Stability of NLMS with zero-phase signal conditioning for acoustic echo cancellation

A problem with hands-free telephones is that the far-end talker experiences an echo of his/her own speech because of acoustic coupling between the microphone and speaker caused by their co-location in a reverberant enclosure such as a car cabin. The echo can be eliminated by using an acoustic echo canceller (AEC). The most popular adaptive filter for AEC is the normalised least-mean squares (NLMS) algorithm. The paper introduces the acausually conditioned-NLMS (AC-NLMS) and shows how the intermittent stability problems experienced with the AC-NLMS can be solved, with little extra complexity (one multiply for α) and in an intuitively attractive way. The modification also allows short-term and long-term convergence properties to be traded off against each other. A direct, stationary application of AC-NLMS is integrating pre-emphasis into NLMS to equalise the 1/f spectrum of speech. However, analysis of the mechanism that causes instability is required and, additionally, the new stable form of AC-NLMS requires extending to the case of nonstationary signals: the piecewise block approach seems most appropriate