低碰撞区跳频序列理论界及其设计
发布时间：2018-08-30 14:17
【摘要】：在跳频通信系统中,跳频序列扮演着非常重要的角色。跳频序列特性的好坏很大程度上决定了跳频通信系统多址干扰的大小,因而直接影响着跳频通信系统性能的优劣。跳频序列的研究主要包括跳频序列的理论界以及跳频序列的设计两个方面。在跳频序列的理论界方面,本文主要研究了低碰撞区跳频序列集关于最大非周期汉明相关函数的理论界、低碰撞区跳频序列集关于最大部分汉明相关函数的理论界以及无碰撞区跳频序列集的理论界等。在跳频序列的设计方面,本文主要研究了具有最优平均周期汉明相关的跳频序列集、具有最优最大周期汉明相关的低碰撞区跳频序列集、具有最优最大周期部分汉明相关的低碰撞区跳频序列集以及最优无碰撞区跳频序列集的构造与性能分析等。首先,建立了低碰撞区跳频序列集的序列数目、频隙个数、序列长度、低碰撞区和低碰撞区内的最大非周期汉明自相关函数值、最大非周期汉明互相关函数值这六个参数所满足的不等式,导出了低碰撞区跳频序列集关于最大非周期汉明相关函数值的新理论界。新界包含了跳频序列集在低碰撞区内的最大非周期汉明自相关函数值和最大非周期汉明互相关函数值的二次项。同时,导出了常规跳频序列集关于最大非周期汉明相关函数值的新理论界。建立了低碰撞区跳频序列集的序列数目、频隙个数、序列长度、低碰撞区和低碰撞区内的最大周期部分汉明自相关函数值、最大周期部分汉明互相关函数值这六个参数所满足的不等式,导出了低碰撞区跳频序列集关于最大周期部分汉明相关函数值的新理论界。这些新理论界与相应的已有的理论界相比较,更精确。另外,给出了无碰撞区跳频序列集的一些重要性质,讨论了现有的无碰撞区跳频序列集理论界,揭示了几个理论界之间的关系,给出了这些理论界之间的等价条件。接着,深入研究了跳频序列集的平均周期汉明相关函数的性质,给出了跳频序列集具有最优平均周期汉明相关的充分必要条件。基于有限域上的多项式理论,构造了一类具有最优平均周期汉明相关的跳频序列集。新型跳频序列集包括已有的3次+常数跳频序列集作为特殊情况。利用交织技术,给出了构造具有最优平均周期汉明相关特性的跳频序列集的新方法。利用新方法,构造了几类具有新参数的最优平均周期汉明相关跳频序列集。该构造方法包括了Chung和Yang的构造方法作为特殊情况。然后,基于m-序列及其抽样序列,分别构造了两类具有最优最大周期汉明相关的低碰撞区跳频序列集。新构造的低碰撞区跳频序列集具有新参数并且包括了Ding和Yin构造的跳频序列集作为特殊情况。另外,给出了构造最优无碰撞区跳频序列集的一般化方法。利用新构造方法,可以生成任意长度的最优无碰撞区跳频序列集。并且,任意一个最优无碰撞区跳频序列集,都可以由该一般化构造方法生成。最后,证明了在一定条件下不存在对所有相关窗长度关于理论界最优的低碰撞区跳频序列集。给出了低碰撞区跳频序列集具有严格最优平均周期部分汉明相关的充分条件。利用交织技术,给出了构造对所有相关窗长度关于理论界最优的低碰撞区跳频序列集的新方法。利用新的交织构造法,得到了几类对所有相关窗长度关于理论界最优的低碰撞区跳频序列集。利用交织技术,基于m-序列,构造了一类对某些特定的相关窗长度关于理论界最优的低碰撞区跳频序列集。另外,利用级联技术,给出了构造对某些特定的相关窗长度关于理论界最优的低碰撞区跳频序列集和具有严格最优平均周期部分汉明相关的低碰撞区跳频序列集的新方法。利用新的级联构造法,得到了几类对某些特定的相关窗长度关于理论界最优的低碰撞区跳频序列集。
[Abstract]:Frequency hopping sequences play a very important role in frequency hopping communication systems. The characteristics of frequency hopping sequences largely determine the size of multiple access interference in frequency hopping communication systems, and thus directly affect the performance of frequency hopping communication systems. In this paper, we mainly study the theoretical bounds of the maximum aperiodic Hamming correlation function, the theoretical bounds of the maximum Hamming correlation function and the frequency hopping sequence set in the low collision region. In this paper, we mainly study the frequency hopping sequence set with the optimal average period Hamming correlation, the frequency hopping sequence set with the optimal maximum period Hamming correlation, the frequency hopping sequence set with the optimal maximum period Hamming correlation, and the construction and performance analysis of the optimal frequency hopping sequence set with the optimal maximum period Hamming correlation. The inequalities of the six parameters of the frequency hopping sequence set in the low collision region, such as the number of sequences, the number of frequency gaps, the length of sequences, the maximum aperiodic Hamming autocorrelation function and the maximum aperiodic Hamming cross correlation function in the low collision region and the low collision region are derived. The new theorem includes the quadratic terms of the maximum aperiodic Hamming autocorrelation function and the maximum aperiodic Hamming cross correlation function of the frequency hopping sequence set in the low impact region. The inequalities satisfied by the six parameters, i.e. the number of columns, the number of frequency