Sequential Matrix Diagonalization Algorithms for Polynomial EVD of Parahermitian Matrices

Abstract

For parahermitian polynomial matrices, which can be used, for example, to characterize space-time covariance in broadband array processing, the conventional eigenvalue decomposition (EVD) can be generalized to a polynomial matrix EVD (PEVD). In this paper, a new iterative PEVD algorithm based on sequential matrix diagonalization (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 diagonalization faster and with lower order operations than existing PEVD algorithms.