Analysis And Application Of The Quaternary Sequences With Low Correlation

Quaternary sequences has found major applications in several situations,and quaternary sequences are preferred to achieve the better correlation bounds than binary sequences with the same families and periods of the sequences,according to the theory.However,quaternary sequences with low correlation has been constructed are not sufficient,as a result this thesis designs a quaternary sequences family based on Galois ring,and determines its correlation distribution,at the same time,constructs families of orthogonal sequences that can be used in CDMA systems using quaternary function.(1)This thesis constructs a family of quaternary sequences with same sequence period and quantity,which based on the generalized maximal length Z₄sequences proposed by Tang et al.The problem of evaluation of exponential sums are equal to finding roots of equations in finite fields by virtue of the Z₄valued quadratic forms over Galois ring,consequently the correlation distribution is completely determined.At last we get a new family of quaternary sequences with good correlation property via adding the generalized maximal length Z₄sequences to our constructed sequences family.(2)This thesis proposes a set of families of orthogonal sequences over Galois ring using the method proposed by Zhang et al.The sequences are orthogonal to each other in the same family,and have low correlation if in different families.Additionally,we allocate the set of families of orthogonal sequences to a regular hexagonal network in CDMA systems while preserving the orthogonality of adjacent cells and the low correlation property between nonadjacent cells,besides the sufficient number of sequences in each cell and the long reuse distance.Meanwhile,the sequences are also allocated to the simple system that all the sequences in cells are orthogonal to each other except the only nonorthogonality comes from the reuse of cells.