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Chip-Asynchronous Version of Welch Bound: Gaussian Pulse Improves BER Performance

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Sequences and Their Applications – SETA 2006 (SETA 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4086))

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Abstract

We give a quadratic form expression of the mean squared multiple-access interference (MAI) averaged over relative time delays for chip-asynchronous DS/CDMA systems. A lower bound on the mean squared MAI is referred to as chip-asynchronous version of Welch bound, which depends on chip pulse shapes. Real analysis tells us that a pair of rectangular and sinc functions is one of Fourier transform and its inverse Fourier transform and vice versa. On the other hand, Gaussian pulses have the self-duality property. Gaussian chip pulses sacrifice inter-symbol interference, however, they give smaller mean squared MAI, as well as lower bit error rate, than the conventional Nyquist pulses.

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References

  1. Welch, L.R.: Lower bounds on the maximum cross correlation of signals. IEEE Trans. Inform. Theory 20, 397–399 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  2. Rupf, M., Massey, J.L.: Optimum sequence multisets for synchronous code-divition multiple-access channels. IEEE Trans. Inform. Theory 40(4), 1261–1266 (1994)

    Article  MATH  Google Scholar 

  3. Sarwate, D.: Meeting the Welch bound with equality. In: Ding, T.H.C., Niederreiter, H. (eds.) Sequences and Their Applications: Proceedings of SETA 1998, Springer, London (1999)

    Google Scholar 

  4. Viswanath, P., Anatharam, V., Tse, D.N.C.: IEEE Trans. Inform. Theory 45(6), 1968–1983 (1999)

    Google Scholar 

  5. Viswanath, P., Anatharam, V.: IEEE Trans. Inform. Theory 45(6), 1984–1991 (1999)

    Google Scholar 

  6. Karystinos, G.N., Pados, D.A.: New bounds on the total squared correlation and optimum design of DS-CDMA binary signature sets. IEEE Trans. Commun., 48–51 (2003)

    Google Scholar 

  7. Karystinos, G.N., Pados, D.A.: The maximum squared correlation, sum capacity, and total asymptotic efficiency of minimum total-squered-correlation binary signature sets. IEEE Trans. Inform. Theory, 348–355 (2005)

    Google Scholar 

  8. Mow, W.H.: On the bounds on odd correlation of sequences. IEEE Trans. Inform. Theory 40(3), 954–955 (1994)

    Article  MATH  Google Scholar 

  9. Pursley, M.B.: Performance evaluation for phase-coded SS multiple-access communication-part-I: system analysis. IEEE Trans. Commun. 25(8), 795–799 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ulukus, S., Yates, R.D.: User capacity of asynchronous CDMA systems with matched filter receivers and optimum signature sequences. IEEE Trans. Inform. Theory, 903–909 (2004)

    Google Scholar 

  11. Mazzini, G., Setti, G., Rovatti, R.: Chaotic complex spreading sequences for asynchronous DS-CDMA -part I: System modeling and results. IEEE Trans. Circuits Syst. I 44(10), 937–947 (1997)

    Article  MathSciNet  Google Scholar 

  12. Mazzini, G., Rovatti, R., Setti, G.: Interference minimisation by autocorrelation shaping in asynchronous DS/CDMA systems: Chaos based spreading is nearly optimal. Electronics Letters, IEE 35, 1054–1055 (1999)

    Article  Google Scholar 

  13. Chen, C.C., Yao, K., Umeno, K., Biglieri, E.: Design of spread-spectrum sequences using chaotic dynamical systems and ergodic theory. IEEE Trans. Circuits Syst. I 48(9), 1110–1114 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kohda, T., Fujisaki, H.: Variances of multiple access interference: Code average against data average. Electronics Letters, IEE 36, 1717–1719 (2000)

    Article  Google Scholar 

  15. Rovatti, R., Setti, G., Mazzini, G.: Pulse shaping and SIR-energy trade-off in chaos-based asynchronous DS-CDMA. In: Proc. of the 2004 Int. Symp. on Circuits and Systems, IV, pp. 613–616 (2004)

    Google Scholar 

  16. Setti, G., Rovatti, R., Mazzini, G.: Performance of chaos-based asynchronous DS-CDMA with different pulse shapes. IEEE Commun. Lett. 8(7), 416–418 (2004)

    Article  Google Scholar 

  17. Cho, J.H., Lehnert, J.S.: An optimal signal design for band-limited asynchronous DS-CDMA communications. IEEE Trans. Inform. Theory 48(5), 1172–1185 (2002)

    Article  MATH  Google Scholar 

  18. Cho, J.H., Gao, W.: Continuous-time equivalents of Welch bound equality sequences. IEEE Trans. Inform. Theory 51, 3176–3185 (2005)

