Convergence properties for frequency-wavenumber estimation

The estimation of the frequency-wavenumber spectrum from the output of a sensor array placed in a homogeneous random field is considered. A generalized estimator that includes the Bartlett and minimum energy estimators is analyzed. The generalized frequency-wavenumber estimator is shown to converge in distribution, and a precise asymptotic expression for the covariance matrix of the limiting distribution is obtained. It is also shown that the estimator converges in the mean-square sense. Examples of the asymptotic variance for a variety of array configurations are presented.<>