Construction of Optimal Zero Correlation Zone Aperiodic Complementary Sequence Sets
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摘要:
该文基于正交序列集，研究了一类新的零相关区(ZCZ)非周期互补序列(ZACS)集构造方法，所得到的序列集参数达到最优，且在满足Z|N的条件下零相关区长度可以灵活选择。该方法所构造的序列具有理想的自相关性能和组内互补特性。通过调整参数q，可得到多个不同的序列集。同时，基于多电平完备序列，给出了一类高斯整数正交序列集的构造方法，得到的高斯整数正交序列集可以用于非周期互补序列集的构造。所提方法构造的零相关区非周期互补序列集用于多载波码分多址系统中可以降低多径干扰、多址干扰，也可以作为训练序列用于多输入多输出信道估计中。
Abstract:The construction of ZCZ Aperiodic Complementary Sequence (ZACS) sets are researched based on orthogonal matrices. The proposed approach can provide optimal ZACS sets and the length of ZCZ can be chosen flexibly under the condition of Z|N. The resultant sequence sets have ideal autocorrelation properties and intra-group complementary properties. By adjusting the parameter q, different ZACS sets can be obtained. Moreover, based on the multilevel perfect sequence over integer, Gaussian integer orthogonal matrix is constructed which can be used as the initial sequence in the construction of ZACS. The sequence sets can be applied to Multi-Carrier Code Division Multiple Access (MC-CDMA) system to remove multipath interference and multiple access interference. Furthermore, it can be used as training sequence in Multiple Input Multiple Output (MIMO) channel estimation.
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表 1 零相关区非周期互补序列集参数比较
文献定理 构造基础 结果序列参数 是否达到最优 ZCZ选择是否灵活 文献[8]方法1 正交矩阵${{A}_{{Q} \times {Q}}}$和${{H}_{{L} \times {L}}}$, $Q = pZ$，$L = NZ$ $(pNZ,Z){\rm{ACS}}_Q^L$ 是 是 文献[9] 格雷序列和正交矩阵${{U}_{{V} \times {V}}}$ $(KL,Z){\rm{ACS}}_N^{KZ}$ $L = N$时最优 是 文献[10] 完备互补序列集${\rm{PC}}(M,L)$和正交矩阵${{A}_{{P} \times {P}}}$ $([M,P],L){\rm{IGC}}_M^{LP}$ 是 否 文献[12] 完备互补序列集${\rm{PC}}(M,L)$ $([{2^n},{2^n}M],Z){\rm{IaGC}}_{{2^n}M}^{{2^n}L}$ 组内最优 否 文献[13]方法1 ZACS序列集参数$(M,Z){\rm{ACS}}_P^N$ $(2M,Z){\rm{ACS}}_{2P}^{2N}$ 否 否 文献[13]方法2 ZACS序列集参数$(M,Z){\rm{ACS}}_{2P}^N$ $(M,2Z){\rm{ACS}}_{2P}^{2N}$ $M = 2P\left\lfloor {{N/Z}} \right\rfloor $时最优 否 文献[14] ZACS序列集参数$(T,Z){\rm{ACS}}_M^N$ $(T,Z){\rm{ACS}}_M^N$ $T = M\left\lfloor {{N/Z}} \right\rfloor $时最优 否 本文 正交矩阵${A_{{N} \times {N}}}$和正交序列集$B$, $N = LZ$, $T = KZ$ $(LT,Z){\rm{ACS}}_N^T$ 是 是 
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