Sequential Matrix Diagonalisation Algorithms for Polynomial EVD of Parahermitian Matrices

For parahermitian polynomial matrices, which can be used, for example, to characterise space-time covariance in broadband array processing, the conventional eigenvalue decomposition (EVD) can be generalised to a polynomial matrix EVD (PEVD). In this paper, a new iterative PEVD algorithm based on sequential matrix diagonalisation (SMD) is introduced. At every step the SMD algorithm shifts the dominant column or row of the polynomial matrix to the zero lag position and eliminates the resulting instantaneous correlation. A proof of convergence is provided, and it is demonstrated that SMD establishes diagonalisation faster and with lower order operations than existing PEVD algorithms.