Research On Multiple Sequence Sets With Good Inter-set Cross-correlations And Gaussian Integer Sequences

Sequences with good correlations have important applications in wireless communications、radar and cryptograph.In wireless communication systems,sequences are used as pilot sequence and spreading code.The inference level in these systems is determined by the correlation amplitude of sequences used.As a result,the performance of a communication system is directly affected by the spreading sequence set used in the system.This dissertation researches the constructions of several classes of sequences with good correlations.Firstly,multiple binary zero correlation zone(ZCZ)sequence sets with inter-set zero correlation zone are investigated.The basic idea is using the generic construction framework of binary ZCZ sequence from binary complementary sequence sets.Mutiple binary complementary sequence sets with good inter-set cross-correlation properties are constructed at first,then multiple ZCZ sequence sets with good inter-set cross-correlation property are obtained by using the ZCZ construction framework accordingly.Concretely,more than 2 binary complementary sequence sets with inter-set orthogonality are constructed from binary orthogonal matrices,based on which more than 2 binary ZCZ sequence sets with inter-set orthogonality are obtained.Futhermore,multiple binary ZCZ sequence sets with inter-set ZCZ are constructed from complementary sequence sets with inter-set ZCZ.Note that all these ZCZ sequence sets are optimal according to the theoretical bounds.The length of inter-set zero cross correlation zone is only 1 less than that of the maximum length according to the theoretical bound.Secondly,multiple polyphose ZCZ sequence sets with inter-set low correlation amplitudes are studied.The basic idea is using the generic construction of ZCZ sequence sets from DFT matrices.We deduce the key factor effecting the inter-set correlation amlitudes from the generic construction,which is the hamming correlations of mapping functions used.Thus,4 classes of mapping functions are proposed by using frequency hopping sequence sets,by which 4 class of multiple polyphase ZCZ sequence sets with inter-set correlation amplitudes are constructed.The presented method will be extended,once new mapping functions are constructed,one can obtain new ZCZ sequence sets from the proposed constructing method accordingly.Then,quasi-complementary sequence sets(QCSSs)with low correlation properties are researched.Based on mapping functions on the finite field GF(p),a class of multiple complete complementary code with inter-set low correlation amplitudes are constructed.An aperiodic QCSS with asymptotically optimal parameters are obtained by combining these complete complementary codes.On the other hand,a construction of binary low correlation zone(LCZ)complementary sequence sets based on binary orthogonal matrices are given.Compared with polyphase sequences,binary sequences are more desired in practice because of easy realization.Finally,the design of Guassian integer sequences is concerned.The basic idea is using the relationship between combinatorial design and Guassian integer sequences.Gaussian integer sequences are defined based on difference sets and difference families,then the sufficient conditions of perfect Gaussian integer sequences and Gaussian integer complementary sequences are deduced.At last,perfect Gaussian integer sequences and Gaussian integer complementary sequences are obtained by searching sutitable Gaussian integers.Concretely,3 class of perfect Gaussian integer sequences are constructed from difference sets.Moreover,Gaussian integer complementary sequences are constructed by using difference families.