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

摘要/Abstract

摘要：

在多小区环境下的准同步码分多址(quasi-synchronous code-division multiple-access, QS-CDMA)系统中，不相关多子集零相关区(zero correlation zone, ZCZ)序列集不仅可以消除一定时延内来自相同小区的信号干扰，而且可以完全消除来自相邻小区的信号干扰。针对如何基于仿酉矩阵构造多子集ZCZ序列集的问题，设计了两种构造方法。具体地，通过构造具有一定特性的多个初始矩阵，再结合仿酉矩阵，进而利用不同的初始矩阵产生不同的ZCZ序列集，且序列集间互不相关。所提方法的核心是多个初始矩阵的设计，方法1通过对离散傅里叶变换(discrete Fourier transform, DFT)矩阵进行分块与叠加实现，方法2利用已有的不相关多子集ZCZ序列集实现。由两种方法得到的构造结果，其参数趋近于最优，为解决多小区环境下的干扰抑制问题提供了新的序列设计方法。

关键词: 准同步码分多址系统, 零相关区, 多子集零相关区序列集, 仿酉矩阵

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

中图分类号:

TN911.2

崔莉, 许成谦. 不相关多子集零相关区序列集的构造[J]. 系统工程与电子技术, 2024, 46(10): 3577-3585.

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

图/表 4

表1

由构造方法1得到的S(z)内各序列"

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)

表1

图1

图2

表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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