Joint 2D direction of arrival estimation using a sparse representation of cross covariance matrix

In this study, the problem of two-dimensional (2D) direction of arrival estimation for uncorrelated signals with an L-shaped array is discussed. The estimated cross covariance matrix (CCM) between the sample data along the x-axis and the z-axis is constructed. The elevation angle of the signal is obtained by finding the sparse coefficients of the estimated CCM based on the discussion of statistical probability distribution of the sample data error. Once the elevation angle is obtained, with the non-coupling between the elevation angle and the azimuth angle, the azimuth angle of each source is estimated by the eigenvalue decomposition of the conjugate transpose matrix of the estimated CCM. The proposed algorithm has better estimation performance in the situation of low signal-to-noise-ratio cases but also the estimated azimuth and elevation angles are paired automatically. The performance of the proposed method is compared with some existing schemes and the effectiveness of the method is demonstrated by computer simulations.