Localization of mixed coherently and incoherently distributed sources based on generalized array manifold

In practice, signals received by an array may be a mixture of coherently distributed (CD) and incoherently distributed (ID) sources, due to some complicated multipath/scattering effects. To localize mixed CD and ID sources, a method based on the generalized array manifold (GAM) is developed in this work. Firstly, source enumeration and source type classification are achieved by jointly employing the minimum description length (MDL) criterion, the covariance matrix difference technique and the second-order statistics of associated eigenvalues. Secondly, with the source enumeration result, the nominal direction of arrival (DOA) of ID sources is estimated by the rank-reduction principle based one-dimensional (1-D) spectral search, where shift invariance of the GAM associated with ID sources is considered. Thirdly, the oblique projection technique is adopted to separate the CD sources from ID ones, and then the nominal DOA of CD sources is estimated via the sparsity-cognizant total least-squares (S-TLS) method. Finally, with aid of the nominal DOA estimates, the corresponding angular spreads are calculated. An analysis of the proposed method is discussed and the approximate Cramér-Rao bound (CRB) is derived. Simulations are provided to demonstrate the performance of the proposed method.