Construction of low-hit-zone frequency hopping sequences with optimal partial Hamming correlation by interleaving techniques

In quasi-synchronous frequency hopping code division multiple-access systems, frequency hopping sequences (FHSs) with low-hit-zone (LHZ) are commonly employed to minimize multiple-access interferences. Usually, the length of correlation window is shorter than the period of the chosen FHSs due to the limited synchronization time or hardware complexity. Thus the study of the partial Hamming correlation properties of LHZ FHSs is of particular importance. In this paper, we prove the nonexistence of LHZ FHS sets with strictly optimal partial Hamming correlation in some conditions. In addition, employing the interleaving techniques, we present a construction of LHZ FHS sets with optimal partial Hamming correlation from m-sequences. The fundamental idea of our design is to use short individual m-sequences together with certain appropriate shift sequences to construct long LHZ FHS sets with optimal partial Hamming correlation. In particular, our construction gives new parameters not covered in the literature.