Research On The Design Theory Of Sequence Pair With Two-level And Three-level Correlation

In modern spread spectrum communication system, the performances ofanti-jamming, anti-interception, multiple access communication and synchronization ofthe system are closely related to the characteristics of the adopted spreading codes.Therefore, research on sequence design and constructing methods of spreading codes withexcellent performance has important theoretical and practical significance to modernspread-spectrum communication system. Aiming at the shortcomings of exist sequencepairs on small space, low energy efficiency, poor property of correlation and balance,several new methods for the construction of binary sequence pairs with two-level andthree-level correlation, quaternary sequence pairs with two-level and three-levelcorrelation and perfect Gaussian integer sequence pairs are proposed in this thesis, basedon the Chinese remainder theorem, combinatorial design theory and interleaved sequencetheory.Firstly, a new construction of ideal two-level correlation binary sequence pairs withinductor and underlying sequences is proposed based on the theory of combinatorialdesign and the Chinese remainder theorem. The required conditions of the row sequencesare given, when the periods are set to be (4m+3)(4m’+3),(4m+1)(4m’+3)and(4m+1)(4m’+1). The performances on correlation, energy effectiveness and balance of thesequences pairs are analyzed, who are constructed using the four typical ideal binarysequences as the row sequences. Nine types of ideal two-level correlation binary sequencepairs are obtained by means of choosing different sequences as the base sequence andinductor sequence. Then, nine types new difference set pairs are derived based on theequal relationship between binary sequence pair with two-level correlation and differenceset pair.Secondly, For the constructions of binary sequence pairs with three-level correlationof period4N, two new construction methods are proposed using cyclotomic classes oforder2and interleaving technique, based on combinatorial design theory and interleavedsequences theory. Based on this, three types of binary sequence pairs with three-levelcorrelation of period4N are obtained, whose out-of-phase correlation values are all {0,-4}. And nine new types of almost difference set pairs are also obtained through the equality ofbinary sequence pairs with three-level correlation and almost difference pair. For theconstruction of binary sequence pairs with three-level correlation of odd period, theconstruction methods based on difference sets and difference set pairs are investigatedrespectively, the properties of balance and correlation of constructed ones are discussed.The concept of almost binary sequence pair is presented, to solve the limited existingspace problem of perfect binary sequence pair with even period (there is only one type ofsuch perfect binary sequence pair whose in-phase correlation value is4), and break thelimitation of the correlation values must be the odd number when the period of binarysequence pair is odd, and the constructions of some types of almost binary sequence pairsare proposed. In addition, the optimal properties such as correlation, balance and energyefficiency of the resultant almost binary sequence pairs are verified.Afterwards，properties of quaternary sequence pairs with even period and three-levelcorrelation are researched, the correlation characteristics of this type of sequence pair areobtained through analysis of its maximum sidelobes. The relationship between binarysequence pairs and quaternary sequence pairs is established by inverse Gray mapping, anda novel construction method is proposed for quaternary sequence pairs with even periodand three-level correlation. With this method, N=2n-1is chosen to be the modulus, idealbinary sequence pairs is chosen to be the characteristic sequences, then quaternarysequence pairs with period of N=4n-2and three-level correlation can be perfectlyconstructed. Furthermore, based on interleaving method, three other types of constructionmethods are proposed by choosing different shift sequence, to obtain quaternary sequencepairs with even period and three-level correlation, who fulfills same correlationcharacteristics. The shift distinctness of constructed quaternary sequence pairs using thethree methods is analyzed.Finally, the links between binary array pair and quaternary pair is established by theinverse Gray mapping. In order to expand the base arrays to construct more perfectquaternary array pairs, the constructions of perfect quaternary array pairs with periodiccomplementary binary array pairs or perfect binary array pairs, and the recursiveconstructions with perfect quaternary array pairs and quasi-perfect array pairs or almost perfect quaternary array pairs are proposed. In order to expand the space of perfectGaussian integer sequences and perfect sequence pairs, the constructions of perfectGaussian integer sequence pairs of odd composite length with perfect Gaussian integersequence of odd length based on the theory of the Chinese remainder theorem andinterleaved sequences are presented. And the constructions of perfect Gaussian integersequence pairs of even length with perfect punctured binary sequence pairs by complextransformation are put forward. Additionally, the shift distinctness of constructed perfectGaussian integer sequence pairs is analyzed when using the different parameters.