Research Paper#Signal Processing, Wireless Communications, Antenna Systems🔬 ResearchAnalyzed: Jan 3, 2026 15:56
Chebyshev Polynomials for Angular Power Spectrum Recovery
Published:Dec 30, 2025 07:24
•1 min read
•ArXiv
Analysis
This paper introduces a novel framework using Chebyshev polynomials to reconstruct the continuous angular power spectrum (APS) from channel covariance data. The approach transforms the ill-posed APS inversion into a manageable linear regression problem, offering advantages in accuracy and enabling downlink covariance prediction from uplink measurements. The use of Chebyshev polynomials allows for effective control of approximation errors and the incorporation of smoothness and non-negativity constraints, making it a valuable contribution to covariance-domain processing in multi-antenna systems.
Key Takeaways
- •Proposes a Chebyshev polynomial expansion framework for APS recovery.
- •Reformulates the ill-posed APS inversion as a finite-dimensional linear regression problem.
- •Provides an exact semidefinite characterization of nonnegative APS.
- •Introduces a derivative-based regularizer for smooth APS profiles.
- •Enables reliable downlink covariance prediction from uplink measurements.
Reference
“The paper derives an exact semidefinite characterization of nonnegative APS and introduces a derivative-based regularizer that promotes smoothly varying APS profiles while preserving transitions of clusters.”