Construction of Two Kinds of Optimal Wide-Gap Frequency-Hopping Sequence Sets

The frequency hopping sequence plays a crucial role in determining the system's anti-jamming performance, in frequency hopping communication systems. If the adjacent frequency points of FHS can ensure wide-gap, it will better improve the anti-interference capability of the FH communication system. Moreover, if the period of the sequence is expanded, and each frequency point does not repeat in the same sequence, the system's ability to resist electromagnetic interference will be enhanced. And a one-coincidence frequency-hopping sequence set consists of FHSs with maximum Hamming autocorrelation 0 and cross-correlation 1. In this paper, we present two constructions of wide-gap frequency-hopping sequence sets. One construction is a new class of wide-gap one-coincidence FHS set, and the other is a WGFHS set with long period. These two WGFHS sets are optimal with respect to WG-Peng-Fan bound. And each sequence of these WGFHS sets is optimal with respect to WG-Lempel-Greenberger bound.