Constructions of Optimal Frequency-Hopping Sequences with Controlled Minimum Gaps

TL;DR

This paper develops new methods for constructing frequency-hopping sequences with optimal correlation properties and controlled minimum gaps, enhancing anti-interference in communication systems.

Contribution

It introduces a general construction framework for optimal uniform wide-gap FHSs with specific lengths, extending previous work and providing recursive methods for sequence construction.

Findings

Proposed a general construction for optimal uniform wide-gap FHSs.

Established recursive methods for constructing FHSs with controlled gaps.

Demonstrated the effectiveness by producing known optimal FHSs with desired properties.

Abstract

Frequency-hopping sequences (FHSs) with low Hamming correlation and wide gaps significantly contribute to the anti-interference performance in FH communication systems. This paper investigates FHSs with optimal Hamming correlation and controlled minimum gaps. We start with the discussion of the upper bounds on the minimum gaps of uniform FHSs and then propose a general construction of optimal uniform wide-gap FHSs with length 2l and 3l, which includes the work by Li et al. in IEEE Trans. Inf. Theory, vol. 68, no. 1, 2022 as a special case. Furthermore, we present a recursive construction of FHSs with length 2l, which concatenate shorter sequences of known minimum gaps. It is shown that the resulting FHSs have the same Hamming correlation as the concatenation-ordering sequences. As applications, several known optimal FHSs are used to produce optimal FHSs with controlled minimum gaps.