2D DOA estimation with sparse uniform circular arrays in the presence of mutual coupling

In this article, we consider the uniform circular arrays (UCAs) with the number of antenna elements insufficient to apply the traditional beamspace-based algorithms, which are labeled as sparse UCAs. For such UCAs, we propose a new hybrid approach for 2D direction-of-arrival (DOA) estimation in the presence of mutual coupling. Using the manifold decomposition technique, we present two new formulations of the steering vector in the presence of mutual coupling for sparse UCAs. Then, we introduce the adaptations to a modified uniform circular array rank reduction algorithm. This leads to an algorithm that is able to estimate the azimuth angle without the exact knowledge of mutual coupling. Next, we use a search-free rooting algorithm which expands the steering into a double Fourier series for each estimated azimuth to obtain the elevation angle estimates. The manifold decomposition technique introduces truncation errors. However, the accuracy of the DOA estimates is strongly affected by these errors when the array has a small number of elements. Therefore, expressions describing the truncation errors in the DOA estimates are derived. This allows us to choose an appropriate truncated degree in the manifold separation transformation to enhance the DOA estimate accuracy. Numerical examples are presented to demonstrate the effectiveness of the proposed method.