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# A novel insight to the SBR2 algorithm for diagonalising Para-Hermitian matrices

 McWhirter, John and Wang, Zeliang 2017. A novel insight to the SBR2 algorithm for diagonalising Para-Hermitian matrices. Presented at: 11th IMA International Conference on Mathematics in Signal Processing, Birmingham, UK, 12 – 14 December 2016. 11th IMA International Conference on Mathematics in Signal Processing.

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## Abstract

The second order sequential best rotation (SBR2) algorithm was originally developed for achieving the strong decorrelation of convolutively mixed sensor array signals. It was observed that the algorithm always seems to produce spectrally majorized output signals, but this property has not previously been proven. In this work, we have taken a fresh look at the SBR2 algorithm in terms of its potential for optimizing the subband coding gain. It is demonstrated how every iteration of the SBR2 algorithm must lead to an increase in the subband coding gain until it comes arbitrarily close to its maximum possible value. Since the algorithm achieves both strong decorrelation and optimal subband coding, it follows that it must also produce spectral majorisation. A new quantity $\gamma$ associated with the coding gain optimization is introduced, and its monotonic behaviour brings a new insight to the convergence of the SBR2 algorithm.

Item Type: Conference or Workshop Item (Poster) Publication In Press Engineering T Technology > TK Electrical engineering. Electronics Nuclear engineering 6 April 2017 09 Jun 2020 01:26 http://orca.cardiff.ac.uk/id/eprint/97499

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