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The covariance matrix for an array associated with a stationary space-time process is completely determined by the individual element locations, the directional responses of those elements, and the spatial spectrum of the process. Assuming the process is stationary in both time and space, there is a well-defined Fourier transform relationship between the elements of the covariance matrix and the spatial spectrum. An estimate of the covariance matrix can be determined from an estimate of the spatial spectrum. This paper compares the performance of adaptive beamformers derived from such structured covariance matrices with those based on the standard sample covariance matrix. Simulations illustrate the performance of this approach for both interference and noise only and correlated signal and interference cases.