Maximum Likelihood Estimation Based Complex-Valued Robust Chinese Remainder Theorem and Its Fast Algorithm
Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Li, Xiaoping, Sun, Shiyang, Liao, Qunying, Xia, Xiang-Gen
Language: English
Subfield: Information Systems
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6910776418