Paper Info
Title
Optimal frequency hopping sequences: auto- and cross-correlation properties
Abstract
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 FH 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 FH sequences are obtained.
Year
DOI
Venue
2009
10.1109/TIT.2008.2009856
IEEE Transactions on Information Theory
Keywords
Field
DocType
cross-correlation property,algebraic construction,algebraic technique,combinatorial approach,single fh sequence,optimal frequency,combinatorial characterization,hamming auto,multiple fh sequence,fh sequence,hamming correlation,maximum hamming correlation,lower bound,frequency hopping spread spectrum,cross correlation,algebra,communication system,spread spectrum communication,gamma function
Hamming code,Discrete mathematics,Combinatorics,Algebraic number,Combinatorial method,Upper and lower bounds,Hamming distance,Trace (linear algebra),Frequency-hopping spread spectrum,Mathematics,Spread spectrum
Journal
Volume
Issue
ISSN
55
2
0018-9448
Citations 
PageRank 
References 
69
2.17
8
Authors
3
Name
Order
Citations
PageRank
Gennian Ge190495.51
Ying Miao249143.85
Zhongxiang Yao3692.17