Optimal Frequency-Hopping Sequences With New Parameters
Optimal Frequency-Hopping Sequences With New Parameters
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DOI：
10.1109/tit.2010.2040888
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发表时间：
2010-04
影响因子：
2.5
通讯作者：
Jin-Ho Chung;Kyeongcheol Yang
中科院分区：
文献类型：
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作者：
Jin-Ho Chung;Kyeongcheol Yang
长度为v、频率集大小为M的跳频序列(FHS)称为(v，M，？)-FHS，如果它的最大异相汉明自相关为？本文提出了三类新的关于Lempel-Greenberger界的最优FHS。首先，当p=mf+1是奇素数且f为偶数且p？3mod4时，构造了新的最优(p，M，f)-FHS。然后，对任意奇素数p和正整数K1、p1(p1+2)、2m-1或p1m-1，给出了最优(Kp，p，k)-FHSs的构造，其中p1和p1+2为奇素数。最后，还提出了几种具有最大异相汉明自相关1或2的新的最优跳频结构。特别地，证明了对于任何整数N？3和任何具有N+1？v？2 N-1的整数v，存在最优的(v，N，1)-FHS，以及对于任何整数N？3，证明了最优的(2N+1，N，2)-FHS的存在性。这些最优FHS具有文献中没有讨论的新参数。
A frequency-hopping sequence (FHS) of length v and frequency set size M is called a (v,M,¿)-FHS if its maximum out-of-phase Hamming autocorrelation is ¿. Three new classes of optimal FHSs with respect to the Lempel-Greenberger bound are presented in this paper. First, new optimal (p,M,f)-FHSs are constructed when p = Mf +1 is an odd prime such that f is even and p ¿ 3 mod 4 . And then, a construction for optimal (kp,p,k)-FHSs is given for any odd prime p and a positive integer K 1,p1(p1 + 2 ),2m -1,or p1 m-1, where p1 and p1+2 are odd primes. Finally, several new optimal FHSs with maximum out-of-phase Hamming autocorrelation 1 or 2 are also presented. In particular, the existence of optimal (v,N,1)-FHSs is proven for any integer N ¿ 3 and any integer v with N +1 ¿ v ¿ 2 N-1, as well as the existence of optimal (2N +1,N,2)-FHSs is shown for any integer N ¿ 3. These classes of optimal FHSs have new parameters which are not covered in the literature.