Error probability analysis for adaptive decision feedback equalizers under slowly fading multipath channels

It is very difficult to analyse the error probability of the adaptive decision feedback equalizer (DFE) when it is operated under a time-varying channel. A decision error not only propagates through the feedback filter affecting the future outputs, but also through the adaptive algorithm updating the tap weights towards a wrong direction. Most of the existing analysis works do not consider the error propagation effect in the adaptive algorithm. We specifically take this effect into account and analyze the error probability of the DFE under slowly fading channels. We consider the most widely used adaptive algorithm, namely, the least mean square (LMS) algorithm. Closed-form expressions are derived for the training mode as well as the decision-directed mode. Finally, the validity of the theoretical results are verified through computer simulations.