An algebraic approach for deriving eigenvalues and eigenvectors of correlation matrices toward the fast DOA estimation

摘要

In this report, we discuss the eigenproblems of correlation matrices in Direction-of-arrival (DOA) algorithms. Such eigenproblems should be quickly processed for the fast data transferring, and the QR decomposition (or the one combined with Householder transformation) is generally used for such processing. This report focuses on the case that the number of the arriving wave is a few, say, the order of the correlation matrix is less than five. Regarding the eigenproblem as solving the fourth-order algebraic polynomial, the eigenvalues and eigenvectors can be obtained in a very short time. Moreover, it is confirmed that the proposed algebraic approach does not make the accuracy worse when it is implemented by finite word-length processors suchlike digital signal processors (DSP).