New Families of Optimal Frequency-Hopping Sequences of Composite Lengths

摘要

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.