Convergence analysis of decision-directed adaptive echo cancellers for baseband data transmission

This article deals with the analysis of a decision-directed echo canceller working in a baseband data communication link. This guided scheme, as known in self-adaptive equalization systems, introduces stable local minima in the error surface thus dissuading any gradient search procedure. Regardless of this drawback, the article studies two stochastic gradient algorithms in a multimodal error surface context. They are based in the minimization of absolute and quadratic norms (L/sub 1/ and L/sub 2/) of an improved error reference signal. The analysis assumes bipolar data contaminated with a residual intersymbol interference plus background white noise. The article introduces a new perspective on the analysis of conditions that guarantees convergence towards any desired steady state even with the existence of local minima. It uses a dynamic bounding function for the adaption step dependent on the residual echo variance that allows tracking of the global convergence-condition in the working range. Furthermore, the analysis makes it also possible to predict whether the algorithm will converge or whether it could be trapped in any stable stationary point. It also shows the risky dependence of the convergence towards an undesired steady state on some internal and working variables, such as initial filter settings, interference level, etc.<>