The design of sub-arrayed phased arrays (PAs) with sub-array-only amplitude and phase controls that afford arbitrary-shaped power patterns matching reference ones is addressed. Such a synthesis problem is formulated in the power pattern domain and an innovative complex-excitations clustering method, which is based on the decomposition of the reference power pattern in a number of elementary patterns equal to the array elements, is presented. A set of representative results is reported to illustrate the features of the proposed approach as well as to assess its effectiveness in comparison with benchmark results from the state-of-the-art (SoA) excitation matching-based clustering methods.