Asymptotic statistics for a generalized frequency-wavenumber estimator

The estimation of the frequency-wavenumber spectrum form the output of a sensor array placed in a homogeneous random field is considered. A generalized estimator which includes the Bartlett and minimum-variance estimators is used. Joint asymptotic normality of this frequency-wavenumber estimator is established; a precise asymptotic expression for the covariance matrix of the limiting distribution is obtained. It is shown that the generalized estimator converges in the mean-square sense. Confidence intervals based on the asymptotic normality results are presented for two array configuration examples