低/零相关区序列设计理论研究
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摘要
码分多址(CDMA)系统利用扩频序列实现多址传输，扩频序列的相关性直接决定了系统的抗干扰能力，因此构造具有良好相关性的扩频序列对于提高CDMA系统的性能和容量具有重要意义。本课题主要在低/零相关区序列设计、周期互补序列集设计、理想自相关序列设计、低/零相关区阵列集设计等方面进行研究。
首先，提出了新的移位不等价的低/零相关区序列集的构造方法。分别给出了长度为2和长度为P的移位序列的构造方法，其中，P大于等于2，满足P|L，L为低/零相关区长度，并利用交织方法构造多个移位不等价的低/零相关区序列集。在基于N2维交织矩阵的构造方法中，计算出不等价移位序列集数量的理论上界；在基于N P维交织矩阵的构造方法中，给出了低/零相关区序列集可以达到理论界的条件。与现有方法相比，两类低/零相关区序列集的构造方法均可以得到更多的适合多小区准同步码分多址通信系统的扩频序列集。
其次，提出了具有良好自相关性的高斯整数序列的设计方法。构造了两类特殊的高斯整数序列，即具有理想自相关性的平衡的四元序列和完备8-QAM/8-QAM+序列。通过对特殊高斯整数序列的研究，给出了一般型完备高斯整数序列的构造方法，该方法基于整数集上的多电平完备序列，并根据其周期的奇偶性，分别利用不同的组合和映射关系构造完备高斯整数序列，利用该方法可以得到新的完备高斯整数序列，从而实现了对现有完备高斯整数序列的数量的扩展。
再次，提出了低/零相关区高斯整数序列集的构造方法。基于不同的映射关系和二元二值自相关序列构造多个具有相同参数的四元低相关区序列集，所得到的低相关区序列集的参数可以灵活选择，同一个序列集中的序列移位不等价，不同的序列集间最多存在一个移位等价的序列；基于完备高斯整数序列构造了两类最佳或几乎最佳的零相关区高斯整数序列集，且序列集中的序列移位不等价；基于高斯整数周期互补序列集和高斯整数零相关区周期互补序列集，通过不同的移位或者映射操作，给出两种零相关区高斯整数周期互补序列集的构造方法。
最后，提出了新的零相关区阵列集的构造方法。基于完备阵列，构造了两类二维零相关区阵列集。两种方法均适用于高斯整数符号集上零相关阵列集的构造，并且所得到的阵列集均为最佳或几乎最佳的，阵列集的参数可以灵活选择以适应不同系统的要求。
In code division multiple access (CDMA) systems, multiple access transmissionactualizes by spreading sequences and the level of the interference is determined by thecorrelation of spreading sequence. Therefore, it is important to construct spreadingsequences with good correlation for the high-performance and the high-capacity of theCDMA system. In this thesis, we give a study on the design of sequence set with low orzero correlation zone (LCZ/ZCZ), periodic complementary sequence, sequence with idealautocorrelation, and LCZ/ZCZ array set.
Firstly, the construction methods of shift distinct LCZ/ZCZ sequence sets areproposed. Constructions of shift sequence with length2and P are proposed, where P2and P|L, L is the length of LCZ/ZCZ. Then multiple shift distinct LCZ/ZCZ sequencesets are constructed by using interleaving technique. The upper bound of the LCZ/ZCZshift sequence sets is computed for the construction based on N2interleaving matrix.The sufficient condition under which the LCZ/ZCZ shift sequence sets are optimal ispresented for the construction based on N Pinterleaving matrix. Compared withprevious constructions, the two new constructions provide more spreading sequences toquasi-synchronous code-division multiple-access (QS-CDMA) systems.
Secondly, the methods of constructing Gaussian integer sequence with goodautocorrelation are proposed. Balanced quaternary sequences with optimal autocorrelationvalue and perfect8-QAM/8-QAM+sequences, which are two classes of special Gaussianinteger sequences, are constructed. Then constructions of perfect Gaussian integersequences are presented. According to the parity of the multilevel perfect sequences overinteger, different mappings and combined methods are used for constructing perfectGaussian integer sequences. New Gaussian integer sequences are generated by theproposed construction and the number of the existing perfect Gaussian integer sequencesis extended.
Thirdly, the construction methods of LCZ/ZCZ Gaussian integer sequences areproposed. Based on a binary sequence with two-level autocorrelation, multiple quaternaryLCZ sequence sets with the same parameters are constructed by using different mappings. The parameters of the resultant LCZ sequence sets can be flexibly chosen. The sequencesfrom one quaternary LCZ sequence set are all shift distinct and there is only one shiftequivalent sequence from different sets. Furthermore, two classes of optimal or almostoptimal Gaussian integer sequence with ZCZ are constructed based on perfect Gaussiansequence. In addition, different shift or mapping operations are applied to Gaussianinteger periodic complementary sequence sets and ZCZ Gaussian integer periodiccomplementary sequence sets, then two classes of Gaussian integer periodiccomplementary sequence with ZCZ are constructed.
