Generalized methods to construct low-hit-zone frequency-hopping sequence sets and optimal constructions

In a quasi-synchronous frequency-hopping multiple-access system, relative time delay between different users within a zone around the origin can be allowed. Therefore, frequency-hopping sequence (FHS) sets with low-hit-zone (LHZ) have attracted great interest of many related scholars. Moreover, on account of the limited synchronous time or hardware complexity, the periodic partial Hamming correlation (PPHC) plays a major role in determining the synchronization performance. In this paper, we first present three new generalized methods to construct LHZ-FHS sets via Cartesian product. Meanwhile, we pay our attention to the maximum periodic Hamming correlation (PHC) of the constructed LHZ-FHS sets in the first generalized method, and to the maximum PPHC of the constructed LHZ-FHS sets in the rest generalized methods. In addition, we also introduce five new classes of optimal LHZ-FHS sets based on these three generalized methods.