Maximum Likelihood Estimation Based Complex-Valued Robust Chinese Remainder Theorem and Its Fast Algorithm
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908480586121216 |
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| author | Li, Xiaoping Sun, Shiyang Liao, Qunying Xia, Xiang-Gen |
| author_facet | Li, Xiaoping Sun, Shiyang Liao, Qunying Xia, Xiang-Gen |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18625 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum Likelihood Estimation Based Complex-Valued Robust Chinese Remainder Theorem and Its Fast Algorithm Li, Xiaoping Sun, Shiyang Liao, Qunying Xia, Xiang-Gen Signal Processing 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. |
| title | Maximum Likelihood Estimation Based Complex-Valued Robust Chinese Remainder Theorem and Its Fast Algorithm |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2503.18625 |