Research On Perfect Guassian Integer And Gaussian Integer Periodic Sequence Set

A Guassian integer sequence is complex sequence of the form a+bj,where a,b?Z.Z represents the integer domain.A Gaussian integer sequence with good correlation characteristics can be Aplied to orthogonal frequency division multiplexing systems and code division multiple access systems as new address codes.Compared with traditional address codes,it has high transmission efficiency and high spectrum utilization.The widely used four-element sequence and Quadrature Amplitude Modulation(QAM)sequence are special forms of Gaussian integer sequences.The possession of good correlation characteristics and the inclusion of a greater number of sequence sets is of great significance for the performance and cAacity of communication systems.This pAer combines the combination design method and the sequence design concept in mathematics,focusing on the design of complete Gaussian integer sequences and Gaussian integer complementary sequence sets.Firstly,based on the concept and properties of the circular class in the combined design a Perfect sequence of Gaussian integers(PGIS)in the form of new parameters is proposed,and the sequence of odd long complete Gaussian integers is extended to even length by coefficient sequence and interleaving method,and a large amount of high energy is obtained.A sequence of efficient Gaussian integers with a maximum energy efficiency close to 1.Secondly,based on the existing complete sequence and periodic sequence set(one is Gaussian integer sequence),a new shift sequence is constructed by Euler's theorem,and then a multiplication coefficient and interleaving shift operation is used to obtain a kind of A method of transitioning from a traditional sequence to a Gaussian integer domain.In order to verify the feasibility of this method,this pAer selects various types of sequences and periodic sequence sets as the base sequence,constructs the corresponding Gaussian integer sequence and Gaussian integer periodic sequence set,and then from the sequence form,low Peak-to-Mean Envelope Power Ratio(PMEPR),theoretical limits of sequence sets and other aspects are analyzed,and compared with the results of other literatures,it is proved that the construction method is feasible.Finally,this pAer combines the nature of the circular idea and the difference set couple,and proposes three kinds of binary complementary sequences.Based on the special binary complementary sequence of construction,a class of Gaussian integer periodic Zero Correlation Zone(ZCZ)Complementary sequence set is obtained by using the zero insertion method and the filtering method.