Fast implementation of root-form eigen-based methods for detecting closely spaced sources

Root-form eigen-based methods for direction-of-arrival (DOA) estimation represent a class of estimators that exhibit a higher resolution capability relative to spectral-form estimators in detecting closely spaced sources with a linear, equally spaced (LES) array. These methods require an eigenvalue decomposition (EVD) and a polynomial rooting. Although the numerical complexity associated with the EVD is greatly reduced with the use of beamspace transformation, large-order polynomial rooting still raises practical difficulties. As a remedy, the author proposes a novel iterative implementation of beamspace root-form methods without the need for large-order polynomial rooting. The new method exploits the banded structure of the augmented noise eigenvector matrix associated with an LES array. It requires only rooting in parallel several small-order polynomials and some minor matrix manipulations at each iteration. It is shown that the proposed method offers the performance of beamspace root-MUSIC