Optimum decision delay of the finite-length DFE

This work 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 v and the decision delay Δ is smaller than the feedforward filter (FFF) length N_f, then only the first Δ+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 v, and if N_b≥v and N_f is long enough, the optimum decision delay that minimizes the MMSE is N_f-1.