Efficient Real-Valued Rank Reduction Algorithm for DOA Estimation of Noncircular Sources under Mutual Coupling

Noncircular sources are widely used in wireless communication array systems, which can offer more accurate estimates and detect more sources. However, in practical array systems, the direction-of-arrival (DOA) estimation performance may be severely degraded by mutual coupling effects. To solve this problem, we propose a real-valued DOA estimation algorithm for noncircular sources under unknown mutual coupling. Based on the sources' noncircularity, an augmented real-valued covariance matrix is constructed. Then, utilizing the banded symmetric and Toeplitz property of the mutual coupling matrix, the middle subarray elements are considered as ideal ones, which have the same array gains. Finally, according to the subspace principle, a rank reduction-based virtual steering vector parameterizing method is derived, which extracts the DOAs from other nuisance parameters. Compared with conventional algorithms, the proposed one not only improves the estimation accuracy but also resolves more sources. Moreover, it is computationally efficient, since it only requires real-valued computations and 1-D spectral search. Numerical simulations demonstrate that the proposed method performs well under unknown mutual coupling and outperforms some of the existing approaches in resolution capability, estimation accuracy, and computational loads.