Fast adaptive digital equalization by recurrent neural networks

Neural networks (NNs) have been extensively applied to many signal processing problems. In particular, due to their capacity to form complex decision regions, NNs have been successfully used in adaptive equalization of digital communication channels. The mean square error (MSE) criterion, which is usually adopted in neural learning, is not directly related to the minimization of the classification error, i.e., bit error rate (BER), which is of interest in channel equalization. Moreover, common gradient-based learning techniques are often characterized by slow speed of convergence and numerical ill conditioning. In this paper, we introduce a novel approach to learning in recurrent neural networks (RNNs) that exploits the principle of discriminative learning, minimizing an error functional that is a direct measure of the classification error. The proposed method extends to RNNs a technique applied with success to fast learning of feedforward NNs and is based on the descent of the error functional in the space of the linear combinations of the neurons (the neuron space); its main features are higher speed of convergence and better numerical conditioning w.r.t. gradient-based approaches, whereas numerical stability is assured by the use of robust least squares solvers. Experiments regarding the equalization of PAM signals in different transmission channels are described, which demonstrate the effectiveness of the proposed approach