Performance analysis of the weighted decision feedback equalizer

In this paper, we analyze the behavior of the weighted decision feedback equalizer (WDFE), mainly from filtering properties aspects. This equalizer offers the advantage of limiting the error propagation phenomenon. It is well known that this problem is the main drawback of decision feedback equalizers (DFEs), and due to this drawback DFEs are not used very often in practice in severe channels (like wireless channels). The WDFE uses a device that computes a reliability value for making the right decision and decreasing the error propagation phenomenon. We illustrate the WDFE convergence through its error function. Moreover regarding the filtering analysis, we propose a Markov model of the error process involved in the WDFE. We also propose a way to reduce the number of states of the model. Our model associated with the reduction method permits to obtain several characteristic parameters such as, error propagation probability (appropriate to qualify the error propagation phenomenon), time recovery and error burst distribution. Since the classical DFE is a particular case of the WDFE (where the reliability is always equal to one); our model can be applied directly to DFE. As a result of the analysis of this process, we show that the error propagation probability of the WDFE is less than that of the classical DFE. Consequently, the length of the burst of errors also decreases with this new WDFE. Our filtering model shows the efficiency of the WDFE.