A method for cancelling/reducing acoustic echoes in speech/audio signal enhancement processing comprises using a received reference signal to excite an adaptive filter wherein the output of the adaptive filter forms a replica signal of acoustic echo; an adaptation step size is controlled for updating the coefficients of the adaptive filter; the adaptation step size is initialized by using an open-loop approach and optimized by using a closed-loop approach; one of the most important parameters with the open-loop approach is an energy ratio between an energy of a returned echo signal in an input microphone signal and an energy of the received reference signal; one of the most important parameters with the closed-loop approach is a normalized correlation or a square of the normalized correlation between the input microphone signal and the replica signal of acoustic echo; the replica signal of acoustic echo is subtracted from the microphone input signal to suppress the acoustic echo in the microphone input signal.