Polynomial GSVD Beamforming for Two-User Frequency-Selective MIMO Channels

Hassan, Diyari; Redif, Soydan; McWhirter, J.G.; Lambotharan, Sangarapillai

doi:10.1109/tsp.2021.3052040

Cited by 8 publications

(4 citation statements)

References 33 publications

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“…This CSD matrix can assist in formulating and solving broadband array problems, including e.g. beamforming [2]- [4], blind source separation [5], multichannel coding [6], [7], speech enhancement [8]- [10], or MIMO system design [11]- [13].…”

Section: Introductionmentioning

confidence: 99%

Eigenvalue Decomposition of a Parahermitian Matrix: Extraction of Analytic Eigenvectors

Weiss

Proudler

Coutts

et al. 2023

IEEE Trans. Signal Process.

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An analytic parahermitian matrix admits in almost all cases an eigenvalue decomposition (EVD) with analytic eigenvalues and eigenvectors. We have previously defined a discrete Fourier transform (DFT) domain algorithm which has been proven to extract the analytic eigenvalues. The selection of the eigenvalues as analytic functions guarantees in turn the existence of unique one-dimensional eigenspaces in which analytic eigenvectors can exist. Determining such eigenvectors is not straightforward, and requires three challenges to be addressed. Firstly, one-dimensional subspaces for eigenvectors have to be woven smoothly across DFT bins where a non-trivial algebraic multiplicity causes ambiguity. Secondly, with the one-dimensional eigenspaces defined, a phase smoothing across DFT bins aims to extract analytic eigenvectors with minimum time domain support. Thirdly, we need to check whether the DFT length, and thus the approximation order, is sufficient. We propose an iterative algorithm for the extraction of analytic eigenvectors and prove that this algorithm converges to the best of a set of stationary points. We provide a number of numerical examples and simulation results, in which the algorithm is demonstrated to extract the ground truth analytic eigenvectors arbitrarily closely.

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Section: Introductionmentioning

confidence: 99%

Eigenvalue Decomposition of a Parahermitian Matrix: Extraction of Analytic Eigenvectors

Weiss

Proudler

Coutts

et al. 2023

IEEE Trans. Signal Process.

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“…Such algorithms can enable a number of applications ranging from e.g. MIMO communications [14], [15], beamforming [16], to filter bank design and paraunitary matrix completion [17]. The Kogbetliantz method in [13] is a powerful approach that generally yields better diagonalisation and lower order factors than those achieved via two PEVDs.…”

Section: Introductionmentioning

confidence: 99%

Generalised Sequential Matrix Diagonalisation for the SVD of Polynomial Matrices

Khattak,

Proudler,

McWhirter

et al. 2023

2023 Sensor Signal Processing for Defence Conference (SSPD)

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To extend the singular value decomposition (SVD) to matrices of polynomials, an existing algorithm -a polynomial version of the Kogbetliantz SVD -iteratively targets the largest off-diagonal elements, and eliminates these through delay and Givens operations. In this paper, we perform a complete diagonalisation of the matrix component that contains this maximum element, thereby transfering more off-diagonal energy per iteration step. This approach is motivated by -and represents a generalisation of -the sequential matrix diagonalisation method for parahermitian matrices. In simulations, we demonstrate the benefit of this generalised SMD over the Kogbetliantz approach, both in terms of diagonalisation and the order of the extracted factors.

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“…This decomposition has found extensive utilisation in signal processing generally [3,4]. The SVD has been particularly attractive for the design of multipleinput multiple-output (MIMO) narrowband communications systems, where A is the channel matrix of complex gain factors [5][6][7][8][9][10][11][12][13][14] . Here, the decomposition afforded by the SVD has been shown to enable solutions for e.g.…”

Section: Introductionmentioning

confidence: 99%

Compact Order Polynomial Singular Value Decomposition of a Matrix of Analytic Functions

Bakhit,

Khattak,

Proudler

et al. 2023

2023 IEEE 9th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

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This paper presents a novel method for calculating a compact order singular value decomposition (SVD) of polynomial matrices, building upon the recently proven existence of an analytic SVD for analytic, non-multiplexed polynomial matrices. The proposed method calculates a conventional SVD in sample points on the unit circle, and then applies phase smoothing Algorithms to establish phase-coherence between adjacent frequency bins. This results in the extraction of compact order singular values and their corresponding singular vectors. The method is evaluated through experiments conducted on an ensemble of randomised polynomial matrices, demonstrating its superior performance in terms of higher decomposition accuracy and lower polynomial order compared to state-of-the-art techniques.

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Polynomial GSVD Beamforming for Two-User Frequency-Selective MIMO Channels

Cited by 8 publications

References 33 publications

Eigenvalue Decomposition of a Parahermitian Matrix: Extraction of Analytic Eigenvectors

Eigenvalue Decomposition of a Parahermitian Matrix: Extraction of Analytic Eigenvectors

Generalised Sequential Matrix Diagonalisation for the SVD of Polynomial Matrices

Compact Order Polynomial Singular Value Decomposition of a Matrix of Analytic Functions

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