# American Institute of Mathematical Sciences

February  2020, 14(1): 1-9. doi: 10.3934/amc.2020001

## 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

* Corresponding author: Yujuan Sun

Received  November 2017 Revised  November 2018 Published  August 2019

Fund Project: This work was supported by the National Natural Science Foundation of China under Grant 61672414 and the National Cryptography Development Fund under Grant MMJJ20170113.

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.

Citation: Chunlei Xie, Yujuan Sun. Construction and assignment of orthogonal sequences and zero correlation zone sequences for applications in CDMA systems. Advances in Mathematics of Communications, 2020, 14 (1) : 1-9. doi: 10.3934/amc.2020001
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##### References:
Assignment of orthogonal sets to a lattice of regular hexagonal cells
Orthogonality between $\overline{f_c}$ and $\mathcal {H}_{a}$
 $\mathcal {H}_{00}$ $\mathcal {H}_{10}$ $\mathcal {H}_{01}$ $\mathcal {H}_{11}$ $\overline{f_{00}}$ $\bot$ $\bot$ $\bot$ $\overline{f_{10}}$ $\bot$ $\bot$ $\overline{f_{01}}$ $\bot$ $\bot$ $\overline{f_{11}}$ $\bot$ $\bot$ $\bot$
 $\mathcal {H}_{00}$ $\mathcal {H}_{10}$ $\mathcal {H}_{01}$ $\mathcal {H}_{11}$ $\overline{f_{00}}$ $\bot$ $\bot$ $\bot$ $\overline{f_{10}}$ $\bot$ $\bot$ $\overline{f_{01}}$ $\bot$ $\bot$ $\overline{f_{11}}$ $\bot$ $\bot$ $\bot$
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