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 structure in systems that combine equalization with coded modulation. With a given symbol rate 1/T and transmit spectrum, the output signal-to-noise ratio SNR(MMSE-DFE,U) of a MMSE-DFE with an unbiased decision rule is a single parameter that characterizes the channel for coding purposes, Indeed, the transmit spectrum that maximizes SNR(MMSE-DFE,U) is the 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 coded system with a MMSE-DFE equalization structure may be accurately estimated using the gain of the coding scheme at a given Pr(E). This performance is shown to be approximately the same as that of a multicarrier system using the same transmit spectrum and similar coding; such systems are known to be able to approach capacity arbitrarily closely. The MMSE-DFE can perform significantly better than a zero-forcing decision-feedback equalizer, particularly at moderate-to-low SNR's and on severe-ISI channels. Simulation results indicate that performance of the 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) be used.