A stable pre-whitened NLMS algorithm for acoustic echo cancellation

This thesis is on a new method for improving the convergence speed of the normalised least mean square (NLMS) algorithm when the input is a coloured signal, such as speech, that can be decorrelated using linear prediction. The proposed method gives a significant improvement in the convergence speed and requires very little additional computation in terms of arithmetic operations and memory space. It is also very easy to implement. An important aspect of the proposed method is its inherent stability irrespective of the order of the prediction-error filter or the manner in which it is adapted. This allows the proposed method to be used without any restrictions beyond those of the conventional NLMS algorithm. Following the stability analysis, a further improvement to the basic proposed method is suggested. This improvement is restricted to the cases where the input signal is decorrelated by a prediction-error filter of up to order two. The proposed method finds immediate application in acoustic echo cancellation in hands-free telephones where the impulse response of the system (echo path) to be identified is very long and the identification has to be done in real time. Such an application requires an algorithm with low computational complexity and a fast rate of convergence. In general, the proposed method can be used where the input coloured signal can be decorrelated using linear prediction.