Skip to main content

Multilevel Codes for OFDM-Like Modulation over Underspread Fading Channels

Abstract

We study the problem of modulation and coding for doubly dispersive, that is, time and frequency selective, fading channels. Using the recent result that underspread linear systems are approximately diagonalized by biorthogonal Weyl-Heisenberg bases, we arrive at a canonical formulation of modulation and code design. For coherent reception with maximum-likelihood decoding, we derive the code design criteria as a function of the channel's scattering function. We use ideas from generalized concatenation to design multilevel codes for this canonical channel model. These codes are based on partitioning a constellation carved out from the integer lattice. Utilizing the block fading interpretation of the doubly dispersive channel, we adapt these partitioning techniques to the richness of the channel. We derive an algebraic framework which enables us to partition in arbitrarily large dimensions.

References

  1. 1.

    Kozek W: Matched Weyl-Heisenberg expansions of nonstationary environments, M.S. thesis. Vienna University of Technology, Vienna, Austria; March 1997.

    Google Scholar 

  2. 2.

    Kozek W: Adaptation of Weyl-Heisenberg frames to underspread environments. In Gabor Analysis and Algorithms: Theory and Applications. Edited by: Feichtinger HG, Strohmer T. Birkhäuser, Boston, Mass, USA; 1998:323–352.

    Google Scholar 

  3. 3.

    Liu K, Kadous T, Sayeed AM: Orthogonal time-frequency signaling over doubly dispersive channels. IEEE Transactions on Information Theory 2004, 50(11):2583–2603. 10.1109/TIT.2004.836931

    MathSciNet  Article  Google Scholar 

  4. 4.

    Giraud X, Boutillon E, Belfiore JC: Algebraic tools to build modulation schemes for fading channels. IEEE Transactions on Information Theory 1997, 43(3):938–952. 10.1109/18.568703

    MathSciNet  Article  Google Scholar 

  5. 5.

    Boutros J, Viterbo E: Signal space diversity: a power- and bandwidth-efficient diversity technique for the Rayleigh fading channel. IEEE Transactions on Information Theory 1998, 44(4):1453–1467. 10.1109/18.681321

    MathSciNet  Article  Google Scholar 

  6. 6.

    Caire G, Taricco G, Biglieri E: Bit-interleaved coded modulation. IEEE Transactions on Information Theory 1998, 44(3):927–946. 10.1109/18.669123

    MathSciNet  Article  Google Scholar 

  7. 7.

    Ungerboeck G: Channel coding with multilevel/phase signals. IEEE Transactions on Information Theory 1982, 28(1):55–66. 10.1109/TIT.1982.1056454

    MathSciNet  Article  Google Scholar 

  8. 8.

    Zadeh L: Time-varying networks, I. Proceedings of IRE 1961, 49: 1488–1503.

    MathSciNet  Article  Google Scholar 

  9. 9.

    Proakis JG: Digital Communications. 4th edition. McGraw-Hill, New York, NY, USA; 2001. chapter 14

    Google Scholar 

  10. 10.

    Matz G, Hlawatsch F: Time-frequency transfer function calculus of linear time-varying systems. In Time-Frequency Signal Analysis and Processing. Edited by: Boashash B. Prentice-Hall, Englewood Cliffs, NJ, USA; 2003.

    Google Scholar 

  11. 11.

    Kozek W, Molisch AF: Nonorthogonal pulseshapes for multicarrier communications in doubly dispersive channels. IEEE Journal on Selected Areas in Communications 1998, 16(8):1579–1589. 10.1109/49.730463

    Article  Google Scholar 

  12. 12.

    Leeuwin-Boulle K, Belfiore JC: The cutoff rate of time correlated fading channels. IEEE Transactions on Information Theory 1993, 39(2):612–617. 10.1109/18.212291

    Article  Google Scholar 

  13. 13.

    Wang Z, Giannakis GB: A simple and general parameterization quantifying performance in fading channels. IEEE Transactions on Communications 2003, 51(8):1389–1398. 10.1109/TCOMM.2003.815053

    Article  Google Scholar 

  14. 14.

    Biglieri E, Proakis J, Shamai S: Fading channels: information-theoretic and communications aspects. IEEE Transactions on Information Theory 1998, 44(6):2619–2692. 10.1109/18.720551

    MathSciNet  Article  Google Scholar 

  15. 15.

    Siwamogsatham S, Fitz MP: Robust space-time codes for correlated Rayleigh fading channels. IEEE Transactions on Signal Processing 2002, 50(10):2408–2416. 10.1109/TSP.2002.803349

    Article  Google Scholar 

  16. 16.

    Imai H, Hirakawa S: A new multilevel coding method using error-correcting codes. IEEE Transactions on Information Theory 1977, 23(3):371–377. 10.1109/TIT.1977.1055718

    Article  Google Scholar 

  17. 17.

    Forney GD Jr., Gallager RG, Lang GR, Longstaff FM, Qureshi SU: Efficient modulation for band-limited channels. IEEE Journal on Selected Areas in Communications 1984, 2(5):632–647. 10.1109/JSAC.1984.1146101

    Article  Google Scholar 

  18. 18.

    Wachsmann U, Fischer RFH, Huber JB: Multilevel codes: theoretical concepts and practical design rules. IEEE Transactions on Information Theory 1999, 45(5):1361–1391. 10.1109/18.771140

    MathSciNet  Article  Google Scholar 

  19. 19.

    Modestino JW, Mui SY: Convolutional code performance in the rician fading channel. IEEE Transactions on Communications 1976, 24(6):592–606. 10.1109/TCOM.1976.1093351

    Article  Google Scholar 

  20. 20.

    Royden HL: Real Analysis. 3rd edition. Prentice-Hall, Englewood Cliffs, NJ, USA; 1988. chapter 4

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Siddhartha Mallik.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Mallik, S., Koetter, R. Multilevel Codes for OFDM-Like Modulation over Underspread Fading Channels. EURASIP J. Adv. Signal Process. 2006, 097210 (2006). https://doi.org/10.1155/ASP/2006/97210

Download citation

Keywords

  • Information Technology
  • Linear System
  • Quantum Information
  • Fading Channel
  • Canonical Formulation