Direction of arrival estimation in sparse arrays in the presence of unknown colored block-correlated noise fields

We address the problem of maximum likelihood (ML) direction-of-arrival (DOA) estimation in unknown spatially correlated noise fields using sensor arrays composed of multiple subarrays on a sparse grid. In such arrays, the noise covariance matrix has a block-diagonal structure which enables the number of nuisance noise parameters to be reduced substantially and the identifiability of the underlying DOA estimation problem to be ensured. A new deterministic ML DOA estimator is derived for the considered class of sparse sensor arrays. The proposed approach concentrates the estimation problem with respect to all nuisance parameters. In contrast to the analytic concentration used in conventional ML techniques, the proposed estimator is based on an iterative procedure, which includes a stepwise concentration of the LL (log-likelihood) function. Our algorithm is free of any further structural constraints or parametric model restrictions which are usually imposed on the noise covariance matrix and received signals in most existing ML-based approaches to DOA estimation in spatially correlated noise.