Computationally Efficient Partial Crosstalk Cancellation in Fast Time-Varying DSL Crosstalk Environments
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Research Article Computationally Efficient Partial Crosstalk Cancellation in Fast Time-Varying DSL Crosstalk Environments Amir R. Forouzan and Lee M. Garth Department of Electrical and Computer Engineering, University of Canterbury, Private Bag 4800, Christchurch 8020, New Zealand Received 3 April 2006; Revised 5 December 2006; Accepted 17 December 2006 Recommended by Markus Rupp Line selection (LS), tone selection (TS), and joint tone-line selection (JTLS) partial crosstalk cancellers have been proposed to reduce the online computational complexity of far-end crosstalk (FEXT) cancellers in digital subscriber lines (DSL). However, when the crosstalk profile changes rapidly over time, there is an additional requirement that the partial crosstalk cancellers, particularly the LS and JTLS schemes, should also provide a low preprocessing complexity. This is in contrast to the case for perfect crosstalk cancellers. In this paper, we propose two novel channel matrix inversion methods, the approximate inverse (AI) and reduced inverse (RI) schemes, which reduce the recurrent complexity of the LS and JTLS schemes. Moreover, we propose two new classes of JTLS algorithms, the subsort and Lagrange JTLS algorithms, with significantly lower computational complexity than the recently proposed optimal greedy JTLS scheme. The computational complexity analysis of our algorithms shows that they provide much lower recurrent complexities than the greedy JTLS algorithm, allowing them to work efficiently in very fast time-varying crosstalk environments. Moreover, the analytical and simulation results demonstrate that our techniques are close to the optimal solution from the crosstalk cancellation point of view. The results also reveal that partial crosstalk cancellation is more beneficial in upstream DSL, particularly for short loops. Copyright © 2007 A. R. Forouzan and L. M. Garth. 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.
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INTRODUCTION
The main impairments in digital subscriber lines (DSL) are loop loss, crosstalk, background noise, impulse noise, and radio ingress. For the short loop lengths of very high-speed digital subscriber lines (VDSL), the dominant impairment is far-end crosstalk (FEXT). Recently, FEXT cancellation techniques in loops with coordination among the transceivers on one side have been proposed. Coordination results in effective FEXT cancellation with higher performance and complexity reduction [1]. However, the method and success of FEXT cancellation techniques strongly depend on the degree of coordination among the DSL transceivers and the available processing power. FEXT cancellation in downstream (DS) and upstream (US) discrete multitone (DMT) DSL can be done by coordinating the transmitter and the receiver modems, respectively. In [2], a vector Tomlinson-Harashima precoder and in [3] a simpler technique called the diagonalizing precompensato
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