Adaptive filtering in data communications with self improved error reference

The observed signals that usually play the role of error references for adaptive echo cancellers and channel equalizers in data communications are basically composed by data plus a residual error. The goal of such systems is to eliminate those errors to enhance the present data. However, in some systems, depending on the convergence stage, the presence of data in the error reference may mask or distort the true error reference (the residual echo or ISI). This paper shows a new perspective on how to use old samples of the observed error to improve the current error reference. It exploits the discrete or the constant envelope nature of the data to build up an error cost function that matches the instantaneous optimal one: their corresponding MLE. These new error surfaces present a more robust (or uniform) behavior during the convergence period since they offer a proper unmasked residual error as error reference