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

This paper is devoted to the maximum likelihood (ML) estimation of multiple sources in the presence of unknown noise. With the noise modeled as a spatial autoregressive (AR) process, a direct and systematic way is developed to find the true ML estimates of all parameters associated with the direction finding problem, including the direction-of-arrival (DOA) angles /spl Theta/, the AR coefficients /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 part, /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 result from Monte Carlo trials, even for small numbers of snapshots.<>