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arXiv · 2512.23506

Affine-Projection Recovery of Continuous Angular Power Spectrum: Geometry and Resolution

Shengsong Luo·Ruilin Wu·Chongbin Xu·Junjie Ma·Xiaojun Yuan·Xin Wang
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Abstract

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.

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Shengsong Luo, Ruilin Wu, Chongbin Xu, Junjie Ma, Xiaojun Yuan, Xin Wang. 2025-12-29. Affine-Projection Recovery of Continuous Angular Power Spectrum: Geometry and Resolution. https://arxiv.org/abs/2512.23506

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