Construction Of Big Orthogonal Sequence Sets Based On Boolean Functions

The design of the codewords in the Spread-Spectrum communication system is one of the most concerned topics in sequence design.Spread-Spectrum technique has been widely ap-plied in both military and civilian communications.The correlation value of the spread spectrum sequences determines the ability of the anti-interference of the system.Thus the sequences should have desirable cross-correlation properties.In order to meet the in-creasingly dense population communications,the sequences also need to ensure that the number of users in each cell is large enough.In this thesis,the definition of Semi-Bent sequence sets and weakly Semi-Bent sequence sets are presented.The Semi-Bent orthogo-nal sequences and weakly Semi-Bent orthogonal sequences which are constructed by using Maiorana-McFarland cryptographic Boolean functions construction technique can be as-signed to a regular tessellation of hexagonal cells,typical for synchronous code-division multiple-access(S-CDMA)systems.It's significant to satisfy that sequences in adjacent cells should be orthogonal to each other and the correlation of sequences in the nonadjacent cell is limited within a certain range.The conclusions are as follows:1)A construction method and two optimization schemes of weakly Semi-Bent orthogo-nal sequence sets are given.Firstly,Compared with Semi-Bent orthogonal sequence sets,the constructed weakly Semi-Bent orthogonal sequence sets double the numbers of each cell at the expense of the increasing correlation of nonorthogonal sequences.Specially,when m is 5(2m is the length of sequence),the number of users per cell is larger than currently best known method.Secondly,a new class of Semi-Bent or-thogonal sequence sets or weakly Semi-Bent orthogonal sequence sets based on the known orthogonal sequence sets is constructed.And Semi-Bent orthogonal sequence sets when m equals to 4 are obtained derived from Semi-Bent orthogonal sequence sets when m is equal to 3,the number of individual cellular users is twice larger than the optimal results.Finally,the class of weakly Semi-Bent orthogonal sequence sets which constructed by combining with the former two methods is optimized,a novel class of Semi-Bent orthogonal sequence sets is constructed which making the interference between non-adjacent cells smaller than weakly Semi-Bent orthogonal sequence sets without reducing the number in each cell.2)A construction of the p-ary Semi-Bent orthogonal sequence sets by extending M-M functions from F2 to Fp is proposed,and two schemes are given to simplify assign-ment of long sequence to cells for a large m.The number of individual cellular users can reach pm-2 for any m>3.In addition,p-ary weakly Semi-Bent and p-ary Semi-Bent orthogonal sequence sets are constructed by using different methods,whose individual cell user numbers are both up to pm-1.Specially,the maximum of user number per cell can be up to 3m-1 when tenary Semi-Bent orthogonal sequence sets are constructed.