Construction of optimal symmetric Z-complementary code set based on extended Boolean function

CHEN Xiaoyu; ZHANG Zhaoyu; DU Yuqiong

doi:10.11959/j.issn.1000-436x.2025104

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Construction of optimal symmetric Z-complementary code set based on extended Boolean function

Papers | 更新时间：2025-07-04

- Construction of optimal symmetric Z-complementary code set based on extended Boolean function
- Journal on Communications Vol. 46, Issue 6, Pages: 209-217(2025)
- 作者机构：
  
  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
- 作者简介：
- 基金信息：
  
  The Natural Science Foundation of Hebei Province(F2025203055)
- DOI：10.11959/j.issn.1000-436x.2025104
  CLC： TN911.2
- Received：06 March 2025，
  
  Revised：2025-05-27，
  
  Published：25 June 2025
- 稿件说明：
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陈晓玉,张兆瑜,杜玉琼.基于扩展布尔函数的最优对称Z互补码集构造[J].通信学报,2025,46(06):209-217.

CHEN Xiaoyu,ZHANG Zhaoyu,DU Yuqiong.Construction of optimal symmetric Z-complementary code set based on extended Boolean function[J].Journal on Communications,2025,46(06):209-217.
陈晓玉,张兆瑜,杜玉琼.基于扩展布尔函数的最优对称Z互补码集构造[J].通信学报,2025,46(06):209-217. DOI： 10.11959/j.issn.1000-436x.2025104.

CHEN Xiaoyu,ZHANG Zhaoyu,DU Yuqiong.Construction of optimal symmetric Z-complementary code set based on extended Boolean function[J].Journal on Communications,2025,46(06):209-217. DOI： 10.11959/j.issn.1000-436x.2025104.

摘要

针对宽带广义空间调制（GSM）系统训练序列数目受限的问题，研究了最优对称Z互补码集（SZCCS）和增强型交叉Z互补集（E-CZCS）的构造方法。提出了一种基于扩展布尔函数（EBF）的最优对称Z互补码集的构造方法，所得序列具有新的参数形式，具体为

</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msup><mo>

</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>

</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>m</mi></mrow></msup><mo stretchy="false">)</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84328740&type=

3.13266683

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84328715&type=

20.65866661

。同时，该序列也是具有大零相关区（ZCZ）的增强型交叉Z互补序列集，且序列的零相关区长度与序列长度比值为1。所得2种序列集参数灵活且不再局限于2的幂次形式。以所提增强型交叉Z互补集为基序列构造广义空间调制系统的训练矩阵，通过仿真实验验证了该增强型交叉Z互补集的信道估计能达到理论最小均方误差（MSE）。

Abstract

Aiming at the problem of the limited number of training sequences in the wideband generalized spatial modulation (GSM) system

the construction methods of the optimal symmetric Z-complementary code set (SZCCS) and the enhanced cross Z-complementary set (E-CZCS) were studied. A new construction method for the optimal symmetric Z complementary code set based on extended Boolean function (EBF) was proposed. The resulting sequence had a new parameter form

which was specifically represented as

</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn mathvariant="normal">1</mn></mrow></msup><mo>

</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>

</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>m</mi></mrow></msup><mo stretchy="false">)</mo></math>

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84328756&type=

3.13266683

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84328757&type=

20.65866661

. At the same time

the construction was also enhanced cross Z-complementary sequence set with large zero correlation zone (ZCZ)

where the ratio of the ZCZ length to the sequence length was 1. The parameters of the two sequence sets obtained were flexible and were no longer limited to powers of 2. Using the proposed enhanced cross Z-complementary set obtained as the base sequence

the training matrix for the generalized space modulation system was constructed. Simulation results demonstrate that the channel estimation of the enhanced cross Z-complementary set can achieve the theoretical minimum mean square error (MSE).

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Keywords

references

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彭秀平 , 刘银娜 , 王毓 , 等 . 面向广义空间调制的增强型交叉Z互补集的新构造 [J ] . 通信学报 , 2024 , 45 ( 12 ): 153 - 161 .

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