低碰撞区跳频序列部分汉明相关特性研究

发布时间：2018-07-13 19:57

【摘要】：由于具有较好的抗干扰性能、安全可靠性以及多址等诸多特性,跳频通信系统在军事通信领域和民用通信领域都有着广泛的应用。另一方面,跳频通信系统多址干扰的大小在一定程度上取决于系统所采用的跳频序列的汉明相关性能的好坏。因此,跳频序列在跳频通信系统中有着很重要的作用。为了满足实际通信环境的要求,低碰撞区跳频序列以及部分汉明相关的概念应运而生。此外,常规跳频序列集是低碰撞区跳频序列集在低碰撞区大小等于序列长度减去1时的特殊情况,而周期汉明相关(或非周期汉明相关)是部分汉明相关在相关窗长度等于序列长度(或序列长度减去时延长度)时的特殊情况。跳频序列的理论研究主要包括跳频序列的理论界以及设计能够达到或者接近理论界的跳频序列两个方面。本文主要研究了跳频序列集部分汉明相关函数平均值的理论界、低碰撞区跳频序列集部分汉明相关函数最大值的理论界、具有优良周期汉明相关性质的低碰撞区跳频序列集、具有最优部分汉明相关性质的低碰撞区跳频序列集以及具有优良非周期汉明相关性质的跳频序列集。首先,研究了常规跳频序列集在给定序列长度、序列个数、频隙个数的情况下,其部分汉明自相关函数的平均值及其部分汉明互相关函数的平均值应受的理论约束,建立了新的常规跳频序列集部分汉明相关函数平均值的理论界。研究了低碰撞区跳频序列集在给定序列长度、序列个数、频隙个数、低碰撞区大小、相关窗长度的情况下,其在低碰撞区内的部分汉明相关函数的最大值应受的理论约束,建立了新的低碰撞区跳频序列集部分汉明相关函数最大值的理论界。和已有的相关跳频序列理论界相比,这两个新的跳频序列理论界更紧。其次,基于m-序列的优异移位相加性质以及理想k元组分布特性,利用m-序列及其抽样序列,构造了两类具有最优周期汉明相关性质的低碰撞区跳频序列集。此外,利用m-序列的抽样序列,构造了一类在所有相关窗长度下都能具有最优部分汉明相关性质的低碰撞区跳频序列集。接着,研究了在有移位序列和没有移位序列的情况下,利用交织技术构造低碰撞区跳频序列集的方法,给出了三类拥有不同参数并且能够具有优良周期汉明相关性质的低碰撞区跳频序列集。然后,利用笛卡尔乘积理论,给出了三种新的低碰撞区跳频序列集的构造。其中,第一种构造重点关注了新构造的跳频序列集在低碰撞区内的周期汉明相关函数的最大值,而剩下的两种构造重点关注了新构造的跳频序列集在低碰撞区内的部分汉明相关函数的最大值。此外,基于有限域中的二次多项式,构造了一类具有最优部分汉明相关性质的跳频序列集并将其作为其中的一类基序列集。基于以上三种低碰撞区跳频序列集的构造,选择合适的基序列集,得到了六类新的低碰撞区跳频序列集。其中,前两类低碰撞区跳频序列集具有最优周期汉明相关性质,而剩下的四类低碰撞区跳频序列集在所有相关窗长度下都能具有最优部分汉明相关性质。最后,利用具有最优部分汉明相关性质的跳频序列集,研究了一种构造新的跳频序列集的方法。利用这种构造方法,我们可以对新的跳频序列集的参数进行灵活地选取,从而得到一大批新的跳频序列集。此外,在某些参数条件下,新的跳频序列集能够具有优良非周期汉明相关性质。基于已有的两类具有最优部分汉明相关性质的跳频序列集,得到了两类新的能够具有优良非周期汉明相关性质的跳频序列集。另外,只要选定了基序列集,借助于Matlab平台,我们可以将所有可能得到的新的跳频序列集的非周期汉明相关性能分析出来。这样就可以为选择合适的新的跳频序列集参数提供很大的便利。
[Abstract]:Because of its good anti-jamming performance, security, reliability and multiple access, frequency hopping communication systems are widely used in both military and civil communication fields. On the other hand, the size of multiple access interference in the frequency hopping communication system depends to some extent on the Hamming performance of the frequency hopping sequence used by the system. Therefore, the frequency hopping sequence plays an important role in the frequency hopping communication system. In order to meet the requirements of the actual communication environment, the frequency hopping sequence of the low collision area and some related concepts of Hamming have emerged. In addition, the conventional frequency hopping sequence set is the special of the low collision region frequency hopping sequence set at the lower collision area for 1 subtracted the sequence length. However, the periodic Hamming correlation (or the correlation of the non periodic Hamming) is the special case of some Hamming related window lengths equal to the length of the sequence (or the length of the sequence minus the length of the delay). The theoretical study of the frequency hopping sequence mainly includes the theoretical circle of the frequency hopping sequence and the design of two frequency hopping sequences that can reach or close to the theoretical circle. In this paper, we mainly study the theorists of the mean value of the Hamming correlation function of the frequency hopping sequence set, the theorists of the maximum value of the Hamming correlation function in the low collision region frequency hopping sequence set, the low collision zone frequency hopping sequence with good periodic Hamming correlation properties, and the low collision frequency hopping sequence set with the best part of the Hamming correlation. First, we study the theoretical constraints of the average value of the autocorrelation function and the mean value of some Hamming intercorrelation functions of the conventional frequency hopping sequence set in the case of the given sequence length, the number of sequence and the number of the frequency gap, and a new conventional frequency hopping