Asymptotically Optimal Golay-ZCZ Sequence Sets with Flexible Length

Abstract

Zero correlation zone (ZCZ) sequences and Golay complementary sequences are two kinds of sequences with different preferable correlation properties. Golay-ZCZ sequences are special kinds of complementary sequences which also possess a large ZCZ and are good candidates for pilots in OFDM systems. Known Golay-ZCZ sequences reported in the literature have a limitation in the length which is the form of a power of 2. In this paper, we propose two constructions of Golay-ZCZ sequence sets with new parameters which generalize the constructions of Gong et al. (IEEE Transaction on Communications 61(9), 2013) and Chen et al (IEEE Transaction on Communications 61(9), 2018). Notably, one of the constructions results in optimal binary Golay-ZCZ sequences, while the other results in asymptotically optimal polyphase Golay-ZCZ sequences as the number of sequences increases.

New Constructions of Mutually Orthogonal Complementary Sets and Z-Complementary Sequence Sets Based on Extended Boolean Functions

“…But both of these methods only have power of two lengths when q = 2. Other methods for designing MOCSs include PU matrices [20,21], interleaving, Kronecker product [22,23], extended correlation [24] and concatenation [40]. However, These methods are hard to be applied in engineering due to their large space and time requirements in hardware generation.…”

“…Apart from these direct constructions of MOCSs, there are some other indirect methods to construct MOCSs such as interleaving, concatenation, paraunitary (PU) matrices, Kronecker product, extended correlation, etc. [19][20][21][22][23][24]. However, the generated MOCSs may not be friendly for hardware generation due to their large space and time requirements.…”