Reduced-complexity direction of arrival estimation with centro-symmetrical arrays and its performance analysis

A fast algorithm is proposed to dramatically reduce the computational complexity of the multiple signal classification (MUSIC) algorithm for direction-of-arrival (DOA) estimate using a centro-symmetrical array (CSA). The CSA is divided into two sub-arrays and a real matrix is constructed with the covariance matrices of the two sub-arrays and their cross-correlation ones. This real matrix is further regarded as the data covariance one observed by a virtual array which has a real array response, and a novel MUSIC-like cost function is derived accordingly. In the developed method, only real-valued computation is required and the spectral search is compressed into half of the total angular field-of-view. Furthermore, the dimensions of noise subspace and those of search vector are both reduced, leading to about 97% complexity reduction as compare to MUSIC. The non-asymptotic statistical performance of the new DOA estimator is analyzed and a closed-form expression is given to predict the mean square error (MSE) of DOA estimation by the new technique. The effectiveness of the presented approach as well as the theoretical analysis is verified through numerical computer simulations, and it is shown that the proposed method is able to provide good accuracy with low signal-to-noise ratio (SNR) and small numbers of snapshots.