ssing signals that are orders of magnitude larger than the ADC’s threshold. To address this issue, the Unlimited Sampling (US) strategy was introduced, which applies a modulo operator prior to sampling to avoid saturation. In this paper, we study LSE via unlimited sampling. By exploiting the oversampling property and proving that the leakage onto the tail frequency can be controlled, we establish an optimization problem in the Fourier and first-order difference domain. We then propose a dynamic programming (DP) based algorithm followed by orthogonal matching pursuit (OMP) method to solve it. In addition, a two stage US LSE (USLSE) is proposed where the line spectral signal is first recovered by iteratively executing DP and OMP, and then the parameters are estimated by applying a state-of-art LSE algorithm. Unlike other works that consider noise added in modulo samples, this paper tackles the more challenging scenario of noise added in original samples. Substantial numerical simulations demonstrate that the proposed algorithm, USLSE, outperforms existing algorithms in such a scenario. In addition, the simulation validates that the first stage of USLSE can also be used to recover bandlimited signals. Finally, we process the real data generated by AWR1642, and the results show that USLSE estimates two people with maximum folding times being 2, and estimates one corner and two people with maximum folding times being 5.This is the joint work with Mr. Qi Zhang in Singapore University of Technology and Design.