Construction and assignment of orthogonal sequences and zero correlation zone sequences for applications in CDMA systems

Chunlei Xie; Yujuan Sun

doi:10.3934/amc.2020001

Article Contents

2020, Volume 14, Issue 1: 1-9. Doi: 10.3934/amc.2020001

This issue Previous Article Next Article New self-dual and formally self-dual codes from group ring constructions

Construction and assignment of orthogonal sequences and zero correlation zone sequences for applications in CDMA systems

Chunlei Xie^1,2, and
Yujuan Sun^1,2, ,

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
^* Corresponding author: Yujuan Sun

Received: November 2017

Revised: November 2018

Published: August 2019

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

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Abstract

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.

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Mathematics Subject Classification: Primary: 11B50, 94A55; Secondary: 11B75.

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Figure 1. Assignment of orthogonal sets to a lattice of regular hexagonal cells

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Table 1. 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 $

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