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.

翻译：当奈奎斯特速率采样不切实际时，高带宽信号的数字采集尤为困难。这引发了对亚奈奎斯特采样方法的广泛研究，主要针对频谱和正弦频率估计。然而，这些方法难以处理可能导致模数转换器（ADC）饱和的高动态范围（HDR）信号。针对此问题，我们提出了一种新颖的亚奈奎斯特频谱估计方法，该方法基于无限传感框架（USF），并利用多通道系统。该亚奈奎斯特USF方法在幅度和频率域均对采样进行混叠，使得逆问题特别具有挑战性。为此，我们的精确恢复定理证明，任意幅度和频率的$K$个正弦波可以从$6K + 4$个模采样中恢复，值得注意的是，这与采样率或折叠阈值无关。秉承亚奈奎斯特采样的真正精神，通过模ADC硬件实验，我们展示了使用Hz范围采样率（0.078%奈奎斯特率）成功估计kHz范围HDR信号的频谱。我们的实验还表明，与常规ADC相比，使用少一位的模ADC可将频率估计精度提高高达33倍。这些发现为频谱估计应用（例如雷达、到达方向估计和认知无线电）开辟了新途径，展示了USF的潜力。