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The design of irregular planar phased arrays ( PA s) characterized by a highly-modular architecture is addressed. By exploiting the property of self-replicating tile shapes, also known as  rep-tiles , the arising array layouts consist of tiles having different sizes, but equal shape, all being generated by assembling a finite number of smaller and congruent copies of a single elementary building-block. Towards this end, a deterministic optimization strategy is used so that the arising rep-tile arrangement of the planar  PA  is an optimal trade-off between complexity, costs, and fitting of user-defined requirements on the radiated power pattern, while guaranteeing the complete overlay of the array aperture. As a representative instance, such a synthesis method is applied to tile rectangular apertures with  L -shaped tromino tiles. A set of representative results is reported for validation purposes, but also to point out the possibility/effectiveness of the proposed approach, unlike state-of-the-art tiling techniques, to reliably handle large-size array apertures.

A Self-Replicating Single-Shape Tiling Technique for the Design of Highly Modular Planar Phased Arrays - The Case of L -Shaped Rep-Tiles