Delay estimation for transform domain acoustical echo cancellation

Acoustic echo cancellation can be used to remove the annoying talker feedback in hands-free (teleconferencing) systems. The echo canceller identifies the response between the loudspeaker and the microphone, and produces an echo replica which is then subtracted from the signal. Adaptive filtering techniques are employed to determine the echo path response. The speech signal (or the reference signal) is used to train the algorithm. Fast convergence and good tracking capabilities can not be achieved by classical transform domain adaptive filtering algorithms when the reference signal has variable rank autocorrelation matrix. In this thesis, we examine the DCT-LMS algorithm and we emphasize on the role played by the Discrete Cosine Transform. This fixed transformation reduces the eigenvalue spread of the input autocorrelation matrix by partially decorrelating the inputs. The autocorrelation matrix of speech signals is often rank-deficient. During the low rank phases, some of the transform-domain tap coefficients become irrelevant to the adaptation process and stop adapting. When the autocorrelation matrix gains full rank, there will be no longer any “frozen” weights. However, the weights that have been frozen are “far” from the optimal point; they require additional convergence time to track again the changes in the room impulse response. In this dissertation, we present a new method that uses the information contained in the other coefficients to move the frozen weights closer to the optimal point and, consequently, reduce the overall convergence time. By modeling the changes in the impulse response that result from an alteration in the spacing between the microphone and the loudspeaker by a single delay, we were able to develop the “Spectrum Delay Update” method. It consists of replacing, during low-rank phase, each frozen coefficient by a delayed version of the previous full-rank solution. To estimate the corresponding delay, a novel DCT-domain delay estimation algorithm was derived. Simulation results demonstrate the efficiency of SDU for acoustic echo cancellation, the gain in Echo Return Loss is substantial. The experimental performance analysis confirms the expected reduction in the Euclidean Distance between the filter weights and the actual room impulse response DCT. Furthermore, it shows that spectrally updating the filter weights reduces the MSE jump when the autocorrelation matrix gains full rank.