A Direct and New Construction of Near-Optimal Multiple ZCZ Sequence Sets

TL;DR

This paper introduces a novel direct construction method for near-optimal multiple ZCZ sequence sets from generalized Boolean functions, partially addressing an open problem and enabling improved multi-cluster QS-CDMA systems.

Contribution

It presents the first direct construction of multiple ZCZ sequence sets with inter-set ZCCZ from Boolean functions, achieving near-optimal union properties.

Findings

Constructed near-optimal multiple ZCZ sequence sets from Boolean functions.

Achieved performance parameter close to 1 for individual and union sets.

Compared favorably with existing state-of-the-art methods.

Abstract

In this paper, for the first time, we present a direct and new construction of multiple zero-correlation zone (ZCZ) sequence sets with inter-set zero-cross correlation zone (ZCCZ) from generalised Boolean function. Tang \emph{et al.} in their 2010 paper, proposed an open problem to construct $N$ binary ZCZ sequence sets such that each of these ZCZ sequence sets is optimal and if the union of these $N$ sets is taken then that union is again an optimal ZCZ sequence set. The proposed construction partially settles this open problem by presenting a construction of optimal ZCZ sequence sets such that their union is a near-optimal ZCZ sequence set. Further, the performance parameter of each binary ZCZ sequence set in the proposed construction is $1$ and tends to $1$ for their union. The proposed construction is presented by a two-layer graphical representation and compared with the existing state-of-the-art. Finally, novel multi-cluster quasi synchronous-code division multiple access (QS-CDMA) system model is provided by using the proposed multiple ZCZ sequence sets.