rate or folding threshold. In the true spirit of sub-Nyquist sampling, via modulo ADC hardware experiments, we demonstrate successful spectrum estimation of HDR signals in the kHz range using Hz range sampling rates (0.078% Nyquist rate). Our experiments also reveal up to a 33-fold improvement in frequency estimation accuracy using one less bit compared to conventional ADCs. These findings open new avenues in spectral estimation applications, e.g., radars, direction-of-arrival (DoA) estimation, and cognitive radio, showcasing the potential of USF.
Date Issued
2024-01-01
Date Acceptance
2024-09-22
Citation
IEEE Transactions on Signal Processing, 2024, 72, pp.5065-5076
ISSN
1053-587X
Publisher
Institute of Electrical and Electronics Engineers
Start Page
5065
End Page
5076
Journal / Book Title
IEEE Transactions on Signal Processing
Volume
72
Copyright Statement
Copyright © 2024 IEEE. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Subjects
Engineering
Estimation
Frequency estimation
Hardware
multi-channel architecture
Noise
Quantization (signal)
Radar imaging
RECOVERY
Signal processing algorithms
spectral estimation
sub-Nyquist sampling
Time-domain analysis
Unlimited sampling
Vectors
Publication Status
Published
Date Publish Online
2024-09-30