Correlation Of Costas Sequence And The Application In LTE

This thesis introduced several common sequences with good correlation properties, such as theGold 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 andthe number theory of principles and methods, the structure, generation methods and characteristicsof these sequences were discussed. In this thesis, the design methods of signals with a goodcorrelation were summarized, the results of all of these sequences in the calculation of theautocorrelation function and the cross-correlation function were explained, and the correspondingsimulation results were given, too. The research of the two-dimensional sequence—Costassequence was focused on in this thesis.Theory of structures of Welch Costas arrays with1-gap row or column and Golomb Costasarrays with1-gap row and1-gap column was established with the study of the properties andmathematical models of Welch Costas and Golomb Costas arrays and their families which areobtained by the cyclic shift method. By conducting a number of researches on the algebraicconstructions and the auto-and cross-correlation properties of Welch Costas arrays with1-gap rowor column and Golomb Costas arrays with1-gap row and1-gap column, certain theorems wereconfirmed. OFDM is one of the key technologies of LTE, and it’s very important to design areasonable frequency hopping code used in OFDM. Based on Costas sequences, an OFDMfrequency hopping signal was designed. The design of frequency hopping codes and the distributionof them to the users were illustrated while the design of frequency hopping patterns was explored inOFDM system with Welch Costas arrays with1-gap row or column and Golomb Costas arrays with1-gap row and1-gap column. By designing fre-quency hopping codes with Welch Costas arrayswith1-gap row or column and Golomb Costas arrays with1-gap row and1-gap column, analgebraically 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 restrictedin a wireless communication system.