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The importance of designing a radar (or communications) receiver to operate effectively in the presence of spatial noise creates the necessity for determining the space-time cross-correlation functions between antenna array elements. A representation of a general, polarized, nonisotropic noise process is used to determine the cross-spectral densities and cross-correlation functions between arbitrarily oriented dipole antenna array elements in the presence of a noise field only. Several examples have been worked out for isotropic noise to show the variation of the cross-correlated noise function vs. the spatial separation of the dipoles. One important result is that the noise cross correlation is shown to be a function of the receiver element spatial orientation when the elements are dipoles. For certain spatial orientations between dipoles it is possible to reduce the noise cross correlation between these antenna array elements to zero.