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

Xiaoping Li

doi:10.1109/JMASS.2025.3640013

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

2026-03-01

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DOI：10.1109/JMASS.2025.3640013

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In this article, we investigate complex-valued Chinese remainder theorem (C-CRT) with erroneous remainders, where the moduli are Gaussian integers and 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 a multichannel self-reset analog-to-digital converter (ADC) system with Gaussian integers as moduli, which enables the recovery of high dynamic range complex-valued bandlimited signals at the Nyquist sampling rate. The results demonstrate that the proposed algorithm outperforms the existing methods.

Keywords:

Maximum likelihood estimation

Frequency modulation

Vectors

Signal processing algorithms

Redundancy

Image reconstruction

Sufficient conditions

Heuristic algorithms

Analog-digital conversion

Gaussian distribution

Chinese remainder theorem (CRT)

complex-valued CRT (C-CRT)

multichannel self-reset (SR) analog-to-digital converter (ADC)

real-valued CRT

residue number system

robust CRT

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

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