不相关多子集零相关区序列集的构造

doi:10.12305/j.issn.1001-506X.2024.10.34

Abstract

Abstract:

In multi-cell quasi-synchronous code-division multiple-access (QS-CDMA) systems, uncorrelated multiple-subset zero correlation zone (ZCZ) sequence sets can not only eliminate signal interference in the same cell within a certain time delay, but also eliminate signal interference from adjacent cells completely. Two construction methods are designed to solve the problem that how to construct multiple-subset ZCZ sequence sets based on paraunitary (PU) matrices. Specifically, by constructing multiple initial matrices with certain characteristics, combined with the PU matrices, different initial matrices are used to yield different ZCZ sequence sets. Furthermore, the obtained ZCZ sequence sets are uncorrelated with each other. The key idea of the construction methods is the design of the multiple initial matrices. Construction method 1 is realized by dividing and stacking the discrete Fourier transform (DFT) matrices, and construction method 2 is implemented by the existing uncorrelated multiple-subset ZCZ sequence sets. The parameter performance of the construction results obtained by the two methods is close to optimal, which provides a new sequence design method for solving the interference suppression problem in a multi-cell environment.

Key words: quasi-synchronous code-division multiple-access (QS-CDMA) system, zero correlation zone (ZCZ), multiple-subset ZCZ sequence sets, paraunitary matrix

CLC Number:

TN911.2

Li CUI, Chengqian XU. Construction of uncorrelated multiple-subset zero correlation zone sequence sets[J]. Systems Engineering and Electronics, 2024, 46(10): 3577-3585.

Figures/Tables 4

Table 1

Sequences of S(z) derived from construction method 1"

