【作者】 赵萌；

【导师】 贾彦国； 张继山；

【作者基本信息】 燕山大学 ， 工程硕士（专业学位）， 2019， 硕士

【摘要】 扩频通信具有抗阻塞性强、隐秘性好、可降低电磁干扰等优势,在蓝牙、移动宽带、测距定位、民用的数字蜂房等领域有着重要应用。因此,对信号的性能要求也在逐步提高,具有理想相关特性的信号逐渐成为学者们的研究重点。但是目前理想序列偶的研究成果还远不能满足工程需要,为此本课题的研究目的就是得到两种理想序列偶,即最佳屏蔽二进序列偶与伪随机屏蔽二进序列偶。首先,设计基于经典分圆和周期为pq的2-2阶广义分圆的屏蔽二进序列偶的搜索算法。经典分圆方法是先构造出屏蔽差集偶,再根据特征序列和屏蔽序列的定义得到屏蔽二进序列偶。周期为pq的2-2阶广义分圆方法中,广义分圆类是分圆类和中国剩余定理的结合。此方法与经典分圆法相比,可搜索出更多形式的屏蔽差集偶,从而扩大了最佳和伪随机屏蔽二进序列偶的搜索范围,得到了更多的实验结果。其次对经典分圆方法的实验数据进行分析归纳,找到(2f+1,f,f+1,f,f/2)、(5f+1,2f+1,4f+1,2f+1,f/2)等不同参数形式的屏蔽差集偶,提出六种最佳屏蔽二进序列偶与二种伪随机屏蔽二进序列偶的普遍规律,其主峰值可按参数表示为f、3f等。结合分圆数及最佳屏蔽二进序列偶、伪随机屏蔽二进序列偶存在的充分必要条件等相关知识,给出了详细的证明过程并列出实例加以说明。最后对广义分圆方法的数据集进行整理,归纳出(pq,(pq+1)/2,(3pq+p-q+1)/4,(pq+p-q+3)/4,(p+1)(q-1)/8)等不同参数形式的屏蔽差集偶,提出三种最佳屏蔽二进序列偶与一种伪随机屏蔽二进序列偶的普遍规律,其主峰值可按参数表示为(pq-p+q-1)/4,q等,并结合相应理论给出证明和实例。文中提出的两种构造方法,不仅可以得到最佳及伪随机屏蔽二进序列偶,也为搜索其它类型的屏蔽序列开辟了新的方向,提供了新的科研思路。更多还原

【Abstract】 Spread spectrum communication has the advantages of strong resistance to blocking,good privacy,and can reduce electromagnetic interference.It has important applications in bluetooth,mobile broadband,ranging and positioning,civil digital hive and other fields.Therefore,the performance requirement of the signal is also gradually improved,and the signal with ideal correlation characteristics has gradually become the research focus of scholars.However,the current research results of ideal sequence pairs are far from meeting the engineering needs.Therefore,the purpose of this study is to obtain two kinds of ideal sequence pairs,namely the perfect punctured binary sequence pairs and the pseudorandom punctured binary sequence pairs.Firstly,a punctured binary sequence pair search algorithm based on classical cyclotomy and 2-2 order generalized cyclotomy with period pq is designed.The method of classical cyclotomy is to first construct the punctured difference set pair and then get the punctured binary sequence pair according to the definition of the feature sequence and the punctured sequence.In the 2-2 order generalized cyclotomy with pq period,the generalized cyclotomic classes is the combination of the cyclotomic classes and the chinese residual theorem.Compared with the classical cyclotomy,this method can search more punctured difference set pairs,so as to expand the search scope of the perfect and pseudorandom punctured binary sequence pairs and obtain more experimental results.Secondly,the experimental data of classical cyclotomy method are analyzed and summarized,and punctured difference set pairs of different parameter forms are found(2f+1,f,f+1,f,f/2),(5f+1,2f+1,4f+1,2f+1,f/2).Six perfect punctured binary sequence pairs and two pseudorandom punctured binary sequence pairs are proposed.Their main peaks can be expressed as f,3f and so on.Combining the knowledge of cyclotomic number and the necessary and sufficient conditions for the existence of perfect punctured binary sequence pairs and pseudorandom punctured binary sequence pairs,a detailed proof process is given and illustrated with examples.Finally,the data sets of the generalized cyclotomy method are sorted out,andpunctured difference set pairs of different parameter forms are concluded(pq,(pq+1)/2,(3pq+p-q+1)/4,(pq+p-q+3)/4,(p+1)(q-1)/8).Three general rules of the perfect punctured binary sequence pairs and a pseudorandom punctured binary sequence pair are proposed.Their main peaks can be expressed as(pq-p+q-1)/4,q and so on.The proofs and realities are given in combination with relevant theories.The two construction methods proposed in this paper can not only obtain the perfect and pseudorandom punctured binary sequence pairs,but also open up a new direction and provide a new scientific research idea for searching other types of punctured sequences.更多还原