sequence is established. The theoretical bounds of the mean value of the part of the Hamming correlation function are discussed. The theoretical constraints on the maximum value of the partial Hamming correlation function in the low collision area should be constrained by the theoretical constraints of the maximum value of the partial Hamming correlation function in the low collision area, and a new low collision Zone frequency hopping is established. The theorists of the maximum value of the partially Hamming correlation function of the sequence set. Compared with the theorists of the related frequency hopping sequences, the two new frequency hopping sequences have more tight theorists. Secondly, based on the excellent shift addition properties of the m- sequences and the distribution characteristics of the ideal K tuples, the two classes of optimal periodic Han Mingxiang are constructed by using the m- sequence and its sampling sequence. In addition, using the sampling sequence of m- sequences, a class of low collision frequency hopping sequences with the best part of Hamming correlation in all the correlation window lengths is constructed. Then, the interleaving technique is used to construct low collision zone jumping with the displaced sequence and no shift sequence. The method of frequency sequence set gives three classes of low collision frequency hopping sequences with different parameters and can have good periodic Hamming correlation properties. Then, three new low collision zone frequency hopping sequences are constructed by using the Descartes product theory. The first kind of construction focuses on the low frequency hopping sequence set in the new construction. The maximum value of the periodic Hamming correlation function in the collision area, while the remaining two structures focus on the maximum value of the partial Hamming correlation function of the new constructed frequency hopping sequence set in the low collision area. In addition, based on the two polynomial in the finite field, a class of frequency hopping sequences with the best part of the Hamming correlation is constructed and it is constructed. As a class of base sequence sets, based on the construction of the three low collision zone frequency hopping sequences, six kinds of new low collision zone frequency hopping sequences are obtained. Among them, the first two types of low collision zone frequency hopping sequences have the optimal periodic Hamming correlation property, while the remaining four class of low collision zone frequency hopping sequences are set at the same time. In the end, a new method of constructing a new frequency hopping sequence set is studied by using the set of frequency hopping sequences with the best part of Hamming correlation. By using this method, we can select a large number of parameters of the new frequency hopping sequence set so as to get a large number of them. In addition, under some parameter conditions, the new frequency hopping sequence sets can have excellent non periodic Hamming correlation properties. Based on the two classes of frequency hopping sequences which have the best part of the Hamming correlation, two classes of new frequency hopping sequences with excellent aperiodic correlation properties are obtained. With the help of the Matlab platform, we can analyze the non periodic Hamming performance of all the possible new frequency hopping sequences. This can provide a great convenience for selecting the appropriate new frequency hopping sequence set parameters.
【学位授予单位】：西南交通大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TN914.41

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