s_{m, n}	序列
s_{0, 0}	(0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 2, 5, 0, 0, 2, 5, 0, 0, 4, 1, 0, 0, 4, 1, 0, 0, 0, 3, 1, 1, 1, 4, 2, 2, 4, 1, 0, 0, 2, 5, 1, 1, 5, 2, 2, 2, 0, 3, 0, 0, 0, 3, 2, 2, 2, 5, 4, 4, 0, 3, 0, 0, 2, 5, 2, 2, 0, 3, 4, 4, 2, 5, 0, 0, 0, 3, 3, 3, 3, 0, 0, 0, 2, 5, 0, 0, 2, 5, 3, 3, 1, 4, 0, 0, 4, 1, 0, 0, 0, 3, 4, 4, 4, 1, 2, 2, 4, 1, 0, 0, 2, 5, 4, 4, 2, 5, 2, 2, 0, 3, 0, 0, 0, 3, 5, 5, 5, 2, 4, 4, 0, 3, 0, 0, 2, 5, 5, 5, 3, 0, 4, 4, 2, 5)
s_{0, 1}	(0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 2, 2, 0, 3, 2, 2, 0, 3, 4, 4, 0, 3, 4, 4, 0, 3, 0, 0, 1, 4, 1, 1, 2, 5, 4, 4, 0, 3, 2, 2, 1, 4, 5, 5, 2, 5, 0, 0, 0, 3, 0, 0, 2, 5, 2, 2, 4, 1, 0, 0, 0, 3, 2, 2, 2, 5, 0, 0, 4, 1, 2, 2, 0, 3, 0, 0, 3, 0, 3, 3, 0, 3, 2, 2, 0, 3, 2, 2, 3, 0, 1, 1, 0, 3, 4, 4, 0, 3, 0, 0, 4, 1, 4, 4, 2, 5, 4, 4, 0, 3, 2, 2, 4, 1, 2, 2, 2, 5, 0, 0, 0, 3, 0, 0, 5, 2, 5, 5, 4, 1, 0, 0, 0, 3, 2, 2, 5, 2, 3, 3, 4, 1, 2, 2)
s_{0, 2}	(0, 0, 0, 3, 2, 2, 2, 5, 0, 0, 4, 1, 4, 4, 0, 3, 4, 4, 2, 5, 2, 2, 4, 1, 0, 0, 0, 3, 3, 3, 3, 0, 2, 2, 0, 3, 4, 4, 0, 3, 5, 5, 3, 0, 4, 4, 0, 3, 0, 0, 0, 3, 4, 4, 4, 1, 4, 4, 2, 5, 4, 4, 0, 3, 0, 0, 4, 1, 0, 0, 2, 5, 0, 0, 0, 3, 5, 5, 5, 2, 0, 0, 4, 1, 4, 4, 0, 3, 1, 1, 5, 2, 2, 2, 4, 1, 0, 0, 0, 3, 0, 0, 0, 3, 2, 2, 0, 3, 4, 4, 0, 3, 2, 2, 0, 3, 4, 4, 0, 3, 0, 0, 0, 3, 1, 1, 1, 4, 4, 4, 2, 5, 4, 4, 0, 3, 3, 3, 1, 4, 0, 0, 2, 5)
s_{0, 3}	(0, 3, 0, 0, 2, 5, 2, 2, 0, 3, 4, 4, 4, 1, 0, 0, 4, 1, 2, 2, 2, 5, 4, 4, 0, 3, 0, 0, 3, 0, 3, 3, 2, 5, 0, 0, 4, 1, 0, 0, 5, 2, 3, 3, 4, 1, 0, 0, 0, 3, 0, 0, 4, 1, 4, 4, 4, 1, 2, 2, 4, 1, 0, 0, 0, 3, 4, 4, 0, 3, 2, 2, 0, 3, 0, 0, 5, 2, 5, 5, 0, 3, 4, 4, 4, 1, 0, 0, 1, 4, 5, 5, 2, 5, 4, 4, 0, 3, 0, 0, 0, 3, 0, 0, 2, 5, 0, 0, 4, 1, 0, 0, 2, 5, 0, 0, 4, 1, 0, 0, 0, 3, 0, 0, 1, 4, 1, 1, 4, 1, 2, 2, 4, 1, 0, 0, 3, 0, 1, 1, 0, 3, 2, 2)
s_{0, 4}	(0, 0, 0, 3, 4, 4, 4, 1, 4, 4, 2, 5, 2, 2, 4, 1, 0, 0, 2, 5, 2, 2, 0, 3, 0, 0, 0, 3, 5, 5, 5, 2, 0, 0, 4, 1, 2, 2, 4, 1, 1, 1, 3, 0, 4, 4, 2, 5, 0, 0, 0, 3, 0, 0, 0, 3, 2, 2, 0, 3, 2, 2, 4, 1, 2, 2, 4, 1, 0, 0, 4, 1, 0, 0, 0, 3, 1, 1, 1, 4, 4, 4, 2, 5, 2, 2, 4, 1, 3, 3, 5, 2, 2, 2, 0, 3, 0, 0, 0, 3, 2, 2, 2, 5, 0, 0, 4, 1, 2, 2, 4, 1, 4, 4, 0, 3, 4, 4, 2, 5, 0, 0, 0, 3, 3, 3, 3, 0, 2, 2, 0, 3, 2, 2, 4, 1, 5, 5, 1, 4, 0, 0, 4, 1)
s_{0, 5}	(0, 3, 0, 0, 4, 1, 4, 4, 4, 1, 2, 2, 2, 5, 4, 4, 0, 3, 2, 2, 2, 5, 0, 0, 0, 3, 0, 0, 5, 2, 5, 5, 0, 3, 4, 4, 2, 5, 4, 4, 1, 4, 3, 3, 4, 1, 2, 2, 0, 3, 0, 0, 0, 3, 0, 0, 2, 5, 0, 0, 2, 5, 4, 4, 2, 5, 4, 4, 0, 3, 4, 4, 0, 3, 0, 0, 1, 4, 1, 1, 4, 1, 2, 2, 2, 5, 4, 4, 3, 0, 5, 5, 2, 5, 0, 0, 0, 3, 0, 0, 2, 5, 2, 2, 0, 3, 4, 4, 2, 5, 4, 4, 4, 1, 0, 0, 4, 1, 2, 2, 0, 3, 0, 0, 3, 0, 3, 3, 2, 5, 0, 0, 2, 5, 4, 4, 5, 2, 1, 1, 0, 3, 4, 4)
