  The design of irregular planar phased arrays (PAs) 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, concerned with ideal and real antenna
models, as well, 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.
