Research On Theory Of Array Pairs And Its Application

With the development of the electric technology, the application of perfect discrete signal design in signal processing is more prevalent. Either signal analysis and correlation analysis, or spread frequency technology and CDMA system all depend on perfect discrete signal design. The study of binary sequence predominates in the conventional perfect discrete signal design. And the application in the actual system is almost binary sequence. But binary sequences seem to can not meet the needs on system capacity's spreading and signal quality's promoting. So it's necessary to search sequences which have good characteristic and large quantities. Fortunately quadriphase sequences have the advantage which binary sequence can't reach in some ways. And a new signal form was given by array pairs theory and mismatched sequence, in which two sequences were regarded as an pairs(or sequence pair). Then, lots of sequences which can be chosen as engineering signal were obtained. So the paper spread the study of quadriphase sequences into the array pair theory. And then PQPAP(perfect quadriphase punctured array pairs), PQCSP(punctured quadriphase complementary sequence pairs) and QOPMS(quadriphase odd periodic mismatched sequence) were acquired.First, the definition of the PQPAP was given, and its property and prerequisite was studied. With the restriction of the prerequisite, computer search was executed in small array volume. 1-dimensional PQPAP with volume from 3to 12 were obtained. But there are only PQS(perfect quadriphase sequence) with volume 8 and 10 in that range. Also two constructions was given which are fold construction and period product construction. By the constructions, multi-dimensional and large volume PQPAP could be obtained.Then, the definition of PQCSP was given, and the property of the PQCSP was studied. Also two constructions were given to construct large length PQCSP.Last, the definition of QOPMS was given, and its property was studied. By solving the equation which contains the matrix by circulating the odd period sequence, the mismatched sequence was obtained. By computer searching, it was found that there are many high energy efficiency sequences on every length. And it was found that QOPMS and QPMS all could be constructed by OPQMS's odd period product which provides other construction for QPMS.CDMA communication system model wan constructed. The property of BER by implementing 1-dimensional PQPAP (also could be called PPQSP), QOPMS were simulated in Matlab respectively.