Least-squares Khatri-Rao factorization of a polynomial matrix

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Khattak, Faizan A. and Asim, Fasal-E- and Weiss, Stephan and de Almeida, André L. F.; (2025) Least-squares Khatri-Rao factorization of a polynomial matrix. In: 2025 33rd European Signal Processing Conference (EUSIPCO). IEEE, ITA, pp. 2292-2296. ISBN 978-9-4645-9362-4

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Abstract

The Khatri-Rao product is extensively used in array processing, tensor decomposition, and multi-way data analysis, where many applications rely on a least-squares (LS) Khatri-Rao factorization. In broadband sensor array problems, polynomial matrices effectively model frequency-dependent behaviors, necessitating extensions of conventional linear algebra techniques. This paper generalizes the LS Khatri-Rao factorization from ordinary to polynomial matrices by applying it to the discrete Fourier transform (DFT) sample points of polynomial matrices. Phase coherence across bin-wise Khatri-Rao factors is ensured via a phase-smoothing algorithm. The proposed phase smoothing method is validated through broadband angle-of-arrival (AoA) estimation for uniform planar arrays (UPAs), where the steering matrix is a polynomial matrix and can be represented as a Khatri-Rao product between decoupled steering matrices in azimuth and elevation directions.

ORCID iDs

Khattak, Faizan A., Asim, Fasal-E-, Weiss, Stephan ORCID logoORCID: https://orcid.org/0000-0002-3486-7206 and de Almeida, André L. F.;
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