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The analytical model is proposed for simulation of the near-field and far-field characteristics of an all-dielectric free-form antenna system. The antenna system is constructed of an array of high-refractive-index dielectric resonators. The model relies on the coupled mode theory and the perturbation theory for the Maxwell?s equations. The model is validated against numerical simulations performed by the ANSYS HFSS electromagnetic solver and microwave experiments. Three designs of the free-form antenna systems are proposed, studied and experimentally tested. The mechanisms of the multiple beam generation and beam steering are demonstrated