UDC 621.394.13 : 621.394.528 Indexing Terms: Equalizers, Digital communication systems A comparison of decision-feedback equalizers for a 9600 bit/s modem Professor A. P. CLARK, MA, PhD, CEng, MIERE* S. N. ABDULLAH, BSc, MSc, PhDt and S. Y. AMEEN, BSc, MSc* * Department of Electronic and Electrical Engineering, Loughborough University of Technology, Loughborough, Leicestershire, LE11 3TU t Department of Electrical Engineering, College of Engineering, University of Baghdad, Baghdad, Iraq. SUMMARY When a digital data signal is received over a linear channel that distorts the signal, the resulting intersymbol-interference can be removed, or at least greatly reduced, by means of a decision-feedback equalizer. A conventional equalizer is adjusted adaptively to minimize the mean-square error in the equalized signal, where the error is caused partly by intersymbol interference and partly by noise. Alternatively, the equalizer may be adjusted adaptively to minimize the noise in the equalized signal, subject to the accurate equalization of the channel. The latter equalizer is usually easier to adjust close to its ideal setting, for both time- invariant and time-varying channels. The paper compares the tolerances to additive white Gaussian noise of the two equalizers, for the particular application of digital data transmission at 9600 bit/s over telephone circuits. Theoretical analysis is used to compare the equalizers, first for the case where there is a very high signal/noise ratio, and then for the case where the channel introduces pure phase distortion. Computer-simulation tests over models of six different telephone circuits are used to compare the equalizers for more general situations where the signal/noise ratio is not very high and where there is amplitude distortion in the received signal. 1 Introduction In the transmission of digital data at a relatively high rate over a practical bandlimited channel, it is normally necessary to employ an equalizer at the receiver in order to correct the signal distortion introduced by the channel. 1 Linear equalizers are often used, but, over channels introducing severe bandlimiting of the data signal, a significantly better performance can be achieved through the use of decision-feedback equalizers. 1 The latter are therefore of considerable importance for such applications. Conventional decision-feedback equalizers employ transversal filters and are of two main types, as follows. 12 An equalizer of the first type minimizes the mean-square error in the equalized signal, and is referred to here as an MMSE equalizer. An equalizer of the second type achieves exact equalization of the channel and, subject to this constraint, it minimizes the mean-square error in the equalized signal. This equalizer is referred to here as a ZF (zero forcing) equalizer. In the MMSE equalizer the error is caused partly by intersymbol interference and partly by noise, whereas in the ZF equalizer it is caused entirely by noise. In practice, exact equalization of a channel cannot normally be achieved, but extensive tests have shown that the approximation to exact equalization can usually be made so close, without requiring an unduly complex equalizer, that exact equalization can be assumed without introducing any significant error. 1 ' 3 Clearly, an MMSE equalizer must have a lower mean-square error in the equalized signal than a ZF equalizer, but it is by no means certain that this necessarily leads to a lower error rate in the detected data symbols. The particular importance of the ZF equalizer is that it can be adjusted directly from an estimate of the sampled impulse-response of the channel. 4 This leads to a more accurate and rapid adjustment of the equalizer, for a given degree of equipment complexity, than is possible by more conventional techniques that attempt to minimize the mean-square error in the equalized signal. 4 " 7 The aim of this paper is to investigate the relative performances of the MMSE and ZF equalizers for the particular application of data transmission at 9600 bit/s over telephone circuits. The paper first describes the two equalizers and then derives the relationship between them, (a) at very high signal/noise ratios, and (b) in the presence of pure phase distortion. Results of computer-simulation tests are next presented, showing the tolerances to additive white Gaussian noise of the two equalizers in the presence of various levels of amplitude and phase distortions in the received signal. The relative merits of the two equalizers are then compared in the light of these results. Since we are concerned primarily with the equalizer rather than with the telephone circuit, we do not consider coding techniques for improving the performance of the QAM system through the use of more signal levels. 8 2 Model of System The model of the data-transmission system considered here is shown in Fig. 1. The information to be transmitted is Journal of the Institution of Electronic and Radio Engineers, Vol. 58, No. 2, pp. 74-83, March/April 1988 ©1988 IERE