A Decision Feedback Recurrent Neural Equalizer as an Infinite Impulse Response Filter

statistic of(4),on the other hand,requires only n multiplications, n01additions,n coefficient storage,and n+1data storage.

A CKNOWLEDGMENT

The authors would like to thank Dr.S.S.Rao for his encour-agement on the initial portion of this work,which was presented at ICASSP’93[9].

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A Decision Feedback Recurrent Neural

Equalizer as an Infinite Impulse Response Filter Sunghwan Ong,Cheolwoo You,Sooyong Choi,and Daesik Hong

Abstract—An adaptive decision feedback recurrent neural equalizer (DFRNE),which models a kind of an IIR structure,is proposed.Its performance is compared with the traditional linear and nonlinear equalizers with FIR structures for various communication channels.The small size and high performance of the DFRNE makes it suitable for high-speed channel equalization.

Index Terms—Adaptive equalizer,FIR digitalfilter,IIR digitalfilter, nonlinear distortion,recurrent neural networks.

I.I NTRODUCTION

Conventional adaptive equalizers,such as a linear equalizer(LE) and a decision feedback equalizer(DFE),usually employ linearfilters Manuscript received August13,1997.This work was supported in part by a research grant of the University supporting program from the Ministry of Information and Communication and the Video Industrial R&D Association of the Republic of Korea.

The authors are with the Department of Electronic Engineering,Yonsei University,Seoul,Korea(e-mail:daesikh@catseye.yonsei.ac.kr). Publisher Item Identifier S1053-587X(97)08070-7.withfinite impulse response(FIR)or lattice structure,whose coeffi-cients are being adjusted to match the channel characteristics.The coefficients of them can be adjusted by several iterative algorithms. The least mean square(LMS)algorithm is one of the algorithms that trains the equalizers modeled by FIRfilters.In the minimization of the mean squared error(MSE),it is found that the optimum equalizer coefficients are determined from the solution of the set of linear equations.

When the channel has a deep spectral null in its bandwidth or introduces nonlinear distortions,the LE performs poorly.The DFE[1]can be employed to improve the performance of the LE.Although the DFE is nonlinear,the nonlinearity lies in the way the transmitted sequence is recovered at the receiver with the channel model being linear.Therefore,when the channel itself has nonlinear characteristics,the DFE cannot recover the corrupted symbols effectively.

If nonlinear channel distortions are too severe to ignore,the aforementioned equalizers modeled by linear FIRfilters suffer from severe performance degradation.Among the techniques proposed to address the nonlinear channel equalization problem are those in [2]–[6].The authors used the feedforward neural networks based on multilayer perceptrons(MLP’s)that generalize nonlinear FIR filters for the equalization of highly nonlinear channels[4]–[6]. These neural equalizers using MLP’s are trained to approximate the correct mapping from delayed channel outputs to transmitted symbols,and they yield a significant improvement in performance relative to the equalizers with linear FIR structures[4]–[8].However, the neural equalizers using MLP’s usually require a large amount of computation,as well as a large amount of storage[9],[10].

To reduce the burdens of the feedforward neural equalizers,Kechri-otis used the recurrent neural network(RNN)for the equalization [11],[12]as well as the recurrent neural equalizer(RNE),which models a nonlinear IIRfilter.Kechriotis showed that the RNE with simple size can be successfully applied to the equalization problems. However,the RNE is very unstable due to the nature of its IIR structure.The real-time recurrent learning(RTRL)is generally used [13]to train the RNE.

In this paper,a decision feedback recurrent neural equalizer (DFRNE)is proposed for the adaptive equalization of the linear and nonlinear channels that introduce severe distortions and is proposed to overcome the limitation of the RNE.The DFRNE realizes a nonlinear IIRfilter,as the RNE does,with some modification in its feedback input part.The DFRNE of reasonable size not only can model the inverse of communication channels accurately but can also overcome the unstableness due to its IIR structure.

This correspondence is organized as follows.In Section II,we describe the proposed DFRNE as well as the modified version of the RTRL algorithm used to train it.In Section III,the performances of the proposed DFNRE through computer simulations for linear and nonlinear channels are illustrated.Finally,Section IV summarizes ourfindings.

II.T HE D ECISION F EEDBACK R ECURRENT N EURAL E QUALIZER

A.The Structure of the DFRNE and Its Learning Algorithm

A generalized DFRNE is shown in Fig.1.Assume that it has m external inputs and n fully interconnected neurons.Any of all the outputs of the neurons in the network can be considered to be the

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