New families of optimal frequency hopping sequence sets

TL;DR

This paper introduces new algebraic and combinatorial methods for constructing optimal frequency hopping sequence sets, enhancing interference mitigation in spread spectrum systems.

Contribution

It presents novel algebraic, combinatorial, and recursive constructions for FHS sets that achieve optimality according to Peng-Fan bounds.

Findings

Produced new series of optimal FHS sets

Constructed FHS sets via algebraic and combinatorial methods

Achieved optimality with respect to Peng-Fan bounds

Abstract

Frequency hopping sequences (FHSs) are employed to mitigate the interferences caused by the hits of frequencies in frequency hopping spread spectrum systems. In this paper, we present some new algebraic and combinatorial constructions for FHS sets, including an algebraic construction via the linear mapping, two direct constructions by using cyclotomic classes and recursive constructions based on cyclic difference matrices. By these constructions, a number of series of new FHS sets are then produced. These FHS sets are optimal with respect to the Peng-Fan bounds.