An asymmetric ZCZ sequence set with inter-subset uncorrelated property and flexible ZCZ length

Longye Wang; Gaoyuan Zhang; Hong Wen; Xiaoli Zeng

doi:10.3934/amc.2018032

Article Contents

2018, Volume 12, Issue 3: 541-552. Doi: 10.3934/amc.2018032

This issue Previous Article On the linear complexities of two classes of quaternary sequences of even length with optimal autocorrelation Next Article A first step towards the skew duadic codes

An asymmetric ZCZ sequence set with inter-subset uncorrelated property and flexible ZCZ length

1.
The National Key Laboratory of Science and Technology on Communications, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China
2.
School of Electronic and Information Engineering, Henan University of Science and Technology, Luoyang, Henan 471022, China
3.
School of Information Science and Technology, Tibet University, Lhasa, Tibet 850000, China

^* Xiaoli Zeng is the corresponding author
^* Xiaoli Zeng is the corresponding author

^† Longye Wang is also affiliated with School of Engineering and Technology, Tibet University, Lhasa, Tibet 850000, China

Received: July 2017

Revised: January 2018

Published: July 2018

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Abstract

In this paper, we propose a novel method for constructing new uncorrelated asymmetric zero correlation zone (UA-ZCZ) sequence sets by interleaving perfect sequences. As a type of ZCZ sequence set, an A-ZCZ sequence set consists of multiple sequence subsets. Different subsets are correlated in conventional A-ZCZ sequence set but uncorrelated in our scheme. In other words, the cross-correlation function (CCF) between two arbitrary sequences which belong to different subsets has quite a large zero cross-correlation zone (ZCCZ). Analytical results demonstrate that the UA-ZCZ sequence set proposed herein is optimal with respect to the upper bound of ZCZ sequence set. Specifically, our scheme enables the flexible selection of ZCZ length, which makes it extremely valuable for designing spreading sequences for quasi-synchronous code-division multiple-access (QS-CDMA) systems.

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Mathematics Subject Classification: Primary: 94A05, 94B60.

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Figure 1. Periodic correlation properties of U-ZCZ sequence set ${B}$.

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Figure 2. Comparison of Different Families of A-ZCZ Sequence Sets

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Table 1. The A-ZCZ Sequence Set $\mathcal{C} = \{{C}^{(0)}, \, {C}^{(1)}, \, {C}^{(2)}, \, {C}^{(3)}\}$

