Research On Perfect Gaussian Integer Sequences With High Energy Efficiency

With the rapid development of the times,people have higher and higher requirements for communication performance,and the quality of communication systems is closely related to sequence design.The Gaussian integer sequence(GIS)is a complex sequence whose real and imaginary parts are integers.GIS with excellent correlation characteristics is regarded as a new type of address code.Compared with traditional address codes,this address code can transmit information through phase and amplitude,resulting in higher spectrum utilization and transmission efficiency,providing more choices of address codes for orthogonal frequency division multiplexing(OFDM)systems and code division multiple access(CDMA)systems.This paper studies perfect Gaussian integer sequence(PGIS)with high energy efficiency,and analyzes its performance and application.The main content of the paper is as follows:Firstly,based on cyclic difference sets,a necessary and sufficient condition for constructing PGIS with unrestricted real and imaginary parts and 2 degrees is proposed.By this necessary and sufficient condition,a PGIS with high energy efficiency is obtained,and a fast algorithm for generating PGIS is obtained by analyzing the PGIS parameters obtained from cyclic difference sets.At the same time,it is proved that the PGIS constructed based on cyclic difference sets does not have equal amplitude properties.In addition,based on the constructed PGIS,a class of optimal Gaussian integer sequence pairs is obtained.Secondly,based on the methods of direct product,filtering,interleaving,and frequency domain analysis,the length of a high-energy efficient PGIS with 2 degrees constructed by cyclic difference sets is extended,and more PGIS with higher energy efficiency and different degrees is obtained.Finally,by cyclic difference sets,we obtain Gaussian integer periodic complementary sequences that can be applied to the OFDM system.At the same time,by the PGIS with high energy efficiency obtained in this article,a Gaussian integer complementary sequence set of low-column PMEPR that can be effectively applied to the MC-CDMA system is obtained by interleaving and shifting methods.