# Modulo Sampling: Performance Guarantees in The Presence of Quantization

arXiv: https://arxiv.org/abs/2501.01506 · HTML: https://mlsanity.com/paper/2501.01506/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 59 references that are in the map.
- First posted on arXiv 2 Jan 2025.

## Builds on (most cited first, 17 of 17)

- [On Unlimited Sampling and Reconstruction](https://mlsanity.com/paper/1905.03901/) (2019)
- [Unlimited Sampling from Theory to Practice: Fourier-Prony Recovery and Prototype ADC](https://mlsanity.com/paper/2105.05818/) (2021)
- [UNO: Unlimited Sampling Meets One-Bit Quantization](https://mlsanity.com/paper/2301.10155/) (2022)
- [Above the Nyquist Rate, Modulo Folding Does Not Hurt](https://mlsanity.com/paper/1903.12289/) (2019)
- [Back in the US-SR: Unlimited Sampling and Sparse Super-Resolution with its Hardware Validation](https://mlsanity.com/paper/2207.13230/) (2022)
- [Generalized Approximate Message Passing for Unlimited Sampling of Sparse Signals](https://mlsanity.com/paper/1807.03182/) (2018)
- [Residual Recovery Algorithm For Modulo Sampling](https://mlsanity.com/paper/2110.03335/) (2021)
- [The Surprising Benefits of Hysteresis in Unlimited Sampling: Theory, Algorithms and Experiments](https://mlsanity.com/paper/2111.12675/) (2021)
- [Modulo Sampling of FRI Signals](https://mlsanity.com/paper/2207.08774/) (2022)
- [Line Spectral Estimation via Unlimited Sampling](https://mlsanity.com/paper/2210.15811/) (2022)
- [Unlimited Dynamic Range Analog-to-Digital Conversion](https://mlsanity.com/paper/1911.09371/) (2019)
- [On Hybrid Radar Fusion for Integrated Sensing and Communication](https://mlsanity.com/paper/2303.05722/) (2023)
- [Compressed Sensing Based Residual Recovery Algorithms and Hardware for Modulo Sampling](https://mlsanity.com/paper/2412.12724/) (2024)
- [On the Identifiability from Modulo Measurements under DFT Sensing Matrix](https://mlsanity.com/paper/2401.00194/) (2023)
- [Short-time Fourier Transform-based Signal Recovery for Modulo Analog-to-Digital Converters](https://mlsanity.com/paper/2410.18757/) (2024)
- [A Modulo Sampling Hardware Prototype and Reconstruction Algorithm Evaluation](https://mlsanity.com/paper/2410.19383/) (2024)
- [Low Dynamic Range for RIS-aided Bistatic Integrated Sensing and Communication](https://mlsanity.com/paper/2411.06117/) (2024)

## Built on by (most cited first, 1 of 1)

- [mSQUID: Model-Based Leanred Modulo Recovery at Low Sampling Rates](https://mlsanity.com/paper/2510.18729/) (2025)

## Abstract (arXiv)

In this paper, we investigate the relationship between the dynamic range and quantization noise power in modulo analog-to-digital converters (ADCs). Two modulo ADC systems are considered: (1) a modulo ADC which outputs the folded samples and an additional 1-bit folding information signal, and (2) a modulo ADC without the 1-bit information. A recovery algorithm that unfolds the quantized modulo samples using the extra 1-bit folding information is analyzed. Using the dithered quantization framework, we show that an oversampling factor of OF > 3 and a quantizer resolution of b > 3 are sufficient conditions to unfold the modulo samples. When these conditions are met, we demonstrate that the mean squared error (MSE) performance of modulo ADC with an extra 1-bit folding information signal is better than that of a conventional ADC with the same number of bits used for amplitude quantization. Since folding information is typically not available in modulo ADCs, we also propose and analyze a recovery algorithm based on orthogonal matching pursuit (OMP) that does not require the 1-bit folding information. In this case, we prove that OF > 3 and b > 3 + log2(δ) for some δ > 1 are sufficient conditions to unfold the modulo samples. For the two systems considered, we show that, with sufficient number of bits for amplitude quantization, the mean squared error (MSE) of a modulo ADC is Oleft(frac1OF3right) whereas that of a conventional ADC is only Oleft(frac1OFright). We extend the analysis to the case of simultaneous acquisition of weak and strong signals occupying different frequency bands. Finally, numerical results are presented to validate the derived performance guarantees.