Design Of Multilevel Optimal Sequence In Integer And 4~n-QAM Complementary Sequence Set

Complementary sequences and perfect sequences are used in communication systems as the optimal sequences with ideal correlation,and can effectively suppress multipath and multiple access interference during signal transmission.As a special form of Gaussian integer sequence,quadrature amplitude modulation(QAM)sequences can use amplitude and phase to transmit information at the same time,greatly improving the data transmission rate.16-QAM and 64-QAM sequences have been applied in the 3GPP communication standard,so the research on QAM sequence is of great significance.This paper has carried out theoretical research on the construction of multilevel periodic complementary pairs(PCPs),multilevel perfect sequences(MPSs)and QAM complementary sequences.First of all,based on the concept and characteristic of cyclotomy in combinational design theory,a kind of multilevel PCPs and MPSs of odd prime length in the integer set is put forward.Moreover,it is proven that under certain conditions,the constituent sequences of a PCP can be used to construct a perfect Gaussian integer sequence.Based on the constructed sequences,the length of multilevel PCPs and MPSs is extended.Secondly,based on binary sequence,a kind of 4~n-QAM mapping method is proposed,and different parameter values are defined for different base sequence lengths.4~n-QAM complementary sequences of even and odd length are constructed,which greatly increases the number of neutron sequences in complementary sequence.When the base sequence is non-binary,the mapping result is the Gaussian integer complementary sequence.Finally,based on binary and quaternary complementary sequence sets,4~n-QAM complementary sequences sets of even and odd length are proposed by filtering method.Two construction methods are proposed for the base sequence sets with odd length,which makes up the shortage of the length of the constructed sequence in the mapping method and provides more address code selection for practical engineering applications.