The Chinese Remainder Theorem (CRT) based frequency estimation has been widely studied during the past two decades. It enables one to estimate frequencies by sub-Nyquist sampling rates, which reduces the cost of hardware in a sensor network. Several studies have been done on the complex waveform; however, few works studied its applications in the real waveform case. Different from the complex waveform, existing CRT methods cannot be straightforwardly applied to handle a real waveform's spectrum due to the spurious peaks. To tackle the ambiguity problem, in this paper, we propose the first polynomial-time closed-form Robust CRT (RCRT) for the single-tone real waveform, which can be considered as a special case of RCRT for arbitrary two numbers. The time complexity of the proposed algorithm is O(L), where L is the number of samplers. Furthermore, our algorithm also matches the optimal error-tolerance bound.
Keywords: error bound; frequency estimation; robust Chinese Remainder Theorem; sensor network; undersampling.