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196 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 58, NO. 1, JANUARY 2011
Performance of DCSK Cooperative Communication
Systems Over Multipath Fading Channels
Weikai Xu, Student Member, IEEE, Lin Wang, Senior Member, IEEE, and Guanrong Chen, Fellow, IEEE
Abstract—A differential chaos shift keying cooperative commu-
nication (DCSK-CC) system with two users is proposed in this
paper, which has an orthogonal subchannel in broadcast phase and
cooperative phase through orthogonal Walsh code sequences as
its multiaccess scheme. The single relay cooperative network with
decode-and-forward relay is investigated in the proposed system
according to two cooperation protocols, namely, conventional
cooperation and space-time cooperation. Unlike conventional
CDMA cooperative communication (CDMA-CC) systems, quite
surprisingly power control devices that consume more energy to
mitigate near-far effects can be avoided in the proposed system,
which is of great importance to energy-constrained networks such
as wireless sensor networks. Simulation results demonstrate that,
through a conventional cooperation mechanism, the proposed
system has a prominent advantage of good bit-error-probability
(BEP) performance over the CDMA-CC systems that have a single
path correlation receiver, at the same data rate with a high SNR
range over multipath Rayleigh fading channels. Meanwhile, it
is found that conventional cooperation is a better cooperation
strategy relative to space-time cooperation in the proposed system.
In addition, a lower bound of BEP performance is derived and
verified by simulations over independent three-ray Rayleigh
fading channels.
Index Terms—Bit error probability (BEP), chaotic communica-
tion, differential chaos shift keying (DCSK) cooperative communi-
cation system, multipath Rayleigh fading channel, near-far effect.
I. INTRODUCTION
BY using a chaotic carrier to spread a digital signal over
a wide bandwidth spectrum, the resulting system inherits
the benefits of spread-spectrum communications such as mitiga-
tion of multipath fading. Based on this observation, a number of
chaos-based communication schemes have been proposed and
analyzed in recent years [1]–[16]. Among all the digital commu-
nication schemes proposed thus far, DCSK and frequency-mod-
ulated (FM )-DCSK show superior capability in terms of anti-in-
terference over multipath fading channels. Compared with the
direct-sequence spread-spectrum CDMA technique, the DCSK
Manuscript received January 18, 2010; revised April 23, 2010; accepted June
16, 2010. Date of publication November 11, 2010; date of current version De-
cember 30, 2010. This work was supported in part by the City University of
Hong Kong under SRG Grant 7002453 and in part by the National Natural Sci-
ence Foundation of China under Grant 60972053 and Grant 61001073. This
paper was recommended by Associate Editor M. Laddomada.
W. Xu and L. Wang are with the Department ofCommunication Engineering,
Xiamen University, Fujian 361005, China (e-mail: xweikai@xmu.edu.cn; wan-
glin@xmu.edu.cn).
G. Chen is with the Department of Electronic Engineering, City University
of Hong Kong, Hong Kong SAR, China (e-mail: eegchen@cityu.edu.hk).
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.2010.2071730
with autocorrelation receiver (AcR) does not need code acqui-
sition and synchronization, nor channel estimation, but only re-
quires frame or symbol rate sampling, which is also desirable
in applications. Based on these advantages, some ultrawide-
band systems based on DCSK or FM-DCSK modulations have
been proposed recently, e.g., for wireless personal area networks
(WPAN) [17]–[21].
In a wireless network, system performance degrading is
mainly attributed to signal fading and intersymbol interfer-
ence (ISI) arising under multipath propagation environments.
In general, signal fading can be mitigated by using a diver-
sity technique by which redundant signals over independent
channel realizations are transmitted so as to obtain anti-fading
performance with suitable receivers. Multiple-antenna (spatial)
diversity techniques are particularly attractive as they can be
easily combined with other forms of diversity, meanwhile
offering significant performance gains even if other forms of
diversity are unavailable. Over the past two decades, mul-
tiple-antenna diversity has been unprecedentedly developed
[22]–[26]. In [27], a single-input multiple-output (SIMO)
system based on FM-DCSK was proposed. Notice, however,
that the multiple-antenna transmission diversity suggested in
[22], [23] is hardly deployed in DCSK due to the variation of
its carrier in different bit periods. Moreover, in wireless sensor
networks (WSN), multiple-antenna diversity is impractical
due to the cost and size of the sensors. In order to overcome
this limit, a new form of spatial diversity—user cooperative
diversity—was proposed by emulating the transmitting antenna
diversity in [28] and [29].
