Optimum decision delay of the finite-length DFE

This letter investigates the optimum decision delay and tap-length of the finite-length decision feedback equalizer. First we show that, if the feedback filter (FBF) length N-b is equal to or larger than the channel memory upsilon and the decision delay Delta is smaller than the feedforward filter (FFF) length N-f, then only the first Delta + 1 elements of the FFF can be nonzero. Based on this result we prove that the maximum effective FBF length is equal to the channel memory upsilon, and if N-b greater than or equal to upsilon and N-f is long enough, the optimum decision delay that minimizes the MMSE is N-f - 1.