A class of optimal frequency hopping sequences based upon the theory of power residues

Daiyuan Peng; Tu Peng; Xiaohu Tang; Xianhua Niu

doi:10.1007/978-3-540-85912-3_18

A class of optimal frequency hopping sequences based upon the theory of power residues

Daiyuan Peng^*, Tu Peng, Xiaohu Tang, Xianhua Niu

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

31 Citations (Scopus)

Abstract

The average Hamming correlation is an important performance indicator of the frequency hopping sequences. In this paper, the theoretical bound on the average Hamming correlation for frequency hopping sequences is established. Besides, a new family of frequency hopping sequences is proposed and investigated. The construction of new frequency hopping sequences is based upon the theory of power residues, and the new frequency hopping sequences are called the power residue frequency hopping sequences. It is shown that new frequency hopping sequences are optimal with respect to both average Hamming correlation family and the optimal maximum Hamming correlation.

Original language	English
Title of host publication	Sequences and Their Applications - SETA 2008 - 5th International Conference, Proceedings
Pages	188-196
Number of pages	9
DOIs	https://doi.org/10.1007/978-3-540-85912-3_18
Publication status	Published - 2008
Externally published	Yes
Event	5th International Conference on Sequences and Their Applications, SETA 2008 - Lexington, KY, United States Duration: 14 Sept 2008 → 18 Sept 2008

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5203 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	5th International Conference on Sequences and Their Applications, SETA 2008
Country/Territory	United States
City	Lexington, KY
Period	14/09/08 → 18/09/08

Keywords

Average Hamming correlation
Frequency hopping sequence
Hamming correlation
Theoretical bound

Access to Document

10.1007/978-3-540-85912-3_18

Cite this

Peng, D., Peng, T., Tang, X., & Niu, X. (2008). A class of optimal frequency hopping sequences based upon the theory of power residues. In Sequences and Their Applications - SETA 2008 - 5th International Conference, Proceedings (pp. 188-196). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5203 LNCS). https://doi.org/10.1007/978-3-540-85912-3_18

Peng, Daiyuan ; Peng, Tu ; Tang, Xiaohu et al. / A class of optimal frequency hopping sequences based upon the theory of power residues. Sequences and Their Applications - SETA 2008 - 5th International Conference, Proceedings. 2008. pp. 188-196 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "The average Hamming correlation is an important performance indicator of the frequency hopping sequences. In this paper, the theoretical bound on the average Hamming correlation for frequency hopping sequences is established. Besides, a new family of frequency hopping sequences is proposed and investigated. The construction of new frequency hopping sequences is based upon the theory of power residues, and the new frequency hopping sequences are called the power residue frequency hopping sequences. It is shown that new frequency hopping sequences are optimal with respect to both average Hamming correlation family and the optimal maximum Hamming correlation.",

keywords = "Average Hamming correlation, Frequency hopping sequence, Hamming correlation, Theoretical bound",

author = "Daiyuan Peng and Tu Peng and Xiaohu Tang and Xianhua Niu",

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language = "English",

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Peng, D, Peng, T, Tang, X & Niu, X 2008, A class of optimal frequency hopping sequences based upon the theory of power residues. in Sequences and Their Applications - SETA 2008 - 5th International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5203 LNCS, pp. 188-196, 5th International Conference on Sequences and Their Applications, SETA 2008, Lexington, KY, United States, 14/09/08. https://doi.org/10.1007/978-3-540-85912-3_18

A class of optimal frequency hopping sequences based upon the theory of power residues. / Peng, Daiyuan; Peng, Tu; Tang, Xiaohu et al.
Sequences and Their Applications - SETA 2008 - 5th International Conference, Proceedings. 2008. p. 188-196 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5203 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Niu, Xianhua

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N2 - The average Hamming correlation is an important performance indicator of the frequency hopping sequences. In this paper, the theoretical bound on the average Hamming correlation for frequency hopping sequences is established. Besides, a new family of frequency hopping sequences is proposed and investigated. The construction of new frequency hopping sequences is based upon the theory of power residues, and the new frequency hopping sequences are called the power residue frequency hopping sequences. It is shown that new frequency hopping sequences are optimal with respect to both average Hamming correlation family and the optimal maximum Hamming correlation.

AB - The average Hamming correlation is an important performance indicator of the frequency hopping sequences. In this paper, the theoretical bound on the average Hamming correlation for frequency hopping sequences is established. Besides, a new family of frequency hopping sequences is proposed and investigated. The construction of new frequency hopping sequences is based upon the theory of power residues, and the new frequency hopping sequences are called the power residue frequency hopping sequences. It is shown that new frequency hopping sequences are optimal with respect to both average Hamming correlation family and the optimal maximum Hamming correlation.

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KW - Frequency hopping sequence

KW - Hamming correlation

KW - Theoretical bound

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DO - 10.1007/978-3-540-85912-3_18

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Peng D, Peng T, Tang X, Niu X. A class of optimal frequency hopping sequences based upon the theory of power residues. In Sequences and Their Applications - SETA 2008 - 5th International Conference, Proceedings. 2008. p. 188-196. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-85912-3_18

A class of optimal frequency hopping sequences based upon the theory of power residues

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