This article presents an ultra-wideband in-band full-duplex antenna system based on a special 3D-printed Vivaldi array. To mitigate grating lobes inherent in such arrays, the single Vivaldi element size is reduced partially at its bottom and its body is exponentially tapered. In the array, this allows bringing the antennas closer together at their bottom parts, reducing the distance between the radiating slots, which translates to grating lobes reduction, especially at higher frequencies. The system can achieve, in simulation, a decade matching bandwidth from 2 to 20 GHz with more than 60 dB of self-interference cancellation and 12.8 dBi of average gain. The grating lobes remain at least 10 dB below the main lobe level throughout the matching bandwidth.