The minimum-SER linear-combiner decision feedback equalizer

The paper considers the conventional decision feedback equalizer (DFE) that employs a linear combination of the channel observations and the past decisions. An expression of the symbol error rate (SER) is derived for the linear-combiner DFE with the general $M$-PAM constellation by utilizing a geometric translation property of decision feedback. A method is developed to optimize the coefficients of the linear-combiner DFE to achieve the minimum-SER (MSER) solution. The performance of this MSER linear-combiner DFE is superior to the usual minimum mean square error (MMSE) solution