周期为合数长屏蔽二元互补序列偶构造方法研究

doi:10.12263/DZXB.20190456

电子学报 ›› 2021, Vol. 49 ›› Issue (8): 1466-1473.DOI: 10.12263/DZXB.20190456

周期为合数长屏蔽二元互补序列偶构造方法研究

彭秀平¹^,²^,³, 郑德亮¹, 冀惠璞¹, 张桂茹⁴, 刘元慧⁵

^1.燕山大学信息科学与工程学院，河北秦皇岛 066004
^2.河北省信息传输与信号处理重点实验室，河北秦皇岛 066004
^3.通信网信息传输与分发技术重点实验室，河北石家庄 050081
^4.河北建材职业技术学院，河北秦皇岛 066004
^5.燕山大学理学院，河北秦皇岛 066004

收稿日期:2019-04-25 修回日期:2020-11-25 出版日期:2021-08-25 发布日期:2021-08-25
作者简介:彭秀平女，1984年9月出生，安徽安庆人．博士，现为燕山大学副教授，硕士生导师，主要研究方向为序列设计、编码理论. E-mail:pengxp@ysu.edu.cn
郑德亮男，1994年12月出生，四川巴中人．2018年9月进入燕山大学信息科学与工程学院攻读硕士学位，研究方向为序列设计、编码理论．
基金资助:
河北省高等学校青年拔尖人才计划(BJ2018018);河北省教育厅高等学校科技计划重点项目(ZD2019039);装备预研重点实验室基金(6142104190109)

Study on the Construction Method of Punctured Binary Complementary Sequence Pairs with Composite Length

Xiu-ping PENG¹^,²^,³, De-liang ZHENG¹, Hui-pu JI¹, Gui-ru ZHANG⁴, Yuan-hui LIU⁵

^1.School of Information Science and Engineering，Yanshan University，Qinhuangdao，Hebei 066004，China
^2.Hebei Province Key Laboratory of Information Transmission and Signal Processing，Qinhuangdao，Hebei 066004，China
^3.Key Laboratory of Communication Network Information Transmission and Distribution Technology，Shijiazhuang，Hebei 050081，China
^4.Hebei Construction Material Vocational and Technical College，Qinhuangdao，Hebei 066004，China
^5.School of Sciences，Yanshan University，Qinhuangdao，Hebei 066004，China

Received:2019-04-25 Revised:2020-11-25 Online:2021-08-25 Published:2021-08-25

摘要/Abstract

摘要：

互补序列应用于多载波码分多址系统因理论上可同时消除多径干扰和多址干扰而备受关注．基于中国剩余定理，本文提出一种周期为合数长的屏蔽二元互补序列偶的构造方法．构造得到的屏蔽二元互补序列偶可扩展互补序列的存在范围．为了进一步研究屏蔽二元互补序列偶，本文提出一种新的区组设计——屏蔽差族偶，并将屏蔽差族偶与屏蔽二元互补序列偶建立了等价关系,为应用屏蔽差族偶这一新的区组设计研究屏蔽二元互补序列偶提供了理论依据．

关键词: 多载波码分多址, 屏蔽序列, 屏蔽二元互补序列偶, 屏蔽差族偶

Abstract:

Complementary sequences (CSs) have attracted more attention in application of multicarrier code-division multiple-access (MC-CDMA) communication system since they are able to remove multipath interference (MPI) and multi-access interference (MAI). Based on Chinese reminder theorem, a construction method of punctured binary complementary sequence pairs (PBCSPs) with composite length has been proposed. This result can greatly extend the range of complementary sequence. To further study PBCSPs, we present a new block design—punctured difference family pair (PDFP), and establish the equivalent relationship between PDFP and PBCSPs, which provides a theoretical basis for the study of PBCSPs by using the new block design of PDFP.

Key words: MC-CDMA, punctured sequence, punctured binary complementary sequence pairs, punctured difference family pair

中图分类号:

TN911.2

彭秀平, 郑德亮, 冀惠璞, 张桂茹, 刘元慧. 周期为合数长屏蔽二元互补序列偶构造方法研究[J]. 电子学报, 2021, 49(8): 1466-1473.

Xiu-ping PENG, De-liang ZHENG, Hui-pu JI, Gui-ru ZHANG, Yuan-hui LIU. Study on the Construction Method of Punctured Binary Complementary Sequence Pairs with Composite Length[J]. Acta Electronica Sinica, 2021, 49(8): 1466-1473.

图/表 2

表1 r∈ZN*在差表中出现的次数

r ∈ Z 24 *

{u 0, m - u 0, n' : u 0, m ∈ U 0, u 0, n' ∈ U 0', u 0, m ≠ u 0, n', 0 ≤ m ≤ 13,0 ≤ n ≤ 11}

{w 0, l - w 0, v' : w 0, l ∈ W 0, w 0, v' ∈ W 0', w 0, l ≠ w 0, v', 0 ≤ l ≤ 9,0 ≤ v ≤ 3}

{u 1, m - u 1, n' : u 1, m ∈ U 1, u 1, n' ∈ U 1', u 1, m ≠ u 1, n', 0 ≤ m ≤ 11,0 ≤ n ≤ 7}

{w 1, l - w 1, v' : w 1, l ∈ W 1, w 1, v' ∈ W 1', w 1, l ≠ w 1, v', 0 ≤ l ≤ 11,0 ≤ v ≤ 7}

｛1，2，4，5，

7，8，10，11，

13，14，16，17，

19，20，22，23｝

｛3，21｝

｛6，9，12，15，18｝

表1 r∈ZN*在差表中出现的次数

r ∈ Z 24 *

{u 0, m - u 0, n' : u 0, m ∈ U 0, u 0, n' ∈ U 0', u 0, m ≠ u 0, n', 0 ≤ m ≤ 13,0 ≤ n ≤ 11}

{w 0, l - w 0, v' : w 0, l ∈ W 0, w 0, v' ∈ W 0', w 0, l ≠ w 0, v', 0 ≤ l ≤ 9,0 ≤ v ≤ 3}

{u 1, m - u 1, n' : u 1, m ∈ U 1, u 1, n' ∈ U 1', u 1, m ≠ u 1, n', 0 ≤ m ≤ 11,0 ≤ n ≤ 7}

{w 1, l - w 1, v' : w 1, l ∈ W 1, w 1, v' ∈ W 1', w 1, l ≠ w 1, v', 0 ≤ l ≤ 11,0 ≤ v ≤ 7}

｛1，2，4，5，

7，8，10，11，

13，14，16，17，

19，20，22，23｝

｛3，21｝

｛6，9，12，15，18｝

表2 已有周期二元互补序列对长度与本文可得二元互补序列偶对长度对比(100以内)

PCS^［4］

2， 4， 8， 10， 16， 20， 26， 32， 34，40，

50， 52， 58， 64， 68， 72， 74， 80， 82

定理2

6，12，14，22，24，28，30，38，44，46，48，

56，60，62，70，76，78，86，88，92，94，96

定理3

10，20，26，34，40，52，58，68，74，80，82，98

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周期为合数长屏蔽二元互补序列偶构造方法研究

Study on the Construction Method of Punctured Binary Complementary Sequence Pairs with Composite Length

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