New Families of Optimal Frequency-Hopping Sequences of Composite Lengths

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 two new constructions for FHS sets. We first give a new construction for FHS sets of length nN for two positive integers n and N with gcd (n,N)=1. We then present another construction for FHS sets of length (q-1)N , where q is a prime power satisfying gcd (q-1,N)=1. By these two constructions, we obtain infinitely many new optimal FHS sets with respect to the Peng-Fan bound as well as new optimal FHSs with respect to the Lempel-Greenberger bound, which have length $nN$ or n(q-1)N. As a result, a great deal of flexibility may be provided in the choice of FHS sets for a given frequency-hopping spread spectrum system.