Minimum mean-squared error decision-feedback equalization for digital subscriber line transmission with possibly correlated line codes

Most of the published theory on the optimal performance of decision-feedback equalization under the MMSE criterion addresses the transmission of i.i.d. symbol sequences only. This paper presents a theory which accommodates the case of correlated symbol sequences. It also considers the use of a fractionally spaced forward filter in the decision-feedback equalizer (DFE). Two limiting conditions are discussed in some detail, both concerning having an infinite-length DFE feedback filter. In one of them the forward filter is of finite length and in the other it is noncausal infinite. Several numerical examples are given, in which we apply the theory to the study of the MMSE transmission performance, at ISDN basic access rates, of a few example subscriber lines using some well-known line codes. In these examples, the near-end crosstalk from identical digital transmission systems is assumed to be the only significant noise. Throughout the study, we ignore the effects of error propagation in a DFE.