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
计量
- 文章访问数: 82
- HTML全文浏览量: 29
- PDF下载量: 19
- 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

HTML全文

图 1 瞬时平均功率比曲线

下载: 全尺寸图片幻灯片

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) $

下载: 导出CSV

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\} $

下载: 导出CSV

参考文献(26)

[1]	GOLAY M. Complementary series[J]. IRE Transactions on Information Theory, 1961, 7(2): 82–87. doi: 10.1109/TIT.1961.1057620.
[2]	TSENG C C and LIU C. Complementary sets of sequences[J]. IEEE Transactions on Information Theory, 1972, 18(5): 644–652. doi: 10.1109/TIT.1972.1054860.
[3]	LI Yuke, ZHOU Yongxing, LI Xueru, et al. Unimodular complete complementary sequence with optimal trade-off between auto- and cross-ambiguity functions for MIMO radars[J]. IEEE Transactions on Intelligent Vehicles, 2024. doi: 10.1109/TIV.2024.3384435.
[4]	ZHU Jiahua, SONG Yongping, JIANG Nan, et al. Enhanced Doppler resolution and sidelobe suppression performance for golay complementary waveforms[J]. Remote Sensing, 2023, 15(9): 2452. doi: 10.3390/rs15092452.
[5]	ZHOU Yajing, ZHOU Zhengchun, LIU Zilong, et al. Symmetrical Z-Complementary code sets for optimal training in generalized spatial modulation[J]. Signal Processing, 2023, 208: 108990. doi: 10.1016/j.sigpro.2023.108990.
[6]	MEN Xinyu, LIU Tao, LI Yubo, et al. Constructions of 2-D Golay complementary array sets with flexible array sizes for omnidirectional precoding in massive MIMO[J]. IEEE Communications Letters, 2023, 27(5): 1302–1306. doi: 10.1109/LCOMM.2023.3263860.
[7]	赵羚岚, 杨奕冉, 刘喜庆, 等. 基于完全互补码扩频的通信雷达一体化系统[J]. 无线电通信技术, 2023, 49(1): 118–125. doi: 10.3969/j.issn.1003-3114.2023.01.014. ZHAO Linglan, YANG Yiran, LIU Xiqing, et al. Integrated communication and radar system based on complete complementary code spread spectrum[J]. Radio Communications Technology, 2023, 49(1): 118–125. doi: 10.3969/j.issn.1003-3114.2023.01.014.
[8]	LIU Kaiqiang, ZHOU Zhengchun, ADHIKARY A R, et al. New sets of non-orthogonal spreading sequences with low correlation and low PAPR using extended Boolean functions[J]. Designs, Codes and Cryptography, 2023, 91(10): 3115–3139. doi: 10.1007/s10623-023-01247-z.
[9]	李玉博, 王亚会, 于丽欣, 等. 免调度非正交多址接入上行链路的非2幂次长度二元扩频序列[J]. 电子与信息学报, 2022, 44(4): 1402–1411. doi: 10.11999/JEIT210293. LI Yubo, WANG Yahui, YU Lixin, et al. Binary spreading sequences of lengths non-power-of-two for uplink grant-free non-orthogonal multiple access[J]. Journal of Electronics & Information Technology, 2022, 44(4): 1402–1411. doi: 10.11999/JEIT210293.
[10]	PATERSON K G. Generalized Reed-Muller codes and power control in OFDM modulation[J]. IEEE Transactions on Information Theory, 2000, 46(1): 104–120. doi: 10.1109/18.817512.
[11]	CHEN Chaoyu. Complementary sets of non-power-of-two length for peak-to-average power ratio reduction in OFDM[J]. IEEE Transactions on Information Theory, 2016, 64(12): 7538–7545. doi: 10.1109/TIT.2016.2613994.
[12]	DAVIS J A and JEDWAB J. Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes[J]. IEEE Transactions on Information Theory, 1999, 45(7): 2397–2417. doi: 10.1109/18.796380.
[13]	ADHIKARY A R and MAJHI S. New constructions of complementary sets of sequences of lengths non-power-of-two[J]. IEEE Communications Letters, 2019, 23(7): 1119–1122. doi: 10.1109/LCOMM.2019.2913382.
[14]	SHEN Bingsheng, YANG Yang, and ZHOU Zhengchun. A construction of binary Golay complementary sets based on even-shift complementary pairs[J]. IEEE Access, 2020, 8: 29882–29890. doi: 10.1109/ACCESS.2020.2972598.
[15]	WANG Gaoxiang, ADHIKARY A R, ZHOU Zhengchun, et al. Generalized constructions of complementary sets of sequences of lengths non-power-of-two[J]. IEEE Signal Processing Letters, 2020, 27: 136–140. doi: 10.1109/LSP.2019.2960155.
[16]	SHEN Bingsheng, YANG Yang, FAN Pingzhi, et al. New Z-complementary/complementary sequence sets with non-power-of-two length and low PAPR[J]. Cryptography and Communications, 2022, 14(4): 817–832. doi: 10.1007/s12095-021-00550-7.
[17]	SHEN Bingsheng, MENG Hua, YANG Yang, et al. New constructions of Z-complementary code sets and mutually orthogonal complementary sequence sets[J]. Designs, Codes and Cryptography, 2023, 91(2): 353–371. doi: 10.1007/s10623-022-01112-5.
[18]	COHEN G, RUBIE D, SEBERRY J, et al. A survey of base sequences, disjoint complementary sequences and $ O D(4 t ; t, t, t, t) $[J]. JCMCC, 1989, 5: 69–104.
[19]	KOUKOUVINOS C, KOUNIAS S, and SOTIRAKOGLOU K. On base and Turyn sequences[J]. Mathematics of Computation, 1990, 55(192): 825–837. doi: 10.1090/S0025-5718-1990-1023764-7.
[20]	KOUKOUVINOS C, KOUNIAS S, SEBERRY J, et al. Multiplication of sequences with zero autocorrelation[J]. Australasian Journal of Combinatorics, 1994, 10: 5–15.
[21]	EDMONDSON G M, SEBERRY J, and ANDERSON M R. On the existence of Turyn sequences of length less than 43[J]. Mathematics of Computation, 1994, 62(205): 351–362. doi: 10.2307/2153414.
[22]	ĐOKOVIĆ D Ž. On the base sequence conjecture[J]. Discrete Mathematics, 2010, 310(13/14): 1956–1964. doi: 10.1016/j.disc.2010.03.007.
[23]	TURYN R J. Hadamard matrices, Baumert-Hall units, four-symbol sequences, pulse compression, and surface wave encodings[J]. Journal of Combinatorial Theory, Series A, 1974, 16(3): 313–333. doi: 10.1016/0097-3165(74)90056-9.
[24]	BEST D, ÐOKOVIĆ D Ž, KHARAGHANI H, et al. Turyn-type sequences: Classification, enumeration, and construction[J]. Journal of Combinatorial Designs, 2013, 21(1): 24–35. doi: 10.1002/jcd.21318.
[25]	LONDON S. Constructing new Turyn type sequences, T-sequences and Hadamard matrices[D]. [Ph. D. dissertation], University of Illinois at Chicago, 2013.
[26]	PAI Chengyu, LIN Y J, and CHEN Chaoyu. Optimal and almost-optimal Golay-ZCZ sequence sets with bounded PAPRs[J]. IEEE Transactions on Communications, 2023, 71(2): 728–740. doi: 10.1109/TCOMM.2022.3228932.