    Article  MathSciNet  Google Scholar 

  19. Jitsumatsu, Y., Kohda, T.: Gaussian chip shaping enhances the superiority of markovian codes in DS/CDMA systems. In: Proc. of 2006 IEEE Int. Symp. on Circuits and Systems, Island of Kos, Greece (2006)

    Google Scholar 

  20. Blahut, R.E.: Digital Transmission of Information. Addison-Wesley, Reading (1990)

    Google Scholar 

  21. Monk, A.M., Davis, M., Milstein, L.B., Helstrom, C.W.: A noise-whitening approach to multiple access noise rejection–part I: Theory and background. IEEE Journal on Selected Area in Communications 12(5), 817–827 (1994)

    Article  Google Scholar 

  22. Huang, Y., Ng, T.S.: A DS-CDMA system using despreading sequences weighted by adjustable chip waveforms. IEEE Trans. Commun. 47(12), 1884–1896 (1999)

    Article  Google Scholar 

  23. Pursley, M.B., Sarwate, D.V., Stark, W.E.: Error probability for direct-sequence spread-spectrum multiple-access communications–part i: Upper and lower bounds (1982)

    Google Scholar 

  24. Morrow, R.K., Lehnert, J.S.: Bit-to-bit error dependence in slotted DS/SSMA packet systems with random signature sequences. IEEE Trans. Commun. 37, 1052–1061 (1989)

    Article  Google Scholar 

  25. Schotten, H.D.: Sequence families with optimum aperiodic mean-square correlation parameters. In: Ding, C., H, T., Niederreiter, H. (eds.) Sequences and Their Applications: Proceedings of SETA 1998, Springer, London (1999)

    Google Scholar 

  26. Ripley, B.D.: Stochastic Simulation. John Wiley & Sons Inc., New York (1987)

    Book  MATH  Google Scholar 

  27. Pursley, M.B., Sarwate, D.V.: Performance evaluation for phase-coded SS multiple-access communication-part–II: code sequence analysis. IEEE Trans. Commun. 25(8), 800–803 (1977)

    Article  MATH  Google Scholar 

  28. Beaulieu, N.C., Tan, C.C., Damen, M.O.: A ”better than” Nyquist pulse. IEEE Commun. Lett. 5(9), 367–368 (2001)

    Article  Google Scholar 

  29. Slepian, D., Pollak, H.O.: Prolate spheroidal wave functions, fourier analysis, and uncertainty-i. Bell Syst. Tech. J. 40(1), 43–46 (1961)

    MATH  MathSciNet  Google Scholar 

  30. Landolsi, M.A., Stark, W.E.: DS-CDMA chip waveform design for minimal interference under bandwidth, phase, and envelope constraints. IEEE Trans. Commun. 47(11), 1737–1746 (1999)

    Article  Google Scholar 

  31. Nguyen, H.H., Shwedyk, E.: A new construction of signature waveforms for synchronous CDMA systems. IEEE Trans. Broadcast 51, 520–529 (2005)

    Article  Google Scholar 

  32. Zhang, H., Zhou, X., Yazdandoost, K.Y., Chlamtac, I.: Multiple signal waveforms adaptation in cognitive ultra-wideband radio evolution. IEEE J. Select. Areas Commun. 24, 878–884 (2006)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Computer Science and Communication Engineering, Kyushu University, 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581, Japan

    Yutaka Jitsumatsu & Tohru Kohda

Authors
  1. Yutaka Jitsumatsu
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  2. Tohru Kohda
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Editor information

Editors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Guang Gong

  2. Department of Informatics, University of Bergen, PB 7803, 5020, Bergen, Norway

    Tor Helleseth

  3. Department of Electrical and Electronic Engineering, Yonsei University, 121-749, Seoul, Korea

    Hong-Yeop Song

  4. Dept. of Electronics and Electrical Engineering, Pohang University of Science and Technology (POSTECH), 790-784, Pohang, Kyungbuk, Korea

    Kyeongcheol Yang

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© 2006 Springer-Verlag Berlin Heidelberg

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Jitsumatsu, Y., Kohda, T. (2006). Chip-Asynchronous Version of Welch Bound: Gaussian Pulse Improves BER Performance. In: Gong, G., Helleseth, T., Song, HY., Yang, K. (eds) Sequences and Their Applications – SETA 2006. SETA 2006. Lecture Notes in Computer Science, vol 4086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11863854_31

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  • DOI: https://doi.org/10.1007/11863854_31

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44523-4

  • Online ISBN: 978-3-540-44524-1

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