Advertisement

Very Low Correlation Sequence Design with Power Control

  • Mostafa Noorbakhsh
  • S. Ahmadreza RazianEmail author
Research paper
  • 4 Downloads

Abstract

Barker sequences and generalized Barker sequences with complex symbols on the unit circle have very limited lengths to achieve maximum aperiodic autocorrelation of 1. In the performed innovation, we consider symbols beyond the unit circle in the complex plain to obtain more degrees of freedom to achieve the desired minimum autocorrelation level with much longer sequences. The sequence symbols are obtained by direct solution of a minimax problem (i.e., minimization of the maximum autocorrelation), with limitation on their maximum power to preserve the sequence randomness. The sequence length is arbitrary and is an input parameter to the algorithm. The developed algorithm leads to excellent results. For instance, sequences with the length of 1000 can simply be obtained with maximum autocorrelation of not only below 1, but even much smaller.

Keywords

Barker sequences Aperiodic correlation Spread spectrum Minimax problem 

References

  1. Barker RH (1953) Group Synchronizing of binary digital systems. Communication theory. Butterworths Sci. Pub, London, pp 273–287Google Scholar
  2. Barton DK, Leonov SA (1998) Radar technology encyclopedia. Artech House, NorwoodzbMATHGoogle Scholar
  3. Bomer L, Antweiler M (1989) Polyphase Barker sequences. Electron Lett 25(23):1577–1579CrossRefGoogle Scholar
  4. Borwein P, Ferguson R (2005) Polyphase sequences with low autocorrelation. IEEE Trans Inf Theory 45(4):1564–1567MathSciNetCrossRefGoogle Scholar
  5. Borwein P, Mossinghoff MJ (2008) Barker sequences and flat polynomials. In: McKee J, Smyth C (eds) Number theory and polynomials (Bristol, 2006), London Math. Soc. Lecture Note Ser., vol. 352, Cambridge University Press, pp 71–88Google Scholar
  6. Brenner AR (1998) Polyphase Barker sequences up to length 45 with small alphabets. Electron Lett 34(16):1576–1577CrossRefGoogle Scholar
  7. Chang N, Golomb SW (1994) On N-phase Barker sequences. IEEE Trans Inf Theory 40(4):1251–1253MathSciNetCrossRefGoogle Scholar
  8. Chang N, Golomb SW (1996) 7200-phase generalized Barker sequences. IEEE Trans Inf Theory 42(4):1236–1238MathSciNetCrossRefGoogle Scholar
  9. Edgar TF, Himmelblau DM, Lasdon LS (2001) Optimization of chemical processes. McGraw-Hill, New YorkGoogle Scholar
  10. Friese M (1996) Polyphase Barker sequences up to length 36. IEEE Trans Inf Theory 42(4):1248–1250CrossRefGoogle Scholar
  11. Friese M, Zottmann H (1994) Polyphase Barker sequences up to length 31. Electron Lett 30(23):1930–1931CrossRefGoogle Scholar
  12. Golomb SW, Scholtz RA (1965) Generalized Barker sequences. IEEE Trans Inf Theory IT-11(4):533–537MathSciNetCrossRefGoogle Scholar
  13. Ho KM, Mow WH (2004) Searching for the best biphase and quadriphase quasi-Barker sequences. In: International conference on communications, circuits and systems. vol 1, pp 43–47Google Scholar
  14. Mow WH (1996) General limit theorem for n phase Barker sequences. Electron Lett 32:1364–1365CrossRefGoogle Scholar
  15. Mutkov VA, Nikolov NR, Tsakov RG, Staneva LA (2009) A survey of the correlation properties of the generalized Barker Codes. In: 17th telecommunications forum TELEFOR 2009, pp 584–587Google Scholar
  16. Schulze H, Luders C (2005) Theory and application of OFDM and CDMA wideband wireless communications. Wiley, HobokenCrossRefGoogle Scholar
  17. Zhang N, Golomb SW (1989) Sixty-phase generalized Barker sequences. IEEE Trans Inf Theory 35(4):911–912CrossRefGoogle Scholar

Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Research Institute for Subsea Science and TechnologyIsfahan University of TechnologyIsfahanIran
  2. 2.Computer Engineering DepartmentUniversity of IsfahanIsfahanIran

Personalised recommendations