Uniform amplitude sparse arrays have recently gained a renewed interest and a number of synthesis techniques, mainly based on global optimization algorithms, have been presented. In this paper, after a discussion about the expected characteristics of such arrays, a simple deterministic approach for the case of pencil beams patterns is proposed and discussed. The approach, which outperforms previous synthesis techniques, takes inspiration from existing (not well-known) density taper procedures to develop a two stages synthesis where the first step is solved in a new closed analytical form, while the second one just requires local refinements or fast 1-D optimizations. As a consequence, the proposed approach avoids the need of multidimensional global optimization procedures and the inherent possibly prohibitive computational costs. Notably the first step, which also exhibits an improved flexibility with respect to other analytical techniques, already outperforms previous approaches in a number of cases of interest. Several numerical results confirm the effectiveness and usefulness of the proposed tools.
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