Optimal Frequency Hopping Sequences: Auto- and Cross-Correlation Properties

被引:104
|
作者
Ge, Gennian [1 ]
Miao, Ying [2 ]
Yao, Zhongxiang [1 ]
机构
[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China
[2] Univ Tsukuba, Dept Social Syst & Management, Grad Sch Syst & Informat Engn, Tsukuba, Ibaraki 3058573, Japan
基金
中国国家自然科学基金;
关键词
Gamma function; character sum; frequency hopping sequence; Hamming correlation; optimality; partition-type balanced nested difference packing; spread-spectrum communication; trace function; LOWER BOUNDS; CONSTRUCTIONS;
D O I
10.1109/TIT.2008.2009856
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
Frequency hopping (FH) sequences play a key role in frequency hopping spread spectrum communication systems. In order to evaluate the performance of FH sequences, Lempel and Greenberger (1974) and Peng and Fan (2004) derived lower bounds on their Hamming auto- and cross-correlations. In this paper, we construct families of Fit sequences with Hamming correlations meeting those bounds by combinatorial and algebraic techniques. We first construct optimal families consisting of a single FH sequence with maximum Hamming correlation equal to 2 from a combinatorial approach. Then we investigate families consisting of multiple FH sequences. We provide a combinatorial characterization for such families, and present a recursive method to construct them by means of this characterization. We also describe two algebraic constructions for such families of FH sequences, generalizing those of Ding, Moisio, and Yuan (2007). As a consequence, many new optimal families of Fit sequences are obtained.
引用
收藏
页码:867 / 879
页数:13
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