Comparison of two nonuniformly-spaced decision feedback equalizers for sparse multipath channels

Performance comparisons between the conventional decision feedback equalizer (DFE) and an alternative design, known as the decision directed feedback equalizer (DDFE), are conducted with nonuniform spacings on sparse multipath channels. The optimum feedforward filters (FFF) of the DDFE and its variant under the minimum mean square error (MMSE) criterion are derived with the constraint of a nonuniformly spaced feedback filter (NU-FBF), and relationships regarding the optimum tap values and the resultant MMSE between FFF with uniform and nonuniform spacings are established. While the bit error rate (BER) results obtained confirm previous claims that the T-spaced NU-DDFE exhibit prominent improvement over the T-spaced NU-DFE in equalizing long sparse channels such as those encountered in high definition television (HDTV) systems, the gain is only minimal, if any, when applied on simpler sparse channels with fewer multipath terms. Moreover, using a T/2-spaced FFF in the NU-DDFE demands a T/2-spaced FBF to mitigate additional intersymbol interference (ISI) caused by the T/2-spaced channel samples, and a better method than the commonly-used thresholding scheme may be required to accurately determine the tap positions of the T/2-spaced NU-FBF.