Extending narrowband descriptions and optimal solutions to broadband sensor arrays

This overview paper motivates the description of broadband sensor array problems by polynomial matrices, directly extending notation that is familiar from the characterisation of narrowband problems. To admit optimal solutions, the approach relies on extending the utility of the eigen- and singular value decompositions, by finding decompositions of such polynomial matrices. Particularly the factorisation of parahermitian polynomial matrices --- including space-time covariance matrices that model the second order statistics of broadband sensor array data --- is important. The paper summarises recent findings on the existence and uniqueness of the eigenvalue decomposition of such parahermitian polynomial matrices, demonstrates some algorithms that implement such factorisations, and highlights key applications where such techniques can provide advantages over state-of-the-art solutions