Study On The Correlation Properties Of Sequence Pair And The Ternary Signal Pair

The perfect discrete signal and its design play an important part in the area of modernistic communication, radar, sonar, navigation and electronically antagonism systems. An abundance of research results were published through several decades. But at present, the range of selecting perfect discrete signal is relatively narrow and the number of the perfect signals is not sufficient. The correlation properties of the sequence pair are the main research object in this paper. The paper integrates the perfect discrete signal design mode of the sequence pair with the ternary signals, and makes further study for the perfect discrete signals on the basis of the predecessor's research. The main work is as following;(1)The basic concepts of sequence pair, the correlation properties of the sequence pair and the applications of the sequence pair in the signal process and communication system are introduced.(2)The concepts of the periodic and aperiodic correlation function of q phase sequence pairs are presented. Based on these concepts, some corresponding quantities are defined. Using Levenshtein method, we deduce the theoretical evaluation of the bounds of correlation quantities of the sequence pairs and expand the bounds to the general sequence sets.(3)A new periodic correlation signal, pseudorandom ternary array pairs, is proposed. At first, some basic definitions are presented. Then the transformation and spectrum properties are studied. To reduce searching range and improve the efficiency, some admissibility conditions are given out. At last its uniqueness is proved. And a construction method is proposed.(4) A new kind of perfect correlate signal is presented in this paper, that is, odd-periodic perfect ternary sequence pairs. The transformation features are studied and the limited conditions are discussed. Based on this, we search out many odd-periodic perfect ternary sequence pairs with small length. The relationship between the odd-periodic perfect and periodic perfect ternary sequence pairs when the length of the sequence pairs is odd is also given. A construction method for periodic perfect ternary sequence pairs by using the odd-periodic perfect ternary sequence pairs is proposed, too.