${C}^{(0)}$	$\mathit{\boldsymbol{c}}^{(0)}_0$	1, 0, 0, 1, 0, 0, -1, 0, 1, -1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, -1, 0, 1, -1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, -1, 0, 1, -1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, -1, 0, 1, -1, 1, 1, 0, 1
	$\mathit{\boldsymbol{c}}^{(0)}_1$	1, 0, 0, -1, 0, 0, -1, 0, 1, 1, 1, -1, 0, -1, 1, 0, 0, -1, 0, 0, -1, 0, 1, 1, 1, -1, 0, -1, 1, 0, 0, -1, 0, 0, -1, 0, 1, 1, 1, -1, 0, -1, 1, 0, 0, -1, 0, 0, -1, 0, 1, 1, 1, -1, 0, -1
	$\mathit{\boldsymbol{c}}^{(0)}_2$	1, 0, 1, -1, 0, 1, 1, 1, 0, 0, 0, 1, -1, 0, 1, 0, 1, -1, 0, 1, 1, 1, 0, 0, 0, 1, -1, 0, 1, 0, 1, -1, 0, 1, 1, 1, 0, 0, 0, 1, -1, 0, 1, 0, 1, -1, 0, 1, 1, 1, 0, 0, 0, 1, -1, 0
	$\mathit{\boldsymbol{c}}^{(0)}_3$	1, 0, 1, 1, 0, -1, 1, -1, 0, 0, 0, -1, -1, 0, 1, 0, 1, 1, 0, -1, 1, -1, 0, 0, 0, -1, -1, 0, 1, 0, 1, 1, 0, -1, 1, -1, 0, 0, 0, -1, -1, 0, 1, 0, 1, 1, 0, -1, 1, -1, 0, 0, 0, -1, -1, 0
${C}^{(1)}$	$\mathit{\boldsymbol{c}}^{(1)}_0$	1, 0, 0, -i, 0, 0, i, 0, 1, 1, i, {-i}, 0, 1, -i, 0, 0, -1, 0, 0, 1, i, -i, -i, 1, -1, i, -i, -1, i, i, i, i, i, -i, i, -1, -1, -i, i, i, -1, i, i, i, 1, i, i, -1, i, i, i, -1, 1, i, i
	$\mathit{\boldsymbol{c}}^{(1)}_1$	1, 0, 0, i, 0, 0, i, 0, 1, -1, i, i, 0, -1, -i, 0, 0, 1, 0, 0, 1, 0, -i, i, 1, 1, 0, i, -1, 0, 0, -i, 0, 0, -i, 0, -1, 1, -i, -i, 0, 1, i, 0, 0, -1, 0, 0, -1, 0, i, -i, -1, -1, 0, -i
	$\mathit{\boldsymbol{c}}^{(1)}_2$	1, 0, i, i, 0, 1, -i, i, 0, 0, 0, -i, 1, 0, -i, 0, 1, 1, 0, -i, -1, 1, 0, 0, 0, -1, -i, 0, -1, 0, -i, -i, 0, -1, i, -i, 0, 0, 0, i, -1, 0, i, 0, -1, -1, 0, i, 1, -1, 0, 0, 0, 1, i, 0
	$\mathit{\boldsymbol{c}}^{(1)}_3$	1, 0, i, -i, 0, -1, -i, -i, 0, 0, 0, i, 1, 0, -i, 0, 1, -1, 0, i, -1, -1, 0, 0, 0, 1, -i, 0, -1, 0, -i, i, 0, 1, i, i, 0, 0, 0, -i, -1, 0, i, 0, -1, 1, 0, -i, 1, 1, 0, 0, 0, -1, i, 0
${C}^{(2)}$	$\mathit{\boldsymbol{c}}^{(2)}_0$	1, 0, 0, i, 0, 0, -i, 0, 1, 1, -i, i, 0, 1, i, 0, 0, -1, 0, 0, 1, 0, i, i, 1, -1, 0, i, -1, 0, 0, -i, 0, 0, i, 0, -1, -1, i, -i, 0, -1, -i, 0, 0, 1, 0, 0, -1, 0, -i, -i, -1, 1, 0, -i
	$\mathit{\boldsymbol{c}}^{(2)}_1$	1, 0, 0, -i, 0, 0, -i, 0, 1, -1, -i, -i, 0, -1, i, 0, 0, 1, 0, 0, 1, 0, i, -i, 1, 1, 0, -i, -1, 0, 0, i, 0, 0, i, 0, -1, 1, i, i, 0, 1, -i, 0, 0, -1, 0, 0, -1, 0, -i, i, -1, -1, 0, i
	$\mathit{\boldsymbol{c}}^{(2)}_2$	1, 0, -i, -i, 0, 1, i, -i, 0, 0, 0, i, 1, 0, i, 0, 1, 1, 0, i, -1, 1, 0, 0, 0, -1, i, 0, -1, 0, i, i, 0, -1, -i, i, 0, 0, 0, -i, -1, 0, -i, 0, -1, -1, 0, -i, 1, -1, 0, 0, 0, 1, -i, 0
	$\mathit{\boldsymbol{c}}^{(2)}_3$	1, 0, -i, i, 0, -1, i, i, 0, 0, 0, -i, 1, 0, i, 0, 1, -1, 0, -i, -1, -1, 0, 0, 0, 1, i, 0, -1, 0, i, -i, 0, 1, -i, -i, 0, 0, 0, i, -1, 0, -i, 0, -1, 1, 0, i, 1, 1, 0, 0, 0, -1, -i, 0
${C}^{(3)}$	$\mathit{\boldsymbol{c}}^{(3)}_0$	1, 0, 0, -1, 0, 0, 1, 0, 1, -1, -1, -1, 0, 1, -1, 0, 0, 1, 0, 0, -1, 0, -1, 1, 1, 1, 0, -1, 1, 0, 0, -1, 0, 0, 1, 0, 1, -1, -1, -1, 0, 1, -1, 0, 0, 1, 0, 0, -1, 0, -1, 1, 1, 1, 0, -1
	$\mathit{\boldsymbol{c}}^{(3)}_1$	1, 0, 0, 1, 0, 0, 1, 0, 1, 1, -1, 1, 0, -1, -1, 0, 0, -1, 0, 0, -1, 0, -1, -1, 1, -1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 1, 1, -1, 1, 0, -1, -1, 0, 0, -1, 0, 0, -1, 0, -1, -1, 1, -1, 0, 1
	$\mathit{\boldsymbol{c}}^{(3)}_2$	1, 0, -1, 1, 0, 1, -1, -1, 0, 0, 0, -1, -1, 0, -1, 0, 1, -1, 0, -1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, -1, 1, 0, 1, -1, -1, 0, 0, 0, -1, -1, 0, -1, 0, 1, -1, 0, -1, 1, 1, 0, 0, 0, 1, 1, 0
	$\mathit{\boldsymbol{c}}^{(3)}_3$	1, 0, -1, -1, 0, -1, -1, 1, 0, 0, 0, 1, -1, 0, -1, 0, 1, 1, 0, 1, 1, -1, 0, 0, 0, -1, 1, 0, 1, 0, -1, -1, 0, -1, -1, 1, 0, 0, 0, 1, -1, 0, -1, 0, 1, 1, 0, 1, 1, -1, 0, 0, 0, -1, 1, 0

