A lower bound on the average Hamming correlation of frequency-hopping sequence sets

The average Hamming correlation is an important indicator of frequency-hopping sequences (FHSs)which measures the average performance of FHSs employed in practical frequency-hopping multiple access (FHMA) communication systems.In this paper, a lower bound on average Hamming auto- andcross correlations of an FHS setis derived. It generalizes and improves the lower bound proposed recently by Peng, Niu and Tang.A simple necessary and sufficientcondition for an FHS set to meet the new bound is given.Based on this condition, two classes of FHS sets whose average Hamming correlations reach the proposed bound are introduced.