By using a novel soliton sampling technique, we demonstrate the suppression of RF power fading over 94 km of single-mode fiber. We transmit a digital data signal that has been multiplexed on a subcarrier wave that ranges from 0.25-14 GHz. A 35-ps soliton pulse train is used to sample the data-modulated subcarrier. These inherently stable soliton pulses are then used to carry the information without suffering from dispersion. By using this technique, RF power fading is reduced from 22 dB to <2 dB over a 10-GHz frequency range.