Pattern synthesis in hybrid antennas using the singular value decomposition of scattering matrices

Given a scattering matrix representation of a hybrid antenna system, the left and right singular vectors have been shown to form orthonormal base sets for the feed and aperture signal spaces. The rank of the matrices, as determined by the number of nonzero singular values, can be used to determine the number of required feed elements. Using the aperture basis vectors, a set of orthogonal far-field basis patterns can be found. These basis patterns span the pattern space that is utilized by a particular hybrid antenna system, and are useful for pattern synthesis. Although the transmit case has been used for illustrations in this paper, it should be clear that similar relationships and conclusions hold for the receive case as well.