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| Hauptverfasser: | , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2512.23506 |
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| _version_ | 1866917173993144320 |
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| author | Luo, Shengsong Wu, Ruilin Xu, Chongbin Ma, Junjie Yuan, Xiaojun Wang, Xin |
| author_facet | Luo, Shengsong Wu, Ruilin Xu, Chongbin Ma, Junjie Yuan, Xiaojun Wang, Xin |
| contents | This paper considers recovering a continuous angular power spectrum (APS) from the channel covariance. Building on the projection-onto-linear-variety (PLV) algorithm, an affine-projection approach introduced by Miretti \emph{et. al.}, we analyze PLV in a well-defined \emph{weighted} Fourier-domain to emphasize its geometric interpretability. This yields an explicit fixed-dimensional trigonometric-polynomial representation and a closed-form solution via a positive-definite matrix, which directly implies uniqueness. We further establish an exact energy identity that yields the APS reconstruction error and leads to a sharp identifiability/resolution characterization: PLV achieves perfect recovery if and only if the ground-truth APS lies in the identified trigonometric-polynomial subspace; otherwise it returns the minimum-energy APS among all covariance-consistent spectra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23506 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Affine-Projection Recovery of Continuous Angular Power Spectrum: Geometry and Resolution Luo, Shengsong Wu, Ruilin Xu, Chongbin Ma, Junjie Yuan, Xiaojun Wang, Xin Information Theory Signal Processing This paper considers recovering a continuous angular power spectrum (APS) from the channel covariance. Building on the projection-onto-linear-variety (PLV) algorithm, an affine-projection approach introduced by Miretti \emph{et. al.}, we analyze PLV in a well-defined \emph{weighted} Fourier-domain to emphasize its geometric interpretability. This yields an explicit fixed-dimensional trigonometric-polynomial representation and a closed-form solution via a positive-definite matrix, which directly implies uniqueness. We further establish an exact energy identity that yields the APS reconstruction error and leads to a sharp identifiability/resolution characterization: PLV achieves perfect recovery if and only if the ground-truth APS lies in the identified trigonometric-polynomial subspace; otherwise it returns the minimum-energy APS among all covariance-consistent spectra. |
| title | Affine-Projection Recovery of Continuous Angular Power Spectrum: Geometry and Resolution |
| topic | Information Theory Signal Processing |
| url | https://arxiv.org/abs/2512.23506 |