On Novel RIP of Windowed Compressed Spectrum Sensing
Compressed spectrum sensing (CSS) offers great advantages in spectral analysis through sub-Nyquist sampling. However, conventional CSS approaches have not sufficiently addressed the effect of spectral leakage (SL) on sensing performance, a problem that fundamentally alters signal sparsity. Although...
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IEEE
2025-01-01
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| Online Access: | https://ieeexplore.ieee.org/document/11014522/ |
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| author | Huiguang Zhang Baoguo Liu Wei Feng |
| author_facet | Huiguang Zhang Baoguo Liu Wei Feng |
| author_sort | Huiguang Zhang |
| collection | DOAJ |
| description | Compressed spectrum sensing (CSS) offers great advantages in spectral analysis through sub-Nyquist sampling. However, conventional CSS approaches have not sufficiently addressed the effect of spectral leakage (SL) on sensing performance, a problem that fundamentally alters signal sparsity. Although WFs (WFs) are widely employed in traditional spectral analysis to mitigate SL, their systematic application within CSS lacks comprehensive analysis, and they have not been theoretically investigated. This study develops a rigorous theoretical framework for analyzing windowed measurement matrices in CSS by introducing two novel metrics: the Edge Zeroing Coefficient (EZC), which quantifies the boundary behavior of WFs and directly correlates with SL suppression, and the Window Scaling Coefficient (WSC), which characterizes how WFs affect the Restricted Isometry Property (RIP) of measurement matrices. By integrating these metrics, we formulate a dual-effects framework that quantitatively characterizes the inherent trade-offs between the accuracy of spectral analysis and the fidelity of signal reconstruction. We extend conventional block-sparsity concepts by explicitly incorporating WF characteristics, providing the first mathematical framework that directly links window properties to resulting signal sparsity patterns. By leveraging subspace counting theory, we establish sampling bounds for windowed CSS under various conditions, including block-sparse signal structures, ultra-sparse frequency distributions, and noisy environments. Our findings demonstrate that although WFs effectively reduce SL, excessively low EZC and WSC values can degrade RIP quality, potentially causing numerical instability during signal reconstruction. This research provides theoretical foundations and practical guidelines for selecting appropriate WFs based on application-specific requirements, enabling more accurate and efficient spectrum sensing across diverse domains. |
| format | Article |
| id | doaj-art-135c6cdd82964ff6bf3e02d229f511ce |
| institution | OA Journals |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-135c6cdd82964ff6bf3e02d229f511ce2025-08-20T02:19:31ZengIEEEIEEE Access2169-35362025-01-0113921809220210.1109/ACCESS.2025.357032811014522On Novel RIP of Windowed Compressed Spectrum SensingHuiguang Zhang0https://orcid.org/0009-0009-5656-2727Baoguo Liu1Wei Feng2School of Mechanical and Electrical Engineering, Henan University of Technology, Zhengzhou, ChinaSchool of Mechanical and Electrical Engineering, Henan University of Technology, Zhengzhou, ChinaSchool of Mechanical and Electrical Engineering, Henan University of Technology, Zhengzhou, ChinaCompressed spectrum sensing (CSS) offers great advantages in spectral analysis through sub-Nyquist sampling. However, conventional CSS approaches have not sufficiently addressed the effect of spectral leakage (SL) on sensing performance, a problem that fundamentally alters signal sparsity. Although WFs (WFs) are widely employed in traditional spectral analysis to mitigate SL, their systematic application within CSS lacks comprehensive analysis, and they have not been theoretically investigated. This study develops a rigorous theoretical framework for analyzing windowed measurement matrices in CSS by introducing two novel metrics: the Edge Zeroing Coefficient (EZC), which quantifies the boundary behavior of WFs and directly correlates with SL suppression, and the Window Scaling Coefficient (WSC), which characterizes how WFs affect the Restricted Isometry Property (RIP) of measurement matrices. By integrating these metrics, we formulate a dual-effects framework that quantitatively characterizes the inherent trade-offs between the accuracy of spectral analysis and the fidelity of signal reconstruction. We extend conventional block-sparsity concepts by explicitly incorporating WF characteristics, providing the first mathematical framework that directly links window properties to resulting signal sparsity patterns. By leveraging subspace counting theory, we establish sampling bounds for windowed CSS under various conditions, including block-sparse signal structures, ultra-sparse frequency distributions, and noisy environments. Our findings demonstrate that although WFs effectively reduce SL, excessively low EZC and WSC values can degrade RIP quality, potentially causing numerical instability during signal reconstruction. This research provides theoretical foundations and practical guidelines for selecting appropriate WFs based on application-specific requirements, enabling more accurate and efficient spectrum sensing across diverse domains.https://ieeexplore.ieee.org/document/11014522/Windowed CSSRIPedge zeroing coefficientwindow scaling coefficientsubspace counting theory |
| spellingShingle | Huiguang Zhang Baoguo Liu Wei Feng On Novel RIP of Windowed Compressed Spectrum Sensing IEEE Access Windowed CSS RIP edge zeroing coefficient window scaling coefficient subspace counting theory |
| title | On Novel RIP of Windowed Compressed Spectrum Sensing |
| title_full | On Novel RIP of Windowed Compressed Spectrum Sensing |
| title_fullStr | On Novel RIP of Windowed Compressed Spectrum Sensing |
| title_full_unstemmed | On Novel RIP of Windowed Compressed Spectrum Sensing |
| title_short | On Novel RIP of Windowed Compressed Spectrum Sensing |
| title_sort | on novel rip of windowed compressed spectrum sensing |
| topic | Windowed CSS RIP edge zeroing coefficient window scaling coefficient subspace counting theory |
| url | https://ieeexplore.ieee.org/document/11014522/ |
| work_keys_str_mv | AT huiguangzhang onnovelripofwindowedcompressedspectrumsensing AT baoguoliu onnovelripofwindowedcompressedspectrumsensing AT weifeng onnovelripofwindowedcompressedspectrumsensing |