Design Of Sequences Or Sequence Sets With Good Correlation

Sequences or sequence sets with good correlation properties have very wide and important practical applications. Sequence with good autocorrelation can be used in the Code Division Multiple Access (CDMA) communacation systems to ensure the receiver acquire the accurate timing information of received signals which can help the receiver to distinguish the users of signals; on the other hand, sequence sets with some kind of low correlation properties can be used in different communation systems to eliminate the interference and improve the performance of the systems. The practical requirements stimulate the development of sequence design, making it become one of popular topics around the world. This work follows the trend of sequence design, and aims at designs of sequences with good autocorrelation and LCZ sequence sets by using different tools. The major contributions of the dissertation are as follows:1. Two constructions of binary sequences with good autocorrelation are proposed. The first construction is based on N x4interleaved structure of sequences and derive two classes of binary sequences by relaxing the conditions on the shift sequence of this kind of structure which are discussed in an earlier paper. The unexpected autocorrelation values of new sequences only occur four times in every period no matter how long the period is. Furthermore, we generalize this construction to N×3interleaved structure and also obtain a class of binary sequences with good autocorrelation whose unexpected autocorrelation values only occur two times in every period no matter how long the period is. The second construction is based on4×N interleaved structure of sequences and break the restriction on the indicator sequences in another earlier work. We find that having an interleaved structure in the indicator sequences is the key property. So by using other sequences which also have an interleaved structure as new indicator sequences, three classes of binary sequences are proposed. The autocorrelation magnitude of new sequences is optimal.2. Based on Whiteman’s generalized cyclotomy, we propose new constructions of quadriphase and almost quadriphase sequences with odd period. The maximum nontrivial autocorrelation values of the quadriphase sequence reach the best known one for quadriphase sequences with odd period and in the case of almost quadriphase sequence, it also does not exceed the magnitude of the known ones.3. Based on Whiteman’s generalized cyclotomy again, we propose a class of perfect Gaussian integer sequences. This is the first class of perfect Gaussian integer sequences with period N, where N is an odd composite integer, more precisely, N=pq and p, q are twin primes in this construction. Furthermore, for every such N, more than one perfect Gaussian integer sequences can be derived by this construction.4. By using inverse Gray mapping and special binary sequence pairs, we construct new quaternary LCZ sequence sets. Although the sequences sets are not optimal in terms of their size, the maximum of the nontrivial autocorrelation and crosscorrelation values is1in the low correlation zone. It is believed that these sets can be used in some particular situation of communication systems which do not have many users but have higher requirement on low interference.