Equalisers for digital communications using generalized distance measurement

It is shown that a previously published algorithm by C.F.N. Cowan (see Proc. 25th Asimolar Conf. on Signals, Systems and Computers, Pacific Grove, CA, USA, IEEE, 1991), for nonlinear equalization involving the measurement of the Mahalanobis distance makes the assumption that the clusters in the underlying observation space have a Gaussian distribution. If this assumption is violated, poor performance may be obtained. However, it is shown that the equalizer structure is capable of generating good approximations to the theoretical optimum decision boundary. It is the use of the Mahalanobis distance which is inappropriate in the non-Gaussian case. By using a more general concept of distance, it is demonstrated that it is possible to obtain significantly better results than those obtained using the Mahalanobis distance measure. The new method and previous algorithms are also extended to cover the case of multilevel transmitted signals