Noncircularity-based generalized shift invariance for estimation of angular parameters of incoherently distributed sources

In this paper, a reduced-rank angular parameters estimation algorithm is proposed for incoherently distributed (ID) noncircular sources based on a uniform linear array (ULA), which addresses the problems of central direction-of-arrival (DOA) estimation and angular spread estimation. Firstly, the noncircularity property of the signals is utilized to establish an extended generalized array manifold (GAM) model based on the first-order Taylor series approximation. Then, the central DOAs of source signals are obtained based on the generalized shift invariance property of the array manifold and the reduced-rank principle. Next, the angular spreads are estimated from the central moments of the angular distribution. Compared with the existing algorithm without exploiting the noncircularity information, the proposed one can achieve a higher accuracy and handle more sources. In addition, it can deal with a general scenario where different sources have different angular distribution shapes. Furthermore, the approximate stochastic Cramer-Rao bound (CRB) of the concerned problem is derived. Simulation results are provided to demonstrate the performance of the proposed algorithm.