New sets of optimal low-hit-zone frequency-hopping sequences based on m-sequences

Two constructions of low-hit-zone frequency-hopping sequence sets

“…It is of great interest to construct optimal sets of LHZ FHSs. There have been a number of optimal LHZ FHS sets satisfying Peng-Fan-Lee bound [22] (see for example [1,11,15,17,18,19,25,28]) and LHZ FHS sets with optimal partial Hamming correlation (PPHC) satisfying Niu-Peng-Liu-Liu bound [16] (see for example [9,10,13,14,24,26,28]). Now we give attention to the earlier constructions that are related to our work.…”

“…Afterwards, Zhou et al gave two generic constructions of optimal FHS sets [29] employing d-form functions with differencebalanced property, and constructed strictly optimal FHS sets [30] by employing sequences with array structure. In 2017 and 2020, Han et al [11,9] constructed several classes of optimal sets of LHZ FHSs based on m-sequences and its decimated sequences. In 2019, Ouyang et al [20] constructed three classes of strictly optimal FHS sets.…”

“…In this paper, we give two constructions of optimal FHS sets with low hit zone with respect to the Peng-Fan-Lee bound and the Niu-Peng-Liu-Liu bound. The first construction can be viewed as a unification and a generalization of the constructions in [11,9,20,27,29,30]. In the first construction, we not only make corrections to Theorem 1 and Theorem 2 of [27] in Remark 4, but also generate several classes of optimal FHS sets with low hit zone with new parameters, which can be seen through Table 1.…”

“…In the first construction, we not only make corrections to Theorem 1 and Theorem 2 of [27] in Remark 4, but also generate several classes of optimal FHS sets with low hit zone with new parameters, which can be seen through Table 1. The second construction can be viewed as a generalization of the constructions in [11,29,27].…”

New classes of strictly optimal low hit zone frequency hopping sequence sets

“…LHZ FHS sets with low Hamming correlation within the fixed zone are useful in quasi-synchronous frequency hopping multiple-access (FHMA) systems wherein relative delays between distinct users are restricted within a zone around the origin [9]. Several optimal LHZ FHS sets with respect to the Peng-Fan-Lee bound [20] have been constructed in literature [4,13,15,18].…”