Stochastic Unbiased Minimum Mean Error Rate Algorithm for Decision Feedback Equalizers

Capitalizing on a well-known minimum mean-square error (MMSE) property for decision feedback equalization (DFE) along with the use of stochastic gradient approach, we formulate an adaptive minimum error rate (MER) algorithm for DFE over M-ary PAM channels to be named as stochastic unbiased minimum mean-error rate (SUMMER). Comparisons are made between our algorithm and existing MER algorithms in the literature. Also, by invoking the central limit theorem, we present an analytical proof that an unbiased MMSE equalizer will approach an MER equalizer when the equalizer length approaches infinity; thereby, we obtain a lower bound expression for MER.