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Construction and assignment of orthogonal sequences and zero correlation zone sequences for applications in CDMA systems
1. | State Key Laboratory of Integrated Services Networks, Xidian University, Xi'an 710071 China |
2. | State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China |
Orthogonal sequences can be assigned to a regular tessellation of hexagonal cells, typical for synchronised code-division multiple-access (S-CDMA) systems. In this paper, we first construct a new class of orthogonal sequences with increasing the number of users per cell to be $ 2^{m-2} $ for even number $ m\geq 4 $ (where $ 2^m $ is the length of the sequences). In addition, based on the above construction we construct a family of orthogonal sequences with zero correlation zone property which can be applied to the quasi-synchronous CDMA (QS-CMDA) spread spectrum systems.
References:
[1] |
A. N. Akansu and R. Poluri,
Walsh-like nonlinear phase orthogonal codes for direct sequence CDMA communications, IEEE Trans. on Signal Processing, 55 (2007), 3800-3806.
doi: 10.1109/TSP.2007.894229. |
[2] |
S. Chee, S. Lee and K. Kim,
Semi-bent functions, Advances in Cryptology-ASIACRYPT'94, 917 (1994), 107-118.
|
[3] |
E. H. Dinan and B. Jabbari,
Spreading codes for direct sequence CDMA and wideband CDMA cellular networks, IEEE Communications Magazine, 36 (1998), 48-54.
doi: 10.1109/35.714616. |
[4] |
P. Z. Fan, N. Suehiro, N. Kuroyanagi and X. Deng,
Class of binary sequences with zero correlation zone, Electronics Letters, 35 (1999), 777-779.
doi: 10.1049/el:19990567. |
[5] |
A. Goldsmith, Wireless Communications, Cambridge University Press, 2005.
doi: 10.1017/CBO9780511841224.![]() |
[6] |
O. S. Rothaus,
On "bent" functions, Journal of Combinatorial Theory, 20 (1976), 300-305.
doi: 10.1016/0097-3165(76)90024-8. |
[7] |
D. H. Smith, R. P. War and S. Perkins,
Gold codes, Hadamard partitions and the security of CDMA systems, Designs, Codes and Cryptography, 51 (2009), 231-243.
doi: 10.1007/s10623-008-9257-8. |
[8] |
D. H. Smith, F. H. Hunt and S. Perkins,
Exploiting spatial separations in CDMA systems with correlation constrained sets of Hadamard matrices, IEEE Transactions on Information Theory, 56 (2010), 5757-5761.
doi: 10.1109/TIT.2010.2070310. |
[9] |
X. H. Tang and P. Fan,
Bounds on aperiodic and odd correlations of spreading sequences with low or zero correlation zone, Electronics Letters, 37 (2001), 1201-1202.
doi: 10.1049/el:20010801. |
[10] |
X. Tang and W. H. Mow, Design of spreading codes for quasi-synchronous CDMA with intercell interference, IEEE Journal on Selected Areas in Communications, 24 (2006), 84-93. Google Scholar |
[11] |
X. H. Tang, P. Z. Fan and J. Lindner,
Multiple binary ZCZ sequence sets with good cross-correlation property based on complementary sequence sets, IEEE Transactions on Information Theory, 56 (2010), 4038-4045.
doi: 10.1109/TIT.2010.2050796. |
[12] |
K. Yang, Y.-K. Kim and P. V. Kumar,
Quasi-orthogonal sequences for code-division multiple-access systems, IEEE Transactions on Information Theory, 46 (2000), 982-993.
doi: 10.1109/18.841175. |
[13] |
W.-G. Zhang, C.-L. Xie and E. Pasalic,
Large sets of orthogonal sequences suitable for applications in CDMA systems, IEEE Transactions on Information Theory, 62 (2016), 3757-3767.
doi: 10.1109/TIT.2016.2550478. |
[14] |
Z. C. Zhou, D. Zhang, T. Helleseth and J. Wen,
A construction of multiple optimal zcz sequence sets with good cross-correlation, IEEE Transactions on Information Theory, 64 (2018), 1340-1346.
doi: 10.1109/TIT.2017.2756845. |
show all references
References:
[1] |
A. N. Akansu and R. Poluri,
Walsh-like nonlinear phase orthogonal codes for direct sequence CDMA communications, IEEE Trans. on Signal Processing, 55 (2007), 3800-3806.
doi: 10.1109/TSP.2007.894229. |
[2] |
S. Chee, S. Lee and K. Kim,
Semi-bent functions, Advances in Cryptology-ASIACRYPT'94, 917 (1994), 107-118.
|
[3] |
E. H. Dinan and B. Jabbari,
Spreading codes for direct sequence CDMA and wideband CDMA cellular networks, IEEE Communications Magazine, 36 (1998), 48-54.
doi: 10.1109/35.714616. |
[4] |
P. Z. Fan, N. Suehiro, N. Kuroyanagi and X. Deng,
Class of binary sequences with zero correlation zone, Electronics Letters, 35 (1999), 777-779.
doi: 10.1049/el:19990567. |
[5] |
A. Goldsmith, Wireless Communications, Cambridge University Press, 2005.
doi: 10.1017/CBO9780511841224.![]() |
[6] |
O. S. Rothaus,
On "bent" functions, Journal of Combinatorial Theory, 20 (1976), 300-305.
doi: 10.1016/0097-3165(76)90024-8. |
[7] |
D. H. Smith, R. P. War and S. Perkins,
Gold codes, Hadamard partitions and the security of CDMA systems, Designs, Codes and Cryptography, 51 (2009), 231-243.
doi: 10.1007/s10623-008-9257-8. |
[8] |
D. H. Smith, F. H. Hunt and S. Perkins,
Exploiting spatial separations in CDMA systems with correlation constrained sets of Hadamard matrices, IEEE Transactions on Information Theory, 56 (2010), 5757-5761.
doi: 10.1109/TIT.2010.2070310. |
[9] |
X. H. Tang and P. Fan,
Bounds on aperiodic and odd correlations of spreading sequences with low or zero correlation zone, Electronics Letters, 37 (2001), 1201-1202.
doi: 10.1049/el:20010801. |
[10] |
X. Tang and W. H. Mow, Design of spreading codes for quasi-synchronous CDMA with intercell interference, IEEE Journal on Selected Areas in Communications, 24 (2006), 84-93. Google Scholar |
[11] |
X. H. Tang, P. Z. Fan and J. Lindner,
Multiple binary ZCZ sequence sets with good cross-correlation property based on complementary sequence sets, IEEE Transactions on Information Theory, 56 (2010), 4038-4045.
doi: 10.1109/TIT.2010.2050796. |
[12] |
K. Yang, Y.-K. Kim and P. V. Kumar,
Quasi-orthogonal sequences for code-division multiple-access systems, IEEE Transactions on Information Theory, 46 (2000), 982-993.
doi: 10.1109/18.841175. |
[13] |
W.-G. Zhang, C.-L. Xie and E. Pasalic,
Large sets of orthogonal sequences suitable for applications in CDMA systems, IEEE Transactions on Information Theory, 62 (2016), 3757-3767.
doi: 10.1109/TIT.2016.2550478. |
[14] |
Z. C. Zhou, D. Zhang, T. Helleseth and J. Wen,
A construction of multiple optimal zcz sequence sets with good cross-correlation, IEEE Transactions on Information Theory, 64 (2018), 1340-1346.
doi: 10.1109/TIT.2017.2756845. |

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