gaps, the length of sequences, the maximum periodic Hamming autocorrelation function in the low collision region and the maximum periodic Hamming cross correlation function in the low collision region, are derived. In addition, some important properties of frequency hopping sequence set in non-collision region are given, the existing theoretical bounds of frequency hopping sequence set in non-collision region are discussed, the relations among several theoretical bounds are revealed, and the equivalent conditions between these theoretical bounds are given. Then, the frequency hopping sequence set is studied in depth. The properties of the average periodic Hamming correlation function of a set are given. The necessary and sufficient conditions for the optimal average periodic Hamming correlation of a set of frequency hopping sequences are given. Based on the polynomial theory over finite fields, a class of frequency hopping sequences with optimal average periodic Hamming correlation is constructed. As a special case, a new method to construct a set of frequency hopping sequences with optimal mean periodic Hamming correlation is presented by using interleaving technique. By using the new method, several optimal mean periodic Hamming correlation frequency hopping sequences with new parameters are constructed. Based on m-sequences and their sampling sequences, two kinds of frequency-hopping sequences with optimal maximum period Hamming correlation are constructed. The newly constructed frequency-hopping sequences with new parameters and the frequency-hopping sequences with Ding and Yin constructions are considered as special cases. In addition, the optimal frequency-hopping sequence set with no collision region is constructed. By using the new construction method, the optimal set of frequency hopping sequences in collision-free region of arbitrary length can be generated. Moreover, any optimal set of frequency hopping sequences in collision-free region can be generated by the generalized construction method. Finally, it is proved that under certain conditions there is no low collision with respect to the optimal length of all correlation windows in the theoretical domain. A set of frequency hopping sequences in the region of low collision is presented. Sufficient conditions are given for the set of frequency hopping sequences in the region of low collision to have a strictly optimal mean periodic partial Hamming correlation. By using interleaving technique, a new method for constructing the set of frequency hopping sequences in the region of low collision with respect to all correlation window lengths is presented. By using interleaving technique and m-sequence, a kind of frequency hopping sequence set in low collision region with respect to the optimal length of some specific correlation windows is constructed. In addition, by using cascade technique, a low collision sequence set with respect to the optimal length of some specific correlation windows is constructed. A new method of frequency hopping sequence set in collision region and frequency hopping sequence set in low collision region with strict optimal mean periodic partial Hamming correlation is presented.
