Optimal Equalizers and Targets for Detection in ISI Channels

In this paper we consider the alternate approach of designing the equalizer and target jointly so that they minimize the overall bit-error rate in the system. Our main result is theoretical analysis that shows that the MMSE equalizer and the monic GPR target do indeed perform the best (compared to other designs) for uncoded inputs. However, for spectrally shaped coded inputs, the proposed design produces filters that are different from those GPR design. Thus, we predict a gain with the new design over the monic GPR design for coded signals.