具有大零相关区宽度的Ⅱ型偶长Z-互补对构造方法

doi:10.11959/j.issn.1000-436x.2023121

通信学报 ›› 2023, Vol. 44 ›› Issue (6): 167-174.doi: 10.11959/j.issn.1000-436x.2023121

具有大零相关区宽度的Ⅱ型偶长Z-互补对构造方法

陈晓玉¹^,², 孙连峰¹^,², 张钇涵¹^,²

¹ 燕山大学信息科学与工程学院，河北秦皇岛 066004
² 燕山大学河北省信息传输与信号处理重点实验室，河北秦皇岛 066004

修回日期:2023-06-05 出版日期:2023-06-25 发布日期:2023-06-01
作者简介:陈晓玉（1983- ），女，内蒙古赤峰人，博士，燕山大学副教授、博士生导师，主要研究方向为序列设计、无线通信技术等
孙连峰（1999- ），男，山东济南人，燕山大学硕士生，主要研究方向为序列设计
张钇涵（1998- ），女，河北邯郸人，燕山大学硕士生，主要研究方向为序列设计
基金资助:
国家自然科学基金资助项目(62241110);河北省自然科学基金资助项目(F2021203078);河北省高等学校科学技术研究基金资助项目(ZD2022026);河北省重点实验室基金资助项目(202250701010046)

Construction method of type-Ⅱ even-length Z-complementary pair with large zero correlation zone width

Xiaoyu CHEN¹^,², Lianfeng SUN¹^,², Yihan ZHANG¹^,²

¹ School of Information Science ＆Engineering, Yanshan University, Qinhuangdao 066004, China
² Hebei Province Key Laboratory of Information Transmission and Signal Processing, Yanshan University, Qinhuangdao 066004, China

Revised:2023-06-05 Online:2023-06-25 Published:2023-06-01
Supported by:
The National Natural Science Foundation of China(62241110);The Natural Science Foundation of Hebei Province(F2021203078);Science and Technology Project of Hebei Province Higher Education(ZD2022026);The Key Laboratory Project of Hebei Province(202250701010046)

摘要/Abstract

摘要：

利用交织技术提出了Ⅱ型偶长Z-互补对的构造方法，提出了以Golay互补对及其互补偶为基础序列的交织结构基本框架，并给出了该框架需要满足的必要条件，以使所得Z-互补对可以具有较大的零相关区宽度。所构造的 Z-互补对的主要参数形式为((2k+1)N,(2k+1)N-k)-ZCP，其中N 为所选 Golay 互补对的长度。所构造的 Z-互补对虽然不能覆盖所有偶数长度，但其零相关区宽度可以达到或接近Ⅱ型偶长二进制 Z-互补对的理论上界，且具有较小的峰均包络功率比，其值小于或等于 4，应用到多载波扩频系统中可以消除更多的异步干扰和减小非线性失真。

关键词: 格雷互补对, 偶长Z-互补对, 零相关区, 峰均包络功率比

Abstract:

The construction method of Type-Ⅱ even-length Z-complementary pair (ZCP) was proposed by using the inter-leaving technique.The basic framework of interleaving structure with Golay complementary pair (GCP) and its mate as the basic sequences was proposed.Furthermore, the necessary conditions were given for the framework in order that the resulting ZCP could have large zero correlation zone (ZCZ) width.The main parameter form of the constructed ZCP was((2k+1)N,(2k+1)N-k)-ZCP, where N was the length of the chosen GCP.Although not all even lengths can be covered, the constructed ZCP has the ZCZ width that can achieve or approach the upper bound of Type-Ⅱ even-length binary ZCP, and has small peak-to-mean envelope power ratio whose value is less than or equal to 4.The resultant sequences can be applied to multi-carrier spread spectrum system to eliminate more asynchronous interference and reduce nonlinear distortion.

Key words: Golay complementary pair, even-length Z-complementary pair, zero correlation zone, peak-to-mean envelope power ratio

中图分类号:

TN911.2

陈晓玉, 孙连峰, 张钇涵. 具有大零相关区宽度的Ⅱ型偶长Z-互补对构造方法[J]. 通信学报, 2023, 44(6): 167-174.

