Adaptive Precoding for Downstream Crosstalk Precancelation in DSL Systems Using Sign-Error Feedback
Abstract
The performance of many very high bit rate digitalsubscriber line (VDSL) systems is limited by the effects of crosstalkamong the wires in a bundle. For the downstream, a precoder cancompensate for this, provided that some crosstalk channel informationis available at the transmitter. In this paper, we investigatethe issue of precoder design based on a particular type of feedback:it is assumed that each receiver sends back the (complex) sign of thenoise on the symbol detection as a way to provide the needed informationon crosstalk channels. We derive an algorithm that makesuse of this limited information in an adaptive way to iterativelycompute the precoder. The performance of the proposed algorithmis extensively analyzed, both with theoretical evaluations and simulationresults. The algorithm is also compared to other solutions,showing the efficient performance for the limited amount of overheadit requires.Index Terms—Adaptive algorithm, channel estimation,crosstalk, precoding, vectored DSL.
I. INTRODUCTION
DUE to the use of higher bandwidths and shorter loops, theFEXT (far end crosstalk) is becoming the main degradationin some DSL systems such as VDSL2 (very high bit ratedigital subscriber line). For this reason, a number of precancelationtechniques have been designed to decrease the effect ofFEXT [1]–[4] in downstream, using the coordination at the centraloffice (CO) or optical network unit (ONU). A suitable precoderis introduced on the vector of transmitted symbols. Thesemethods assume that a good estimate of the crosstalk channelmatrix is available. Essentially, the precoder is the inverse ofthis matrix.We focus on downstream in this paper, as the upstream issueis simpler to solve. Due to the nature of the DSL network, thetransmitters in the downstream are collocated and can be “coordinated”at the central office, while the receivers are physicallyseparated and thus are uncoordinated. To be able to com pute the precoder, combined knowledge on the crosstalk channelcharacteristics of each transmitter towards each user is required.Thus, it is necessary to centralize the available information thatis present only distributed at the independent receivers. This requiresfeedback from the receivers.One straightforward way to solve the problem is to use a setof pilot symbols, sent periodically, to perform the tracking ofthe downstream channels at the CPE. An example of this solution,applied to the VDSL system is analyzed in [5]. In [6], itis proposed to simplify the precoder to its off-diagonal elementsonly, and an LMS tracking algorithm is proposed that convergesto the optimal off-diagonal solution. This is also essentially apilot-based solution. These methods use part of the useful bitrate as pilot symbols and, in addition, the information about theestimates needs to be sent back to the CO periodically to updatethe precoder. So this may lead to a large overhead. In order to tryto limit this overhead, some methods have been proposed thatonly require to feedback the sign of the error samples (slicer errors)at the receiver [7], [8]. The entire estimation processing istransferred at the central office. Recently, it has also been proposedin [9] to use SNR measurements, introducing small perturbationson the transmitted signal, and observing their effecton the received SNR, seen from the CPE side.In this paper, we revisit the method that was briefly describedin [8], and that is based on the feedback of the sign of the errorsamples from the receiver. In this method, the transmitter usesthe combination of the feedback and of the knowledge of thetransmitted symbols to iteratively compute the precoder. Wepropose a modified version of the algorithm that considerablydecrease the complexity with respect to what was presentedin [8], and we analyze the performance of the proposed (simplified)method. Approximate performance expressions are derivedto quantify the potential of the method, and they are comparedto simulation results to be validated. It is shown how theseexpressions can also easily be used to help setting the parametersof the method. Finally, the performance is compared to otherexisting methods.

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