Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.20866 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908795500756992 |
|---|---|
| author | Zhang, Huiguang |
| author_facet | Zhang, Huiguang |
| contents | The synchronous Nyquist folding generalized eigenvalue method (SNGEM) realizes full frequency/amplitude/phase estimation of multitone signals at extreme sub-Nyquist rates by jointly processing the original signals and their time derivatives. In this paper, accurate Cramer-Rao bounds for amplitude ratio parameter R=A/B=1/(2\pif) are derived for two channels with equal SNR. Monte-Carlo simulations confirm that SNGEM achieves machine accuracy in noise-free conditions and closely approaches the derived CRB at all SNR levels, even at 10- 20x compression, whereas classical compressive sensing OMP exhibits irreducible error flattening due to DFT grid bias and aliasing noise. These results establish SNGEM as a statistically nearly optimal deterministic sub-Nyquist parameter spectrum analysis |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20866 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cramér-Rao Bound Analysis and Near-Optimal Performance of the Synchronous Nyquist-Folding Generalized Eigenvalue Method (SNGEM) for Sub-Nyquist Multi-Tone Parameter Estimation Zhang, Huiguang Information Theory The synchronous Nyquist folding generalized eigenvalue method (SNGEM) realizes full frequency/amplitude/phase estimation of multitone signals at extreme sub-Nyquist rates by jointly processing the original signals and their time derivatives. In this paper, accurate Cramer-Rao bounds for amplitude ratio parameter R=A/B=1/(2\pif) are derived for two channels with equal SNR. Monte-Carlo simulations confirm that SNGEM achieves machine accuracy in noise-free conditions and closely approaches the derived CRB at all SNR levels, even at 10- 20x compression, whereas classical compressive sensing OMP exhibits irreducible error flattening due to DFT grid bias and aliasing noise. These results establish SNGEM as a statistically nearly optimal deterministic sub-Nyquist parameter spectrum analysis |
| title | Cramér-Rao Bound Analysis and Near-Optimal Performance of the Synchronous Nyquist-Folding Generalized Eigenvalue Method (SNGEM) for Sub-Nyquist Multi-Tone Parameter Estimation |
| topic | Information Theory |
| url | https://arxiv.org/abs/2601.20866 |