Theory of Minimum Mean-Square-Error QAM Systems Employing Decision Feedback Equalization

Interest has recent]}' intensified in receiver structures which hopefully will permit higher data symbol rates than are possible with con1821 1822 T H E B E L L S Y S T E M TECHNICAL JOURNAL, D E C E M B E R 1 9 7 3 ventional demodulator/linear equalizer structures having the same error probability. The decision feedback equalizer is an example of a receiver component that can have important performance advantages over a linear equalizer operating over dispersive channels with additive noise. 1-7 The basic structure of a decision feedback equalizer (DFE) is shown in Fig. 1. The function of the filter in the feedback path is to cancel "postcursors" of the channel's impulse response; that is, intersymbol interference components arising from previously decided symbols. Thus, the job of the linear filter in the forward path is to minimize (according to some criterion) "precursors" of the channel's impulse response which cause intersymbol interference from future data symbols. Of course, there is a possibility of error propagation with this nonlinear feedback structure. We avoid this intractable problem by assuming that no erroneous decisions pass into the feedback filter. Thus, our results provide a performance lower bound. Earlier experimental studies indicated that error propagation is not a serious problem on some channels.3,4 Price6 (whose bibliography on the subject is extensive) has derived asymptotic formulas (allowing for an infinite number of equalizer taps) for error probability, optimum transmitter pulse spectrum, and communication efficiency for the "zero-forcing" DFE, which minimizes the noise variance at the D F E output subject to the constraint that the intersymbol interference is zero at the receiver's sampling instants.