Sub-Nyquist USF Spectral Estimation: $K$ Frequencies with $6K + 4$ Modulo Samples
<|reference_start|>Sub-Nyquist USF Spectral Estimation: $K$ Frequencies with $6K + 4$ Modulo Samples: 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.<|reference_end|>
@article{guo2024sub-nyquist,
    title={Sub-Nyquist USF Spectral Estimation: $K$ Frequencies with $6K + 4$
  Modulo Samples},
    author={Ruiming Guo, Yuliang Zhu and Ayush Bhandari},
    journal={arXiv preprint arXiv:2409.16472},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.16472},
    primaryClass={cs.IT eess.SP math.IT}
}