Optimal Bounds for Partial Hamming Correlation of Multi-Timeslot Wide-Gap Frequency-Hopping Sequence Sets

Abstract

Frequency-hopping multiple access (FHMA) systems offer significant advantages such as jamming resistance, multi-user capability, and enhanced security, making them crucial for secure communications and wireless networks. This letter establishes new theoretical bounds on the maximum periodic Hamming autocorrelation (PHAC) and periodic partial Hamming autocorrelation (PPHAC) for multi-timeslot wide-gap frequency-hopping sequences (MTWGFHSs), along with the maximum periodic partial Hamming correlation (PPHC) for MTWGFHS sets. These advancements address the challenges posed by dynamic channels and intelligent jamming, contributing to a robust FHMA system.