On Pseudo-Random and Orthogonal Binary Spreading Sequences
Different pseudo-random or pseudo-noise (PN) as well as orthogonal sequences that can be used as spreading codes for code division multiple access (CDMA) cellular networks or can be used for encrypting speech signals to reduce the residual intelligence are investigated. We briefly review the theoretical background for direct sequence CDMA systems and describe the main characteristics of the maximal length, Gold, Barker, and Kasami sequences. We also discuss about variable- and fixed-length orthogonal codes like Walsh- Hadamard codes. The equivalence of PN and orthogonal codes are also derived. Finally, a new PN sequence is proposed which is shown to have certain better properties than the existing codes.
[1] A. J. Viterbi, CDMA: Principles of Spread Spectrum Communication,
Addison-Wesley, 1995.
[2] W. Diffe and M. E. Hellman, "New directions in cryptography," IEEE
Trans. Inform. Theory, vol. 22, pp. 644-654, Nov. 1976.
[3] R. L. Pickholtz, D. L. Schilling and L. B. Milstein, "Theory of spread
spectrum communications- A tutorial," IEEE Trans. Commun., vol.
COM-30, no. 5, May 1982.
[4] E. H. Dinan and B. Jabbari, "Spreading codes for direct sequence CDMA
and wideband CDMA cellular networks," IEEE Commun. Magazine, vol.
36, no. 4, pp. 48-54, Sep. 1998.
[5] B. Sklar, Digital Communications: Fundamentals and Applications, 2nd
Ed., Prentice Hall, 2001.
[6] J. H. Lindholm, "An analysis of the pseudo randomness properties of
the subsequences of long m-sequences," IEEE Trans. Inform. Theory,
vol. IT-14, pp. 569-576, July 1968.
[7] I. Oppermann and B. S. Vucetic, "Complex spreading sequences with a
wide range of correlation properties," IEEE Trans. Commun., vol. COM-
45, pp. 365-375, March 1997.
[8] L. T. Wang and E. J. McCluskey, "Linear feedback shift register design
using cyclic codes," IEEE Trans. Comput., vol. 37, pp. 1302-1306, Oct.
1988.
[9] A. Fuster and L. J. Garcia, "An efficient algorithm to generate binary
sequences for cryptographic purposes," Theoretical Computer Science,
vol. 259, pp. 679-688, May 2001.
[10] D. V. Sarwate and M. B. Pursley, "Correlation properties of pseudo
random and related sequences," Proc. IEEE, vol. 68, no. 5, pp. 593-
619, May 1980.
[11] S. W. Golomb and R. A. Scholtz, "Generalized Barker sequences," IEEE
Trans. Inform. Theory, vol. IT-11, no. 4, pp. 533-537, Oct. 1965.
[12] R. Turyn and J. E. Storer, "On binary sequences," Proc. Am. Math. Soc,
vol. 12, pp. 394-399, June 1961.
[13] D. G. Luenberger, "On Barker codes of even length," Proc. IEEE, vol.
51, pp. 230-231, Jan. 1963.
[14] C. K. Chan and W. H. Lam, "Generalised Barker-like PN sequences
for quasisynchronous spread spectrum multiple access communication
systems," IEE Proc. Commun., vol. 142, no. 2, pp. 91-98, April 1995.
[15] X. Wang, Y. Wu and B. Caron, "Transmitter identification using embedded
pseudo random sequences," IEEE Tran. Broadcasting, vol. 50, no.
3, pp. 244-252, Sep. 2004.
[16] V. Milosevic, V. Delic and V. Senk, "Hadamard transform application
in speech scrambling," Proc. IEEE, vol. 1, pp. 361-364, July 1997.
[17] Tai-Kuo Woo, "Orthogonal variable spreading codes for wideband
CDMA," IEEE Trans. Vehicular Techn., vol. 51, no. 4, pp. 700-709,
July 2002.
[18] E. J. Watson, "Primitive Polynomials (mod 2)," Mathematics of Computation,
vol. 16, pp. 368-369, 1962.
[19] B. Wysocki and T. A. Wysocki, "Modified Walsh Hadamard
sequences for DS-CDMA wireless systems," School of
Electrical, Computer and Telecommunications Engineering,
University of Wollongong, Australia. (Online) Available:
www.elec.uow.edu.au/staff/wysocki/publications/J1.pdf.
[1] A. J. Viterbi, CDMA: Principles of Spread Spectrum Communication,
Addison-Wesley, 1995.
