The design of phased arrays able to generate arbitrary-shaped beams through a sub-arrayed architecture is addressed here. The synthesis problem is cast in the excitation matching framework, so as to yield clustered phased arrays providing optimal trade-offs between the complexity of the array architecture (i.e., the minimum number of control points at the sub-array level) and the matching of a reference pattern. A synthesis tool based on the k-means algorithm is proposed for jointly optimizing the sub-array configuration and the complex sub-array coefficients. Selected numerical results, including pencil beams with sidelobe notches and asymmetric lobes as well as shaped main lobes, are reported and discussed to highlight the peculiarities of the proposed approach also in comparison with some extensions to complex excitations of state-of-the-art sub-array design methods.
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