New Bounds for Aperiodic Wide-Gap Frequency Hopping Sequences∗

Frequency hopping sequences (FHSs) play a significant role in modern frequency hopping spread spectrum communication and radar systems. In terms of application, the aperiodic Hamming correlation (HC) holds greater significance compared to the periodic HC as it directly impacts the communication performance. In addition, it is crucial for each user's FHS to have a substantial wide-gap (WG) in order to prevent the received signals from interfering with each other. In this letter, we obtain a new bound by extending the aperiodic bound proposed by Peng-Fan and the WG FHS bound introduced by Li-Fan-Yang-Wang. The proposed bound is strict since they can be verified using specific parameters of aperiodic WG FHSs.