【学位授予单位】：西南交通大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN914.41
[Abstract]:Frequency hopping sequences play a very important role in frequency hopping communication systems. The characteristics of frequency hopping sequences largely determine the size of multiple access interference in frequency hopping communication systems, and thus directly affect the performance of frequency hopping communication systems. In this paper, we mainly study the theoretical bounds of the maximum aperiodic Hamming correlation function, the theoretical bounds of the maximum Hamming correlation function and the frequency hopping sequence set in the low collision region. In this paper, we mainly study the frequency hopping sequence set with the optimal average period Hamming correlation, the frequency hopping sequence set with the optimal maximum period Hamming correlation, the frequency hopping sequence set with the optimal maximum period Hamming correlation, and the construction and performance analysis of the optimal frequency hopping sequence set with the optimal maximum period Hamming correlation. The inequalities of the six parameters of the frequency hopping sequence set in the low collision region, such as the number of sequences, the number of frequency gaps, the length of sequences, the maximum aperiodic Hamming autocorrelation function and the maximum aperiodic Hamming cross correlation function in the low collision region and the low collision region are derived. The new theorem includes the quadratic terms of the maximum aperiodic Hamming autocorrelation function and the maximum aperiodic Hamming cross correlation function of the frequency hopping sequence set in the low impact region. The inequalities satisfied by the six parameters, i.e. the number of columns, the number of frequency gaps, the length of sequences, the maximum periodic Hamming autocorrelation function in the low collision region and the maximum periodic Hamming cross correlation function in the low collision region, are derived. In addition, some important properties of frequency hopping sequence set in non-collision region are given, the existing theoretical bounds of frequency hopping sequence set in non-collision region are discussed, the relations among several theoretical bounds are revealed, and the equivalent conditions between these theoretical bounds are given. Then, the frequency hopping sequence set is studied in depth. The properties of the average periodic Hamming correlation function of a set are given. The necessary and sufficient conditions for the optimal average periodic Hamming correlation of a set of frequency hopping sequences are given. Based on the polynomial theory over finite fields, a class of frequency hopping sequences with optimal average periodic Hamming correlation is constructed. As a special case, a new method to construct a set of frequency hopping sequences with optimal mean periodic Hamming correlation is presented by using interleaving technique. By using the new method, several optimal mean periodic Hamming correlation frequency hopping sequences with new parameters are constructed. Based on m-sequences and their sampling sequences, two kinds of frequency-hopping sequences with optimal maximum period Hamming correlation are constructed. The newly constructed frequency-hopping sequences with new parameters and the frequency-hopping sequences with Ding and Yin constructions are considered as special cases. In addition, the optimal frequency-hopping sequence set with no collision region is constructed. By using the new construction method, the optimal set of frequency hopping sequences in collision-free region of arbitrary length can be generated. Moreover, any optimal set of frequency hopping sequences in collision-free region can be generated by the generalized construction method. Finally, it is proved that under certain conditions there is no low collision with respect to the optimal length of all correlation windows in the theoretical domain. A set of frequency hopping sequences in the region of low collision is presented. Sufficient conditions are given for the set of frequency hopping sequences in the region of low collision to have a strictly optimal mean periodic partial Hamming correlation. By using interleaving technique, a new method for constructing the set of frequency hopping sequences in the region of low collision with respect to all correlation window lengths is presented. By using interleaving technique and m-sequence, a kind of frequency hopping sequence set in low collision region with respect to the optimal length of some specific correlation windows is constructed. In addition, by using cascade technique, a low collision sequence set with respect to the optimal length of some specific correlation windows is constructed. A new method of frequency hopping sequence set in collision region and frequency hopping sequence set in low collision region with strict optimal mean periodic partial Hamming correlation is presented.
【学位授予单位】：西南交通大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：TN914.41
【参考文献】
相关期刊论文 前6条
1 刘方;彭代渊;;一类具有最优平均汉明相关特性的跳频序列族[J];电子与信息学报;2010年05期
2 冯莉芳,汪晓宁,叶文霞,彭代渊;基于无碰撞区跳频码的准同步组网方案[J];西南交通大学学报;2004年06期
3 梅文华,杨义先,周炯i，
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