New Families of Optimal Frequency-Hopping Sequences of Composite Lengths

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.