Generalized polynomial deflation method for rooting-based DOA estimators using greatest common divisor

Abstract

Given a uniform linear array (ULA) with M sensors, most rooting-based direction of arrival (DOA) estimators used to solve polynomials with high degree 2(M−1) for source DOAs, which is time-consuming with large ULAs. In this paper, we propose a novel polynomial deflation method which can be generally used for all coefficient-symmetric rooting-based DOA estimators, e.g., root-MUSIC, unitary root-MUSIC (U-root-MUSIC), real-valued root-MUSIC (RV-root-MUSIC), etc. We prove that for L<M sources, the greatest common divisor (GCD) of original polynomial and its derivative contains DOA information and has reduced degree about L. Therefore, DOA can be obtained by GCD directly. Numerical simulations are conducted to demonstrate that with significantly reduced complexity, such a GCD method can provide satisfactory performance close to the Crame´r-Rao Lower Bound (CRLB).