The paper presents the optimization of a reflector-backed Vivaldi antenna which was designed to operate at the 1.8, 2.1, and 3.5 GHz frequencies used in the fourth and fifth generation of wireless systems. Reducing antenna back radiation is the primary goal of the optimization; at the same time, however, antenna impedance matching has to be preserved for the considered set of frequencies, this way generating a conflict of goals. The proposed design method is based on a minimax formulation of each goal against frequency and a Pareto-like tradeoff of solutions. Both goals were achieved as a consequence of the optimization process, and the antenna now exhibits a voltage standing wave ratio below 3, front-to-back ratio of 14 dB and a gain in the front direction not smaller than 8 dBi.
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