Research On ZCZ Array Pair And Complementary Sequence Pair Theory

The perfect discrete signal and its design plays an very important role in modern communications, radar, space ranging and controlling, signal processing, information encryption and electronically countermeasures design optimization. Therefore, an in-depth research on the characters of sequences or arrays and providing more perfect discrete signals with good correlation character for engineering application is of very importance both in theory and applications.Combined with newly proposed zero correlation zone(ZCZ) sequence and array theory and the signal design idea based on array pair correlation, the problems of ZCZ array pair theory and several kinds of complementary sequence pairs theory is mainly studied in this thesis. The primary results include:1) The concept of ZCZ array pair is proposed, and it's properties and construction methods are presented with theory confirmation. By using perfect periodic autocorrelation array pair and orthogonal matrix, several ZCZ array pair sets with rectangle zero correlation zone can be obtained based on inteleaved method. ZCZ array pairs set with certain volume, family size and zero correlation zone can be synthesized through choosing suitable shift sequences. The proposed technique not only can expand the exist scope of ZCZ array pair, but also can be applied to the construction of ternary, quaternary, polyphase ZCZ array pair and ZCZ array.2) The concept of binary complementary sequence pair sets is defined, the properties and construction methods are studied also. Based on these techniques, binary complementary sequence pair sets with larger sequence pair number and length can be synthesized, the theoretical proof and examples are proposed also. The research results show that a great many binary complementary sequence pair sets can be constructed through these methods.3) A new concept of binary complementary sequence pair set's mate is defined under aperiodic correlation condition. Several construction methods for mate are proposed and proved by using concatenation and interleaving techniques. Through these methods a great many binary complementary sequence pair sets and mates can be generated. By using some examples these methods are illustrated. Compared with traditional complementary sequence set, it has wider existence space. Some construction methods for binary complementary sequence pair sets based on set's mate are proposed also.4) The concept of odd-periodic binary complementary sequence pair is proposed, its transformation properties and the relationship with aperiodic and periodic binary complementary sequence pair are studied. Several construction methods are presented, and some odd-periodic binary complementary sequence pair with small volume are searched out through the method of eliminating equivalent classes. Some conjectures and conlusions are obtained by the analization of searching results. The concept of odd-periodic binary complementary sequence pair sets and mates is defined, and several construction methodes are proposed. The research results show that lots of odd-periodic binary complementary sequence pair sets and mates can be obtained through these methods.All the results above are important, for they perfected the theory of array pair and extended the select scope of perfect discrete signal.