Constructions of Two Optimal Zero Correlation Zone Aperiodic Complementary Sequence Sets
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摘要: 该文基于正交矩阵，通过不同的矩阵变换的方法，提出两类零相关区(ZCZ)非周期互补序列集(ZACSS)的构造方法。在正交矩阵的阶能够被零相关区长度整除的条件下，所得序列集参数均能达到最优，且零相关区长度可以灵活选择。第1种方法构造的序列集具有理想的自相关互补性，通过进一步分组，可以得到多个组内互补的序列集。利用初始矩阵和正交矩阵的多样性能够构造出大量的最优零相关区非周期互补序列集，可应用于多载波码分多址(MC-CDMA)系统作为用户地址码来消除多径干扰和多址干扰。Abstract: Based on orthogonal matrices, constructions of two Zero Correlation Zone (ZCZ) Aperiodic Complementary Sequence Sets (ZACSS) are proposed through different matrix transformation methods. Under the condition that the order of the orthogonal matrices can be evenly divided by the length of the zero-correlation zone, the parameters of obtained sequence sets are optimal, and the length of the ZCZ can be chosen flexibly. The sequence sets are constructed by the first method have ideal autocorrelation complementarity, and by further grouping, a set of intra-group complementary sequence sets can be obtained. A large number of optimal ZACSS can be constructed by different kinds of initial matrices and orthogonal matrices. The resultant sequence sets proposed in this paper can be applied to Multi-Carrier Code Division Multiple Access (MC-CDMA) systems as user address codes to eliminate multipath interference and multiple access interference.
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表 1 ZACSS构造方法的比较
文献构造方法 构造基础 构造结果参数 是否达到最优 ZCZ长度 文献[10] 两个$N \times N$的正交矩阵 $\left( {[{N \mathord{\left/ {\vphantom {N Z}} \right. } Z},N],Z} \right) - {\text{IGC}}_N^N$ 是 灵活：$Z$ 文献[11]
构造方法1$Q \times Q$和$L \times L$的正交矩阵，$Q = pZ$, $L = NZ$ $\left( {pNZ,Z} \right){\text{ACS}}_Q^L$ 是 灵活：$Z$ 文献[11]
构造方法2$Q \times Q$和$L \times L$的正交矩阵，$Q = {p^n}Z$, $L = NZ$ $\left( {{p^n}NZ,Z} \right){\text{ACS}}_Q^L$ 是 灵活：$Z$ 文献[13] 2元$\left( {T,Z} \right){\text{ACS}}_M^N$ 4元$\left( {T,Z} \right){\text{ACS}}_M^N$ $T = M\left\lfloor {{N \mathord{\left/ {\vphantom {N Z}} \right. } Z}} \right\rfloor $时最优 固定：Z 文献[14]
构造方法1$D \times D$的正交矩阵，$\left( {M,L} \right){\text{ACS}}_N^L$且$\gcd \left( {L,D} \right) = 1$ $\left( {MD,L} \right){\text{ACS}}_N^{LD}$ $M = N$时
最优固定：L 文献[16] 完备互补序列集${\text{PC}}\left( {M,L} \right)$ $\left( {[{2^n},{2^n}M],Z} \right){\text{IaGC}}_{{2^n}M}^{{2^n}L}$ 组内最优 $\left\{ {1,2,4, \cdots ,{2^{n - 1}}} \right\}$ 文献[19] ${2^n} \times {2^n}$Hadamard矩阵，长度为$N$，ZCZ长度为$Z$ 的2元互补序列偶，$ N = {2^\alpha }{10^\beta }{26^\gamma } + 1 $ $\left( {{2^{n + 1}},Z} \right){\text{ACS}}_{{2^{n + 1}}}^N$ 是 固定：$Z$ 本文
构造方法1矩阵$ {{\mathbf{U}}_{H \times Z}} $和${{\mathbf{V}}_{H \times H}}$，两个$Q$阶正交矩阵,$Z|Q$ $\left( {HQ,Z} \right){\text{ACS}}_Q^Q$ 是 灵活：可任意 本文
构造方法2正交矩阵${{\mathbf{A}}_{Q \times Q}}$和${{\mathbf{B}}_{L \times L}}$,$L = NZ$, $ Q=HZ $ $\left( {HL,Z} \right){\text{ACS}}_Q^L$ 是 灵活：可任意 
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