2182 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS–I: REGULAR PAPERS, VOL. 64, NO. 8, AUGUST 2017
Multi-Carrier Chaos Shift Keying: System Design
and Performance Analysis
Hua Yang, Member, IEEE, Wallace K. S. Tang, Senior Member, IEEE, Guanrong Chen, Fellow, IEEE,
and Guo-Ping Jiang, Senior Member, IEEE
Abstract—Based on multi-carrier transmission and multi-level
chaos shift keying modulation, a novel multi-carrier chaos shift
keying (MC-CSK) modulation system is proposed and designed
in this paper. The new system adopts multiple subcarriers,
on which all chaotic basis signals along with multiple data-
bearing signals are transmitted simultaneously. The data-bearing
signals and their references, though sharing the same subcarriers,
are separated by I/Q channels. As a consequence, the MC-CSK
system can achieve higher bit rate and better spectral efficiency
compared with the MC-DCSK system. It can also dispense with
chaos synchronization and threshold shifting that are required in
conventional CSK systems, and achieve a delay-line-free design in
both transmitters and receivers. Also, the performance of the pro-
posed system is further improved by normalizing all chaotic basis
signals and making them strictly orthogonal using the Gram–
Schmidt algorithm. Moreover, the bit error rates (BERs) of the
MC-CSK system over additive white Gaussian noise and multi-
path Rayleigh fading channels are derived. Finally, simulations
are performed under different channel conditions and the effects
of system parameters on the BER performance are evaluated.
Both analytical and simulation results confirm that the MC-CSK
system outperforms differential CSK (DCSK) and MC-DCSK
systems in BER performance, except a rare case when the
number of subcarriers is very small.
Index Terms—Chaos-based communications, multi-carrier
chaos shift keying, spectral efficiency, non-coherent detector,
bit error rate.
I. INTRODUCTION
D
ISTINGISHED for their excellent communication secu-
rity, simplicity in circuit design, strong resistance to
self-interference, low probability of interception and high
robustness to multipath degradation, many chaos-based digital
Manuscript received January 2, 2017; revised February 22, 2017; accepted
March 13, 2017. Date of publication April 3, 2017; date of current ver-
sion July 26, 2017. This work was supported in part by the National
Natural Science Foundation of China under Grant 61401226 and Grant
61374180, in part by the Hong Kong Research Grants Council under Grant
GRF CityU11234916, in part by the City University of Hong Kong under
Grant 7004422, in part by the Jiangsu Government Scholarship for Oversea
Studies, and in part by the University Science Research Project of Jiangsu
Province under Grant 16KJB510045. This paper was recommended by
Associate Editor G. Jovanovic Dolecek.
H. Yang is with the School of Electronic Science and Engineering, Nanjing
University of Posts and Telecommunications, Nanjing 210023, China (e-mail:
yangh@njupt.edu.cn).
W. K. S. Tang and G. R. Chen are with the Department of Electronic
Engineering, City University of Hong Kong, Hong Kong (e-mail:
eekstang@cityu.edu.hk; eegchen@cityu.edu.hk).
G.-P. Jiang is with the School of Automation, Nanjing University of
Posts and Telecommunications, Nanjing 210023, China (e-mail: jianggp@
njupt.edu.cn).
Color versions of one or more of the figures in this paper are available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TCSI.2017.2685344
modulation schemes have been proposed, investigated and
optimized in the past two decades [1]–[12]. The basic idea
behind these schemes is to map binary/M-ary data symbols
into different non-periodic and wideband chaotic basis signals.
Generally, the chaos-based digital modulation schemes can
be classified as coherent and non-coherent schemes. For a
coherent scheme, chaos synchronization is required and this
stringent requirement is unfortunately impractical for real
world applications. Therefore, schemes using non-coherent
detectors are more popular. As a typical non-coherent system,
differential chaos shift keying (DCSK) system [3] as well
as its revised version named frequency-modulated differen-
tial chaos shift keying (FM-DCSK) system [4] has received
great attention in recent years [13]–[20]. In both systems,
transmitted-reference (T-R) technique is adopted to bypass the
requirements of chaos synchronization and channel estimation.
The data and reference signals are separated in a time division
multiple access (TDMA) fashion, and therefore demodulation
could be performed by evaluating correlations between the
first and the second halves of the received signal in one
symbol duration. Compared to other non-coherent systems,
DCSK/FM-DCSK systems can achieve much better perfor-
mances under various channel conditions [5]–[8], but at the
cost of low data rate and low energy efficiency in general.
In order to increase the data rate or to obtain higher energy
efficiency, several enhanced versions of DCSK have been
designed, including quadrature chaos shift keying (QCSK) [9],
multi-level DCSK/FM-DCSK [10], high-efficiency differential
chaos shift keying (HE-DCSK) [11] and orthogonal chaotic
vector shift keying (OCVSK) [12] systems. However, these
solutions along with DCSK/FM-DCSK are not applicable
to ultra wideband (UWB) communications because of the
need for wideband delay lines. Implementing transceivers with
wideband delay lines is practically difficult [21]. It will result
in extremely high power consumption based on digital imple-
mentation, while analog wideband delay lines are too long and
rather difficult to integrate with the CMOS technology.
To resolve the above difficulty in implementation, the wide-
band delay lines are removed from receivers in [22] and [23]
by separating data and reference signals with different Walsh
codes in the DCSK. Later, in [24], Walsh codes are substituted
by chaotic codes to gain a higher data rate. For the similar pur-
pose, a single carrier multi-level DCSK modulation system is
proposed in [25], where Walsh codes and Hilbert transform are
utilized to build multiple orthogonal basis functions. Differing
from those in [22]–[24], however, the system in [25] separates
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