Decision feedback equalization

As real world communication channels are stressed with higher data rates, intersymbol interference (ISI) becomes a dominant limiting factor. One way to combat this effect that has recently received considerable attention is the use of a decision feedback equalizer (DFE) in the receiver. The action of the DFE is to feed back a weighted sum of past decision to cancel the ISI they cause in the present signaling interval. This paper summarizes the work in this area beginning with the linear equalizer. Three performance criteria have been used to derive optimum systems; 1) minimize the noise variance under a "zero forcing" (ZF) constraint i.e., insist that all intersymbol interference is cancelled, 2) minimize the mean-square error (MMSE) between the true sample and the observed signal just prior to the decision threshold, and 3) minimize the probability of error (Min Pe). The transmitter can be fixed and the receiver optimized or one can obtain the joint optimum transmitter and receiver. The number of past decisions used in the feedback equalization can be finite or infinite. The infinite case is easier to handle analytically. In addition to reviewing the work done in the area, we show that the linear equalizer is in fact a portion of the DFE receiver and that the processing done by the DFE is exactly equivalent to the general problem of linear prediction. Other similarities in the various system structures are also shown. The effect of error propagation due to incorrect decisions is discussed, and the coaxial cable channel is used as an example to demonstrate the improvement available using DFE.