Finally, the construction methods of ZCZ array set are proposed. Based on perfectsequence, two classes of two dimensional ZCZ array sets are constructed. Both methodscan be used for constructing ZCZ array set over Gaussian integers. Moreover, the resultantarray sets are optimal or almost optimal and the parameters of the array sets can beflexibly chosen so as to meet different requirements in the application.
首先，提出了新的移位不等价的低/零相关区序列集的构造方法。分别给出了长度为2和长度为P的移位序列的构造方法，其中，P大于等于2，满足P|L，L为低/零相关区长度，并利用交织方法构造多个移位不等价的低/零相关区序列集。在基于N2维交织矩阵的构造方法中，计算出不等价移位序列集数量的理论上界；在基于N P维交织矩阵的构造方法中，给出了低/零相关区序列集可以达到理论界的条件。与现有方法相比，两类低/零相关区序列集的构造方法均可以得到更多的适合多小区准同步码分多址通信系统的扩频序列集。
其次，提出了具有良好自相关性的高斯整数序列的设计方法。构造了两类特殊的高斯整数序列，即具有理想自相关性的平衡的四元序列和完备8-QAM/8-QAM+序列。通过对特殊高斯整数序列的研究，给出了一般型完备高斯整数序列的构造方法，该方法基于整数集上的多电平完备序列，并根据其周期的奇偶性，分别利用不同的组合和映射关系构造完备高斯整数序列，利用该方法可以得到新的完备高斯整数序列，从而实现了对现有完备高斯整数序列的数量的扩展。
再次，提出了低/零相关区高斯整数序列集的构造方法。基于不同的映射关系和二元二值自相关序列构造多个具有相同参数的四元低相关区序列集，所得到的低相关区序列集的参数可以灵活选择，同一个序列集中的序列移位不等价，不同的序列集间最多存在一个移位等价的序列；基于完备高斯整数序列构造了两类最佳或几乎最佳的零相关区高斯整数序列集，且序列集中的序列移位不等价；基于高斯整数周期互补序列集和高斯整数零相关区周期互补序列集，通过不同的移位或者映射操作，给出两种零相关区高斯整数周期互补序列集的构造方法。
最后，提出了新的零相关区阵列集的构造方法。基于完备阵列，构造了两类二维零相关区阵列集。两种方法均适用于高斯整数符号集上零相关阵列集的构造，并且所得到的阵列集均为最佳或几乎最佳的，阵列集的参数可以灵活选择以适应不同系统的要求。
In code division multiple access (CDMA) systems, multiple access transmissionactualizes by spreading sequences and the level of the interference is determined by thecorrelation of spreading sequence. Therefore, it is important to construct spreadingsequences with good correlation for the high-performance and the high-capacity of theCDMA system. In this thesis, we give a study on the design of sequence set with low orzero correlation zone (LCZ/ZCZ), periodic complementary sequence, sequence with idealautocorrelation, and LCZ/ZCZ array set.
Firstly, the construction methods of shift distinct LCZ/ZCZ sequence sets areproposed. Constructions of shift sequence with length2and P are proposed, where P2and P|L, L is the length of LCZ/ZCZ. Then multiple shift distinct LCZ/ZCZ sequencesets are constructed by using interleaving technique. The upper bound of the LCZ/ZCZshift sequence sets is computed for the construction based on N2interleaving matrix.The sufficient condition under which the LCZ/ZCZ shift sequence sets are optimal ispresented for the construction based on N Pinterleaving matrix. Compared withprevious constructions, the two new constructions provide more spreading sequences toquasi-synchronous code-division multiple-access (QS-CDMA) systems.
Secondly, the methods of constructing Gaussian integer sequence with goodautocorrelation are proposed. Balanced quaternary sequences with optimal autocorrelationvalue and perfect8-QAM/8-QAM+sequences, which are two classes of special Gaussianinteger sequences, are constructed. Then constructions of perfect Gaussian integersequences are presented. According to the parity of the multilevel perfect sequences overinteger, different mappings and combined methods are used for constructing perfectGaussian integer sequences. New Gaussian integer sequences are generated by theproposed construction and the number of the existing perfect Gaussian integer sequencesis extended.
Thirdly, the construction methods of LCZ/ZCZ Gaussian integer sequences areproposed. Based on a binary sequence with two-level autocorrelation, multiple quaternaryLCZ sequence sets with the same parameters are constructed by using different mappings. The parameters of the resultant LCZ sequence sets can be flexibly chosen. The sequencesfrom one quaternary LCZ sequence set are all shift distinct and there is only one shiftequivalent sequence from different sets. Furthermore, two classes of optimal or almostoptimal Gaussian integer sequence with ZCZ are constructed based on perfect Gaussiansequence. In addition, different shift or mapping operations are applied to Gaussianinteger periodic complementary sequence sets and ZCZ Gaussian integer periodiccomplementary sequence sets, then two classes of Gaussian integer periodiccomplementary sequence with ZCZ are constructed.
Finally, the construction methods of ZCZ array set are proposed. Based on perfectsequence, two classes of two dimensional ZCZ array sets are constructed. Both methodscan be used for constructing ZCZ array set over Gaussian integers. Moreover, the resultantarray sets are optimal or almost optimal and the parameters of the array sets can beflexibly chosen so as to meet different requirements in the application.
引文
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