Optimal and near-optimal frequency-hopping sequences based on Gaussian period

被引：0

作者：

Wang, Yan ^{[1
]}

Fu, Yanxi ^{[1
]}

Li, Nian ^{[2
]}

Wang, Huanyu ^{[1
]}

机构：

[1] Xian Univ Architecture & Technol, Sch Sci, Caosi East Rd, Xian 710311, Shaanxi, Peoples R China

[2] Hubei Univ, Sch Cyber Sci & Technol, Hubei Key Lab Appl Math, Wuhan 430062, Hubei, Peoples R China

来源：

AIMS MATHEMATICS | 2023年 / 8卷 / 12期

基金：

中国国家自然科学基金;

关键词：

frequency-hopping sequence (FHS); trace function; Gaussian period; Lempel-Greenberger bound; CONSTRUCTIONS; SETS;

D O I：

10.3934/math.20231493

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Frequency-hopping sequences (FHSs) have a decisive influence on the whole frequencyhopping communication system. The Hamming correlation function plays an important role in evaluating the performance of FHSs. Constructing FHS sets that meet the theoretical bounds is crucial for the research and development of frequency-hopping communication systems. In this paper, three new classes of optimal FHSs based on trace functions are constructed. Two of them are optimal FHSs and the corresponding periodic Hamming autocorrelation value is calculated by using the known Gaussian period. It is shown that the new FHSs are optimal according to the Lempel-Greenberger bound. The third class of FHSs is the near-optimal FHSs.

引用

页码：29158 / 29170

页数：13

共 24 条

[1] Optimal frequency-hopping sequences via cyclotomy [J].

Chu, WS ;

Colbourn, CJ .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2005, 51 (03) :1139-1141

[2] k-Fold Cyclotomy and Its Application to Frequency-Hopping Sequences [J].

Chung, Jin-Ho ;

Yang, Kyeongcheol .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (04) :2306-2317

[3] Optimal Frequency-Hopping Sequences With New Parameters [J].

Chung, Jin-Ho ;

Yang, Kyeongcheol .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2010, 56 (04) :1685-1693

[4] New Classes of Optimal Frequency-Hopping Sequences by Interleaving Techniques [J].

Chung, Jin-Ho ;

Han, Yun Kyoung ;

Yang, Kyeongcheol .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2009, 55 (12) :5783-5791

[5] Sets of optimal frequency-hopping sequences [J].

Ding, Cunsheng ;

Yin, Jianxing .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2008, 54 (08) :3741-3745

[6] Algebraic constructions of optimal frequency-hopping sequences [J].

Ding, Cunsheng ;

Moisio, Marko J. ;

Yuan, Jin .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2007, 53 (07) :2606-2610

[7] Optimal frequency hopping sequences: A combinatorial approach [J].

Fuji-Hara, R ;

Miao, Y ;

Mishima, M .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2004, 50 (10) :2408-2420

[8] Further combinatorial constructions for optimal frequency-hopping sequences [J].

Ge, Gennian ;

Fuji-Hara, Ryoh ;

Miao, Ying .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2006, 113 (08) :1699-1718

[9] Optimal Frequency Hopping Sequences: Auto- and Cross-Correlation Properties [J].

Ge, Gennian ;

Miao, Ying ;

Yao, Zhongxiang .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2009, 55 (02) :867-879

[10]

Han YK, 2008, IEEE INT SYMP INFO, P2593, DOI 10.1109/ISIT.2008.4595460

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