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Table 2. Periodic correlation properties of UA-ZCZ sequence set $\mathcal{C}$.

Constructions	Parameters	Uncorrelated or not	Flexible ZCZ or not
Theorem^$\ast$1 in [12]	$\mathcal{Z}_A(LP, [L, N], [M-1, 2M-1])$	No	No
Theorem^†2 in [12]	$\mathcal{Z}_A(TL, \, [T, N], \, [M, TL])$	Yes	No
Theorem^‡2 in [16]	$\mathcal{Z}_A(TLP, \, [L, T], \, [P, TLP])$ or $\mathcal{Z}_A(TLP, \, [L, T], \, [P-1, TLP])$	Yes	No
Theorem^$\sharp$3.4	$\mathcal{Z}_A(2TP, \, [2M, T], \, [Z, 2TP])$	Yes	Yes
^$\ast$ $L$ is the order of orthogonal matrix $O_L$, $P$ is length of perfect sequence, and $L=KM$, $N=\lfloor\frac{T}{M}\rfloor>1$, $K>1$, $M>1$.
^† $T$ is the order of DFT matrix $H_T$, $L$ is the order of orthogonal matrix $O_L$, and $L=KM$, $N=\lfloor\frac{T}{M}\rfloor>1$, $K>1$, $M>1$.
^‡ $T$ is the order of DFT matrix $H_T$, $L$ is the order of orthogonal matrix $O_L$, $P$ is length of perfect sequence, and $\gcd{(T, P)}=1$, $\gcd{(L, P)}=1$ (or $L\|P$ or $P\|L$).
^$\sharp$ $T$ is the order of DFT matrix $H_T$, $P$ is length of perfect sequence, and $Z\leq2$, $M=\lfloor\frac{P-2}{Z}\rfloor$ or $M=\lfloor\frac{P-1}{Z}\rfloor$.

