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

Abstract

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

CLC Number:

TN911.2

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.

Figures/Tables 4

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)

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	$N = 2^{α} 10^{β} 26^{γ}$

References 16

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	CHEN X Y , SUN L F , ZHANG J K ,et al. Construction of new even-length type-Ⅱ Z-complementary pair[J. Journal on Communications, 2023,44(3): 138-144.
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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

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

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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

[1]	Xiaoyu CHEN, Lianfeng SUN, Jiekun ZHANG, Yubo LI. Construction of new even-length type-II Z-complementary pair [J]. Journal on Communications, 2023, 44(3): 138-144.
[2]	Xiaoyu CHEN,Xichao GAO,Yongjie LI. Construction of optimal zero correlation zone sequence set [J]. Journal on Communications, 2020, 41(8): 215-222.
[3]	Yu-bo LI,Jia-an SUN,Nan JING. Construction of zero correlation zone Gaussian integer sequence set [J]. Journal on Communications, 2017, 38(9): 25-30.
[4]	Yu-bo LI,Cheng-qian XU,Nan JING,Gang LI,Kai LIU,Hao-chen HU. Construction of ZCZ periodic complementary sequence set with flexible subsequences [J]. Journal on Communications, 2015, 36(2): 200-203.
[5]	Jun-ping GAO,Qi LI,Ju-feng DAI,Li LIU. Research of ZCZ array pair and its construction methods [J]. Journal on Communications, 2008, 29(9): 62-67.
[6]	Xin TONG,Qiao-yan WEN. New class of ternary two dimensional array sets with a zero correlation zone [J]. Journal on Communications, 2008, 29(3): 124-129.