Xiaoyu CHEN, Lianfeng SUN, Yihan ZHANG. Construction method of type-Ⅱ even-length Z-complementary pair with large zero correlation zone width[J]. Journal on Communications, 2023, 44(6): 167-174.

图/表 4

表1

表2

本文所得部分Ⅱ型EB-ZCP的具体PMEPR"

GCP的长度N	$(e_{2}, f_{2})$ 的PMEPR值（定理2式(9)）	$(e_{3}, f_{3})$ 的PMEPR值（定理3）	$(e_{4}, f_{4})$ 的PMEPR值（推论1式(12)）	$(e_{5}, f_{5})$ 的PMEPR值（推论2式(13)）
2	(2.692 8, 2.245 9)	(1.991 6, 3.600 0)	(1.693 1, 2.571 4)	(2.486 7, 2.338 3)
4	(2.575 2, 3.024 9)	(2.657 3, 3.424 4)	(3.526 2, 3.571 4)	(2.399 9, 2.451 1)
8	(2.808 1, 3.066 8)	(3.600 0, 3.363 1)	(3.383 0, 3.227 1)	(2.537 9, 2.507 3)
10	(3.333 3, 2.852 2)	(3.547 7, 3.412 4)	(2.800 0, 3.558 5)	(2.561 2, 2.661 7)
16	(3.296 1, 3.197 8)	(3.456 5, 3.418 1)	(3.571 4, 3.447 6)	(2.596 5, 2.609 9)

表2

表3

Ⅱ型EB-ZCP构造方法比较"

文献	ZCP长度	ZCZ宽度	参数限制
文献[12]定理1	2^{k+ 2}N	(2^k+2-1)N	$k \geq 1, N = 2^{α} 10^{β} 26^{γ}$
文献[12]定理2	2N+2	$\frac{3 N}{2} + 2$	$N = 2^{α} 10^{β} 26^{γ}$
文献[12]定理3	2^k+1N+2^k+1	$2^{k + 1} N + 2^{k + 1} - \frac{N}{2}$	$k \geq 1, N = 2^{α} 10^{β} 26^{γ}$
文献[13]定理2	2^kN+2^k1	2^kN+2^k-1-N	$N \in ℤ^{+}, k \geq 2$
文献[13]定理3	3N	3N 1	$N = 2^{α} 10^{β} 26^{γ}$
文献[13]定理3	14N	14N 1	$N = 2^{α} 10^{β} 26^{γ}$
文献[14]	2^mP	2^mP+1-P	$m, P \geq 1$
本文定理2	2N	2N-1	$N = 2^{α} 10^{β} 26^{γ}$
本文定理2	3N	3N-1	$N = 2^{α} 10^{β} 26^{γ}$
本文定理3	5N	5N-2	$N = 2^{α} 10^{β} 26^{γ}$
本文推论1	7N	7N-3	$N = 2^{α} 10^{β} 26^{γ}$
本文推论2	9N	9N-4	$N = 2^{α} 10^{β} 26^{γ}$

表3

表4

参考文献 16

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具有大零相关区宽度的Ⅱ型偶长Z-互补对构造方法

Construction method of type-Ⅱ even-length Z-complementary pair with large zero correlation zone width

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图/表 4

参考文献 16

相关文章 8

Metrics

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类型	ZCP长度	ZCZ宽度	PMEPR界限
定理2	2N	2N-1	4
定理2	3N	3N-1	3.33
定理3	5N	5N-2	3.6
推论1	7N	7N-3	3.71
推论2	9N	9N-4	3.77

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ZCP长度	文献[13]定理2	文献[14]	本文定理	理论上界
20	18	16	18	19
28	25	22	25	27
36	32	28	32	35
50	38	26	48	49
70	53	36	67	69
90	68	46	86	89
130	98	66	128	129
182	137	92	179	181
200	188	176	198	199
234	176	118	230	233
260	228	196	258	259
364	319	274	361	363
468	410	352	464	467
500	438	376	498	499
900	788	676	896	899