Frequency hopping sequences with optimal partial Hamming correlation by interleaving techniques

In order to evaluate the goodness of frequency hopping (FH) 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 FH sequence, so the study of the partial Hamming correlation of FH sequence is particularly important. In this paper, we first prove that there does not exist a strictly optimal FH sequence set of family size M and length N over a frequency slot set of size q with respect to the partial Hamming correlation bound when N > q² over M and q ≥ 2. In addition, we give a construction of FH sequences with optimal partial Hamming correlation by utilizing interleaving techniques.