Skip to main content
  • Research Article
  • Open access
  • Published:

Wireless Multicarrier Communications via Multipulse Gabor Riesz Bases

Abstract

We introduce multipulse multicarrier (MPMC) modulation, a wireless communication scheme that augments traditional single-pulse multicarrier systems by using multiple pulses at the transmitter and the receiver. The mathematical foundation of MPMC systems is established by the novel concept of multipulse Gabor Riesz bases. We adapt Zak-Fourier domain tools previously developed for multiwindow Gabor frames to analyze and design (bi)orthogonal multipulse Gabor Riesz bases and the corresponding MPMC systems in a computationally efficient manner. Furthermore, explicit expressions for the interference power and the spectral efficiency in MPMC transmissions over time-varying multipath channels are derived. The superiority of MPMC modulation over single-pulse multicarrier systems is finally demonstrated via numerical simulations.

References

  1. Chang RW: Synthesis of band-limited orthogonal signals for multi-channel data transmission. Bell System Technical Journal 1966, 45(10):1775–1796.

    Article  Google Scholar 

  2. Bingham JAC: Multicarrier modulation for data transmission: an idea whose time has come. IEEE Communications Magazine 1990, 28(5):5–14. 10.1109/35.54342

    Article  Google Scholar 

  3. Le Floch B, Alard M, Berrou C: Coded orthogonal frequency division multiplex. Proceedings of the IEEE 1995, 83(6):982–996. 10.1109/5.387096

    Article  Google Scholar 

  4. Weinstein SB, Ebert PM: Data transmission by frequency division multiplexing using the discrete Fourier transform. IEEE Transactions on Communications 1971, 19(5, part 1):628–634. 10.1109/TCOM.1971.1090705

    Article  Google Scholar 

  5. Cimini L Jr.: Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing. IEEE Transactions on Communications 1985, 33(7):665–675. 10.1109/TCOM.1985.1096357

    Article  Google Scholar 

  6. Peled A, Ruiz A: Frequency domain data transmission using reduced computational complexity algorithms. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '80), April 1980, Denver, Colo, USA 5: 964–967.

    Article  Google Scholar 

  7. Smulders P: Exploiting the 60 GHz band for local wireless multimedia access: prospects and future directions. IEEE Communications Magazine 2002, 40(1):140–147. 10.1109/35.978061

    Article  Google Scholar 

  8. Haas R, Belfiore J-C: A time-frequency well-localized pulse for multiple carrier transmission. Wireless Personal Communications 1997, 5(1):1–18. 10.1023/A:1008859809455

    Article  Google Scholar 

  9. Bölcskei H: Efficient design of pulse-shaping filters for OFDM systems. Wavelet Applications in Signal and Image Processing VII, July 1999, Denver, Colo, USA, Proceedings of SPIE 3813: 625–636.

    Article  Google Scholar 

  10. 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 

  11. Schafhuber D, Matz G, Hlawatsch F: Pulse-shaping OFDM/BFDM systems for time-varying channels: ISI/ICI analysis, optimal pulse design, and efficient implementation. Proceedings of 13th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (PIMRC '02), September 2002, Lisbon, Portugal 3: 1012–1016.

    Article  Google Scholar 

  12. Siclet C, Siohan P, Pinchon D: Oversampled orthogonal and biorthogonal multicarrier modulations with perfect reconstruction. Proceedings of IEEE 14th International Conference on Digital Signal Processing (DSP '02), July 2002, Santorini, Greece 2: 647–650.

    Article  Google Scholar 

  13. Hartmann MM, Matz G, Schafhuber D: Theory and design of multipulse multicarrier systems for wireless communications. Proceedings of 37th IEEE Asilomar Conference on Signals, Systems and Computers (ACSSC '03), November 2003, Pacific Grove, Calif, USA 1: 492–496.

    Google Scholar 

  14. Zibulski M, Zeevi YY: Analysis of multiwindow Gabor-type schemes by frame methods. Applied and Computational Harmonic Analysis 1997, 4(2):188–221. 10.1006/acha.1997.0209

    Article  MathSciNet  Google Scholar 

  15. Gröchenig K: Foundations of Time-Frequency Analysis. Birkhäuser, Boston, Mass, USA; 2001.

    Book  Google Scholar 

  16. Feichtinger HG, Strohmer T (Eds): Gabor Analysis and Algorithms: Theory and Applications. Birkhäuser, Boston, Mass, USA; 1998.

    Book  Google Scholar 

  17. Hartmann MM, Matz G, Schafhuber D: Multipulse multicarrier communications over time-varying fading channels: performance analysis and system optimization. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '04), May 2004, Montreal, Quebec, Canada 3: 805–808.

    Google Scholar 

  18. Hartmann MM, Matz G, Schafhuber D: Transceiver design for precoded multipulse multicarrier packet transmissions over time-varying fading channels. Proceedings of IEEE Global Telecommunications Conference (GLOBECOM '04), November–December 2004, Dallas, Tex, USA 4: 2409–2413.

