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The fact of being bulky and not very cost-efficient made lens antennas not to be taken much into account in the past. Nowadays, this kind of antennas has attracted more attention due to the increasing demand of higher frequencies in 5G, where lenses become considerably smaller. Moreover, the advances achieved in manufacturing techniques such as 3D printing have reduced the costs to a great extent. Lenses can be used to transform the \ac{EM} waves coming from a source into any desired radiation pattern. For example, a directive beam in any specific direction could counteract the higher path losses at the new frequency bands used in 5G. In order to feed the lens, a transition from a coaxial cable to a waveguide or horn antenna working at the desired frequency band has been used as the source. However, most of the time, these feeds are only able to support a single polarization, thus not exploiting the capabilities, such as the increase in capacity, of using \ac{PDM}. In this thesis, a system composed of a dual-polarized array feed and a Gutman lens operating at the frequency band of 28 GHz is designed and simulated in order to analyze its performance. Commercial software CST Microwave Studio is used for that purpose. Some prototype ideas to be manufactured in the future are also analyzed.