Echo Cancellation - A Likelihood Ratio Test for Double-talk Versus Channel Change

Abstract

Echo cancellers are in wide use in both electrical (four wire to two wire mismatch) and acoustic (speaker-microphone coupling) applications. One of the main design problems is the control logic for adaptation. Basically, the algorithm weights should be frozen in the presence of double-talk and adapt quickly in the absence of double-talk. The control logic can be quite complicated since it is often not easy to discriminate between the echo signal and the near-end speaker. This paper derives a log likelihood ratio test (LRT) for deciding between double-talk (freeze weights) and a channel change (adapt quickly) using a stationary Gaussian stochastic input signal model. The probability density function of a sufficient statistic under each hypothesis is obtained and the performance of the test is evaluated as a function of the system parameters. The receiver operating characteristics (ROCs) indicate that it is difficult to correctly decide between double-talk and a channel change based upon a single look. However, post-detection integration of approximately one hundred sufficient statistic samples yields a detection probability close to unity (0.99) with a small false alarm probability (0.01).