In this paper, the two-user cooperative diversity technique is
introduced into the DCSK system. The Walsh code sequences
with excellent cross-correlation characteristics are adopted as
user multiple access [30]. Compared with the cooperative di-
versity system based on CDMA [28], [29], the proposed system
obtains both multipath diversity gain and cooperative diversity
gain using a simpler AcR.
The remainder of this paper is organized as follows. The
principle of DCSK and the two-user cooperative system based
on DCSK are presented in Section II. The bit error proba-
bility (BEP) lower bound of the proposed system is analyzed
in Section III. Then, simulation results and discussions are
presented in Section IV. Finally, conclusions are drawn in
Section V.
II. SYSTEM MODEL
This section reviews the related system models, based on
which the proposed system is developed.
1549-8328/$26.00 © 2010 IEEE
XU et al.: PERFORMANCE OF DCSK COOPERATIVE COMMUNICATION SYSTEMS OVER MULTIPATH FADING CHANNELS 197
Fig. 1. Block diagram of DCSK transceiver. (a) Transmitter. (b) Receiver.
A. Principle of DCSK
DCSK uses a chaotic signal as the carrier, with a differential
shift keying modulator, for transmission. The chaotic signal is
generated by a chaotic mapping method [31], and the simple
Logistic chaotic map is chosen here for implementation. Fig. 1
shows the block diagram of the binary DCSK communication
system. The binary DCSK modulation unit transmits a refer-
ence segment of the chaotic signal in the first half of the symbol
duration, and repeats or reverses the segment in the last half of
the symbol duration, according to the digital information “1” or
“0,” respectively. The modulated signal is represented by two
orthogonal basis functions, and , as follows
(1)
Here, is modulated signal for transmission and is the bit
energy. The two orthogonal basis functions are
,(2)
where is the bit duration and is the chaotic signal.
In DCSK, each basis function consists of a reference and an
information-bearing segment. The receiver can be implemented
using a suboptimum AcR. In AcR, the observation signal is
given by
(3)
where is the received signal into the AcR.
B. Multiple-User System Based on Walsh Codes
For a multiple user or nonbinary DCSK communication
system, the orthogonal Walsh code sequences were adopted for
implementation [30].
Let be a -order Walsh code sequence, ,
. The -order Walsh code sequences are
recursively constructed as follows:
(4)
Fig. 2. DCSK demodulator using GML detection.
For example, for, , second- and fourth-order Walsh
code sequences are, respectively,
(5)
During the demodulation process, the generalized maximum
likelihood (GML) detection rule may be applied [32]. As a
universal method, second-order Walsh code is used for binary
DCSK and higher order Walsh code is employed for multiuser
or nonbinary DCSK. The binary DCSK demodulator using
GML detection is illustrated in Fig. 2.
As shown in Fig. 2, the weighted energy received is
(6)
where is the bit duration, is the received signal, and
are the corresponding elements in the second-
order Walsh code, which are being multiplied as the weights
during the modulation. The demodulator needs to find the index
that maximizes , and then make a decision on the
bit, either “1” or “0.”
The above-described Walsh code-based DCSK modulation
scheme is now extended to a multiple-access system. Consider
a system with users. Let denote the length of each carrier
segment, and denote the global spread-spectrum factor. One
may use -order Walsh code to accommodate the users.
During the modulation, one forces so as to make
sure that the global spread-spectrum factor f is kept constant.
The transmitted signal of the user can be expressed by the
-order orthogonal Walsh code, as follows:
(7)
where , is a row vector of the -order
Walsh code.
The demodulation process of multiple users based on the
Walsh code can be readily extended further from binary DCSK
198 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 58, NO. 1, JANUARY 2011
Fig. 3. Block diagram of the -user receiver.
Fig. 4. The cooperative transmission scheme (a) Odd period, transmit self data
(b) Even period, relay the data of partner’s.
with GML detection rule. The block diagram of the demodu-
lator of the user is shown in Fig. 3, and the weighted energy
combined of the -user bit is expressed as
(8)
where ( or 1) denotes the decision statistic of the
user.
C. Two-User Cooperation Model
For exposition, consider a cellular system in which two mo-
biles are communicating with a base station. The channels be-
tween each user and the base station (the uplink channel) are
independent, so are the channels between the two users (the
interuser channel). Due to the advantages of DCSK over fre-
quency-selective channels, all channels are assumed to subject
to static block frequency-selective fading; that is, the channel
state remains constant during each cooperative period. It is as-
sumed that a cooperative period is divided into broadcast phase
and cooperative phase, denoted as odd period and even period,
respectively. The transceiver model used is illustrated by Fig. 4.
