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Slot-ring antennas have been mainly used in mobile communications, since they can radiate power at low elevation angles. These antennas present narrow bandwidth and high input impedance at their first resonance frequency. A rectangular slot ring antenna (RSRA) with two concentric rings is proposed and it is proved that such a structure has a lower reflection coefficient and higher bandwidth than the single RSRA. A formal analysis is presented using design of experiments (DOE) and functional data analysis (FDA). Two levels, high and low, are set for each factor considered. On the basis of a T-test, it is possible to learn the significant factors that improve the antenna response. According to the results, the best design conditions are: substrate relative permittivity, εr, high; slot width, W, low; outer slot ring perimeter, Ll, low. Moreover, the open circuit stub length has a low impact over the reflection coefficient in this experiment. Finally, the 32 experiments performed were analyzed in order to find a behavior pattern. It is possible to state the factors that decrease the reflection coefficient and increase the antenna bandwidth. A multiband behavior is found when the factor Ll is set high and the levels of the other factors are "do not care". This multiband operation occurred when the two rings are near each other.