Line Spectral Estimation via Unlimited Sampling

Line spectral estimation (LSE) is a fundamental problem in signal processing due to its wide applications. For signals that are orders of magnitude larger than the dynamic range of the analog-to-digital (ADC) threshold, conventional ADC will clip or saturate, leading to significant information loss. The Unlimited Sensing Framework (USF) was introduced to avoid saturation through sampling of the signal modulo. Motivated by the USF, we study the LSE from modulo samples. By exploiting oversampling and the bounded spectral property, the US-LSE is proposed to recover the folding instants and perform LSE. Our numerical simulations show that for oversampling factor $\gamma\geq 10$, the US-LSE is more stable in a lower signal to noise scenario, in the range of $20\sim30$ dB, compared to the existing algorithm. Besides, we process the real data generated by AWR1642, and show that US-LSE estimates the ranges of two corners with SNRs of $12$ dB and $23$ dB for oversampling factor $\gamma= 10$, and the normalized dynamic range ${\rm DR}=\beta_g/\lambda\approx 3$, where $\beta_g$ is the infinity norm of the signal.