An Algorithm for Polynomial Matrix Eigenvalue Decomposition

Speaker: John McWhirter

4th May 2005 , 2pm , Room 519 Claremont Tower

Abstract

Space time adaptive processing is an important topic which arises in broadband sensor array signal processing. The space time correlation matrix requires (at least) three dimensions but may be represented very effectively as a para Hermitian symmetric (Laurent) polynomial matrix. A stable technique for computing the eigenvalue decomposition (EVD) of such a matrix is important for many applications including; broadband subspace identification; independent component analysis (ICA) applied to convolutive mixtures; space time coding for multiple antenna (MIMO) communicaton channels. This paper presents a novel algorithm for computing the polynomial matrix EVD. It involves diagonalising the polynomial space-time correlation matrix by means of a paraunitary "similarity" transformation. It makes use of "elementary paraunitary transformations" and constitutes a generalisation of the classical Jacobi algorithm. A proof of convergence has been obtained. Impressive results have been obtained for a range of practical applications using both simulated experimental data. Some of these will be presented.