Underdetermined Wideband DOA Estimation Utilizing Noncircular Complex Gaussian Distribution

With the emerging of sparsely spaced sensor arrays, the study on underdetermined direction-of-arrival (DOA) estimation methods has drawn much attention. In most of the existing methods, the vectorized sample covariance matrix was considered as circularly symmetric Gaussian by default. However, the sample covariance vector is in fact noncircular, and its pseudo covariance matrix has not yet been utilized for underdetermined DOA estimation. On account of the wide usage of wideband signals nowadays, in this letter, the underdetermined DOA estimation problem for wideband signals is addressed, where the noncircularity of the sample covariance vectors is exploited. Moreover, a hierarchical Bayesian model is established, modeling the noncircular sample covariance vectors, the nonnegative group-sparse signal variance vectors, the auto-estimated regularization parameter and the off-grid difference, which were not considered simultaneously in the existing methods. A sparse Bayesian learning algorithm is derived via expectation-maximization, and numerical simulations show that the proposed method outperforms the methods that do not consider the noncircularity of sample covariance vectors.