Lower Bounds on the Maximum Partial Correlations of Frequency Hopping Sequence Set with Low Hit Zone

Xianhua NIU  Daiyuan PENG  Fang LIU  Xing LIU  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A   No.11   pp.2227-2231
Publication Date: 2010/11/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.2227
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Signal Design and its Application in Communications)
Category: Sequences
frequency hopping sequences,  correlation window,  low hit zone,  maximum partial Hamming correlation,  

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In order to evaluate the goodness of frequency hopping sequence design, the periodic Hamming correlation function is used as an important measure. Usually, the length of correlation window is shorter than the period of the chosen frequency hopping sequence, so the study of the partial Hamming correlation of frequency hopping sequence is particularly important. In this paper, the maximum partial Hamming correlation lower bounds of frequency hopping sequences with low hit zone, with respect to the size of the frequency slot set, the length of correlation window, the family size, the low hit zone, the maximum partial Hamming autocorrelation and the maximum partial Hamming crosscorrelation are established. It is shown that the new bounds include the known Lempel-Greenberger bound, Peng-Fan bounds, Eun-Jin-Hong-Song bound and Peng-Fan-Lee bounds as special cases.