The effect of decision delay in finite-length decision feedback equalization

In this correspondence we derive the finite-length, minimum mean-squared error decision feedback equalizer (MMSE-DFE). We include decision delay as an explicit parameter. Our derivation yields an algebraic interpretation of the effect of decision delay on DFE performance (measured by mean-squared error). It also allows the fast computation of the MMSE-DFE for several different values of both decision delay and the number of feedback taps. Our approach is especially useful for short filter lengths, when the decision delay can significantly affect DFE performance.