On The Average Partial Hamming Correlation of Frequency-Hopping Sequences

Wenli REN  Fang-Wei FU  Zhengchun ZHOU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.5   pp.1010-1013
Publication Date: 2013/05/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.1010
Print ISSN: 0916-8508
Type of Manuscript: LETTER
Category: Communication Theory and Signals
frequency-hopping sequence,  Hamming correlation,  partial correlation,  average correlation,  

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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≤υ, where υ is the sequence period, and generalizes the bound developed by Peng et al which is valid only when ω=υ. 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.