A Dual Decomposition Approach to Partial Crosstalk Cancelation in a Multiuser DMT-xDSL Environment
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Research Article A Dual Decomposition Approach to Partial Crosstalk Cancelation in a Multiuser DMT-xDSL Environment Jan Vangorp,1 Paschalis Tsiaflakis,1 Marc Moonen,1 Jan Verlinden,2 and Geert Ysebaert2 1 Department 2 DSL
of Electrical Engineering, Katholieke Universiteit Leuven, 3001 Leuven, Belgium Experts Team, Alcatel-Lucent, 2018 Antwerpen, Belgium
Received 21 September 2006; Accepted 14 May 2007 Recommended by Sudharman Jayaweera In modern DSL systems, far-end crosstalk is a major source of performance degradation. Crosstalk cancelation schemes have been proposed to mitigate the effect of crosstalk. However, the complexity of crosstalk cancelation grows with the square of the number of lines in the binder. Fortunately, most of the crosstalk originates from a limited number of lines and, for DMT-based xDSL systems, on a limited number of tones. As a result, a fraction of the complexity of full crosstalk cancelation suffices to cancel most of the crosstalk. The challenge is then to determine which crosstalk to cancel on which tones, given a complexity constraint. This paper presents an algorithm based on a dual decomposition to optimally solve this problem. The proposed algorithm naturally incorporates rate constraints and the complexity of the algorithm compares favorably to a known resource allocation algorithm, where a multiuser extension is made to incorporate the rate constraints. Copyright © 2007 Jan Vangorp et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
1.
INTRODUCTION
Far-end crosstalk (FEXT), which is typically 10–15 dB larger than the background noise, is a major source of performance degradation in xDSL systems. One strategy for dealing with this crosstalk is crosstalk cancellation. Several crosstalk cancellation schemes have been proposed. Linear pre- and post filtering [1, 2] requires coordination at both the transmitters and receivers. Successive interference cancellation or precompensation [3, 4] can be used if there is only coordination available at the receivers or transmitters, respectively, for example, in the case of crosstalk cancellation in an upstream VDSL scenario. For this level of coordination, it is shown in [5, 6] that a simple linear zero-forcing canceller or linear precompensator performs near-optimally in an xDSL environment. Even for these simple linear cancellers, the complexity grows with the square of the number of lines. For example, in a binder of 8 VDSL lines transmitting on 4096 tones at a block rate of 4000 blocks per second, the runtime complexity of crosstalk cancellation exceeds 1 billion multiplications per second. However, crosstalk exhibits space and tone selectivity [7]. Measurements show that most of the crosstalk originates from a limited number of lines, for example, those in close
proximity. Moreover, crosstalk coupling is heavily dependent on the frequency. Because most of the crosstal
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