Lower Bounds on the Average Partial Hamming Correlations of Frequency Hopping Sequences with Low Hit Zone

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Average Hamming correlation is an important performance indicator of frequency hopping sequences. Usually, the length of correlation window is shorter than the period of the chosen frequency hopping sequence, so the study of the partial Hamming correlations of frequency hopping sequences is particularly important. In this paper, the average partial Hamming correlation lower bounds of frequency hopping sequences with low hit zone, with respect to the size of frequency slot set, length of correlation window, family size, low hit zone, average partial Hamming autocorrelation and average partial Hamming crosscorrelation are established. It is shown that the new bounds include the Peng-Peng-Tang-Niu bounds for the conventional frequency hopping sequences as special cases.

This work was supported by the National Science Foundation of China (NSFC, 60872015).