A stable pre-whitened NLMS algorithm for acoustic echo cancellation
NdunguEdward Nganga
2014
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.