Study On Signals With Good Correlation

This thesis introduced several common sequences with good correlation properties, such as the Gold sequence, GMW sequences, Kasami sequence, Bent sequences, Barker sequence, m sequences, Costas sequence, which were widely used in data encryption, spread spectrum communication, radar, sonar and wireless communication. By using the knowledge of shift registers, finite fields and the number theory of principles and methods, the structure, generation methods and characteristics of these sequences were discussed. In this thesis, the design methods of signals with a good correlation were summarized, the results of all of these sequences in the calculation of the autocorrelation function and the cross-correlation function were explained, and the corresponding simulation results were given, too. The research of the two-dimensional sequence-Costas sequence was focused on in this thesis.Theory of structures of Welch Costas arrays with 1-gap row or column and Golomb Costas arrays with 1-gap row and 1-gap column was established with the study of the properties and mathematical models of Welch Costas and Golomb Costas arrays and their families which are obtained by the cyclic shift method. By conducting a number of researches on the algebraic constructions and the auto- and cross-correlation properties of Welch Costas arrays with 1-gap row or column and Golomb Costas arrays with 1-gap row and 1-gap column, certain theorems were confirmed. The design of frequency hopping codes and the distribution of them to the users were illustrated while the design of frequency hopping patterns was explored in OFDM system with Welch Costas arrays with 1-gap row or column and Golomb Costas arrays with 1-gap row and 1-gap column. By designing fre-quency hopping codes with Welch Costas arrays with 1-gap row or column and Golomb Costas arrays with 1-gap row and 1-gap column, an algebraically constructed fre-quency hop code family can achieve ideal auto-correlation properties. And excellent cross-correlation performance can be obtained when the Doppler shifts are restricted in a wireless communication system.