Gain optimization for arbitrary antenna arrays subject to random fluctuations

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Abstract
A general procedure is formulated for the maximization of the expected directive gain for arbitrary antenna arrays whose excitation amplitudes and phases as well as element positions are subject to random errors. Correlations are allowed to exist between the random fluctuations, and the general formulation imposes no restrictions on either the magnitude or the probability distribution of the fluctuations. Numerical examples are given which illustrate the dependence of the expected gain, the main-beam radiation efficiency, the radiation pattern, and the optimum element excitations on the standard deviation and correlation distance of the parameter errors. It is shown that, in typical cases, the properly optimized array yields not only a higher directive gain and a higher mainbeam radiation efficiency but also a better radiation pattern than an array which is "optimized" under the assumption of no random errors.

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