s_{1, 0}	(0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 2, 5, 0, 0, 2, 5, 0, 0, 4, 1, 0, 0, 4, 1, 3, 3, 3, 0, 4, 4, 4, 1, 5, 5, 1, 4, 3, 3, 5, 2, 4, 4, 2, 5, 5, 5, 3, 0, 0, 0, 0, 3, 2, 2, 2, 5, 4, 4, 0, 3, 0, 0, 2, 5, 2, 2, 0, 3, 4, 4, 2, 5, 3, 3, 3, 0, 0, 0, 0, 3, 3, 3, 5, 2, 3, 3, 5, 2, 0, 0, 4, 1, 3, 3, 1, 4, 0, 0, 0, 3, 4, 4, 4, 1, 2, 2, 4, 1, 0, 0, 2, 5, 4, 4, 2, 5, 2, 2, 0, 3, 3, 3, 3, 0, 2, 2, 2, 5, 1, 1, 3, 0, 3, 3, 5, 2, 2, 2, 0, 3, 1, 1, 5, 2)
s_{1, 1}	(0, 3, 0, 0, 0, 3, 0, 0, 0, 3, 2, 2, 0, 3, 2, 2, 0, 3, 4, 4, 0, 3, 4, 4, 3, 0, 3, 3, 4, 1, 4, 4, 5, 2, 1, 1, 3, 0, 5, 5, 4, 1, 2, 2, 5, 2, 3, 3, 0, 3, 0, 0, 2, 5, 2, 2, 4, 1, 0, 0, 0, 3, 2, 2, 2, 5, 0, 0, 4, 1, 2, 2, 3, 0, 3, 3, 0, 3, 0, 0, 3, 0, 5, 5, 3, 0, 5, 5, 0, 3, 4, 4, 3, 0, 1, 1, 0, 3, 0, 0, 4, 1, 4, 4, 2, 5, 4, 4, 0, 3, 2, 2, 4, 1, 2, 2, 2, 5, 0, 0, 3, 0, 3, 3, 2, 5, 2, 2, 1, 4, 3, 3, 3, 0, 5, 5, 2, 5, 0, 0, 1, 4, 5, 5)
s_{1, 2}	(0, 0, 0, 3, 2, 2, 2, 5, 0, 0, 4, 1, 4, 4, 0, 3, 4, 4, 2, 5, 2, 2, 4, 1, 3, 3, 3, 0, 0, 0, 0, 3, 5, 5, 3, 0, 1, 1, 3, 0, 2, 2, 0, 3, 1, 1, 3, 0, 0, 0, 0, 3, 4, 4, 4, 1, 4, 4, 2, 5, 4, 4, 0, 3, 0, 0, 4, 1, 0, 0, 2, 5, 3, 3, 3, 0, 2, 2, 2, 5, 3, 3, 1, 4, 1, 1, 3, 0, 4, 4, 2, 5, 5, 5, 1, 4, 0, 0, 0, 3, 0, 0, 0, 3, 2, 2, 0, 3, 4, 4, 0, 3, 2, 2, 0, 3, 4, 4, 0, 3, 3, 3, 3, 0, 4, 4, 4, 1, 1, 1, 5, 2, 1, 1, 3, 0, 0, 0, 4, 1, 3, 3, 5, 2)
s_{1, 3}	(0, 3, 0, 0, 2, 5, 2, 2, 0, 3, 4, 4, 4, 1, 0, 0, 4, 1, 2, 2, 2, 5, 4, 4, 3, 0, 3, 3, 0, 3, 0, 0, 5, 2, 3, 3, 1, 4, 3, 3, 2, 5, 0, 0, 1, 4, 3, 3, 0, 3, 0, 0, 4, 1, 4, 4, 4, 1, 2, 2, 4, 1, 0, 0, 0, 3, 4, 4, 0, 3, 2, 2, 3, 0, 3, 3, 2, 5, 2, 2, 3, 0, 1, 1, 1, 4, 3, 3, 4, 1, 2, 2, 5, 2, 1, 1, 0, 3, 0, 0, 0, 3, 0, 0, 2, 5, 0, 0, 4, 1, 0, 0, 2, 5, 0, 0, 4, 1, 0, 0, 3, 0, 3, 3, 4, 1, 4, 4, 1, 4, 5, 5, 1, 4, 3, 3, 0, 3, 4, 4, 3, 0, 5, 5)
s_{1, 4}	(0, 0, 0, 3, 4, 4, 4, 1, 4, 4, 2, 5, 2, 2, 4, 1, 0, 0, 2, 5, 2, 2, 0, 3, 3, 3, 3, 0, 2, 2, 2, 5, 3, 3, 1, 4, 5, 5, 1, 4, 4, 4, 0, 3, 1, 1, 5, 2, 0, 0, 0, 3, 0, 0, 0, 3, 2, 2, 0, 3, 2, 2, 4, 1, 2, 2, 4, 1, 0, 0, 4, 1, 3, 3, 3, 0, 4, 4, 4, 1, 1, 1, 5, 2, 5, 5, 1, 4, 0, 0, 2, 5, 5, 5, 3, 0, 0, 0, 0, 3, 2, 2, 2, 5, 0, 0, 4, 1, 2, 2, 4, 1, 4, 4, 0, 3, 4, 4, 2, 5, 3, 3, 3, 0, 0, 0, 0, 3, 5, 5, 3, 0, 5, 5, 1, 4, 2, 2, 4, 1, 3, 3, 1, 4)
s_{1, 5}	(0, 3, 0, 0, 4, 1, 4, 4, 4, 1, 2, 2, 2, 5, 4, 4, 0, 3, 2, 2, 2, 5, 0, 0, 3, 0, 3, 3, 2, 5, 2, 2, 3, 0, 1, 1, 5, 2, 1, 1, 4, 1, 0, 0, 1, 4, 5, 5, 0, 3, 0, 0, 0, 3, 0, 0, 2, 5, 0, 0, 2, 5, 4, 4, 2, 5, 4, 4, 0, 3, 4, 4, 3, 0, 3, 3, 4, 1, 4, 4, 1, 4, 5, 5, 5, 2, 1, 1, 0, 3, 2, 2, 5, 2, 3, 3, 0, 3, 0, 0, 2, 5, 2, 2, 0, 3, 4, 4, 2, 5, 4, 4, 4, 1, 0, 0, 4, 1, 2, 2, 3, 0, 3, 3, 0, 3, 0, 0, 5, 2, 3, 3, 5, 2, 1, 1, 2, 5, 4, 4, 3, 0, 1, 1)

