基于基序列构造二元互补序列集

沈炳声; 周正春; 杨洋; 范平志

doi:10.11999/JEIT240309

基于基序列构造二元互补序列集

doi: 10.11999/JEIT240309

1.
西南交通大学信息科学与技术学院成都 611756
2.
西南交通大学数学学院成都 611756

基金项目: 国家自然科学基金(12401695, U23A20274, 62171389)，四川省自然科学基金创新研究群体(2024NSFTD0015)，中央高校基本科研业务费(2682024CX027)

详细信息

作者简介:
沈炳声：男，博士，研究方向为序列编码设计、通信雷达一体化

周正春：男，教授，研究方向为编码理论、通信/雷达波形设计、电子信息对抗

杨洋：男，教授，研究方向为序列编码设计、通信/雷达波形设计

范平志：男，教授，研究方向为高移动性宽带无线通信、信号设计与处理、信息理论与编码、无线频谱资源管理

通讯作者:
沈炳声　bsshen9527@swjtu.edu.cn

中图分类号: TN911.2
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- 被引次数: 0
出版历程
- 收稿日期: 2024-04-22
- 修回日期: 2024-08-28
- 网络出版日期: 2024-09-01
- 刊出日期: 2024-09-26

Constructions of Binary Complementary Sequence Set Based on Base Sequences

1.
School of Information Science and Technology, Southwest Jiaotong University, Chengdu 611756, China
2.
School of Mathematics, Southwest Jiaotong University, Chengdu 611756, China

Funds: The National Natural Science Foundation of China (12401695, U23A20274, 62171389), Sichuan Natural Science Foundation Innovation Research Group (2024NSFTD0015), The Fundamental Research Funds for the Central Universities (2682024CX027)

摘要

摘要: 互补序列集凭借其理想的非周期自相关函数特性，在通信与感知领域得到广泛应用。针对互补序列集长度受限的问题，该文以基序列为初始序列，利用级联算子和交织算子提出两类二元互补序列集的新构造方法。所提构造填补了二元互补序列集在特定长度上的空白，并解决了由Adhikary和Majhi提出的公开问题。
- 互补序列集 /
- 基序列 /
- 交织算子 /
- 级联算子
Abstract: Complementary Sequence Sets (CSS) have ideal aperiodic auto-correlation functions and are widely used in the field of communication and sensing. In order to solve the problem of limited length of complementary sequence sets, two new constructions of binary complementary sequence sets are proposed using concatenation operator and interleaving operator, with the base sequence as the initial sequence. The proposed construction fills the gap in the length of the binary complementary sequence set and solves the public problem proposed by Adhikary and Majhi.
- Complementary Sequence Set (CSS) /
- Base sequence /
- Concatenation operator /
- Interleaving operator

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图 1 瞬时平均功率比曲线

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表 1 短长度Turyn序列

L	序列	L	序列
1	$ \left( {\begin{array}{*{20}{c}} { + - } \\ { + + } \\ + \\ + \end{array}} \right) $	6	$ \left( {\begin{array}{*{20}{c}} { + + + - + + + } \\ { + + - - - + - } \\ { + + - + - - } \\ { + + - + + - } \end{array}} \right) $
2	$ \left( {\begin{array}{*{20}{c}} { + + + } \\ { + + - } \\ { + - } \\ { + - } \end{array}} \right) $	7	$ \left( {\begin{array}{*{20}{c}} { + + - + - + - - } \\ { + + + + - - - + } \\ { + + + - + + + } \\ { + - - + - - + } \end{array}} \right) $
3	$ \left( {\begin{array}{*{20}{c}} { + + - - } \\ { + + - + } \\ { + + + } \\ { + - + } \end{array}} \right) $	12	$ \left( {\begin{array}{*{20}{c}} { + + + + - + - + - + + + + } \\ { + + + - - + - + - - + + - } \\ { + + + - + + - - + - - - } \\ { + + + - - + - + + - - - } \end{array}} \right) $
4	$ \left( {\begin{array}{*{20}{c}} { + + - + + } \\ { + + + + - } \\ { + + - - } \\ { + - + - } \end{array}} \right) $	14	$ \left( {\begin{array}{*{20}{c}} { + + - + + + - + - + + + - + + } \\ { + + + - + + - - - + + - + + - } \\ { + + + + - - + - + + - - - - } \\ { + - - - - + - + - + + + + - } \end{array}} \right) $
5	$ \left( {\begin{array}{*{20}{c}} { + + + - - - } \\ { + + - + - + } \\ { + + - + + } \\ { + + - + + } \end{array}} \right) $

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表 2 集合大小为4的二元互补序列集

来源	长度	限制
文献[11]	${2^{m - 1}} + {2^v}$	$m \ge 2,{\text{ }}v \le m - 1$
文献[13]	$L + 1,{\text{ }}L + 2$	$L$的Golay数
文献[14]	$kL$	$k$是偶移位互补对存在的长度， $L$是Golay数
文献[15]	${L_1} + {L_2}$	${L_1}$和${L_2}$都是Golay数
注4(本文)	$2L + 1$	$ L\in \{1,2,\cdots ,38\}\cup \{x:x是\text{Golay}数\} $
注5(本文)	${2^k}L + {2^k} - 1$	$L \in \{ 1,2,3,4,5,6,7,12,14\} ,{\text{ }}k \ge 1$
注6(本文)	$3L - 1$	$ L\in \{x:2\le x\le 40且x是偶数\} $

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参考文献(26)

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