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Various techniques for optimizing the performance indices of antenna arrays are discussed. In particular, methods for maximizing array directivity and signal-to-noise power ratio are reviewed. These performance indices are expressible as a ratio of two Hermitian forms, which has a certain special property to enable the facile determination of both its maximum value and the conditions under which this maximum is attained. Special maximization procedures by excitation amplitude and phase adjustments, by spacing perturbation, by phase adjustments only, and by a coordinate transformation with constraints on the array pattern are examined. For wire antennas the method of moments using a subsectioning technique can be applied to obtain numerical answers which include mutual-coupling effects. Methods for considering large arrays and for the maximization of power gain are indicated.
D.K. Cheng (1971) studied this question.