Information Technology Reference
In-Depth Information
A Class of Optimal Frequency Hopping
Sequences Based upon
the Theory of Power Residues
Daiyuan Peng
1
,TuPeng
2
,
Xiaohu Tang
1
,andXianhuaNiu
1
1
Key Laboratory of Information Coding and Transmission, Southwest
Jiaotong University, Chengdu, Sichuan 610031, P.R. of China
dypeng@swjtu.edu.cn, xhutang@ieee.org,
cow flower1212@yahoo.com.cn
2
Department of Computer Science, University of Texas at Dallas,
Ricardson, TX 75080-3021 USA
pengtutu@gmail.com
Abstract.
The average Hamming correlation is an important perfor-
mance indicator of the frequency hopping sequences. In this paper, the
theoretical bound on the average Hamming correlation for frequency hop-
ping sequences is established. Besides, a new family of frequency hop-
ping 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 se-
quences are optimal with respect to both average Hamming correlation
family and the optimal maximum Hamming correlation.
Keywords:
average Hamming correlation, Hamming correlation, fre-
quency hopping sequence, theoretical bound.
1
Introduction
The design of frequency hopping (FH) sequences is suitable for frequency hop-
ping or time hopping (TH) CDMA systems, multi-user radar and sonar systems
which remain of great interest in recent years [1,2]. In FH CDMA systems, the
address assignment must be achieved in such a way that there is no ambiguity
about the sender and the information it transmits, and the received signal must
interfere as negligible as possible to the reception of other users' signals. The
mutual interference in FH CDMA is mainly controlled by the Hamming cross-
correlation of the hopping sequences. The need for finding FH sequences which
