Golay-ZCZ Sequence Sets with Flexible Lengths Based on Matrices of Polynomials

In this paper, we develop a generalized construction framework of zero-correlation zone (ZCZ) sequence sets based on para-unitary (PU) matrices. We show that any square PU matrix with unimodular sequences can generate ZCZ sequence sets by perfectly controlling its expanded product form, thereby improving upon existing results. The key idea is to impose specific conditions on the expanded product forms of PU matrices to enable accurate computation of periodic correlation functions. In addition, each constructed ZCZ sequence set is a PU column vector and hence it represents a Golay complementary set (GCS). In this work, we call them Golay-ZCZ sequence sets. The lengths, set sizes and ZCZ widths of the constructed Golay-ZCZ sequence sets are all flexible with the form of non-power-of-two. These Golay-ZCZ sequence sets can be directly applied to practical training-based channel estimation schemes in multiple-antenna systems.