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Maximum Likelihood Direction Finding in Spatially Colored Noise Fields



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1048 IEEE TRANSACTIONS ON SIGNAL PROCESSING VOL 59 NO 3 MARCH 2011 Maximum Likelihood Direction Finding in Spatially Colored Noise Fields Using Sparse Sensor Arrays Tao Li and Arye Nehorai Fellow IEEE Abstract 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 Cram r 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 Index Terms Cram r Rao bound CRB direction of arrival DOA estimation maximum likelihood estimation spatially colored noise I INTRODUCTION RRAY processing for direction of arrival DOA estimation has been a topic of intensive research interest during the past two decades Many proposed estimators assume spatially white noise see 1 5 for examples such that the array noise covariance matrix is proportional to an identity matrix However this assumption is not realistic in many practical applications 6 12 where the noise fields are spatially colored The spatial correlation or nonuniformity in the colored noise may significantly degrade the performance of the estimators assuming spatially white noise 13 14 In these applications it is beneficial to take the spatial color of the noise into account to improve the



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