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Inversion of Parahermitian matrices

Weiss, Stephan and Millar, Andrew P. and Stewart, Robert W. (2010) Inversion of Parahermitian matrices. In: 18th European Signal Processing Conference, 2010-08-23 - 2010-08-28.

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Parahermitian matrices arise in broadband multiple-input multiple-output (MIMO) systems or array processing, and require inversion in some instances. In this paper, we apply a polynomial eigenvalue decomposition obtained by the sequential best rotation algorithm to decompose a parahermitian matrix into a product of two paraunitary, i.e.lossless and easily invertible matrices, and a diagonal polynomial matrix. The inversion of the overall parahermitian matrix therefore reduces to the inversion of auto-correlation sequences in this diagonal matrix. We investigate a number of different approaches to obtain this inversion, and and assessment of the numerical stability and complexity of the inversion process.