A Real-Valued Polynomial Rooting Method for Fast Direction of Arrival Estimation With Large Uniform Linear Arrays

When used for direction of arrival (DOA) estimation with large uniform linear arrays (ULAs), both root-MUSIC and unitary root-MUSIC (U-root-MUSIC) involve high-dimension eigenvalue decomposition (EVD) and high-degree polynomial rooting computations. In this paper, we propose a novel real-valued modification of root-MUSIC to reduce the computational complexity. We first divide the large ULA into two moderate subarrays and exploit the subarray structure to extract a real noise matrix with reduced-dimension EVD. Using this real noise matrix, we construct a real polynomial, and further employ a variable substitution technique to transform the real polynomial to a new one with reduced degree equivalently. As such, both tasks of EVD and polynomial rooting can be computed efficiently. We finally show by numerical simulations that with significantly reduced computational complexity, the proposed method sacrifices statistically nonsignificant accuracy that is acceptable.