    Article  Google Scholar 

  19. Strohmer T, Beaver S: Optimal OFDM design for time-frequency dispersive channels. IEEE Transactions on Communications 2003, 51(7):1111–1122. 10.1109/TCOMM.2003.814200

    Article  Google Scholar 

  20. Hirosaki B: An orthogonally multiplexed QAM system using the discrete Fourier transform. IEEE Transactions on Communications 1981, 29(7):982–989. 10.1109/TCOM.1981.1095093

    Article  Google Scholar 

  21. Bölcskei H, Duhamel P, Hleiss R: Design of pulse shaping OFDM/OQAM systems for high data-rate transmission over wireless channels. Proceedings of IEEE International Conference on Communications (ICC '99), June 1999, Vancouver, British Columbia, Canada 1: 559–564.

    Google Scholar 

  22. Siohan P, Siclet C, Lacaille N: Analysis and design of OFDM/OQAM systems based on filterbank theory. IEEE Transactions on Signal Processing 2002, 50(5):1170–1183. 10.1109/78.995073

    Article  Google Scholar 

  23. Hara S, Prasad R: Overview of multicarrier CDMA. IEEE Communications Magazine 1997, 35(12):126–133. 10.1109/35.642841

    Article  Google Scholar 

  24. Zibulski M, Zeevi YY: Discrete multiwindow Gabor-type transforms. IEEE Transactions on Signal Processing 1997, 45(6):1428–1442. 10.1109/78.599955

    Article  Google Scholar 

  25. Christensen O: An Introduction to Frames and Riesz Bases. Birkhäuser, Boston, Mass, USA; 2003.

    Book  Google Scholar 

  26. Young RM: An Introduction to Nonharmonic Fourier Series. Academic Press, New York, NY, USA; 1980.

    MATH  Google Scholar 

  27. Naylor AW, Sell GR: Linear Operator Theory in Engineering and Science. 2nd edition. Springer, New York, NY, USA; 1982.

    Book  Google Scholar 

  28. Proakis JG: Digital Communications. 3rd edition. McGraw-Hill, New York, NY, USA; 1995.

    MATH  Google Scholar 

  29. Janssen AJEM: Duality and biorthogonality for Weyl-Heisenberg frames. Journal of Fourier Analysis and Applications 1995, 1(4):403–436.

    Article  MathSciNet  Google Scholar 

  30. Bello PA: Characterization of randomly time-variant linear channels. IEEE Transactions on Communications Systems 1963, 11(4):360–393. 10.1109/TCOM.1963.1088793

    Article  Google Scholar 

  31. Matz G, Hlawatsch F: Time-frequency characterization of random time-varying channels. In Time-Frequency Signal Analysis and Processing: A Comprehensive Reference. Edited by: Boashash B. Elsevier, Oxford, UK; 2003:410–419. chapter 9.5

    Google Scholar 

  32. Hlawatsch F: Time-Frequency Analysis and Synthesis of Linear Signal Spaces: Time-Frequency Filters, Signal Detection and Estimation, and Range-Doppler Estimation. Kluwer Academic, Boston, Mass, USA; 1998.

    Book  Google Scholar 

  33. Cover TM, Thomas JA: Elements of Information Theory. John Wiley & Sons, New York, NY, USA; 1991.

    Book  Google Scholar 

  34. Pinchon D, Siohan P, Siclet C: Design techniques for orthogonal modulated filterbanks based on a compact representation. IEEE Transactions on Signal Processing 2004, 52(6):1682–1692. 10.1109/TSP.2004.827193

    Article  MathSciNet  Google Scholar 

  35. Bölcskei H, Janssen AJEM: Gabor frames, unimodularity, and window decay. Journal of Fourier Analysis and Applications 2000, 6(3):255–276. 10.1007/BF02511155

    Article  MathSciNet  Google Scholar 

  36. Janssen AJEM, Strohmer T: Characterization and computation of canonical tight windows for Gabor frames. Journal of Fourier Analysis and Applications 2002, 8(1):1–28. 10.1007/s00041-002-0001-x

    Article  MathSciNet  Google Scholar 

  37. Horn RA, Johnson CR: Topics in Matrix Analysis. Cambridge University Press, Cambridge, UK; 1994.

    MATH  Google Scholar 

  38. Golub GH, Van Loan CF: Matrix Computations. 2nd edition. Johns Hopkins University Press, Baltimore, Md, USA; 1989.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Manfred M Hartmann.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Hartmann, M.M., Matz, G. & Schafhuber, D. Wireless Multicarrier Communications via Multipulse Gabor Riesz Bases. EURASIP J. Adv. Signal Process. 2006, 023818 (2006). https://doi.org/10.1155/ASP/2006/23818

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1155/ASP/2006/23818

Keywords