MMSE DECISION-FEEDBACK EQUALIZERS AND CODING .2. CODING RESULTS

The minimum-mean-squared-error decision-feedback equalizer (MMSE-DFE) has properties that suggest that it is a canonical equalization struct ure in systems that combine equalization with coded modulation. With a given symbol rate 1/T and transmit spectrum, the output signal-to-noi se ratio SNR(MMSE-DFE,U) of a MMSE-DFE with an unbiased decision rule is a single parameter that characterizes the channel for coding purpos es, Indeed, the transmit spectrum that maximizes SNR(MMSE-DFE,U) is th e capacity-achieving (water-pouring) spectrum, and the capacity C(T) ( in bits per two dimensions) is given by C(T) = log(2)[1 + SNR(MMSE-DFE ,U)] regardless of the channel characteristics. The performance of a c oded system with a MMSE-DFE equalization structure may be accurately e stimated using the gain of the coding scheme at a given Pr(E). This pe rformance is shown to be approximately the same as that of a multicarr ier system using the same transmit spectrum and similar coding; such s ystems are known to be able to approach capacity arbitrarily closely. The MMSE-DFE can perform significantly better than a zero-forcing deci sion-feedback equalizer, particularly at moderate-to-low SNR's and on severe-ISI channels. Simulation results indicate that performance of t he MMSE-DFE is surprisingly insensitive to transmit spectral shaping, as long as the transmit spectrum exceeds the capacity-achieving band, but that there is an optimal symbol rate that should (approximately) b e used.