A modified likelihood function approach to DOA estimation in the presence of unknown spatially correlated Gaussian noise using a uniform linear array

The problem of modified ML estimation of DOA's of multiple source signals i ncident on a uniform linear array (ULA) in the presence of unknown, spatial ly correlated Gaussian noise is addressed here. Unlike previous work, the p roposed method does not impose any structural constraints or parameterizati on of the signal and noise covariances. It is shown that the characterizati on suggested here provides a very convenient framework for obtaining an int uitively appealing estimate of the unknown noise covariance matrix via a su itable projection of the observed covariance matrix onto a subspace that is orthogonal complement of the so-called signal subspace, This leads to a fo rmulation of an expression for a so-called modified likelihood function, wh ich can be maximized to obtain the unknown DOA's, For the case of an arbitr ary array geometry, this function has explicit dependence on the unknown no ise covariance matrix. This explicit dependence can be avoided for the spec ial case of a uniform line array by using a simple polynomial characterizat ion of the latter. A simple approximate version of this function is then de veloped that can be maximized via the well-known IQML algorithm or its rece nt variants, An exact estimate based on the maximization of the modified li kelihood function is obtained by using nonlinear optimization techniques wh ere the approximate estimates are used for initialization, The proposed est imator is shown to outperform the MAP estimator of Kelly et al., Extensive simulations have been carried out to show the validity of the proposed algo rithm and tc, compare it with some previous solutions.