New Spectrally Constrained Sequence Sets with Optimal {Periodic} Cross-Correlation

TL;DR

This paper introduces a new framework for constructing spectrally constrained sequences with optimal periodic cross-correlation properties, crucial for modern communication and radar systems operating over non-contiguous spectrum.

Contribution

It proposes a unifying construction method for unimodular SCS families using circular Florentine rectangles and interleaving, achieving a tighter correlation lower bound.

Findings

Achieves a new lower bound for periodic correlation of SCSs.

Constructs multiple SCS sets with zero correlation zone properties.

Demonstrates the optimality of the proposed SCS families.

Abstract

Spectrally constrained sequences (SCSs) play an important role in modern communication and radar systems operating over non-contiguous spectrum. Despite numerous research attempts over the past years, very few works are known on the constructions of optimal SCSs with low cross-correlations. In this paper, we address such a major problem by introducing a unifying framework to construct unimodular SCS families using circular Florentine rectangles (CFRs) and interleaving techniques. By leveraging the uniform power allocation in the frequency domain for all the admissible carriers (a necessary condition for beating the existing periodic correlation lower bound of SCSs), we present a tighter correlation lower bound and show that it is achievable by our proposed SCS families including multiple SCS sets with zero correlation zone properties.