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Polynomial matrix eigenvalue decomposition techniques for multichannel signal processing

Wang, Zeliang 2017. Polynomial matrix eigenvalue decomposition techniques for multichannel signal processing. PhD Thesis, Cardiff University.
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Polynomial eigenvalue decomposition (PEVD) is an extension of the eigenvalue decomposition (EVD) for para-Hermitian polynomial matrices, and it has been shown to be a powerful tool for broadband extensions of narrowband signal processing problems. In the context of broadband sensor arrays, the PEVD allows the para-Hermitian matrix that results from the calculation of a space-time covariance matrix of the convolutively mixed signals to be diagonalised. Once the matrix is diagonalised, not only can the correlation between different sensor signals be removed but the signal and noise subspaces can also be identified. This process is referred to as broadband subspace decomposition, and it plays a very important role in many areas that require signal separation techniques for multichannel convolutive mixtures, such as speech recognition, radar clutter suppression, underwater acoustics, etc. The multiple shift second order sequential best rotation (MS-SBR2) algorithm, built on the most established SBR2 algorithm, is proposed to compute the PEVD of para-Hermitian matrices. By annihilating multiple off-diagonal elements per iteration, the MS-SBR2 algorithm shows a potential advantage over its predecessor (SBR2) in terms of the computational speed. Furthermore, the MS-SBR2 algorithm permits us to minimise the order growth of polynomial matrices by shifting rows (or columns) in the same direction across iterations, which can potentially reduce the computational load of the algorithm. The effectiveness of the proposed MS-SBR2 algorithm is demonstrated by various para-Hermitian matrix examples, including randomly generated matrices with different sizes and matrices generated from source models with different dynamic ranges and relations between the sources’ power spectral densities. A worked example is presented to demonstrate how the MS-SBR2 algorithm can be used to strongly decorrelate a set of convolutively mixed signals. Furthermore, the performance metrics and computational complexity of MS-SBR2 are analysed and compared to other existing PEVD algorithms by means of numerical examples. Finally, two potential applications of theMS-SBR2 algorithm, includingmultichannel spectral factorisation and decoupling of broadband multiple-input multiple-output (MIMO) systems, are demonstrated in this dissertation.

Item Type: Thesis (PhD)
Date Type: Completion
Status: Unpublished
Schools: Engineering
Uncontrolled Keywords: Polynomial Matrix Eigenvalue Decomposition; Broadband Subspace Decomposition; MS-SBR2 Algorithm; Spectral Factorisation; MIMO Systems; PEVD Algorithms.
Date of First Compliant Deposit: 18 January 2018
Last Modified: 20 May 2021 09:32

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