New theoretical bounds on the aperiodic correlation functions of binary sequences

  • Peng Daiyuan 
  • Fan Pingzhi 


In order to reduce or eliminate the multiple access interference in code division multiple access (CDMA) systems, we need to design a set of spreading sequences with good autocorrelation functions (ACF) and crosscorrelation functions (CCF). The importance of the spreading codes to CDMA systems cannot be overemphasized, for the type of the code used, its length, and its chip rate set bounds on the capability of the system that can be changed only by changing the code. Several new lower bounds which are stronger than the well-known Sarwate bounds, Welch bounds and Levenshtein bounds for binary sequence set with respect to the spreading sequence length, family size, maximum aperiodic autocorrelation sidelobe and maximum aperiodic crosscorrelation value are established.


aperiodic correlation functions binary sequences Levenshtein bounds Sarwate bounds Welch bounds Sidelnikov bounds 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Fan, P. Z., Darnell, M., Sequence Design for Communications Applications, New York: Wiley, 1996.Google Scholar
  2. 2.
    Pursley, M. B., Sarwate, D. V., Performance evaluation for phase-coded spread spectrum multiple-access communications-Part I: System analysis, IEEE Trans. Commun., 1977, COM-25: 795–799.CrossRefGoogle Scholar
  3. 3.
    Sarwate, D. V., Pursley, M. B., Crosscorrelation properties of pseudonoise and related sequences, Proceedings of IEEE, 1980, 68(5): 593–619.CrossRefGoogle Scholar
  4. 4.
    Sarwate, D. V., Bounds on crosscorrelation and autocorrelation of sequences, IEEE Trans. Inform. Theory, 1979, 25: 720–724.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Welch, L. R., Lower bounds on the maximum crosscorrelation of signals, IEEE Trans. Inform. Theory, 1974, IT-20: 397–399.CrossRefMathSciNetGoogle Scholar
  6. 6.
    Sidelnikov, V. M., Crosscorrelation of sequences, Probl. Kybem (in Russian), 1971, 24: 15–42.MathSciNetGoogle Scholar
  7. 7.
    Sidelnikov, V. M., On mutual correlation of sequences, Soviet Math Doklady, 1971, 12: 197–201.Google Scholar
  8. 8.
    Massey, J. L., On Welch’s Bound for the crosscorrelation of a sequence set, Proceedings of EEE ISIT’90, Sept. 1990, 385.Google Scholar
  9. 9.
    Levenshtein, V. I., New lower bounds on aperiodic crosscorrelation of binary codes, IEEE Trans. Inform. Theory, 1999, 45(1): 284–288.MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Peng, D. Y., Fan, P. Z., Bounds on Aperiodic auto- and cross-correlations of binary sequences with low or zero correlation zone, PDCAT’2003 Proceedings, IEEE Press, August, 2003, 882–886.Google Scholar
  11. 11.
    Fan, P. Z., Hao, L., Generalized orthogonal sequences and their applications in synchronous CDMA systems, IEICE Trans. Fundamentals, 2000, E83-A(11): 1–16.Google Scholar
  12. 12.
    Tang, X. H., Fan, P. Z., A class of pseudonoise sequences over GF(P) with low correlation zone, IEEE Trans. on Information Theory, 2001, 47(4): 1033–1039.CrossRefMathSciNetGoogle Scholar
  13. 13.
    Suehiro, N., A signal design without co-channel interference for approximately synchronized CDMA system, IEEE J. Sel. Areas Commun., 1994, 12: 837–841.CrossRefGoogle Scholar
  14. 14.
    Li, D. B., The perspective of large area synchronous CDMA technology for the fourth-generation mobile radio, IEEE Communication Magazine, March 2003, 114–118.Google Scholar
  15. 15.
    Li, W. C. Y., The most spectrum-efficient duplexing system: CDD, IEEE Communication Magazine, March 2002, 163–166.Google Scholar

Copyright information

© Science in China Press 2005 2005

Authors and Affiliations

  1. 1.Institute of Mobile CommunicationsSouthwest Jiaotong UniversityChengduChina

Personalised recommendations