Basic Equalizers

The problem of equalization can be divided into sequence estimation and symbol decesion equalization. The optimal solution for the sequence estimation equalizer is the maximum likelihood sequence estimation (MLSE) [1]. The problem with this approach is that it is computationally very expensive and it also requires the knowledge of channel at the receiving end. The symbol decesion equalizers are relatively simple to implement and they are computationaly less complex than the MLSE. The two common types of are the linear transversal equalizer (LTE) and the decesion 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 least mean square (LMS) algorithm. The adaptive filter here finds the channel inverse in the presence of noise providing linear decesion boundary.

The decesion function of the optimal equalizer is basically non-linear in nature. The problem of equalization can also be considered as a classification problem wherethe equalizer classifies the recieved signal vector to one of the signal constellations. Thus we can treat equalization as a non-linear classification problems, and so the performance of linear equalizers are far from optimal. Thus the only option remains is to go for non-linear equalizers.

Non-linear equalizers using artificial neural networks (ANN) [13] and radial basis functions [4][5][7] have been sucessfully developed. The ANN equalizer provides a non-linear decesion function but the convergence rate is slow. Also it suffers prblem of not attaining optimal solution because on multimodal local minima. If they are overtrained then they may also diverge to give a very high value. The RBF equalizers on the other hand provides localized functional behaviour demanded by the optimal equalizer decesion function but training of the centres is difficult. However orthogonal least square algorithm (OLMS) [6] or the k means clustering [7] can be used to train the centres. Clustering in mutidimensional space is computationally complex and requires long training sequances. This has lead to search of other non-linear equalization techniques. A fuzzy equalizer based on fuzzy adaptive filter was proposed in [10] while equalizer based on fuzzy system was proposed in [12]. These equalizers performed well, but could not provide optimal decesion boundry. Also the equalizer based on Fuzzy filter were computationally expensive. Here a novel idea is used for equalization using fuzzy logic.

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