Localization of Mixed Far-Field and Near-Field Incoherently Distributed Sources Using Two-Stage RARE Estimator

In this article, a mixed source localization method utilizing a two-stage rank-reduction (RARE) estimator is investigated. Different from the existing methods, the proposed one is built on the incoherently distributed (ID) source model, which is more appropriate for multipath and fast time-varying channels. Firstly, a general array manifold (GAM) model is established, where nominal direction of arrivals (DOAs) and nominal ranges are extracted from the initial array manifold. By exploiting the shift invariance property of the far-field (FF) GAM and combining virtual source enumeration result, nominal FF DOA estimation is achieved by a 1-D RARE spectral search. Secondly, the oblique projection operation is adopted to separate near-field (NF) sources, and the nominal DOA and range parameters of NF sources are subsequently obtained by jointly utilizing the manifold separation technique and another two 1-D spectral searches. With the estimated nominal DOA and range parameters, the angular spread and range spread are then successfully estimated. Moreover, the Cramér–Rao bound for the considered case is also derived. Simulation results are presented to validate the effectiveness of the proposed method.