Theoretical Research On Complementary Sequences And Quasi-complementary Sequences

Sequences with good properties have important applications in wireless communications,cryptography,radar,sonar,ultra-wideband wireless positioning technology and compressed sensing.This thesis focuses on the design of complementary sequences and quasi-complementary sequences with excellent correlation properties for multi-carrier wireless communication systems,including mutual orthogonal complementary sequence sets(MOCSSs),low/zero-correlation zone complementary sequence sets(LCZ/ZCZ-CSSs),and low-correlation complementary sequence sets(LC-CSSs).Firstly,based on quadratic generalized Boolean functions(GBFs),direct constructions of complete complementary sequence sets(CCSSs)and MOCSSs with flexible lengths are investigated.By analyzing the allocation scheme of complementary sequences for multicarrier code-division multiple-access(MC-CDMA)systems,the problem of high peak-to-average power ratio(PAPR)is studied.By using coding techniques,the PAPR can be effectively controlled below 3 d B.Further,a set of complementary sequences with ZCZ properties is studied using quadratic GBFs and graph theory.The constructed sequence sets include multiple subsets,each of which is a CCSS.It is worth pointing out that the sequences within the same subset have ideal aperiodic autocorrelation and cross-correlation properties,and the sequences from different subsets have ideal aperiodic cross-correlation properties within a ZCZ.In addition,the constructed sequence sets are optimal according to the theoretical bounds of ZCZ-CSSs.Secondly,two classes of aperiodic ZCZ-CSSs with good cross-correlatin subsets are investigated via paraunitary(PU)matrices.Specifically,by establishing the connection between different PU matrices using special permutation matrices,a construction of multiple CCSSs with inter-set ZCZ property is proposed.The resultant sequence sets are optimal in terms of the theoretical bounds of ZCZ-CSSs.Then,by decomposing a PU matrix using sparse matrices,a construction of aperiodic inter-group complementary sequence sets(IG-CSSs)is proposed.The obtained sequence sets contain several groups(or called subsets),in which the lengths of sequences from different groups can be set flexibly and take different values.Each group is an aperiodic ZCZ-CSS,thus the sequences within a group have ideal aperiodic autocorrelation and cross-correlation properties within a ZCZ,and the sequences from different groups have ideal aperiodic cross-correlation properties.Then,three frameworks of periodic LC-CSSs are developed associated with characters of finite fields.By analyzing the relations between parameters of the constructed sequence sets,several classes of periodic LC-CSSs are further designed using cyclic difference sets,binary m sequences,binary Sidelnikov sequences,relative difference sets,almost difference sets,cyclotomic classes,and Kate sets respectively.The research results show that the proposed periodic LC-CSSs have new parameters uncovered in the literature and asymptotically achieve the theoretical bounds.As a result,they can provide more choices for different application scenarios.Finally,three classes of aperiodic LC-CSSs are investigated over complex unit roots,which are asymptotically optimal with respect to the related theoretical bounds.Besides,considering the local correlation performance,a class of aperiodic LCZ-CSSs is provided,which are asymptotically optimal in some cases and contain a larger number of sequences.Notably,all the constructed aperiodic quasi-complementary sequence sets have new parameters.