Analysis of Inverse Crosstalk Channel Estimation

Abstract— Digital subscriber line (DSL) data rates for shortloops are typically limited by crosstalk between adjacent linesrather than by background noise. Precoding can reduce crosstalkin the downstream from the access node to the customer premisesequipment significantly if an accurate estimate of the inversecrosstalk channel is provided. Recently, a backward-compatiblemethod has been proposed for estimating downstream crosstalkchannels using standardized signal-to-noise ratio (SNR) reports.This paper develops a probabilistic model of the estimationprocess and, within this model, provides conditions under whichsuccessive updates of the precoder are guaranteed to converge tothe ideal inverse precoder. Bounds on estimator variance and con-vergence times are obtained and optimized with respect to systemparameters.Theanalysiscanbeappliedtothesituationinwhichanew line is being activated and added to a group of precoded linesseamlessly, that is, with controlled impact on the SNR of the activelines. Two phases are proposed to achieve seamless activation; theprotection phase is used to let the active lines learn the crosstalkfrom the activating line and the acquisition phase is used to let theactivating line learn the crosstalk from the active lines. Results ofthe analysis are illustrated by numerical simulations.