The signals at the receiver can be expressed as (9) and (10) at the
bottom of the page. Here, is the convolution operator, ,
and are the baseband model of signals at the base
station, user 1 and user 2, respectively, during a frame period.
Moreover, is the signal transmitted by user , , and
is a white Gaussian noise random process with zero mean
and two-sided power spectral density , . The
channel multipath impulse response are modeled as a linear
time-invariant process, , where
Fig. 5. Cooperation protocol of the two-user DCSK-CC system (a) Conven-
tional cooperation (b) Space-time cooperation.
and denote the attenuation and delay of the -path, respec-
tively, and is the number of the multipath components. It is
typically assumed that the channel multipath impulse responses
are same for both odd periods and even periods. User 1 recon-
structs the partner’s information into through in
odd periods, user 2 uses in a similar fashion to reconstruct
the partner’s information into . Then, the two users co-
operate to both send their messages to the base station in even
periods.
In general, user-cooperative algorithms at relay, such as
amplify-and-forward (AF) or decode-and-forward (DF), were
applied [33]. In the case of AF, the user simply amplifies
its partner’s signal and then forwards it to the destination,
whereas in the case of DF, the partner’s signal is decoded,
reencoded, and then forwarded to the destination. Although
both full-duplex and half-duplex relay channels can be im-
plemented for user cooperative schemes [33], this paper only
discusses half-duplex transmission. Unlike the conventional
time-division or frequency-division relay channels, a pair of
orthogonal sequences of fourth-order Walsh code is allocated to
each user in the DCSK-CC system. Fig. 5 shows conventional
cooperation and space-time cooperation, respectively.
III. PERFORMANCE LOWER BOUND
As a lower bound, BEP of the DCSK-CC system is analyzed
under the ideal condition, namely, error-free DF at the relay
user. During the whole cooperative period, there is a distinction
between “odd” and “even” periods. During the “odd” period,
each user sends only its own data, which are received and de-
tected by the base station and by its partner, respectively. The
(9)
(10)
XU et al.: PERFORMANCE OF DCSK COOPERATIVE COMMUNICATION SYSTEMS OVER MULTIPATH FADING CHANNELS 199
signal transmitted by user 1 is as seen in (9). It is received
by its partner according to , and
by the base station according to
, respectively. Adopting the GML de-
modulation algorithm based on Walsh codes, the partner uses
to form a hard estimate of of user 1, whereas the base
station depends on its received signal to make a soft decision of
. The BEP of the partner’s hard decision estimate of is
equal to
(11)
where is the conditional BEP over a fading multipath
channel, and is the instantaneous signal-to-noise ratio (SNR)
of the fading multipath channel. Assuming that bit “1” is trans-
mitted, can be expressed as
(12)
According to the GML algorithm, where and are
weighted energies of bit “0” and bit “1” of user 1, respectively.
With DCSK modulation, for a large spread-spectrum factor and
if the logistic map is used, the corresponding can be
simplified as [34]
(13)
Denoting ,
and , and assuming is the inde-
pendent and identically-distributed(i.i.d.) Rayleigh distribution
random variables, one can verify that is an i.i.d. exponen-
tial distribution random variable, with probability density func-
tion (PDF) . The BEP of the partner’s
hard decision estimate of is calculated by (11) and (13). The
PDF of can be obtained, as
(14)
where is the PDF of the instantaneous signal-to-noise
ratio (SNR) of the path component. To simplify the analysis,
a three-path channel is assumed, whose power delay profile is
. From (14), the PDF
of is expressed by
(15)
For , the function can be approximately ex-
pressed by
(16)
Substituting (13), (15), and (16) into (11), the BEP of user 1
at the partner is approximately expressed as (17) at the bottom
of the page. So, the BEP can be evaluated through numerical
integral of (17).
On the other hand, due to the orthogonality of Walsh code
sequences, the base station makes a soft decision in the “odd”
period by calculating
(18)
During the “even” period, the two users both send to the base
station a cooperative signal consisting of what each user esti-
mates from its partner’s bit in the “odd” period. The transmitted
signals of the two partners are
(19)
where and are the estimated bits of user 1 and user 2 at
their partners in the “odd” period, respectively. The base station
receives signal and extracts a soft decision statistic by
calculating
(20)
At the base station, assuming transmitted bit , the prob-
ability of bit error of user 1 is calculated by
(21)
where denotes the weighted energy of user 1, which is
a combination of the “odd” period and the “even” period. De-
note as a combined weight for the relay link decision
statistics at the base station, (21) is expressed in more detail as
(22) at the bottom of the page. When , the combination
(17)
200 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 58, NO. 1, JANUARY 2011
manner collapses to combined equal gains; that is, the even pe-
riod has the same combination weight as the odd period. More
specifically, if the interuser channel is perfect, i.e., ,
then the lower bound of BEP is approximately estimated as
(23)
where and are SNR conditioned channels between
user 1 to the base station and between user 2 to the base station.
