阵列偶及阵列偶相关理论研究

The perfect signal and its design play an important part in the optimizing design in the area of modernistic communication, radar, sonar, navigation, space ranging and controlling and electronically antagonism systems. It is of theoretical and application importance to study all kinds of sequence and array properties in depth. The most important application of the sequences and arrays is based on the coorelation properties of them,but such researches have some limitation because they are based on the research of the autocoorelation of single sequence or the crosscoorelation of multi-sequences.The theory of array pairs coorelation breaks out the concept of former equences,present to form the array pairs by two arrays, the autocoorelaiton function of the array pairs is defined by the crosscoorelation function of the two arrays. The concept of array paris extends the exist areas of the perfect signal,and the former perfect signal become its special types.Therefore,the theory of array pairs provide more perfect signal to the application areas such as communication engineering and so on.This project obtained many theory achievements in the area of array pairs, inclued:On the basis of perfect binary array pairs theory , the concepts of quasiperfect binary array pairs and doubly quasiperfect binary array pairs are presented ,the properties, construction and the relationship between them and perfect binary array pairs are studied.So the new construction of perfect binary array pairs are obtained. A new form of sequence pairs-punctured binary sequence pairs was defined,so the concepts of perfect punctured binary sequence pairs and odd-periodic perfect punctured binary sequence pairs are presented,and the propreties and construction are studied. A new form of array pairs-punctured binary array pairs was defined,so the concepts of perfect punctured binary array pairs and partial periodic perfect punctured binary sequence pairs are presented.,and the propreties and construction are studied. The quasi-perfect punctured binary array pairs and doubly quasi-perfect punctured binary array pairs are defined.Their properties and construction are studied,the realationship between them and perfect punctured binary array pairs is presented.The aperiodic auto-coorelation function of punctured binary sequence pairs is defined,the punctured binary comolementary sequence pairs is presented,and the properties and construction are studied. A new bolck design-differences set pairs is defined.The properties is studied.The relationship between differernces set pairs and perfect binary array pairs is given.The periodic complementary binary sequence pairs and differences family pairs are defined.The properties ,construction,and their relationship are studied. The optimization of binary sequences using genetic algorithms is presented.The high efficient searching algorithm of array pairs is designed,and the perfect binary array pairs ,quasi-perfect binary array pairs and other array pairs with certain volume are obtained.These theory achievements completed the theory of array pairs,enriched the perfect signal design theory,and provided more selectable signals for engineering application.

目前阵列偶和阵列偶相关理论的研究还不够深入和系统。本项目的研究内容是：创建一般情况下阵列偶相关函数的性质和特点；针对工程应用的需求，定义多种形式的最佳阵列偶（如循环相关、非循环相关、汉明相关、并元相关条件下，或多元条件下的最佳阵列偶），并研究它们的性质、构造方法和相互关系，以及工程应用等相关问题。