Maximum likelihood direction finding in spatially colored noise fields using sparse sensor arrays

We consider the problem of maximum likelihood (ML) direction-of-arrival (DOA) estimation of narrowband signals using sparse sensor arrays, which consist of widely separated subarrays such that the unknown spatially colored noise field is uncorrelated between different subarrays. We develop ML DOA estimators under the assumptions of zero-mean and non-zero-mean Gaussian signals based on an Expectation-Maximization (EM) framework. For DOA estimation of non-zero-mean Gaussian signals, we derive the Cramér-Rao bound (CRB) as well as the asymptotic error covariance matrix of the ML estimator that improperly assumes zero-mean Gaussian signals. We provide analytical and numerical performance comparisons for the existing deterministic and the proposed stochastic ML estimators. The results show that the proposed estimators normally provide better accuracy than the existing deterministic estimator, and that the nonzero means in the signals improve the accuracy of DOA estimation.