New Constructions of Golay Complementary Pair/Array with Large Zero Correlation Zone

TL;DR

This paper introduces new methods for constructing Golay complementary pairs and arrays with large zero correlation zones, extending their lengths and dimensions beyond previous limitations, which benefits applications like OFDM systems.

Contribution

It proposes novel constructions of Golay pairs and arrays with large ZCZ, including new lengths and two-dimensional arrays, surpassing prior length restrictions.

Findings

Constructed GCPs with length 4N and ZCZ width N+1.

Extended to two-dimensional Golay arrays with large ZCZ.

Demonstrated improved correlation properties for practical applications.

Abstract

Zero correlation zone (ZCZ) sequences and Golay sequences are two kinds of sequences with different preferable correlation properties. It was shown by Gong \textit{et al.} and Chen \textit{et al.} that some Golay sequences also possess a large ZCZ and are good candidates for pilots in OFDM systems. Known Golay sequences with ZCZ reported in the literature have a limitation in the length which is the form of a power of 2. One objective of this paper is to propose a construction of Golay complementary pairs (GCPs) with new lengths whose periodic autocorrelation of each of the Golay sequences and periodic corss-correlation of the pair displays a zero correlation zone (ZCZ) around the in-phase position. Specifically, the proposed GCPs have length $4N$ (where, $N$ is the length of a GCP) and ZCZ width $N+1$. Another objective of this paper is to extend the construction to two-dimensional Golay complementary array pairs (GCAPs). Interestingly the periodic corss-correlation of the proposed GACPs also have large ZCZs around the in-phase position.