【作者】 刘涛；

【导师】 许成谦；

【作者基本信息】 燕山大学 ， 电子科学与技术， 2020， 博士

【摘要】 具有良好相关性能的序列在无线通信、雷达、密码等众多领域都有着十分重要的应用。在无线通信系统中往往采用序列来做为导频信号或扩频码,序列相关函数值的大小直接决定了系统干扰水平的高低,因而序列相关性能的好坏影响着通信系统的性能。本文针对几类具有良好相关性的序列设计方法展开研究。首先,研究了具有集间零相关区的二元ZCZ序列集构造方法。基本思路是根据基于互补序列的ZCZ序列集构造框架,通过构造具有良好集间互相关性的二元互补序列集,从而对应得到具有良好集间互相关性能的二元ZCZ序列集。具体的,一方面利用二元正交矩阵构造了集合数目大于2的多个二元互补序列集,不同集合间具有正交性,进而利用ZCZ序列集的构造框架得到了集合数目大于2的具有集间正交性的二元ZCZ序列集。另一方面通过构造具有集间零相关区的二元互补序列集,进而构造了具有集间零相关区的二元ZCZ序列集。每个ZCZ序列集参数都是最优的,集间零相关区长度仅比理论最大值小1。其次,研究了具有集间低相关性的多相ZCZ序列集构造方法。基本思路是根据基于DFT矩阵的多相ZCZ序列集构造框架,通过推导得到影响ZCZ序列集集间互相关函数值大小的关键因素,即集间互相关函数幅度值与映射函数的汉明相关性有关。通过利用跳频序列集构造了4类映射函数,进而对应构造出4类具有集间低相关性的多相ZCZ序列集,每个ZCZ序列集参数都是最优的。该构造方法可以进行推广,只要构造出其他满足条件的映射函数,就可以利用本方法得到新的具有集间低相关性的ZCZ序列集。再次,研究了具有低相关性的准互补序列集构造方法。一方面,基于有限域GF(p)上的映射函数构造了一类具有多子集结构的互补序列集。不同子集间具有低相关性质,将多个子集合并则可以得到一个参数达到渐进最优的非周期低相关互补序列集。另一方面,基于二元正交矩阵,提出了一类二元非周期低相关区互补序列集构造方法,得到的序列集参数也是达到渐进最优的。与多相序列相比,二元序列具有方便应用的优点,因而在实际的通信系统中应用价值更大。最后,研究了高斯整数集上的序列构造方法。基本思想是利用序列与组合设计之间的联系,利用差集、差族等集合定义高斯整数序列、高斯整数互补序列,进而利用组合设计理论推导出完备高斯整数序列、高斯整数互补序列的存在条件,最终通过寻找满足条件的高斯整数来赋值得到相应的完备高斯整数序列和高斯整数互补序列。具体的,利用差集构造了三类具有不同参数的完备高斯整数序列。基于差族构造了周期性高斯整数互补序列。更多还原

【Abstract】 Sequences with good correlations have important applications in wireless communications、radar and cryptograph.In wireless communication systems,sequences are used as pilot sequence and spreading code.The inference level in these systems is determined by the correlation amplitude of sequences used.As a result,the performance of a communication system is directly affected by the spreading sequence set used in the system.This dissertation researches the constructions of several classes of sequences with good correlations.Firstly,multiple binary zero correlation zone(ZCZ)sequence sets with inter-set zero correlation zone are investigated.The basic idea is using the generic construction framework of binary ZCZ sequence from binary complementary sequence sets.Mutiple binary complementary sequence sets with good inter-set cross-correlation properties are constructed at first,then multiple ZCZ sequence sets with good inter-set cross-correlation property are obtained by using the ZCZ construction framework accordingly.Concretely,more than 2 binary complementary sequence sets with inter-set orthogonality are constructed from binary orthogonal matrices,based on which more than 2 binary ZCZ sequence sets with inter-set orthogonality are obtained.Futhermore,multiple binary ZCZ sequence sets with inter-set ZCZ are constructed from complementary sequence sets with inter-set ZCZ.Note that all these ZCZ sequence sets are optimal according to the theoretical bounds.The length of inter-set zero cross correlation zone is only 1 less than that of the maximum length according to the theoretical bound.Secondly,multiple polyphose ZCZ sequence sets with inter-set low correlation amplitudes are studied.The basic idea is using the generic construction of ZCZ sequence sets from DFT matrices.We deduce the key factor effecting the inter-set correlation amlitudes from the generic construction,which is the hamming correlations of mapping functions used.Thus,4 classes of mapping functions are proposed by using frequency hopping sequence sets,by which 4 class of multiple polyphase ZCZ sequence sets with inter-set correlation amplitudes are constructed.The presented method will be extended,once new mapping functions are constructed,one can obtain new ZCZ sequence sets from the proposed constructing method accordingly.Then,quasi-complementary sequence sets(QCSSs)with low correlation properties are researched.Based on mapping functions on the finite field GF(p),a class of multiple complete complementary code with inter-set low correlation amplitudes are constructed.An aperiodic QCSS with asymptotically optimal parameters are obtained by combining these complete complementary codes.On the other hand,a construction of binary low correlation zone(LCZ)complementary sequence sets based on binary orthogonal matrices are given.Compared with polyphase sequences,binary sequences are more desired in practice because of easy realization.Finally,the design of Guassian integer sequences is concerned.The basic idea is using the relationship between combinatorial design and Guassian integer sequences.Gaussian integer sequences are defined based on difference sets and difference families,then the sufficient conditions of perfect Gaussian integer sequences and Gaussian integer complementary sequences are deduced.At last,perfect Gaussian integer sequences and Gaussian integer complementary sequences are obtained by searching sutitable Gaussian integers.Concretely,3 class of perfect Gaussian integer sequences are constructed from difference sets.Moreover,Gaussian integer complementary sequences are constructed by using difference families.更多还原