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 Θ, the AR coefficients α, the signal covariance Φ_s and the noise power σ². We show that the estimates of the linear part of the parameter set, Φ_s and σ², can be separated from the nonlinear part, Θ and α. This results in a significant reduction in the dimensionality of the nonlinear optimization problem. Asymptotic analysis is performed on the estimates of Θ and α 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