In the wireless communication systems, the objective of using array antennas is to extract the desired signal while filtering out the unwanted interferences. New methods are developed for the optimization and synthesis, in terms of the directivity and the side lobe level. For the optimization of the array pattern, it is proposed to adjust both the excitation and the spacing of the antenna elements. The determination of the optimal excitation and spacing is shown to be a polynomial problem; this is described in terms of a unified mathematical approach to nonlinear optimization of multidimensional array geometries. The approach utilizes a class of limiting properties of Legendre functions that are dictated by the array geometry addressed. The objective of this paper is to describe a unified mathematical approach to nonlinear optimization of multidimensional array geometries.
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