Lower bounds on the periodic partial correlations of frequency hopping sequences with partial low hit zone

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 periodic partial Hamming correlation of frequency hopping sequence is particularly important. In this paper, the periodic partial Hamming correlation lower bounds for frequency hopping sequences with partial low hit zone, with respect to the size of the frequency slot set, the length of correlation window, the family size, the partial low hit zone, the maximum periodic partial Hamming autocorrelation and the maximum periodic partial Hamming crosscorrelation are established. It is shown that the new bound include the known Lempel-Greenberger bound, Peng-Fan bound and Eun-Jin-Hong-Song bound for the conventional frequency hopping sequences as special cases.