Decoupled estimation of DOA and angular spread for spatially distributed sources

We consider the problem of estimating the parameters (direction-of-arrival (DOA) and angular spread) of a spatially distributed source, using a uniform linear array. A two-step procedure which enables decoupling the estimation of the DOA from that of the angular spread is proposed. This method combines a covariance matching algorithm with the use of the extended invariance principle (EXIP). More exactly, the first step makes use of an unstructured model for the part of the covariance matrix that depends on the angular spread. Then, the solution is refined by invoking the EXIP. Instead of a 2-D search, the proposed scheme requires two successive 1-D searches. Additionally, the DOA estimate is robust to mismodelling the spatial distribution of the scatterers. A statistical analysis is carried out and a formula for the asymptotic variance of the estimates is derived. Numerical examples illustrate the performance of the method.