Sub-Nyquist USF Spectral Estimation: $K$ Frequencies with $6K + 4$ Modulo Samples
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929514864443392 |
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| author | Guo, Ruiming Zhu, Yuliang Bhandari, Ayush |
| author_facet | Guo, Ruiming Zhu, Yuliang Bhandari, Ayush |
| contents | Digital acquisition of high bandwidth signals 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16472 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sub-Nyquist USF Spectral Estimation: $K$ Frequencies with $6K + 4$ Modulo Samples Guo, Ruiming Zhu, Yuliang Bhandari, Ayush Information Theory Signal Processing Digital acquisition of high bandwidth signals 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. |
| title | Sub-Nyquist USF Spectral Estimation: $K$ Frequencies with $6K + 4$ Modulo Samples |
| topic | Information Theory Signal Processing |
| url | https://arxiv.org/abs/2409.16472 |