Turbo DFE algorithm with imperfect decision feedback

In this letter, we propose a new turbo decision feedback equalizer (DFE) algorithm that takes into account decision feedback error propagation. We derive the exact mathematical expression for the probability density function (pdf) of soft decision feedback symbols, assuming that soft outputs from channel decoder are independent identically distributed Gaussian random variables with known mean and variance. We find a new set of "imperfect" turbo minimum mean-square error DFE coefficients based on the derived pdf. The proposed turbo detector outperforms other turbo equalization algorithms of similar computational complexity in terms of bit-error rate. The achieved improvement is up to 3.8 dB for severe frequency-selective channels.