Constructions of Gaussian Integer Periodic Complementary Sequences Based on Difference Families
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摘要:
该文给出了基于差族的高斯整数互补序列构造方法。利用差族与互补序列之间的联系，首先推导出高斯整数互补序列存在的充分条件，进而直接构造了阶数为2的高斯整数互补序列。为进一步增加高斯整数互补序列数目，又利用映射方法构造了阶数为4的高斯整数互补序列。同传统的2元互补序列相比，高斯整数互补序列的存在数目很多，因此该文方法可以为通信系统提供大量的互补序列。
Abstract:Constructions of Gaussian integer periodic complementary sequences are presented in this paper. Based on the relationship between periodic complementary sequences and difference families, the sufficient condition of the existence of Gaussian integer periodic complementary sequences is proposed at first, then Gaussian integer periodic complementary sequences with degree 2 are constructed directly. To extend the number of Gaussian integer complementary sequences, Gaussian integer complementary sequences with degree 4 are constructed based on mappings. Compared with binary complementary sequences, there are more Gaussian integer complementary sequences, as a result, the presented methods will propose an abundance of complementary sequences for communication systems.
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表 1 满足式(6)的高斯整数
${\alpha _0}$ ${\alpha _1}$ ${\beta _0}$ ${\beta _1}$ –2 –1 1 0 –2 –1 1 2 –2 1 1 –2 –2 1 1 0 –1 –2 0 1 –1 –2 2 1 –1 2 0 –1 –1 2 2 –1 1 –2 –2 1 1 –2 0 1 1 2 –2 –1 1 2 0 –1 2 –1 –1 0 2 –1 –1 2 2 1 –1 –2 
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