On Noise-Sensitivity of Unlimited Sampling in Line Spectral Estimation

The unlimited sampling framework, utilizing modulo analog-to-digital converters (ADCs), has recently been introduced to mitigate the information loss caused by the dynamic range limitations of traditional ADCs. In this paper, we evaluate the noise sensitivity of unlimited sampling in line spectral estimation by deriving the Cramér–Rao bound (CRB) and show that estimation based solely the modulo measurements can be sensitive to noise. To address this issue, we propose integrating the modulo ADC-based unlimited sampling with the sign information of the original signal. We compare the CRBs of different unlimited sampling frameworks and show the benefit of enhanced robustness to noise by the sign-aided approach.