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  • Research Article
  • Open Access

The Worst-Case Interference in DSL Systems Employing Dynamic Spectrum Management

EURASIP Journal on Advances in Signal Processing20062006:078524

  • Received: 1 December 2004
  • Accepted: 31 July 2005
  • Published:


Dynamic spectrum management (DSM) has been proposed to achieve next-generation rates on digital subscriber lines (DSL). Because the copper twisted-pair plant is an interference-constrained environment, the multiuser performance and spectral compatibility of DSM schemes are of primary concern in such systems. While the analysis of multiuser interference has been standardized for current static spectrum-management (SSM) techniques, at present no corresponding standard DSM analysis has been established. This paper examines a multiuser spectrum-allocation problem and formulates a lower bound to the achievable rate of a DSL modem that is tight in the presence of the worst-case interference. A game-theoretic analysis shows that the rate-maximizing strategy under the worst-case interference (WCI) in the DSM setting corresponds to a Nash equilibrium in pure strategies of a certain strictly competitive game. A Nash equilibrium is shown to exist under very mild conditions, and the rate-adaptive waterfilling algorithm is demonstrated to give the optimal strategy in response to the WCI under a frequency-division (FDM) condition. Numerical results are presented for two important scenarios: an upstream VDSL deployment exhibiting the near-far effect, and an ADSL RT deployment with long CO lines. The results show that the performance improvement of DSM over SSM techniques in these channels can be preserved by appropriate distributed power control, even in worst-case interference environments.


  • Nash Equilibrium
  • Nash
  • Quantum Information
  • Power Control
  • Pure Strategy

Authors’ Affiliations

Department of Electrical Engineering, Stanford University, Stanford, CA 94305-9515, USA


