New frequency-hopping sequence sets with optimal average and good maximum Hamming correlations

In frequency-hopping multiple-access systems, the average Hamming correlation (AHC) among frequency-hopping sequences (FHSs) as well as the maximum Hamming correlation (MHC) is an important performance measure. Moreover, each FHS is required to be balanced for its robustness against jamming or fading environments. In this study, the authors investigate FHS sets with optimal AHC and (near-)optimal MHC, whose FHSs are balanced. The authors first show that any uniformly distributed FHS set has optimal AHC with respect to the Peng-Niu-Tang bound. The authors also present two classes of FHS sets with optimal AHC and (near-)optimal MHC, whose FHSs are (perfectly) balanced. The authors then analyse the AHC of FHS sets constructed by interleaving techniques, and present some new FHS sets with optimal AHC and MHC, whose FHSs are perfectly balanced.