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References

[1]	P. Z. Fan and L. Hao, Generalized orthogonal sequences and their applications in synchronous CDMA systems, IEICE Trans. Fund., E83-A (2000), 2054-2069.
[2]	G. Gong, New designs for signal sets with low cross correlation balance property and large linear span: GF(p) case, IEEE Trans. Inf. Theory, 48 (2002), 2847-2867. doi: 10.1109/TIT.2002.804044.
[3]	T. Hayashi, Zero-correlation zone sequence set constructed from a perfect sequence, IEICE Trans. Fund., E90-A (2007), 1-5. doi: 10.1109/CIT.2007.192.
[4]	T. Hayashi, T. Maeda, S. Matsufuji and S. Okawa, A ternary zero-correlation zone sequence set having wide inter-subset zero-correlation zone, IEICE Trans. Fund., E94-A (2011), 2230-2235.
[5]	T. Hayashi, T. Maeda and S. Okawa, A generalized construction of zero-correlation zone sequence set with sequence subsets, IEICE Trans. Fund., E94-A (2011), 1597-1602.
[6]	P. H. Ke and Z. C. Zhou, A generic construction of Z-periodic complementary sequence sets with flexible flock size and zero correlation zone length, IEEE Signal Process. Lett., 22 (2015), 1462-1466. doi: 10.1109/LSP.2014.2369512.
[7]	S. Matsufuji, N. Kuroyanagi, N. Suehiro and P. Z. Fan, Two types polyphase sequence sets for approximately synchronized CDMA systems, IEICE Trans. Fund., E86-A (2003), 229-234.
[8]	X. H. Tang, P. Z. Fan and S. Matsufuji, Lower bounds on correlation of spreading sequence set with low or zero correlation zone, Electronics Letters, 36 (2000), 551-552. doi: 10.1049/el:20000462.
[9]	X. H. Tang and H. M. Wai, A new systematic construction of zero correlation zone sequences based on interleaved perfect sequences, IEEE Trans. Inf. Theory, 54 (2008), 5729-5734. doi: 10.1109/TIT.2008.2006574.
[10]	X. H. Tang, P. Fan and J. Lindner, Multiple binary ZCZ sequence sets with good cross-correlation property based on complementary sequence sets, IEEE Trans. Inf. Theory, 56 (2010), 4038-4045. doi: 10.1109/TIT.2010.2050796.
[11]	H. Torii, T. Matsumoto and M. Nakamura, A new method for constructing asymmetric {ZCZ} sequence sets, IEICE Trans. Fund., E95-A (2012), 1577-1586.
[12]	H. Torii, T. Matsumoto and M. Nakamura, Extension of methods for constructing polyphase asymmetric ZCZ sequence sets, IEICE Trans. Fund., E96-A (2013), 2244-2252.
[13]	H. Torii, M. Nakamurai and Makoto, Optimal polyphase asymmetric ZCZ sets including uncorrelated sequences, Journal of Signal Processing, 16 (2012), 487-494.
[14]	L. Y. Wang, X. L. Zeng and H. Wen, A novel construction of asymmetric ZCZ sequence sets from interleaving perfect sequence, IEICE Trans. Fund., E97-A (2014), 2556-2561.
[15]	L. Y. Wang, X. L. Zeng and H. Wen, Families of asymmetric sequence pair set with zero-correlation zone via interleaved technique, IET Commun., 10 (2016), 229-234. doi: 10.1049/iet-com.2015.0075.
[16]	L. Y. Wang, X. L. Zeng and H. Wen, Asymmetric ZCZ sequence sets with inter-subset uncorrelated sequences via interleaved technique, IEICE Trans. Fund., E100-A (2017), 751-756.
[17]	Z. C. Zhou, Z. Pan and X. H. Tang, New families of optimal zero correlation zone sequences based on interleaved technique and perfect, IEICE Trans. Fund., E91-A (2008), 3691-3697.
[18]	Z. C. Zhou, X. H. Tang and G. Gong, A new class of sequences with zero or low correlation zone based on interleaving technique, IEEE Trans. Inf. Theory, 54 (2008), 4267-4273. doi: 10.1109/TIT.2008.928256.