Lower Bounds on the Aperiodic Hamming Correlations of Frequency Hopping Sequences

Xing LIU  Daiyuan PENG  Xianhua NIU  Fang LIU  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.6   pp.1445-1450
Publication Date: 2013/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.1445
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Spread Spectrum Technologies and Applications
Keyword: 
frequency hopping sequences,  frequency hopping spread spectrum,  aperiodic Hamming correlation,  the Peng-Fan bound,  lower bound,  

Full Text: PDF>>
Buy this Article




Summary: 
In order to evaluate the goodness of frequency hopping (FH) sequence design, the periodic Hamming correlation function is used as an important measure. But aperiodic Hamming correlation of FH sequences matters in real applications, while it received little attraction in the literature compared with periodic Hamming correlation. In this paper, the new aperiodic Hamming correlation lower bounds for FH sequences, with respect to the size of the frequency slot set, the sequence length, the family size, the maximum aperiodic Hamming autocorrelation and the maximum aperiodic Hamming crosscorrelation are established. The new aperiodic bounds are tighter than the Peng-Fan bounds. In addition, the new bounds include the second powers of the maximum aperiodic Hamming autocorrelation and the maximum aperiodic Hamming crosscorrelation but the Peng-Fan bounds do not include them. For the given sequence length, the family size and the frequency slot set size, the values of the maximum aperiodic Hamming autocorrelation and the maximum aperiodic Hamming crosscorrelation are inside of an ellipse which is given by the new aperiodic bounds.