On the equivalence of the simultaneous and separate MMSE optimizations of a DFE FFF and FBF

There is great interest in the use of decision feedback equalization (DFE) to mitigate the effects of intersymbol interference (ISI) on wireless multipath fading channels. The coefficients of a DFE feedforward filter (FFF) and feedback filter (FBF) are usually adjusted based on the minimum mean square error (MMSE) criterion. The equalizer coefficients can be calculated by recursive adaptation or by direct computation based on a channel estimate. The equivalence of the simultaneous and separate MMSE optimization of the FFF and FBF of a finite-length DFE is established.