Low-hit-zone frequency hopping sequence sets with optimal partial Hamming correlation properties

Construction of optimal low-hit-zone frequency hopping sequence sets under periodic partial Hamming correlation

“…Thus, E is an (11,11,11, W 0 , W0 11 ) FHS set with optimal PPHC property with respect to the bound (2).…”

“…Choose p = 11 such that gcd(p, q(q m − 1)) = 1. We can obtain an (11,11,11, W 0 , W0 11 ) one-coincidence FHS set E as shown in Example 2. Then based on Construction 1, we can get an LHZ FHS set G as follows: g 0 = {(α 0 , 0), (α 18 , 4), (α 3 , 1), (α 3 , 2), (α 12 , 7), (α 24 , 5), (α 6 , 7), (α 3 , 2), · · · }, g 1 = {(α 0 , 1), (α 18 , 5), (α 3 , 2), (α 3 , 3), (α 12 , 8), (α 24 , 6), (α 6 , 8), (α 3 , 3), · · · }, · · · g 98 = {(α 7 , 10), (α 22 , 3), (α 20 , 0), (α 20 , 1), (α 6 , 6), (α 10 , 4), (α 14 , 6), · · · }.…”

“…(j 1 L 1 , k 1 N 1 , r 1 , W 2 , z 1 − 1, W2 T1 ) k 1 z 1 = L 1 , gcd(z 1 +1, T 1 ) = 1, j 1 (z 1 +1) ≡ 1( mod L 1 ), j 1 = λz 1 + 1, λ ≥ 1 [11] (lL 2 , N 2 , r 2 , W 3 , L 2 − 1, γ) l > 0 [9] (L 3 L 4 , p 4 , p 3 p 4 , W 6 , min{L 3 , L 4 }− 1, W6 T3L4 ) gcd(L 3 , L 4 ) = 1, p 3 ( L3 T3 − 1 + η)(min{L 3 , L 4 }p 4 − 1) = L 3 L 4 (min{L 3 , L 4 } − p 3 ), 0 < η ≤ 1 [17] (pq(q m − 1), pq m−1 , pq m , W, min{p, q(q m − 1)} − 1, W p(q m −1) ) pq m+1 +p 2 −pq −q −p 2 q m−1 + 1 < 0 if p = min{p, q(q m − 1)} This paper…”

“…After that, Chung et al [6] introduced constructions of optimal LHZ FHS sets through Cartesian product in 2013. Moreover, the first construction of LHZ FHS sets with optimal PPHC property was presented by Liu et al [11] in 2013. Then Han et al [9] proposed constructions of LHZ FHS sets with optimal PPHC property through concatenated construction method in 2014.…”

Near Optimal Low-hit-zone Frequency Hopping Sequence Set with Partial Hamming Correlation Property

“…Now, very few of LHZ-PPHC FHS sets were covered in the literature. In 2013, Xing Liu et al [15] constructed a class of LHZ-PPHC FHS set based on interleaving. In 2015, Ch.…”