Research On Sequence Pairs Design

The perfect discrete signal has been widely employed in spread spectrumcommunication, sonar, navigation, CDMA and so on. When the perfect discrete signal isapplied in location, navigation and common communication, the key and hot point iswhether the signals have good correlation. Therefore, the construction of the perfectdiscrete signals with good correlation has important theory significance and applicationsignificance. Several perfect sequence pairs are researched in this paper.The construction methods of of pseudo-random sequence are studied. A newconstruction method called cyclotomic class is proposed. The difference set pairs isconstructed by using cyclotomic class. The existence conditions of the construction of thedifference set pairs through cyclotomic class are studied. Several construction methods ofdifference set pairs through cyclotomic class are given and proved. A newpseudo-random sequence pair is constructed by applying the equal relation between thedifference set pairs and the pseudo-random sequence pair. And this sequence has goodautocorrelation and equilibrium performance of"0"and"1". Some examples are given toprove it.A newly defined block design called complementary difference set pairs is proposed.Complementary difference set pairs is constructed by using cyclotomic class. Theexistence conditions of the construction of the complementary difference set pairsthrough cyclotomic class are studied. Several construction methods of complementarydifference set pairs through cyclotomic class are given and proved. A new binarycomplementary sequence is constructed by applying the equal relation between thecomplementary difference set pairs and the binary complementary sequence. And thissequence has good autocorrelation and equilibrium performance of"0"and"1". However,the existence space of the sequence is extended.A new kind of pseudo-random sequence called perfect three-value autocorrelationsequence pair is proposed. First, the constant weight difference almost set pair isconstructed through cyclotomic class. Then the perfect three-value autocorrelation sequence pair corresponding to the constant weight difference almost set pair is getaccording to the equal relation between different set and sequence. Research of theoryindicates that the new sequence pair has the same good autocorrelation and equilibriumperformance of"0"and"1"with the perfect three-value autocorrelation sequence pairconstructed by Ding and so on.A new block design called punctured difference set pair is put forward. Theproperties of punctured difference set pair are studied. A special kind of punctureddifference set pairs equal to perfect punctured binary sequence pair is gained. Withdifference set, the punctured difference set pairs which is content with the equivalentcondition is constructed, and then the corresponding perfect punctured binary sequencepair is get; the equivalent relation between a special kind of punctured difference set pairsand pseudo-random punctured binary sequence pair is obtained. The sufficient andnecessary conditions and the necessary conditions of the pseudo-random puncturedbinary sequence pair are studied. Finally a pseudo-random punctured binary sequencepair is constructed through difference set.The family of perfect odd-periodic complementary binary sequence pair is putforward, its properties are studied, and its spectrum is analyzed. The existence conditionsof the family of perfect odd-periodic complementary binary sequence pair are obtained.Two construction methods of the family of perfect odd-periodic complementary binarysequence pair are given and proved. And it means that two construction methods of thefamily of perfect odd-periodic complementary binary sequence pair are gained equally.Based on the family of perfect periodic complementary binary sequence pair,several construction methods are proposed. Using the polynomial properties of the familyof perfect periodic complementary binary sequence pair, a family of perfect periodiccomplementary binary sequence pair with the length of MN can be constructed bycombing two families of perfect periodic complementary binary sequence pair with thelength of N and M. And the length of the new family of perfect periodic complementarybinary sequence pair be odd numbers; Using the properties of the approximately perfectbinary array, a new family of perfect periodic complementary binary sequence pair withthe length of 2N and the group number of 2Q can be constructed by combining a family of perfect periodic complementary binary sequence pair with the length of N and thegroup number of Q with a two-dimension Q*N approximately perfect binary array; Usingthe properties of dyadic theoryï¿¡known family of perfect periodic complementary binarysequence pair can be used to construct more new family of perfect periodiccomplementary binary sequence pair with the same performances through dyadictransformation.