Research On Sequence With Zero Correlation Zone And Sequence Pair With Zero Correlation Zone

In code division multiple access (CDMA) systems, the correlation properties of the spreading sequences employed play an important role on the level of the interference, therefore directly influence the performance and capacity of the CDMA systems. The spreading sequences design is one of the key points of the CDMA systems.The theoretic bounds and the design of spreading sequences are two main issues in the theory of spreading sequences. In this thesis, several kinds of sequence sets with zero correlation zone are constructed. Based on difference set pair, several kinds of sequence pairs are constructed.The construction methods of ternary sequence set with aperiodic zero correlation zone are studied. A new method for constructing ternary sequence set with aperiodic zero correlation zone is proposed, which is based on two arbitrary Hadamard matrices of common size. A series of ternary sequence sets with aperiodic zero correlation zone are constructed by a recursive method. Furthermore, two of this kind of sequence sets are constructed which are mutually orthogonal. The energy efficiency of the proposed sequences is higher than 80%.The construction methods of perfect ZCZ sequence set are improved, which are based on perfect sequences and orthogonal matrices. In the proposed method, all of the perfect sequences with even period can be used to constructed perfect ZCZ sequence set and most of the perfect sequences with odd period can be used to constructed perfect ZCZ sequence set . The size of the orthogonal matrices used in the proposed method is 2×2 or 3×3. The new construction methods of shift sequence are proposed. In addition, the construction methods of perfect ZCZ sequence pair set are studied. Because the length of perfect sequence is limited, the length of perfect sequence pair hasn't such limitation.The construction methods of sequence set with group-wise zero correlation zone are studied. A new method for constructing sequence set with group-wise zero correlation zone is proposed, which is based on a Hadamard matrix of size N×N and a pair of Hadamard matrices of size M×M. The proposed sequence sets have a group-wise zero correlation zone for both periodic and aperiodic cross-correlation functions.The construction methods of perfect binary sequence pair are studied, which are based on difference set pair. An in-depth research into difference set pairs was done. As a result, several construction methods of difference set pair are proposed, which are corresponding with perfect binary sequence pair.In order to do further research on almost perfect binary sequence pair, a new block design (divisible difference set pair) is presented. The properties of divisible difference set pair are studied. Using Hall polynomial, the necessary and sufficient conditions for the existence of divisible difference set pair are proved. The equivalent relationship between almost perfect binary sequence pair and the new block design is given. Several admissibility conditions for almost perfect binary sequence pair are presented.