A wireless repeater includes an input antenna for receiving an input signal, an output antenna for outputting an amplified signal, and an amplifier for amplifying the received input signal and providing the output amplified signal to the output antenna. Radiated coupling between the input and output antennas causes echoes to be transmitted by the repeater. A filter is used for applying a weighting function to a power spectrum of a measured signal in the wireless repeater thereby obtaining a weighted power spectrum of the measured signal. An internal feedback path is employed for adaptively canceling the echo by implementing an adaptive algorithm based on a autocorrelation of the input signal employing the weighted power spectrum of the measured signal.