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Linear array synthesis: a complex Lagrange multipliers approach

An intuitive approach to the synthesis of linear arrays is presented. The algorithm, based on the complex Lagrange multipliers, is optimum in a minimum-mean-square-error sense as originally proposed by Frost (1972). This algorithm does not require apriori knowledge of a mathematical function that describes the desired pattern. The method proposed here uniquely defines side lobes and nulls anywhere in the pattern without the use of template functions. Beam, side lobe, and null shaping is accomplished through the use of derivative constraints (slopes on the pattern). The solution vector is found by solving a simple system of complex linear equations.