DOA Estimation Under Mutual Coupling of Uniform Linear Arrays Using Sparse Reconstruction

• Published in: IEEE wireless communications letters Vol. 8; no. 4; pp. 1004 - 1007
• Main Authors: Wang, Yuexian, Wang, Ling, Xie, Jian, Trinkle, Matthew, Ng, Brian W.-H.
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 01.08.2019; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: convex optimization; Covariance matrices; Direction of arrival; Direction of arrival (DOA); Direction-of-arrival estimation; Estimation; Linear arrays; Linear transformations; Manifolds; Mathematical analysis; Matrix methods; Mutual coupling; Reconstruction; Redundant components; Sparse matrices; sparse reconstruction; Symmetric matrices
• ISSN: 2162-2337; 2162-2345
• DOI: 10.1109/LWC.2019.2903497

A novel sparse reconstruction method is developed for direction of arrival (DOA) estimation in the presence of unknown mutual coupling of uniform linear arrays. In the proposed method, a sparse representation for single measurement vector (SMV) is first derived. Then, it is shown that the problem size can be reduced by a linear transformation to eliminate the redundant components in the SMV. Finally, by taking advantage of the banded symmetric Toeplitz structure of the mutual coupling matrix, a reweighted ℓ 1 -norm minimization subject to an error-constrained ℓ 2 -norm is introduced to determine the DOA estimates without mutual coupling compensation, further enhancing the sparsity and providing a robustness against the noise. Simulation results demonstrate the superiority of the proposed method over its state-of-the-art counterparts.