  Frequency Modulated Continuous Wave (FMCW) radar has been widely applied in
automotive anti-collision systems, automatic cruise control, and indoor
monitoring. However, conventional analog-to-digital converters (ADCs) can
suffer from significant information loss when strong and weak targets coexist
in ranging applications. To address this issue, the Unlimited Sampling (US)
strategy was proposed, which applies a modulo operator prior to sampling. In
this paper, we investigate the range estimation problem using FMCW radar in the
context of US, which can be formulated as a one-dimensional line spectral
estimation (LSE) via US. By exploiting the oversampling property and proving
that the leakage onto a certain frequency band can be controlled, we establish
an integer optimization problem in the Fourier and first-order difference
domain. We then propose a dynamic programming (DP) based algorithm followed by
the 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-the-art LSE algorithm. Substantial numerical
simulations and real experiments demonstrate that the proposed algorithm,
USLSE, outperforms existing algorithms.
