New Constructions of Zero-Correlation Zone Sequences

TL;DR

This paper introduces three systematic methods for constructing zero-correlation zone sequences that can achieve optimal family sizes and ZCZ widths, offering flexible parameters and nested properties for various applications.

Contribution

The paper presents three novel, systematic approaches for constructing ZCZ sequence families that reach theoretical bounds and offer flexible, nested, and diverse sequence parameters.

Findings

Achieve upper bounds on family size and ZCZ width for given sequence length

Produce binary and polyphase ZCZ families with flexible parameters

Sequences exhibit nested-like properties for scalable applications

Abstract

In this paper, we propose three classes of systematic approaches for constructing zero correlation zone (ZCZ) sequence families. In most cases, these approaches are capable of generating sequence families that achieve the upper bounds on the family size ($K$) and the ZCZ width ($T$) for a given sequence period ($N$). Our approaches can produce various binary and polyphase ZCZ families with desired parameters $(N,K,T)$ and alphabet size. They also provide additional tradeoffs amongst the above four system parameters and are less constrained by the alphabet size. Furthermore, the constructed families have nested-like property that can be either decomposed or combined to constitute smaller or larger ZCZ sequence sets. We make detailed comparisons with related works and present some extended properties. For each approach, we provide examples to numerically illustrate the proposed construction procedure.