New Bounds on the Aperiodic Hamming Correlation of Wide-Gap Frequency-Hopping Sequence Sets

Wide-gap frequency-hopping sequences (WGFHSs) require a sufficiently large frequency gap between adjacent frequency points, which grants them inherent resistance against tracking jamming, barrage jamming, and multipath fading. Such sequences constitute a critical building block for enhancing the anti-jamming performance of frequency-hopping communication systems operating in complex electromagnetic environments. In practical systems, the aperiodic Hamming correlation of sequences directly affects receiver synchronization and sequence acquisition performance. Hence it bears greater practical significance than periodic Hamming correlation. However, owing to the complexity of application scenarios, related research is challenging, and existing results remain limited. In this paper, we extend the traditional Peng-Fan aperiodic bound to WGFHSs, and derive two lower bounds on the maximum aperiodic Hamming correlation of WGFHS sets. Numerical examples demonstrate that the proposed bounds are tighter than the traditional Peng–Fan aperiodic bound. This provides a more rigorous theoretical foundation for the design of WGFHS sets.