Analysis of inverse crosstalk channel estimation using SNR feedback

Digital subscriber line (DSL) data rates for short loops are typically limited by crosstalk between adjacent lines rather than by background noise. Precoding can reduce crosstalk in the downstream from the access node to the customer premises equipment significantly if an accurate estimate of the inverse crosstalk channel is provided. Recently, a backward-compatible method has been proposed for estimating downstream crosstalk channels using standardized signal-to-noise ratio (SNR) reports. This paper develops a probabilistic model of the estimation process and, within this model, provides conditions under which successive updates of the precoder are guaranteed to converge to the ideal inverse precoder. Bounds on estimator variance and convergence times are obtained and optimized with respect to system parameters. The analysis can be applied to the situation in which a new line is being activated and added to a group of precoded lines seamlessly, that is, with controlled impact on the SNR of the active lines. Two phases are proposed to achieve seamless activation; the protection phase is used to let the active lines learn the crosstalk from the activating line and the acquisition phase is used to let the activating line learn the crosstalk from the active lines. Results of the analysis are illustrated by numerical simulations.