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Main Authors: Luo, Shengsong, Wu, Ruilin, Xu, Chongbin, Ma, Junjie, Yuan, Xiaojun, Wang, Xin
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2512.24039
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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 proposes a Chebyshev polynomial expansion framework for the recovery of a continuous angular power spectrum (APS) from channel covariance. By exploiting the orthogonality of Chebyshev polynomials in a transformed domain, we derive an exact series representation of the covariance and reformulate the inherently ill-posed APS inversion as a finite-dimensional linear regression problem via truncation. The associated approximation error is directly controlled by the tail of the APS's Chebyshev series and decays rapidly with increasing angular smoothness. Building on this representation, we derive an exact semidefinite characterization of nonnegative APS and introduce a derivative-based regularizer that promotes smoothly varying APS profiles while preserving transitions of clusters. Simulation results show that the proposed Chebyshev-based framework yields accurate APS reconstruction, and enables reliable downlink (DL) covariance prediction from uplink (UL) measurements in a frequency division duplex (FDD) setting. These findings indicate that jointly exploiting smoothness and nonnegativity in a Chebyshev domain provides an effective tool for covariance-domain processing in multi-antenna systems.
format Preprint
id arxiv_https___arxiv_org_abs_2512_24039
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Continuous Angular Power Spectrum Recovery From Channel Covariance via Chebyshev Polynomials
Luo, Shengsong
Wu, Ruilin
Xu, Chongbin
Ma, Junjie
Yuan, Xiaojun
Wang, Xin
Information Theory
Signal Processing
This paper proposes a Chebyshev polynomial expansion framework for the recovery of a continuous angular power spectrum (APS) from channel covariance. By exploiting the orthogonality of Chebyshev polynomials in a transformed domain, we derive an exact series representation of the covariance and reformulate the inherently ill-posed APS inversion as a finite-dimensional linear regression problem via truncation. The associated approximation error is directly controlled by the tail of the APS's Chebyshev series and decays rapidly with increasing angular smoothness. Building on this representation, we derive an exact semidefinite characterization of nonnegative APS and introduce a derivative-based regularizer that promotes smoothly varying APS profiles while preserving transitions of clusters. Simulation results show that the proposed Chebyshev-based framework yields accurate APS reconstruction, and enables reliable downlink (DL) covariance prediction from uplink (UL) measurements in a frequency division duplex (FDD) setting. These findings indicate that jointly exploiting smoothness and nonnegativity in a Chebyshev domain provides an effective tool for covariance-domain processing in multi-antenna systems.
title Continuous Angular Power Spectrum Recovery From Channel Covariance via Chebyshev Polynomials
topic Information Theory
Signal Processing
url https://arxiv.org/abs/2512.24039