Maximum likelihood DOA estimation and asymptotic Cramer-Rao bounds for additive unknown colored noise

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Abstract
This paper is devoted to the maximum likelihood estimation of multiple sources in the presence of unknown noise. With the spatial noise covariance modeled as a function of certain unknown parameters, e.g., an autoregressive (AR) model, a direct and systematic way is developed to find the exact maximum likelihood (ML) estimates of all parameters associated with the direction finding problem, including the direction-of-arrival (DOA) angles /spl Theta/, the noise parameters /spl alpha/, the signal covariance /spl Phi//sub s/, and the noise power /spl sigma//sup 2/. We show that the estimates of the linear part of the parameter set /spl Phi//sub s/ and /spl sigma//sup 2/ can be separated from the nonlinear parts /spl Theta/ and /spl alpha/. Thus, the estimates of /spl Phi//sub s/ and /spl sigma//sup 2/ become explicit functions of /spl Theta/ and /spl alpha/. This results in a significant reduction in the dimensionality of the nonlinear optimization problem. Asymptotic analysis is performed on the estimates of /spl Theta/ and /spl alpha/, and compact formulas are obtained for the Cramer-Rao bounds (CRB's). Finally, a Newton-type algorithm is designed to solve the nonlinear optimization problem, and simulations show that the asymptotic CRB agrees well with the results from Monte Carlo trials, even for small numbers of snapshots.<>

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