Research On The Design Of Complete Gaussian Integer Sequence Based On Cyclotomic Class And Difference Set

Complete Gaussian integer sequences have many applications in channel estimation,radar ranging,wireless communication and other fields.Gaussian integer sequences belong to the category of complex value sequences,the actual and imaginary parts are integers.Compared with the traditional unit circle complex root sequence,Gaussian integer sequences get rid of the sequence amplitude value constraint.In all sequences of the same length,Gaussian integer sequences are characterized by fast data transfer rates.In recent years,the construction of Gaussian integer sequences has attracted much attention,and Gaussian integer sequences with complete autocorrelation performance have become a research hotspot.Based on the analysis of the research status of Gaussian integer sequences and complete Gaussian integer sequences,this paper mainly studies the construction method of complete Gaussian integer sequences based on cyclotomic class and cyclic difference set.The main research contents are as follows:Firstly,two methods for constructing complete Gaussian integer sequences are introduced,one based on the classical cyclotomic class.Complete sequences of Gaussian integers of the third and fifth order are constructed by using the second-and fourth-order cyclotomic classes,respectively.The other is based on the cyclic difference set.The sufficient necessary conditions for the construction of a complete Gaussian integer sequence are clarified,and the second-order complete Gaussian integer sequence is obtained by selecting appropriate parameters,and extended to the third order by using the upsampling and filtering method.The correctness of the two construction methods is illustrated through theoretical derivation and program search examples,and the paper compares them with the construction methods in the existing literature.Secondly,on the basis of the above well-constructed Gaussian integer sequence,Second-order cyclotomic class is used to construct odd length complete Gaussian integer sequences..After analysis,the constructed odd-length complete Gaussian integer sequence has higher energy efficiency than the odd-length complete Gaussian integer sequence of the same length in the existing literature.Then,the interleaved method is used to extend the complete Gaussian integer sequence of odd orders to even levels,and derivations and examples are given.Finally,a near-complete Gaussian integer sequence is constructed based on a pseudo-random sequence,which has a small number of non-zero values in the sidelobe of the autocorrelation function,and the sequence has good balance.The correctness of the construction is proved by theoretical derivation and some examples are given.