MAXIMUM-LIKELIHOOD DOA ESTIMATION AND ASYMPTOTIC CRAMER-RAO BOUNDS FOR ADDITIVE UNKNOWN COLORED NOISE

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 Theta, the noise parameters alpha, the signal covariance Phi(s), and the noise power sigma(2). We show that the estimates of the linear part of the parameter set Phi(s) and sigma(2) can be separated from the nonlinear parts Theta and alpha. Thus, the estimates of Phi(s), and sigma(2) become explicit functions of Theta and alpha. This results in a significant reduction in the dimensionality of the nonlinear optimization problem. Asymptotic analysis is performed on the estimates of Theta and 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.