Minimizing BER in DFE's with the Adatron algorithm

In this paper we apply the Structural Risk Minimization (SRM) principle to minimize the Bit Error Rate in Decision Feedback Equalizers (DFE). We consider both linear discriminant (Optimal Hyperplane) and nonlinear discriminant (Support Vector Machine) classifiers as an alternative to the linear MMSE-DFE and Radial Basis Function (RBF) networks, respectively. A fast and simple adaptive algorithm called the Adatron is applied to obtain the linear or nonlinear classifier. In this way we avoid the high computational cost of quadratic programming. We also study the performance of soft margin classifiers: it is shown that to consider a regularized problem improves the BER, mainly at low SNR's. Furthermore, an adaptive implementation is discussed. Some simulation examples show the advantages of the proposed linear (OH) and nonlinear (SVM) DFE's: a better performance in comparison to the linear MMSE-DFE and a simpler structure in comparison to the RBF-DFE.