Title :
Convergence analysis of decision-directed adaptive echo cancellers for baseband data transmission
Author :
Paez Borrallo, J.M. ; Speranzini, F.L.
Author_Institution :
Dept. de Senales, Systemas y Telecommun., Univ. Politecnica de Madrid, Spain
Abstract :
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.<>
Keywords :
adaptive signal processing; convergence of numerical methods; data communication; echo suppression; intersymbol interference; minimisation; stochastic processes; subscriber loops; telecommunication links; white noise; background white noise; baseband data communication link; baseband data transmission; bipolar data; convergence analysis; decision-directed adaptive echo cancellers; dynamic bounding function; error reference signal; global convergence-condition; initial filter settings; interference level; multimodal error surface; residual echo variance; residual intersymbol interference; self-adaptive equalization systems; stable stationary point; steady state; stochastic gradient algorithms; subscriber loops; tracking; Baseband; Context; Convergence; Data analysis; Data communication; Echo cancellers; Intersymbol interference; Steady-state; Stochastic processes; Surface contamination;
Journal_Title :
Communications, IEEE Transactions on