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首页新参数下最优跳频序列构造方法
本文主要探讨了一类具有新参数的最佳跳频序列(Optimal Frequency Hopping Sequences, OFHS)的研究。在当前的通信系统中,如超宽带、军事通信和蓝牙技术中,频率跳变多址(Frequency Hopping Multiple Access, FHMA)是一种常见的干扰管理策略。为了减少多址干扰,关键在于设计一组具有低汉明相关性和交叉相关性的跳频序列,这通常涉及到寻找最优的跳频序列集合。 文章的核心贡献是提出了一种交错构造(Interleaving Construction)方法,这种方法是从已知的最佳跳频序列中衍生出新的跳频序列集。作者首先选择适合的已知最优跳频序列作为基础,然后通过递归应用所提出的构造策略,能够生成具有新颖参数的最优跳频序列和序列集合。这种创新的构造方式不仅保留了原始序列的优良特性,还能够扩展其性能,适应更广泛的通信需求。 文章引用了诸如汉明相关性(Hamming Correlation)、莱姆佩尔-格林伯格界限(Lempel-Greenberger Bound)以及彭-范界限(Peng-Fan Bound)等理论,这些理论在评估跳频序列的性能和优化过程中起着关键作用。通过这些理论分析,研究人员能够在保证通信系统的安全性与有效性的同时,设计出具有更好性能指标的新一代跳频序列。 本文的研究对于改进现有的跳频通信系统具有重要意义,特别是在提高抗干扰能力、优化频谱利用率和增强多用户环境下的通信效率方面。随着技术的发展,这类具有新参数的最佳跳频序列可能会成为未来通信系统设计中的重要组成部分。
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IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 58, NO. 7, JULY 2012 4899
A Class of Optimal Frequency Hopping
Sequences with New Parameters
Xiangyong Zeng, Han Cai, Xiaohu Tang, Member, IEEE, and Yang Yang
Abstract—In this paper, we propose an interleaving construction
of new sets of frequency hopping sequences from the known ones.
By choosing suitable known optimal frequency hopping sequences
and sets of frequency hopping sequences and then recursively ap-
plying the proposed construction, optimal frequency hopping se-
quences and sets of frequency hopping sequences with new param-
eters can be obtained.
Index Terms—Frequency hopping sequence (FHS), Hamming
correlation, interleaving technique, Lempel–Greenberger bound,
Peng–Fan bound.
I. INTRODUCTION
F
REQUENCY hopping multiple-access is widely used in
modern communication systems suc
h as ultrawideband,
military communications, Bluetooth, and so on [21]. In those
systems, we have to minimize the maximum of Hamming
out-of-phase autocorrel
ation and cross correlation of the set
of frequency hopping sequences (FHSs) to reduce the mul-
tiple-access interference. To accomm odate many users, it is also
very desirable that s
izeoftheFHSsetsisaslargeaspossible.
However, the param eters of the FHS sets are subjected to some
theoretic bounds, fo r example, the Lempel– Greenberger b ound
[18], the Peng–F
an bound [20], or the coding th eory bounds [7].
Therefore, it is of great interest to construct optimal FHSs with
respect to the bounds. During the decades, numerous algebraic
and combin
atorial constru ctions of optimal FHSs and FHS sets
have been proposed (see [1]–[10], [13]–[18], [22]–[25], an d
references therein).
The inte
rleaving technique is a method to construct a long
sequence of length
from sequences of length .They
have been widely u s ed in constructing sequences with goo d
per
iodic correlation [11], [1 2]. In 2010, Chung et al. intro-
duced interleaving technique to the design of FHSs with good
Hamming correlation [2]. Based on known optimal FHS sets,
they presented new classes of optimal FHSs with respect to
the Lempel–Greenberger bound and the Peng–Fan bound via
Manuscript received January 03, 2012; revised April 08, 2012; accepted April
10, 2012. Date of publication May 03, 2012; date of current version June 12,
2012. The work of X. Zeng and H. Cai was supported by the National Science
Foundation of China (NSFC) under Grant 61170257. The work of X. Tang and
Y. Yang was supported by the NSFC under Grant 61171095.
X. Zeng and H. Cai are with the Faculty of Mathematics and Computer Sc i-
ence, Hubei University, Wuhan 430062, China (e-mail: xiangyongzeng@yahoo.
com.cn; h ancai_s@ yahoo.cn).
X. Tang and Y . Yang are with the Provincial Key Lab of Information
Coding and Tr an smissio n, Institute of Mobile Communications, Southwest
Jiaotong University, Chengdu 610031, China (e-mail: xhutang@ieee.org;
yang-data@yahoo.cn).
Communicated by T. Helleseth, Associate Editor for Sequences.
Di
gital Object Identifier 10.1109/TIT.2012.2195771
interleaving the known FHS sets. E ach FHS in the new optimal
FHS set constructed by their method can be arranged into a
matrix such that each column of the new FHS is exactly an FHS
in the corresp onding known FHS set. Comp ared to the original
one, the new set has longer sequence length, larger Hamming
correlation, the same alphabet, and less number of sequences.
The purpose of this paper is to present a new construction
of optimal FHSs and FHS sets with new param eters by means
of interleaving technique. We present a construction of FHS
sets based on kno wn ones, which results in new FHS sets
having a longer sequence length, the same maxim um no ntrivial
Hamming correlation, and the sam e number of sequences but a
larger size of alphabet. Roughly speaking, in contrast to Chung
et al.’s method, our interleaving approach improves the size of
sequence sets but with larger alphabet, if applied to the same
known FHS sets. In our study, some known optimal FHSs
(respectively, optimal sets of FHSs) are used in the proposed
construction to construct new optimal FHSs (respectively,
optimal sets of FHSs). We list the parameters of some optimal
FHSs and sets of FHSs obtained by the proposed construc-
tion in Section IV. Furthermore, if the parameters of these
sequences satisfy some e xtra conditions, then they can be used
to recursively construct more optimal FHSs and sets of FHSs,
whose param eters have not been reported in the literature.
The remainder of this paper is organized as follows. In
Section II, we recall some prelim inaries. A construction of FHS
sets is proposed in S ection III, and the properties of these FHS
sets are also analyzed. In Section IV, some optimal FHSs and
sets of FHSs are obtained based on known optimal FH Ss and
sets of FHSs, respectively. Section V co nclu des the study.
II. P
RELIMINARIES
For a positive integer ,let be a set
of
available frequencies, also called the alphabet. A sequence
is called an FHS of length over if
for all .FortwoFHSs and
of length over ,theirHamming correlation
is defined by
(1)
where
if , and 0 otherwise, and the addi-
tion in the subscript is performed modulo
.If for all
,thenwesay and call the
Hamming autocorrelation of
, denoted by for short.
Define
as
0018-9448/$31.00 © 2012 IEEE
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