Recently, Chung et al. gave a general method to construct frequency-hopping sequence set(FHS set) with low-hit-zone(LHZ FHS set) by the Cartesian product. In their paper, Theorems 5 and 8 claim that k FHS sets whose m...Recently, Chung et al. gave a general method to construct frequency-hopping sequence set(FHS set) with low-hit-zone(LHZ FHS set) by the Cartesian product. In their paper, Theorems 5 and 8 claim that k FHS sets whose maximum periodic Hamming correlation is 0 at the origin result in an LHZ FHS set based on the Cartesian product, and Proposition 4 presented an upper bound of the maximum periodic Hamming correlation of FHSs. However, their statements are imperfect or incorrect. In this paper, we give counterexamples and make corrections to them. Furthermore, based on the Cartesian product, we construct two classes of LHZ FHS sets with optimal maximum periodic partial Hamming correlation property. It is shown that new FHS sets are optimal by the maximum periodic partial Hamming correlation bound of LHZ FHS set.展开更多
In this paper, several periodic Hamming correlation lower bounds for frequency hopping sequences with low hit zone, with respect to the size p of the frequency slot set, the sequence length L, the family size M, low h...In this paper, several periodic Hamming correlation lower bounds for frequency hopping sequences with low hit zone, with respect to the size p of the frequency slot set, the sequence length L, the family size M, low hit zone LH （ or no hit zone NH ）, the maximum periodic Hamming autocorrelation sidelobe Ha and the maximum periodic Hamming crosscorrelation He, are established. It is shown that the new bounds include the known LempeI-Greenberger bounds, T.S. Seay bounds and Peng-Fan bounds for the conventional frequency hopping sequences as special cases.展开更多
基金supported by National Natural Science Foundation of China(Grant No.61271244)Key Grant Project of Ministry of Education of China(Grant No.311031 100)Young Innovative Research Team of Sichuan Province(Grant No.2011JTD0007)
文摘Recently, Chung et al. gave a general method to construct frequency-hopping sequence set(FHS set) with low-hit-zone(LHZ FHS set) by the Cartesian product. In their paper, Theorems 5 and 8 claim that k FHS sets whose maximum periodic Hamming correlation is 0 at the origin result in an LHZ FHS set based on the Cartesian product, and Proposition 4 presented an upper bound of the maximum periodic Hamming correlation of FHSs. However, their statements are imperfect or incorrect. In this paper, we give counterexamples and make corrections to them. Furthermore, based on the Cartesian product, we construct two classes of LHZ FHS sets with optimal maximum periodic partial Hamming correlation property. It is shown that new FHS sets are optimal by the maximum periodic partial Hamming correlation bound of LHZ FHS set.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 60572142） the NSFC/RFBR Joint Research Scheme, the NSFC/K0SEF Joint Research Scheme, and IITA, South Korea.
文摘In this paper, several periodic Hamming correlation lower bounds for frequency hopping sequences with low hit zone, with respect to the size p of the frequency slot set, the sequence length L, the family size M, low hit zone LH （ or no hit zone NH ）, the maximum periodic Hamming autocorrelation sidelobe Ha and the maximum periodic Hamming crosscorrelation He, are established. It is shown that the new bounds include the known LempeI-Greenberger bounds, T.S. Seay bounds and Peng-Fan bounds for the conventional frequency hopping sequences as special cases.
