Abstract
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.
Highlights
Large arrays are widely used in many applications such as radar, sonar and wireless communication, etc, to gain predominance in detection range and spatial resolution capability [1]∼ [3]
To realize thorough real-valued computations for both tasks of eigenvalue decomposition (EVD) and polynomial rooting, we have proposed another real-valued formulation of root-multiple signal classification (MUSIC) for fast DOA
We show by numerical simulations our algorithm can provide a similar performance to ESPRIT [20], and it provides an efficient trade-off between complexity and accuracy
Summary
Large arrays are widely used in many applications such as radar, sonar and wireless communication, etc, to gain predominance in detection range and spatial resolution capability [1]∼ [3]. When large arrays are used, this method still requires high complexity, and there is a wide gap to further reduce the high computational complexity for super-resolution DOA estimation with large ULAs. the main motivation of this paper is to propose a novel modified root-MUSIC algorithm which can be used for low-complexity DOA estimation with large arrays. The main motivation of this paper is to propose a novel modified root-MUSIC algorithm which can be used for low-complexity DOA estimation with large arrays To this end, we first divide a standard ULA into two subarrays and exploit the subarray structure to extract a real noise matrix by real-valued EVD computation on a real-valued matrix which has half-reduced dimensions [18]. (·)H is conjugate transpose, E [·] is mathematical expectation, Re(·) is the real part of the embraced element, span(·) denotes the column space of the embraced matrix, and (·) stands for the angle of the embraced complex number
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