[2] W. Diffe and M. E. Hellman, "New directions in cryptography," IEEE
Trans. Inform. Theory, vol. 22, pp. 644-654, Nov. 1976.
[3] R. L. Pickholtz, D. L. Schilling and L. B. Milstein, "Theory of spread
spectrum communications- A tutorial," IEEE Trans. Commun., vol.
COM-30, no. 5, May 1982.
[4] E. H. Dinan and B. Jabbari, "Spreading codes for direct sequence CDMA
and wideband CDMA cellular networks," IEEE Commun. Magazine, vol.
36, no. 4, pp. 48-54, Sep. 1998.
[5] B. Sklar, Digital Communications: Fundamentals and Applications, 2nd
Ed., Prentice Hall, 2001.
[6] J. H. Lindholm, "An analysis of the pseudo randomness properties of
the subsequences of long m-sequences," IEEE Trans. Inform. Theory,
vol. IT-14, pp. 569-576, July 1968.
[7] I. Oppermann and B. S. Vucetic, "Complex spreading sequences with a
wide range of correlation properties," IEEE Trans. Commun., vol. COM-
45, pp. 365-375, March 1997.
[8] L. T. Wang and E. J. McCluskey, "Linear feedback shift register design
using cyclic codes," IEEE Trans. Comput., vol. 37, pp. 1302-1306, Oct.
1988.
[9] A. Fuster and L. J. Garcia, "An efficient algorithm to generate binary
sequences for cryptographic purposes," Theoretical Computer Science,
vol. 259, pp. 679-688, May 2001.
[10] D. V. Sarwate and M. B. Pursley, "Correlation properties of pseudo
random and related sequences," Proc. IEEE, vol. 68, no. 5, pp. 593-
619, May 1980.
[11] S. W. Golomb and R. A. Scholtz, "Generalized Barker sequences," IEEE
Trans. Inform. Theory, vol. IT-11, no. 4, pp. 533-537, Oct. 1965.
[12] R. Turyn and J. E. Storer, "On binary sequences," Proc. Am. Math. Soc,
vol. 12, pp. 394-399, June 1961.
[13] D. G. Luenberger, "On Barker codes of even length," Proc. IEEE, vol.
51, pp. 230-231, Jan. 1963.
[14] C. K. Chan and W. H. Lam, "Generalised Barker-like PN sequences
for quasisynchronous spread spectrum multiple access communication
systems," IEE Proc. Commun., vol. 142, no. 2, pp. 91-98, April 1995.
[15] X. Wang, Y. Wu and B. Caron, "Transmitter identification using embedded
pseudo random sequences," IEEE Tran. Broadcasting, vol. 50, no.
3, pp. 244-252, Sep. 2004.
[16] V. Milosevic, V. Delic and V. Senk, "Hadamard transform application
in speech scrambling," Proc. IEEE, vol. 1, pp. 361-364, July 1997.
[17] Tai-Kuo Woo, "Orthogonal variable spreading codes for wideband
CDMA," IEEE Trans. Vehicular Techn., vol. 51, no. 4, pp. 700-709,
July 2002.
[18] E. J. Watson, "Primitive Polynomials (mod 2)," Mathematics of Computation,
vol. 16, pp. 368-369, 1962.
[19] B. Wysocki and T. A. Wysocki, "Modified Walsh Hadamard
sequences for DS-CDMA wireless systems," School of
Electrical, Computer and Telecommunications Engineering,
University of Wollongong, Australia. (Online) Available:
www.elec.uow.edu.au/staff/wysocki/publications/J1.pdf.
@article{"International Journal of Electrical, Electronic and Communication Sciences:62725", author = "Abhijit Mitra", title = "On Pseudo-Random and Orthogonal Binary Spreading Sequences", abstract = "Different pseudo-random or pseudo-noise (PN) as well as orthogonal sequences that can be used as spreading codes for code division multiple access (CDMA) cellular networks or can be used for encrypting speech signals to reduce the residual intelligence are investigated. We briefly review the theoretical background for direct sequence CDMA systems and describe the main characteristics of the maximal length, Gold, Barker, and Kasami sequences. We also discuss about variable- and fixed-length orthogonal codes like Walsh- Hadamard codes. The equivalence of PN and orthogonal codes are also derived. Finally, a new PN sequence is proposed which is shown to have certain better properties than the existing codes.
", keywords = "Code division multiple access, pseudo-noise codes,maximal length, Gold, Barker, Kasami, Walsh-Hadamard, autocorrelation,crosscorrelation, figure of merit.", volume = "2", number = "12", pages = "2875-8", }