  1. Spectrum management for loop transmission systems ANSI Std. T1.417, 2002Google Scholar
  2. Sason I: On achievable rate regions for the Gaussian interference channel. IEEE Transactions on Information Theory 2004, 50(6):1345–1356. 10.1109/TIT.2004.828151MathSciNetView ArticleGoogle Scholar
  3. Peng WC: Some communication jamming games, M.S. thesis. University of Southern California, Los Angeles, Calif, USA; 1986.Google Scholar
  4. Hegde MV, Stark WE, Teneketzis D: On the capacity of channels with unknown interference. IEEE Transactions on Information Theory 1989, 35(4):770–783. 10.1109/18.32154MathSciNetView ArticleGoogle Scholar
  5. Han T, Kobayashi K: A new achievable rate region for the interference channel. IEEE Transactions on Information Theory 1981, 27(1):49–60. 10.1109/TIT.1981.1056307MathSciNetView ArticleGoogle Scholar
  6. Chung ST, Cioffi JM: The capacity region of frequency-selective Gaussian interference channels under strong interference. Proceedings of IEEE International Conference on Communications (ICC '03), May 2003, Anchorage, Alaska, USA 4: 2753–2757.View ArticleGoogle Scholar
  7. Song KB, Chung ST, Ginis G, Cioffi JM: Dynamic spectrum management for next-generation DSL systems. IEEE Communications Magazine 2002, 40(10):101–109. 10.1109/MCOM.2002.1039864View ArticleGoogle Scholar
  8. Kerpez KJ, Waring DL, Galli S, Dixon J, Madon P: Advanced DSL management. IEEE Communications Magazine 2003, 41(9):116–123. 10.1109/MCOM.2003.1232246View ArticleGoogle Scholar
  9. Starr T, Sorbara M, Cioffi JM, Silverman PJ: DSL Advances. Prentice-Hall PTR, Upper Saddle River, NJ, USA; 2003.Google Scholar
  10. Chung ST, Kim SJ, Lee J, Cioffi JM: A game-theoretic approach to power allocation in frequency-selective Gaussian interference channels. Proceedings of IEEE International Symposium on Information Theory (ISIT '03), June–July 2003, Pacifico Yokohama, Kanagawa, Japan 316–316.Google Scholar
  11. Cendrillon R, Moonen M, Verliden J, Bostoen T, Yu W: Optimal multiuser spectrum management for digital subscriber lines. Proceedings of IEEE International Conference on Communications (ICC '04), June 2004, Paris, France 1: 1–5.Google Scholar
  12. Statovci D, Nordstrom T: Adaptive subcarrier allocation, power control, and power allocation for multiuser FDD-DMT systems. Proceedings of IEEE International Conference on Communications (ICC '04), June 2004, Paris, France 1: 11–15.Google Scholar
  13. Cherubini G: Optimum upstream power back-off and multiuser detection for VDSL. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '01), November 2001, San Antonio, Tex, USA 1: 375–380.View ArticleGoogle Scholar
  14. Lee J, Sonalkar RV, Cioffi JM: Multi-user discrete bit-loading for DMT-based DSL systems. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '02), November 2002, Taipei, Taiwan 2: 1259–1263.Google Scholar
  15. Jacobsen KS: Methods of upstream power backoff on very high speed digital subscriber lines. IEEE Communications Magazine 2001, 39(3):210–216. 10.1109/35.910609View ArticleGoogle Scholar
  16. Schelstraete S: Defining upstream power backoff for VDSL. IEEE Journal on Selected Areas in Communications 2002, 20(5):1064–1074. 10.1109/JSAC.2002.1007387View ArticleGoogle Scholar
  17. Kang K-M, Im G-H: Upstream power back-off method for VDSL transmission systems. IEE Electronics Letters 2003, 39(7):634–635. 10.1049/el:20030423View ArticleGoogle Scholar
  18. Yu W, Ginis G, Cioffi JM: Distributed multiuser power control for digital subscriber lines. IEEE Journal on Selected Areas in Communications 2002, 20(5):1105–1115. 10.1109/JSAC.2002.1007390View ArticleGoogle Scholar
  19. Ho M, Cioffi JM, Bingham JAC: Discrete multitone echo cancelation. IEEE Transactions on Communications 1996, 44(7):817–825. 10.1109/26.508301View ArticleGoogle Scholar
  20. Van Acker K, Moonen M, Pollet T: Per-tone echo cancellation for DMT-based systems. IEEE Transactions on Communications 2003, 51(9):1582–1590. 10.1109/TCOMM.2003.816983View ArticleGoogle Scholar
  21. Ysebaert G, Vanbleu K, Cuypers G, Moonen M, Verlinden J: Echo cancellation for discrete multitone frame-asynchronous ADSL transceivers. Proceedings of IEEE International Conference on Communications (ICC '03), May 2003, Anchorage, Alaska, USA 4: 2421–2425.View ArticleGoogle Scholar
  22. Jones DC: Frequency domain echo cancellation for discrete multitone asymmetric digital subscriber line transceivers. IEEE Transactions on Communications 1995, 43(2–4):1663–1672.View ArticleGoogle Scholar
  23. Cover TM, Thomas JA: Elements of Information Theory. John Wiley & Sons, New York, NY, USA; 1991.View ArticleGoogle Scholar
  24. Schelestrate ed S: Very high speed digital subscriber lines, part 3: Multicarrier modulation (MCM) specification. ANSI Std. T1.424, 2002Google Scholar
  25. Widrow B, Streams SD: Adaptive Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, USA; 1985.Google Scholar
  26. Cioffi JM: Incentive-based spectrum management. T1.E1 Contribution 2004/480R2, August 2004Google Scholar
  27. Boyd S, Vandenberghe L: Convex Optimization. Cambridge University Press, Cambridge, UK; 2004.View ArticleGoogle Scholar
  28. Basar T, Olsder GJ: Dynamic Noncooperative Game Theory. Academic Press, New York, NY, USA; 1982.MATHGoogle Scholar
  29. Very high speed digital subscriber lines, part 1: Metallic interface ANSI T1.424 (Draft), February 2004Google Scholar
  30. ITR Recommendations G.992.1 : Asymmetric digital subscriber line (ADSL) transceivers. ITU, June 1999Google Scholar


© M. H. Brady and J. M. Cioffi. 2006

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.