Maximum Likelihood Estimation Based Complex-Valued Robust Chinese Remainder Theorem and Its Fast Algorithm

2025/03/24 by Li, Xiaoping, Sun, Shiyang, Liao, Qunying +1 · 2 citations
#FOS: Electrical engineering #Signal Processing (eess.SP) #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2503.18625

Abstract

Recently, a multi-channel self-reset analog-to-digital converter (ADC) system with complex-valued moduli has been proposed. This system enables the recovery of high dynamic range complex-valued bandlimited signals at low sampling rates via the Chinese remainder theorem (CRT). In this paper, we investigate complex-valued CRT (C-CRT) with erroneous remainders, where the errors follow wrapped complex Gaussian distributions. Based on the existing real-valued CRT utilizing maximum likelihood estimation (MLE), we propose a fast MLE-based C-CRT (MLE C-CRT). The proposed algorithm requires only 2L searches to obtain the optimal estimate of the common remainder, where L is the number of moduli. Once the common remainder is estimated, the complex number can be determined using the C-CRT. Furthermore, we obtain a necessary and sufficient condition for the fast MLE C-CRT to achieve robust estimation. Finally, we apply the proposed algorithm to ADCs. The results demonstrate that the proposed algorithm outperforms the existing methods.

Cited by

• Moduli Selection in Robust Chinese Remainder Theorem: Closed-Form Solutions and Layered Design
• A Generalized Multidimensional Chinese Remainder Theorem (MD-CRT) for Multiple Integer Vectors

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