On the Average Hamming Correlation of Frequency-Hopping Sequence Sets with Low Hit Zone

In frequency-hopping sequence (FHS) design, the average Hamming correlation is an important performance indicator. In this paper, the average Hamming correlation of low-hit-zone (LHZ) FHS sets, which has not yet been reported previously, is studied. A lower bound on the average Hamming auto-correlation and the average Hamming cross-correlation of LHZ FHS sets is firstly derived. The new lower bound includes the bound for conventional FHS sets derived by Peng et al. as special case. Then a sufficient and necessary condition for an LHZ FHS set with optimal average Hamming correlation is given. Further, a construction of LHZ FHS sets with optimal average Hamming correlation is presented, whose parameters meet the lower bound on the average Hamming correlation of LHZ FHS sets.