Frequency-hopping sequence sets with no-hit-zone through Cartesian product

Abstract

For quasi-synchronous (QS) frequency-hopping multiple access (FHMA) systems, relative time delay between different users can be allowed to vary in a domain around the origin. On the other hand, for frequency-hopping sequence (FHS) sets with no-hit-zone (NHZ), there will be no hit between different sequences in case their time delay does not exceed a certain region known as NHZ. In such circumstances, NHZ-FHS sets can be well applied in QS-FHMA systems to eliminate the mutual interference (MI) and have great practical significance. In this paper, based on Cartesian product theory, three designs of NHZ-FHS sets are presented. It turns out that the newly constructed NHZ-FHS sets have optimal periodic Hamming correlation (PHC) properties and can offer help in improving the corresponding communication system performances in practice.