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In this work, a specific type of UWB monopole antenna is presented. This type of antenna makes use of a dielectric coating for the monopole which is used both as a radome and to configure the radiation characteristics of the antenna itself. Making use of a dielectric material with a relatively high dielectric constant but easy to work with (for manufacturing purposes), fields radiated from the monopole can be focused as in the case of a lens. In order to satisfy previously defined criteria, the profile of this dielectric coating must be conformed so that fields are focused in a proper way. To make this possible, a global optimization of the profile of the dielectric using the simulated annealing algorithm and the finite element method as the analysis technique is performed. In order to minimize losses as well, not only the profile of the dielectric coating but also the profile of the monopole itself would be subject of the global optimization.