Two Classes of Z-Complementary Code Sets With Good Cross-Correlation Subsets via Paraunitary Matrices

Z-complementary code sets (ZCCSs), extended from complete complementary codes (CCCs), have ideal correlations within a zone around the in-phase position named zero correlation zone (ZCZ). In this article, two classes of aperiodic ZCCSs with good cross-correlation subsets are investigated. They are multiple CCCs with inter-set zero cross-correlation zone (ZCCZ) property and multiple aperiodic ZCCSs with ideal inter-set aperiodic cross-correlation property respectively, the latter is referred to as an aperiodic inter-group complementary (IGC) code set and each ZCCS is called a group. First of all, based on polyphase paraunitary (PU) matrices and special permutation matrices, a construction of multiple polyphase CCCs with an inter-set ZCCZ is proposed. The obtained multiple CCCs have potential applications in interference-free multi-cell environments to support a large number of users. In addition, a construction of aperiodic polyphase IGC code sets is presented from polyphase PU matrices. We remark that different groups of the derived IGC code sets yield different constituent sequence lengths, thus they could provide a variety of quality of service (QoS) in quasi-synchronous multi-cell multi-rate communication systems. To the best of our knowledge, the aforementioned constructions of ZCCSs with good cross-correlation subsets based on PU matrices have not been reported in the literature.