基于二阶分圆类的高能量效率完备高斯整数序列设计

赵伟; 黄雷; 贾彦国; 沈秀敏

doi:10.11999/JEIT220591

基于二阶分圆类的高能量效率完备高斯整数序列设计

doi: 10.11999/JEIT220591

燕山大学信息科学与工程学院河北省计算机虚拟技术与系统集成重点实验室秦皇岛 066004

基金项目: 国家自然科学基金(61601401)，河北省自然科学基金(F2018203057, F2020203043)，河北省高等学校科学技术研究项目(QN2021144)，河北省创新能力提升计划项目(22567626H)

详细信息

作者简介:
赵伟：男，博士生，研究方向为差集偶、二进制序列偶

黄雷：男，硕士生，研究方向为编码理论、密码学

贾彦国：男，教授，博士生导师，研究方向为编码理论、智能补货、量子计算

沈秀敏：女，讲师，硕士生导师，研究方向为编码理论、序列设计

通讯作者:
贾彦国　jyg@ysu.edu.cn

中图分类号: TN911.23
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出版历程
- 收稿日期: 2022-05-10
- 修回日期: 2022-06-22
- 网络出版日期: 2022-06-25
- 刊出日期: 2023-06-10

High Energy Efficient Perfect Gaussian Integer Sequence Design Based on Second Order Cyclotomic Classes

School of Information Science and Engineering, The Key Laboratory for Computer Virtual Technology and System Integration of Hebei Province, Yanshan University, Qinhuangdao 066004, China

Funds: The National Natural Science Foundation of China (61601401), The Natural Science Foundation of Hebei Province (F2018203057, F2020203043), The Research Project for Science and Technology in Higher Education of Hebei (QN2021144), The Innovation Capability Improvement Plan Project of Hebei Province (22567626H)

摘要

摘要: 完备高斯整数序列(PGIS)因其良好的抗干扰性、高传输率和频谱利用率，如今已被广泛应用于码分复用(CDM)系统和正交频分复用(OFDM)系统。该文将高斯整数序列(GIS)分解成实部序列和虚部序列，再通过对实部序列和虚部序列2阶分圆构造出2阶和3阶的PGIS，并提出一种新的将奇数长PGIS扩展成偶数长PGIS的方法，该文构造出的多数PGIS能量效率高于95%，扩大了扩频通信系统的地址选择空间，对于工程实践具有重要意义。
- 完备高斯整数序列 /
- 分圆类 /
- 自相关函数 /
- 互相关函数 /
- 能量效率
Abstract: Perfect Gaussian Integer Sequence (PGIS) has been widely used in Code Division Multiplexing (CDM) systems and Orthogonal Frequency Division Multiplexing (OFDM) systems because of its good anti-interference, high transmission rate and high frequency spectrum utilization. In this paper, Gaussian Integer Sequence (GIS) is decomposed into real part sequence and imaginary part sequence, and then second-order and third-order PGIS are constructed by second-order cyclotomy of real part sequence and imaginary part sequence. A new method of extending odd length PGIS to even length PGIS is proposed. The energy efficiency of most PGIS constructed in this paper is higher than 95%, and expands the address selection space of spread spectrum communication system, which is of great significance to engineering practice.
- Perfect Gaussian Integer Sequence(PGIS) /
- Cyclotomic classes /
- Autocorrelation function /
- Cross correlation function /
- Energy efficiency

