The Design Of Perfect Gaussian Integer Sequence With High Energy Efficiency Based On Cyclotomic Classes

With the increasing number of users and business types in the field of wireless communication,we have higher requirements for the capacity and performance of communication systems.Spread spectrum communication technology has gradually become the mainstream technology in the field of wireless communication due to its strong anti-interference and concealment.The optimal sequence has good autocorrelation and cross correlation,and can achieve good balance and equality for different symbol numbers.Therefore,it occupies an important position in the field of spread spectrum communication.The Perfect Gaussian Integer Sequence(PGIS)studied in this paper is one of the optimal sequences.This paper studies how to construct Perfect Gaussian Integer Sequences based on the classical cyclotomic class.Using the necessary and sufficient conditions derived from the definition of Perfect Gaussian Integer Sequences,the Gaussian Integer Sequences(GIS)are decomposed into real part sequences and imaginary part sequences,and then combined with the classical cyclotomic class to assign values respectively,thereby obtaining a new method for constructing Perfect Gaussian Integer Sequences.First of all,starting with the second order classical cyclotomic classes,based on even order cyclotomic,the conditions that a Perfect Gaussian Integer Sequence should meet are transformed into autocorrelation functions and cross correlation functions that real and imaginary part sequences should meet.The construction method of a Perfect Gaussian Integer Sequence based on the second order cyclotomic classes is studied,and the method is solved by using a computer within a limited sequence length and element value range,A Perfect Gaussian Integer Sequence with high energy efficiency is obtained.Secondly,a Perfect Gaussian Integer Sequence is constructed based on the third order classical cyclotomic classes,which represents the research on odd order classical cyclotomic in this design concept.By decomposing a Gaussian Integer Sequence into real part sequences and imaginary part sequences,a direct construction method based on third order classical cyclotomic is studied,and a computer is used to solve and verify the construction method to obtain a Perfect Gaussian Integer Sequence with high energy efficiency.Finally,the indirect construction method of Perfect Gaussian Integer Sequences is studied.This method obtains a shift sequence by shifting and interleaving a Perfect Gaussian Integer Sequence,and then modifies the coefficient matrix to obtain a new Perfect Gaussian Integer Sequence.It is also possible to construct a new Perfect Gaussian Integer Sequence with unchanged energy efficiency by constraining the absolute values of the expansion coefficients to be equal.