Skip to content


  • Research Article
  • Open Access

Computationally Efficient Partial Crosstalk Cancellation in Fast Time-Varying DSL Crosstalk Environments

EURASIP Journal on Advances in Signal Processing20072007:072041

  • Received: 3 April 2006
  • Accepted: 17 December 2006
  • Published:


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.


  • Computational Complexity
  • Quantum Information
  • Inversion Method
  • Additional Requirement
  • Matrix Inversion

Authors’ Affiliations

Department of Electrical and Computer Engineering, University of Canterbury, Private Bag 4800, Christchurch, 8020, New Zealand


  1. Starr TM, Sorbara M, Cioffi JM, Silverman PJ: DSL Advances. Prentice-Hall, Upper Saddle River, NJ, USA; 2003.Google Scholar
  2. Ginis G, Cioffi JM: Vectored transmission for digital subscriber line systems. IEEE Journal on Selected Areas in Communications 2002,20(5):1085-1104. 10.1109/JSAC.2002.1007389View ArticleGoogle Scholar
  3. Cendrillon R, Moonen M, Verlinden J, Bostoen T, Ginis G: Improved linear crosstalk precompensation for DSL. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '04), May 2004, Montreal, Canada 4: 1053–1056.Google Scholar
  4. Cendrillon R, Moonen M, Van Den Bogaert E, Ginis G: The linear zero-forcing crosstalk canceler is near-optimal in DSL channels. Proccedings of IEEE Global Telecommunications Conference (GLOBECOM '04), November-December 2004, Dallas, Tex, USA 4: 2334–2338.View ArticleGoogle Scholar
  5. Cendrillon R, Moonen M, Ginis G, Van Acker K, Bostoen T, Vandaele P: Partial crosstalk cancellation for upstream VDSL. EURASIP Journal on Applied Signal Processing 2004,2004(10):1520-1535. 10.1155/S1110865704309273Google Scholar
  6. Cendrillon R, Ginis G, Moonen M, Van Acker K: Partial crosstalk precompensation in downstream VDSL. Signal Processing 2004,84(11):2005-2019. 10.1016/j.sigpro.2004.07.013View ArticleGoogle Scholar
  7. Salvekar AA, Louveaux J, Aldana C, Fang JL, de Carvalho E, Cioffi JM: Profile detection in multiuser digital subscriber line systems. IEEE Journal on Selected Areas in Communications 2002,20(5):1116-1125. 10.1109/JSAC.2002.1007391View ArticleGoogle Scholar
  8. Spectrum management for loop transmission systems In (Draft) ANSI Standard T1.417-2003. ANSI, Washington, DC, USA; 2003.Google Scholar
  9. Cioffi J: Very-high-speed digital subscriber lines - system requirements. In Tech. Rep. T1E1.4/98 Contribution 043R6. ANSI, Washington, DC, USA; 1998.Google Scholar
  10. Zeng C, Aldana C, Salvekar AA, Cioffi JM: Crosstalk identification in xDSL systems. IEEE Journal on Selected Areas in Communications 2001,19(8):1488-1496. 10.1109/49.942511View ArticleGoogle Scholar
  11. Tsiaflakis P, Vangorp J, Moonen M, Verlinden J, Ysebaert G: Partial crosstalk cancellation in a multi-user xDSL environment. Proceedings of IEEE International Conference on Communications (ICC '06), June 2006, Istanbul, Turkey 7: 3264–3269.MATHGoogle Scholar
  12. Leshem A, Youming L: A low complexity coordinated FEXT cancellation for VDSL. Proceedings of the 11th IEEE International Conference on Electronics, Circuits and Systems (ICECS '04), December 2004, Tel Aviv, Israel 338–341.Google Scholar
  13. Ginis G: Multi-line coordinated communication for broadband access networks, Ph.D. dissertation. Stanford University, Stanford, Calif, USA, 2002.Google Scholar
  14. Cendrillon R, Moonen M, Gore D, Paulraj A: Low complexity crosstalk cancellation through line selection in upstream VDSL. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '03), April 2003, Hong Kong 4: 692–695.Google Scholar
  15. Starr TM, Cioffi JM, Silverman PJ: Understanding Digital Subscriber Line Technology. Prentice-Hall, Upper Saddle River, NJ, USA; 1999.Google Scholar
  16. Boyd S, Vandenberghe L: Convex Optimization. Cambridge University Press, Cambridge, UK; 2004.View ArticleGoogle Scholar
  17. Cendrillon R, Moonen M, Verliden J, Bostoen T, Yu W: Optimal multi-user spectrum management for digital subscriber lines. Proceedings of IEEE International Conference on Communications (ICC '04), June 2004, Paris, France 1: 1–5.Google Scholar
  18. Yu W, Lui R, Cendrillon R: Dual optimization methods for multiuser orthogonal frequency division multiplex systems. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '04), November-December 2004, Dallas, Tex, USA 1: 225–229.View ArticleGoogle Scholar
  19. Sedgewick R: Algorithms. 2nd edition. Addison-Wesley, Reading, Mass, USA; 1988.MATHGoogle Scholar
  20. ETSI : Transmission and Multiplexing (TM); access transmission systems on metallic access cables; very high speed digital subscriber line (VDSL)—part I: functional requirements. ETSI Std. TS 101 270-1, Rev. V.1.3.1 2003.Google Scholar
  21. Cendrillon R, Moonen M, Suciu R, Ginis G: Simplified Power Allocation and TX/RX Structure for MIMO-DSL. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '03), December 2003, San Francisco, Calif, USA 4: 1842–1846.View ArticleGoogle Scholar
  22. Weisstein EW: Perron's theorem.
  23. Gradshteyn IS, Ryzhik IM: Tables of Integrals, Series, and Products. Academic Press, San Diego, Calif, USA; 2000.MATHGoogle Scholar


© A. R. Forouzan and L. M. Garth 2007

This article is published under license to BioMed Central Ltd. 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.