Fast adaptive digital equalization by recurrent neural networks

Abstract

In recent years, neural networks (NN's) have been extensively applied to many signal processing problems. In particular, due to their capacity to form complex decision regions, NN's 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 (RNN's) 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 RNN's a technique applied with success to fast learning of feedforward NN's 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 PARI signals in different transmission channels are described, which demonstrate the effectiveness of the proposed approach

Adaptive multidimensional spline neural network for digital equalization

“…But, this is not true in practical situation when only few control points for each neuron are locally updated to obtain a good approximation and, at the same time, the number of hidden units and connection weights are drastically reduced. The proposed neural architecture is then applied for the digital equalization task to reduce the effects of intersymbol interference (ISI) and nonlinear channel distortions [6]- [10]. Experimental trials on different channel models and symbol alphabets confirmed the validity of this architecture, from the points of view of both the average symbol error and the convergence speed.…”

Complex discriminative learning Bayesian neural equalizer

“…Traditional equalizers attempt to invert the channel response to recover the original signal sequence before the ÿnal decision [13]. In alternative, in the last years neural networks have been successfully applied to the equalization task [1,2,11,12,14]. Acting as nonlinear maps between received samples and training symbols [5], in fact, neural nets are able to enhance the received signal before demodulation [6].…”

“…As a matter of fact, in these cases the channel inversion is an ill-posed problem, due to a loss of information in the transmission path [1,2,11,12,15]. Bayesian (BA) and maximum likelihood (ML) equalizers are commonly adopted to face this problem [11] and are based on the knowledge of the multidimensional mapping performed by the channel from transmitted symbol sequences onto symbol clusters, deÿned in a proper output space [2,11].…”

“…However, RBF networks are hampered by low speed and limited robustness of the clustering phase [12], which is a critical step of the adaptation process. In fact, if estimated centroids are far from the true positions, local convergence of the algorithm can dramatically slow down or fail.…”

“…Alternatively, multilayer feedforward [1,5,9,14] or recurrent [10,12] neural networks can be used as classiÿers, using the mean square error (MSE) criterion. However, MSE minimization does not imply a reduced bit error rate (BER) [9] and alternative error functionals may be devised.…”