Research On The Design Of Gaussian Integer Sequence Set And Complementary Sequence Set Based On Filtering

The design of the spreading sequences on Gaussian integer rings which have good correlation has attracted scholars' attention both at home and abroad and Gaussian integer sequences play a particularly important role in CDMA systems,orthogonal frequency division multiplexing systems as well as MIMO space-time coding systems and so on.The design of spreading sequences which have good correlation and spreading sequence sets which have more sub-sequences is of great significance for improving the performance and capacity of the communication systems.In this thesis,we give a theoretical study on the Gaussian integer periodic sequence sets with zero correlation zone and Gaussian integer periodic complementary sequence sets with zero correlation zone,mainly.First of all,based on binary or quaternary periodic sequence sets with zero correlation zone and perfect sequences which meet certain conditions,we construct a class of 16-QAM periodic sequence sets with zero correlation zone by the filtering operation,which achieve an expansion of the number of the existing 16-QAM periodic sequence sets with zero correlation zone.Secondly,based on binary,ternary,quaternary as well as QAM periodic sequence sets with zero correlation zone and perfect sequences,we construct a class of Gaussian integer periodic sequence sets with zero correlation zone with the same parameters as the based sequence sets,which can get close to or reach the theoretical bound.In particular,based on two perfect sequences,we can obtain perfect Gaussian integer sequences,which can have odd and even period.Finally,based on periodic complementary sequence sets with zero correlation zone and perfect sequences,we construct a class of Gaussian integer periodic complementary sequence sets with zero correlation zone and with the same parameters as the based sequence sets,that is,those parameters depend on the based sequence sets;based on periodic sequence sets with zero correlation zone and periodic complementary sequences,we construct a class of Gaussian integer periodiccomplementary sequence sets with zero correlation zone,which can get closed to but not reach the theoretical bound;based on periodic complementary sequence sets with zero correlation zone and periodic complementary sequences,we construct a class of Gaussian integer periodic complementary sequence sets with zero correlation zone,which have more sequences.Those constructed sequence sets can provide more address choices for quasi synchronous code division multiple access systems.