“…Moreover, the modularity is advantageous in phased array antenna manufacturing since it enables the implementation of light and low profile structures [17], an easy maintenance, and integrated cooling systems [18]. The constrained clustering is also referred to as array tiling [14], tiles (i.e., physically contiguous clusters of elements) with the same shape (i.e., single-shape tiling [16,[19][20][21][22][23][24][25]) or a limited number of shapes (i.e., multi-shape tiling [12-14, 26, 27]), being used to cover the whole antenna aperture without overlapping and any gaps or leaving the minimum one. As a matter of fact, while a suitable shape/dimension of the antenna aperture is necessary to comply with the design constraints, modern radar/communication applications usually require high directive beams, which are admissible only when assuring the entire aperture overlay.…”