Ternary Signal Pairs And Supplementary Quaternary Array Theory

The perfect discrete signal and its design plays an increasingly important role in modern communications, radar, sonar, navigation, space ranging and controlling, and electronically countermeasures design optimization of other wired and wireless systems. Well-structured signals can enhance system's properties of anti-interference, anti-noise, anti-doubts, the decline of perform- ance such as resistance to the system, and increase data confidentiality and CDMA communications and synchronous communication and rapture can be achieved. Therefore, an in-depth study of the perfect discrete signals is of vital importance both in theory and applications. Over the past decades, the research has made great achievements and further in-depth study is underway at present.Perfect discrete signal research includes period-related signal, aperiod- related signal, related signal based on pairs and other such aspects. Perfect ternary sequence pairs, ternary complementary sequence pairs, periodic complementary ternary sequences, perfect complementary quaternary arrays are discussed in this thesis. This thesis only studied the theoretical issues rather than its engineering applications.In the research of signal pairs, a new kind of discrete signal is presented in this paper, which is perfect ternary sequence pairs and ternary complementary sequence pairs. The definition and its exiting necessary conditions of perfect ternary sequence pairs and ternary complementary sequence pairs were presented; Polynomial character of perfect ternary sequence pairs was given; The construction of perfect ternary sequence pairs by using array transform, Kronecker product, period product, foled transform, by recursion and other methods were presented; we also deduced the same, 2N and 2MN length ternary complementary sequence pairs by using its polynomial character.In the research of periodic complementary ternary sequences, the exiting necessary conditions of periodic complementary ternary sequences were discussed; Polynomial character of periodic complementary ternary sequences was given; The construction of periodic complementary ternary sequences by using period product and period product complementary companion sequences.In the research of two-dimensional perfect supplementary quaternary array, polynomial character of two-dimensional quasiperfect supplementary quatern- ary array was given; A new method for constructing two-dimensional perfect supplementary quaternary array by using of the properties of the two- dimensional perfect supplementary quaternary array and two-dimensional quasiperfect supplementary quaternary array.