Joint multidimensional optimization for blind DOA estimation of uniform circular arrays with unknown mutual coupling

Abstract

Mutual coupling distorts the array manifold and can severely degrade direction-of-arrival (DOA) estimation by subspace-based methods. This paper develops a blind DOA-estimation framework for uniform circular arrays with unknown mutual coupling. By exploiting the complex symmetric circulant structure of the coupling matrix, the ambiguity mechanisms associated with conventional one-dimensional searches are first characterized, and practical criteria are established to reject spurious solutions. It is then shown that existing one-dimensional formulations estimate source directions separately and fail to fully exploit the coupling vector shared by all true DOAs. To address this limitation, two joint multidimensional optimization models are formulated to incorporate the common coupling structure. Newton-based and alternating-optimization procedures are derived, using the one-dimensional estimates for initialization. Simulation studies involving two to four sources demonstrate that the proposed joint formulations improve DOA-estimation accuracy over their one-dimensional counterparts under representative signal-to-noise ratios, array configurations, and coupling conditions, without requiring calibration sources or prior knowledge of the coupling coefficients. These results show that exploiting the shared coupling structure provides an effective approach to blind DOA estimation for uniform circular arrays.