A wireless repeater employing echo cancellation uses a non-linear element in digital baseband to compress the digital transmit signal waveform, thereby allowing distortions in the transmitter circuit as well as interference to be cancelled. In one embodiment, the repeater applies non-linear baseband compression to the digital transmit signal in the digital domain to reduce the peak-to-average amplitude of the digital transmit signal prior to digital-to-analog conversion and prior to over-the-air transmission and prior to sampling of the digital transmit signal for use as the reference signal for echo cancellation. The intentionally introduced non-linear distortion in the transmit signal improves echo cancellation and stability of the repeater. In one embodiment, the non-linear compression is applied only when the digital transmit signal is at or exceed a given power level or a given gain level.