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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2503.23187 |
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| _version_ | 1866917971895517184 |
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| author | Khattak, Faizan A. Fazal-E-Asim Weiss, Stephan de Almeida, Andre L. F. |
| author_facet | Khattak, Faizan A. Fazal-E-Asim Weiss, Stephan de Almeida, Andre L. F. |
| contents | The Khatri-Rao product is extensively used in array processing, tensor decomposition, and multi-way data analysis. Many applications require 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 LS Khatri-Rao factorization from ordinary to polynomial matrices by applying it to the discrete Fourier transform (DFT) samples of polynomial matrices. Phase coherence across bin-wise Khatri-Rao factors is ensured via a phasesmoothing algorithm. The proposed method is validated through broadband angle-of-arrival (AoA) estimation for uniform planar arrays (UPAs), where the steering matrix is a polynomial matrix, which can be represented as a Khatri-Rao product between steering matrix in azimuth and elevation directions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_23187 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Least-Squares Khatri-Rao Factorization of a Polynomial Matrix Khattak, Faizan A. Fazal-E-Asim Weiss, Stephan de Almeida, Andre L. F. Signal Processing The Khatri-Rao product is extensively used in array processing, tensor decomposition, and multi-way data analysis. Many applications require 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 LS Khatri-Rao factorization from ordinary to polynomial matrices by applying it to the discrete Fourier transform (DFT) samples of polynomial matrices. Phase coherence across bin-wise Khatri-Rao factors is ensured via a phasesmoothing algorithm. The proposed method is validated through broadband angle-of-arrival (AoA) estimation for uniform planar arrays (UPAs), where the steering matrix is a polynomial matrix, which can be represented as a Khatri-Rao product between steering matrix in azimuth and elevation directions. |
| title | Least-Squares Khatri-Rao Factorization of a Polynomial Matrix |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2503.23187 |