The symbol decision equalizers are relatively simple to implement and they are computationally less complex than the MLSE. The two common types of symbol decision equalizers are the linear transversal equalizer (LTE) and the decision feedback equalizer (DFE). They are both simple to implement and can be made adaptive by updating their weights with the help of simple adaptive algorithms like the least mean square (LMS), and recursive least square (RLS). The adaptive filter here finds the channel inverse in the presence of noise providing linear decision boundary.
The optimal solution for a symbol equalizer can be formed from Bayes probability theory [11] and is termed as the Bayesian equalizer. The decision function of the optimal equalizer is non-linear in nature. The problem of equalization can also be considered as a classification problem where the equalizer classifies the received signal vector to one of the signal constellations.
Non-linear equalizers using artificial neural networks (ANN) [12] and radial basis functions [3][4][6] have been successfully developed. The ANN equalizer provides a non-linear decision function but the convergence rate is slow. Also it suffers problem of not attaining optimal solution because of multi-modal local minima. If they are over-trained then they may also diverge to give a very high value. The RBF equalizers on the other hand provides localized functional behavior demanded by the optimal equalizer decision function but training of the centres is difficult. However orthogonal least square algorithm (OLMS) [5] or the k means clustering [6] can be used to train the centres.