Optimal and Almost-Optimal Golay-ZCZ Sequence Sets With Bounded PAPRs

This paper aims to present novel constructions of Golay-ZCZ sequence sets with various set sizes and flexible lengths. A Golay-ZCZ sequence set is not only a Golay complementary set (GCS) but also a zero correlation zone (ZCZ) sequence set. Golay-ZCZ sequence sets have been employed in OFDM systems due to their low peak-to-average power ratios (PAPRs) which are upper bounded by the set sizes. Although several constructions of Golay-ZCZ sequence sets have been proposed in the literature, the known Golay-ZCZ sets cannot attain the theoretical upper bound on the ZCZ width for non-binary cases. Also, for the Golay-ZCZ sets constructed by generalized Boolean functions, parameters are limited to powers of two, such as set sizes, sequence lengths, and ZCZ widths. In this paper, constructions of Golay-ZCZ sequence sets based on the extended generalized Boolean functions are proposed, where set sizes, sequence lengths, and ZCZ widths are all flexible and not necessary to be power-of-two. Since the constructed Golay-ZCZ sets have various set sizes, their PAPR upper bounds can be tighter. In addition, the proposed Golay-ZCZ sequence sets can achieve the upper bound on the ZCZ width. Therefore, optimal and almost-optimal Golay-ZCZ sequence sets can be obtained by the proposed methods.