On the use of non-Euclidean cost functions in adaptive echo cancellers

The application of adaptive filters considered is that of data echo cancellers. This is now a common way of achieving full duplex data transmission over a single wire pair by utilising the adaptive filter in its simplest, system modelling, configuration. Such an arrangement is shown. The authors take a rather different approach by looking at the fundamental nature of the adaptation algorithm itself. It should in fact be fairly obvious that in this case, where the input signal is data, the signal statistics are not Gaussian, rather they are multivariate. Therefore, it is logical to conclude that the mean square error is not an optimum objective function in this case. They therefore propose to redesign the adaptation algorithm based on an error criterion other than the square. This has been previously investigated for multilayer perceptron (MLP) architectures for equalisation