This paper presents an iterative algorithm for the synthesis of the three-dimensional\n(3D) radiation pattern generated by an antenna array of arbitrary geometry. The algorithm is\nconceived to operate in fifth-generation (5G) millimeter-wave scenarios, thus enabling the support of\nmulti-user mobile streaming and massive peer-to-peer communications, which require the possibility\nto synthesize 3D patterns with wide null regions and multiple main beams. Moreover, the proposed\nsolution adopts a phase-only control approach to reduce the complexity of the feeding network\nand is characterized by a low computational cost, thanks to the closed-form expressions derived\nto estimate the phase of each element at the generic iteration. These expressions are obtained from\nthe minimization of a weighted cost function that includes all the necessary constraints. To finally\ncheck its versatility in a 5G environment, the developed method is validated by numerical examples\ninvolving planar and conformal arrays, considering desired patterns with different numbers of main\nbeams and nulls.
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