Fast Direction of Arrival Estimation for Uniform Circular Arrays with a Virtual Signal Subspace

In this paper, an augmented subspace-based algorithm for detecting the direction of arrival (DOA) of signals is presented. In the developed scheme, a uniform circular antenna array with a full range of lateral capacity is firstly transformed into a uniform linear antenna array in which the steering matrix has a Vandermonde form. This kind of structure can be exploited to formulate computationally efficient search-free estimation methods. In the process of virtual transformation, a novel DOA unit matrix of an assumed sector where the signals to be detected are located is built and optimized to find response matrices of the real and virtual antenna arrays to signals from the sector. By utilizing singular value decomposition (SVD) of the response matrix of the real antenna array to possible signals from the sector, a stable virtual transformation matrix between the real and virtual antenna arrays is obtained. Meanwhile, the aperture of the original array is also expanded during this process. Then, a virtual cyclic optimization algorithm is introduced to thoroughly mine information from the correlation matrices of the virtual antenna array receiving data and to optimize the signal subspace. Subsequently, the DOA can be efficiently determined through the reconstruction of the steering matrix. In the experimental part of the study, root mean square errors and probability of success are used to evaluate the performance of the algorithms. In particular, simulation results demonstrate that the proposed methods provide significant accuracy improvements especially for low signal-to-noise ratio thresholds.