A Multi-Dimensional Block-Circulant Perfect Array Construction

TL;DR

This paper generalizes a 2D block-circulant perfect array construction to N dimensions, maintaining zero correlation zone properties using perfect autocorrelation sequences with array orthogonality.

Contribution

It introduces an N-dimensional extension of existing array constructions, preserving zero correlation zone properties and utilizing array orthogonality with perfect autocorrelation sequences.

Findings

N-dimensional arrays with zero correlation zones

Preservation of array orthogonality in higher dimensions

Extension of 2D construction to N dimensions

Abstract

We present a $N$-dimensional generalization of the two-dimensional block-circulant perfect array construction by \cite{Blake2013}. As in \cite{Blake2013}, the families of $N$-dimensional arrays possess pairwise \textit{good} zero correlation zone (ZCZ) cross-correlation. Both constructions use a perfect autocorrelation sequence with the array orthogonality property (AOP).