Table 1

Fig.1

Fig.2

Table 2

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来源	构造结果	集间性能参数	限定条件	构造基础
[23]	(LM, [M, N], [M, LM)-ZCZ	当$M=\lfloor L / N\rfloor$时, η=1	$N=\lfloor L / M\rfloor$	L×L阶DFT矩阵
[24]	(KLM, [KM, N], [M, KLM)-ZCZ	当$M=\lfloor L / N\rfloor$时, η=1	$N=\lfloor L / M\rfloor$，N≥2	L×L阶DFT矩阵, KM×KM阶正交矩阵
[25]	(TLP, [T, L], [P, TLP])-ZCZ	当gcd(T, P)=1时, η=1	gcd(L, P)=1	T×T阶正交矩阵, L×L阶DFT矩阵, 长度为P的完备序列
[26]	(2LP, [2M, L], [Z, 2LP])-ZCZ	当Z为偶数, $1< \left \lfloor \frac { P }{ Z }\right \rfloor < \frac { Z }{2 L }$且4L < Z 时, η=1; 当Z为奇数, $0 <\left \lfloor \frac { P }{ Z }\right \rfloor <\frac { Z }{2 L }$且2L < Z时, η=1	Z为偶数时, $ M =\left \lfloor \frac { P -2}{ Z }\right \rfloor $; Z为奇数时, $ M =\left \lfloor \frac { P -1}{ Z }\right \rfloor $; gcd(L, P)=1	L × L阶矩阵, 长度为P的完备序列
定理1	(QNL, [N, M], [(Z－1)L+1, QNL])-ZCZ	当L≠1时, $\eta>1-\frac{1}{Z}$; 当L=1时, η=1	Q=MZ, Z\|N, T>1	长度为L的N×N阶PU矩阵, Q×Q阶DFT矩阵
定理2	(QNL, [N, M], [(Z－1)NL+1, QNL])-ZCZ	$\eta \leqslant 1-\frac{1}{Z}$	-	长度矩阵, (Q, [N, M], [Z, Q])-PUZ和LZCZ

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Construction of uncorrelated multiple-subset zero correlation zone sequence sets

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