On The Average Partial Hamming Correlation of Frequency-Hopping Sequences

Abstract

The average Hamming correlation is an important performance indicator of frequency-hopping sequences (FHSs). In this letter, the average partial Hamming correlation (APHC) properties of FHSs are discussed. Firstly, the theoretical bound on the average partial Hamming correlation of FHSs is established. It works for any correlation window with length 1≤ω≤v, where v is the sequence period, and generalizes the bound developed by Peng et al which is valid only when ω=v. A sufficient and necessary condition for a set of FHSs having optimal APHC for any correlation window is then given. Finally, sets of FHSs with optimal APHC are presented.