Construction of New Optimal Z-Complementary Code Sets from Z-Paraunitary Matrices

In this paper, we first introduce a novel concept, called Z-paraunitary (ZPU) matrices. These ZPU matrices include conventional PU matrices as a special case. Then, we show that there exists an equivalence between a ZPU matrix and a Z-complementary code set (ZCCS) when the latter is expressed as a matrix with polynomial entries. The proposed ZPU matrix has an advantage over the conventional PU matrix with regard to the availability of wider range of matrix sizes and sequence lengths. In addition, the proposed construction framework can accommodate more choices of ZCCS parameters compared to the existing works

Near-Optimal Zero Correlation Zone Sequence Sets from Paraunitary Matrices

Zero correlation zone (ZCZ) sequence sets play an important role in interference-free quasi-synchronous code-division multiple access communications. In this paper, for the first time, we investigate the periodic correlation properties of polyphase sequences obtained from paraunitary (PU) matrices, which shows the inherent relationship between PU matrix and ZCZ sequence sets. Our investigation suggests that any arbitrary PU matrix can produce ZCZ sequence sets by controlling its expanded form. The key idea is to impose certain restrictions on the expanded forms of the PU matrices to enable precise computation of the periodic correlation functions of the constructed sequences. We show that our proposed construction leads to near-optimal ZCZ sequence sets with regard to the ZCZ set size upper bound