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A new method for shaped-beam synthesis is proposed by taking the phases of the desired radiation field as design variables (notably not the usual element excitations). The number of design variables is significantly reduced. To solve the constructed array optimization problem, a fast descent search algorithm is provided, where the convergence is proven theoretically. Several widely used patterns are used to evaluate the effectiveness of the proposed method. Experimental results show that the proposed formula is easier to solve than the conventional one, the proposed algorithm is superior to or competitive with typical mathematical optimizers, and the obtained objective values are very close to those obtained by a global optimization algorithm.
Zeng et al. (2023) studied this question.