Generalized Bounds on Partial Aperiodic Correlation of Complex Roots of Unity Sequences

  • Lifang Feng
  • Pingzhi Fan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4086)


Partial correlation properties of sets of sequences are important in CDMA system as well as in ranging, channel estimation and synchronization applications. In general, it is desirable to have sequence sets with small absolute values of partial correlations. In this paper, generalized lower bounds on partial aperiodic correlation of complex roots of unity sequence sets with respect to family size, sequence length, subsequence length, maximum partial aperiodic autocorrelation sidelobe, maximum partial aperiodic crosscorrelation value and the zero or low correlation zone are derived. It is shown that the previous aperiodic sequence bounds such as Sarwate bounds, Welch bounds, Levenshtein bounds, Tang-Fan bounds and Peng-Fan bounds can be considered as special cases of the new partial aperiodic bounds derived.


Partial Correlation Channel Estimation Binary Sequence Complex Root CDMA System 
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  1. 1.
    Welch, L.R.: Lower bounds on the maximum cross-correlation of signals. IEEE Trans. Information Theory 20, 397–399 (1974)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Tang, X.H., Fan, P.Z., Matsufuji, S.: Lower bounds on maximum correlation of sequence set with low or zero correlation zone. Electronics Letter 36(6), 551–552 (2000)CrossRefGoogle Scholar
  3. 3.
    Peng, D.Y., Fan, P.Z.: Generalized Sarwate bounds on the periodic correlation of complex roots of unity sequences. In: Proc. of IEEE Int. Symp. on Personal, Indoor and Mobile Radio Comms. (PIMRC 2003), Beijing, China, pp. 449–452. IEEE Press, Los Alamitos (2003)Google Scholar
  4. 4.
    Peng, D.Y., Fan, P.Z.: Generalized Sarwate bounds on periodic autocorrelations and cross-correlations of binary sequences. IEE Electronics Letters 38(24), 1521–1523 (2002)CrossRefGoogle Scholar
  5. 5.
    Sarwate, D.V.: Bounds on crosscorrelation and auto- correlation of sequences. IEEE Trans. Inform. Theory 25, 720–724 (1979)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Peng, D., Fan, P.: Generalised Sarwate bounds on the aperiodic correlation of sequences over complex roots of unity. IEE Proc.-Commun. 151(4), 375–382 (2004)CrossRefGoogle Scholar
  7. 7.
    Peng, D., Fan, P., Suehiro, N.: Bounds on aperiodic autocorrelation and crosscorrelation of binary LCZ/ZCZ sequences. IEICE Trans. on Fundamentals, pp. 1–9 (2005)Google Scholar
  8. 8.
    Peng, D., Fan, P.: Bounds on aperiodic auto- and cross-correlation of binary sequences with low or zero correlation zone. IEEE 0-7803-7840-7/03, pp. 882–886 (2003)Google Scholar
  9. 9.
    Pursley, M.B.: On the mean-square partial correlation of periodic sequences. In: Proc. Conf. Information Science and Systems, Johns Hopkins Univ., Baltimore MD, pp. 377–379 (1979)Google Scholar
  10. 10.
    Pursley, M.B., Sarwate, D.V., Basar, T.U.: Partial correlation effects in direct-sequence spread-spectrum multiple-access communications systems. IEEE Trans. Commun. COM-32, 567–573 (1984)Google Scholar
  11. 11.
    Cartier, D.E.: Partial correlation properties of pseudonoise (PN) codes in noncoherent synchronization/detection schemes. IEEE Trans. On Commun., 898–903 (1976)Google Scholar
  12. 12.
    Lee, Y.-H., Tantaratana, S.: Sequential acquisition of PN sequences for DS/SS communications: design and performance. IEEE Journal on selected areas in communications 10(4), 750–759 (1992)CrossRefGoogle Scholar
  13. 13.
    Paterson, K.G., Lothian, P.J.G.: Bounds on partial correlations of sequences. IEEE Trans. Information Theory 44(3), 1164–1175 (1998)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Fan, P.Z., Suehiro, N., Kuroyanagi, N., Deng, X.M.: A class of binary sequences with zero correlation zone. IEE Electron. Lett. 35, 777–779 (1999)CrossRefGoogle Scholar
  15. 15.
    Fan, P., Hao, L.: Generalized orthogonal sequences and their applications in synchronous CDMA. IEICE Trans. Fundamental E83-A(11), 2054–2069 (2000)Google Scholar
  16. 16.
    Deng, X., Fan, P.: Spreading sequence sets with zero and low correlation zone for quasi-synchronous CDMA communication systems. IEEE 0-7803-6507-0/00, pp. 1698–1703 (2000)Google Scholar
  17. 17.
    Torii, H., Nakamura, M., Suehiro, N.: A new class of zero-correlation zone sequences. IEEE Transactions On Information Theory 50(3), 559–565 (2004)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Tang, X.H., Fan, P.Z., Li, D.B., Suehiro, N.: Binary array set with zero correlation zone. IEE Electronics Letters 37(13), 841–842 (2001)CrossRefGoogle Scholar
  19. 19.
    Fan, P.Z.: Spreading sequence design and theoretical limits for quasis-ynchronous CDMA systems. EURASIP Journal on Wireless Communications and Networking (JWCN, USA) 1(1), 19–31 (2004)CrossRefGoogle Scholar
  20. 20.
    Levenshtein, V.I.: New lower bounds on aperiodic crosscorrelation of binary codes. IEEE Trans. on Information Theory 45(1), 284–288 (1999)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lifang Feng
    • 1
  • Pingzhi Fan
    • 1
  1. 1.Institute of Mobile CommunicationsSouthwest Jiaotong UniversityChengduChina

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