Research On Several Complementary Sequences On The Set Of Complex Numbers

The rapid development of today’s society requires more and more communication technology.As the foundation of communication technology,the design of spread spectrum codes plays a crucial role.The Gaussian integer sequence can send information using the phase and amplitude at the same time.Compared with the traditional address codes,it has high transmission efficiency and spectrum utilization.The quaternary sequences and Quadrature Amplitude Modulation(QAM)sequences widely used in communication are special forms of Gaussian integer sequence,but the design of the Gaussian integer complementary sequences is not a lot.In addition,with the commercial application of the Fifth generation mobile communications(5G),good inter-group characteristics can eliminate the information interference between multiple cells in practical applications.Designing more spread spectrum codes with inter-group characteristics has a great significance for the development of communication technology.In this paper,we construct several complementary sequences and complementary sequence sets on the set of complex numbers.First of all,we can obtain the sufficient and necessary conditions for the existence of Gaussian integer periodic complementary pairs and perfect Gaussian integer periodic sequence pairs based on the relation between cyclic difference sets and Gaussian integer periodic complementary pairs and the relation between cyclic difference set pairs and perfect Gaussian integer periodic sequence pairs respectively.When the conditions satisfied by using the computer search parameters,we can obtain Gaussian integer periodic complementary pairs and perfect Gaussian integer periodic sequence pairs.When the length of the sequence is odd,Gaussian integer periodic complementary pairs and perfect periodic sequence pairs are transformed into Gaussian integer odd-periodic complementary pairs and perfect odd-periodic sequence pairs by using the even-odd transformation,and they expand the number of sequences on the set of Gaussian integers.Secondly,we construct Inter-group Zero Correlation Zone Complementary(IGZC)sequence sets based on zero correlation zone sequence sets and integer sets.Using the method of grouping and linear phase transformation,we can obtain periodic IGZC sequence sets,which have a great significance for the application in multi-cell communication.Finally,based on the mapping method of three Quadrature Phase Shift Keying(QPSK)signals,a 64-QAM symbol can generated.Moreover,we present three methods to get more 64-QAM almost complementary sequences using three kinds of nonlinear offsets,the Peak-to-Mean Envelope Power Ratio(PMEPR)of which lies between 2.15 to 2.99,expanding the number of the 64-QAM almost complementary sequences and improving the code rate.