Two-dimensional angular parameter estimation for noncircular incoherently distributed sources based on an L-shaped array

In this paper, a two-stage reduced-rank estimator is proposed for two-dimensional (2D) direction estimation of incoherently distributed (ID) noncircular sources, including their center directions of arrival (DOAs) and angular spreads, based on an L-shaped array. Firstly, based on the first-order Taylor series approximation, a noncircularity-based extended generalized array manifold (GAM) model is established. Then, the 2D center DOAs of incident ID signals are obtained separately with the noncircularity-based generalized shift-invariance property of the array manifold and the reduced-rank principle. The pairing of the two center DOAs is completed by searching for the minimum value of a cost function. Secondly, the 2D angular spreads can be obtained in closed-form solution from the central moments of the angular distribution. The proposed estimator achieves higher accuracy in angle estimation that manages more sources and shows promising results in the general scenario, where different sources possess different angular distributions. Furthermore, the approximate noncircular stochastic Cramer-Rao bound (CRB) of the concerned problem is derived as a benchmark. Numerical analysis proves that the proposed algorithm achieves better estimation performance in both 2D center DOAs and 2D angular spreads than an existing estimator.