New Construction of Optimal Interference-Free ZCZ Sequence Sets by Zak Transform

TL;DR

This paper introduces a novel method for constructing optimal interference-free zero correlation zone sequence sets using Zak transform lattice tessellation, improving spectral structure and computational efficiency.

Contribution

It presents a new construction method for IF-ZCZ sequences that is different from existing approaches, achieving optimality and structured spectral properties.

Findings

Sequences have optimal zero correlation zone length according to Tang-Fan-Matsufuji bound.

Sequences exhibit sparse, highly structured Zak and Fourier spectra.

Construction reduces computational complexity of matched filter banks.

Abstract

In this paper, a new construction of interference-free zero correlation zone (IF-ZCZ) sequence sets is proposed by well designed finite Zak transform lattice tessellation. Each set is characterized by the period of sequences $KM^2$, the set size $K$ and the length of zero correlation zone $M^2-1$, which is optimal with respect to the Tang-Fan-Matsufuji bound. In particular, all sequences in these sets have sparse and highly structured Zak and Fourier spectra, which can decrease the computational complexity of the implementation of the banks of matched filters. Moreover, for the parameters proposed in this paper, the new construction is essentially different from the general construction of optimal IF-ZCZ sequence sets given by Popovic.