HTML全文

表 1 PGIS的能量效率比较

文献	定理	长度	电平数	能量效率(%)	构造实例
文献[6]	定理1	13	3	50.3	例2
文献[6]	定理1	19	3	70.8	例1
文献[7]	定理4	19	3	70.8	例1
文献[7]	定理5	19	2	68.4	例3
文献[11]	定理1	19	2	91.3	表1(行6)
		19	3	80.4	表1(行7)
		19	3	90.0	表1(行8)
本文	定理1	13	3	98.3	$\begin{gathered} (19,{\text{ } } - 8 - {\rm{j} }20,{\text{ } } - 8 + {\rm{j} }20,{\text{ } } - 8 - {\rm{j} }20,{\text{ } } - 8 - {\rm{j} }20,{\text{ } } - 8 + {\rm{j} }20,{\text{ } } - 8 + {\rm{j} }20,{\text{ } } \\ - 8 + {\rm{j} }20,{\text{ } } - 8 + {\rm{j} }20,{\text{ } } - 8 - {\rm{j} }20,{\text{ } } - 8 - {\rm{j} }20,{\text{ } } - 8 + {\rm{j} }20,{\text{ } } - 8 - {\rm{j} }20) \\ \end{gathered}$
		19	2	99.2	$\begin{gathered} (9 + {\rm{j} }11,{\text{ } }9 + {\rm{j} }11,{\text{ } } - 13 - {\rm{j} }6,{\text{ } } - 13 - {\rm{j} }6,{\text{ } }9 + {\rm{j} }11,{\text{ } }9 + {\rm{j} }11,{\text{ } }9 + {\rm{j} }11,{\text{ } } \\ 9 + {\rm{j} }11,{\text{ } } - 13 - {\rm{j} }6,{\text{ } }9 + {\rm{j} }11,{\text{ } } - 13 - {\rm{j} }6,{\text{ } }9 + {\rm{j} }11,{\text{ } } - 13 - {\rm{j} }6,{\text{ } } - 13 - {\rm{j} }6,{\text{ } } \\ - 13 - {\rm{j} }6,{\text{ } } - 13 - {\rm{j} }6,{\text{ } }9 + {\rm{j} }11,{\text{ } }9 + {\rm{j} }11,{\text{ } } - 13 - {\rm{j} }6) \\ \end{gathered}$
		19	2	99.2	$\begin{gathered} ( - 20 - {\rm{j} }2,{\text{ } }19 - {\rm{j} }7,{\text{ } } - 20 - {\rm{j} }2,{\text{ } } - 20 - {\rm{j} }2,{\text{ } }19 - {\rm{j} }7,{\text{ } }19 - {\rm{j} }7,{\text{ } }19 - {\rm{j} }7,{\text{ } } \\ 19 - {\rm{j} }7,{\text{ } } - 20 - {\rm{j} }2,{\text{ } }19 - {\rm{j} }7,{\text{ } } - 20 - {\rm{j} }2,{\text{ } }19 - {\rm{j} }7,{\text{ } } - 20 - {\rm{j} }2,{\text{ } } - 20 - {\rm{j} }2, \\ - 20 - {\rm{j} }2,{\text{ } } - 20 - {\rm{j} }2,{\text{ } }19 - {\rm{j} }7,{\text{ } }19 - {\rm{j} }7,{\text{ } } - 20 - {\rm{j} }2) \\ \end{gathered}$
		19	2	99.6	$\begin{gathered} ( - 18 - {\rm{j} }2,{\text{ } } - 18 - {\rm{j} }2,{\text{ } }17 - {\rm{j} }6,{\text{ } }17 - {\rm{j} }6,{\text{ } } - 18 - {\rm{j} }2,{\text{ } } - 18 - {\rm{j} }2,{\text{ } } - 18 - {\rm{j} }2,{\text{ } } \\ - 18 - {\rm{j} }2,{\text{ } }17 - {\rm{j} }6,{\text{ } } - 18 - {\rm{j} }2,{\text{ } }17 - {\rm{j} }6,{\text{ } } - 18 - {\rm{j} }2,{\text{ } }17 - {\rm{j} }6,{\text{ } }17 - {\rm{j} }6, \\ 17 - {\rm{j} }6,{\text{ } }17 - {\rm{j} }6,{\text{ } } - 18 - {\rm{j} }2,{\text{ } } - 18 - {\rm{j} }2,{\text{ } }17 - {\rm{j} }6) \\ \end{gathered}$

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表 2 PGIS扩展前后的能量效率比较

	长度	能量效率(%)	实例
原序列	3	99.9	$(4 - {\rm{j} }15,11 + {\rm{j} }11,11 + {\rm{j} }11)$
$a = 1,b = - 1$	6	99.9	$( - 19 - {\rm{j} }11,22,{\rm{j} }22, - 11 + {\rm{j} }19,{\rm{j} }22,22)$
$a = 2,b = 2$	6	99.9	$(38 + {\rm{j} }22,44, - {\rm{j} }44{\rm{j} }, - 22 + {\rm{j} }38, - {\rm{j} }44,44)$

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