It is assumed that the power delay profile of channels between
user 1 and user 2 and between the users and the base station
are all the same. Thus, the conditioned SNRs ( and )
are i.i.d. random variables. The distribution of SNR at the base
station is given as
(24)
Substituting (15) into (24), the conditioned SNR becomes
(25) at the bottom of the page, where
Substituting (13) and (25) into (11) and exploiting (16), the ap-
proximate BEP lower bound can be easily evaluated by numer-
ical computation.
IV. RESULTS AND DISCUSSIONS
A. BEP Lower Bound of the Two-User Cooperative System
The BEP lower bound given above is a benchmark of the
DCSK-CC system in wireless multipath environment. Herein,
numerical and simulated results are provided for evaluating this
BEP lower bound. In Fig. 6, the numerical BEP lower bound and
Fig. 6. BEP curves of the DCSK-CC system with error-free or error for-
warding.
simulated results of the two-user DCSK-CC system are plotted
for and , respectively. The numerical results are
obtained by numerical computation using (11), (13), and (25),
while the simulated results are obtained by the Monte Carlo
method assuming error-free DF at the relay user. It can be seen
that the approximately BEP lower bound well agrees with the
simulation results.
The effect of the spread spectrum factor on numerical results
of the BEP lower bound is shown in Fig. 6. Here, when is
32, the numerical results do not agree well with the simulated
ones, since in the derivation of the BEP lower bound, the spread
spectrum factor is assumed to be much higher than the multi-
path time delay so that ISI could be neglected. Under this as-
sumption, for a given fixed multipath time delay, the greater the
spread spectrum factor is, the better the agreement of numerical
results and simulation results is.
In addition, the BEP curves of the DCSK-CC System with
error DF in an equal user distance situation are provided in
Fig. 6. It shows that there is a large gap between BEP lower
bounds of the DCSK-CC and BEP of DCSK-CC with error DF;
(22)
(25)
XU et al.: PERFORMANCE OF DCSK COOPERATIVE COMMUNICATION SYSTEMS OVER MULTIPATH FADING CHANNELS 201
namely, between the two different groups of curves. This is be-
cause there are errors when relay user forwards information in
the actual cooperative system. How can the gap between the
lower bound and a real system be reduced? One method is to
use the adaptive decode-forward protocol that the cyclic redun-
dancy check (CRC) are adopted for parity check at the relay
user. The relay user does not relay partner’s data if the parity
check is not satisfied. Correspondingly, the complexity of the
relay user and the delay of data transmission will be increased.
B. Performance Comparison Between the DCSK-CC System
and the CDMA-CC System
The user-cooperative scheme was proposed as an efficient
wireless diversity technique and introduced into CDMA
systems in [28] and [29], where performance of two-user coop-
erative diversity was studied over flat Rayleigh fading channels.
For convenient comparison with DCSK-CC, the CDMA-CC
system is extended over to frequency-selective Rayleigh fading
channels. The Gold-sequences are adopted as spread-spec-
trum sequences. Notice that the length of a Gold-sequence
is always odd, whereas the global spread-spectrum factor of
the DCSK-CC system is always even. Therefore, similarly to
the standard IMT-2000 [35], an extra “0” is added at the end
of each Gold-sequence to match the spread-spectrum factor,
thereby ensuring the same bandwidth efficiency of the two
systems. Thus, the comparison between the DCSK-CC and the
CDMA-CC can be easily carried out and clearly shown. At
the receiver, the conventional receive algorithm, i.e., the single
path correlation receiver, is adopted.
The near-far effect is a common phenomenon in wireless
communication systems (in particular, CDMA). To mitigate the
near-far effect, power control is an effective strategy for CDMA
systems. Assume that the path loss of all links is proportional to
, where d denotes the link distance between two users. The
near-far effect corresponds to the effect of relay’s location in
a user cooperative communication system. Assume that source,
relay, and destination terminals are located in a two-dimensional
plane, with , , and denoting the link distances of
source to destination, source to relay and relay to destination,
respectively. All distances are normalized by the distance ,
so the distance ratio represents the geometric
positions of all users. So, except for the distance ratio of 1:1:1,
there are near-far effects. The performance comparison between
DCSK-CC and CDMA-CC based on conventional cooperation
schemes [cooperation pattern of Fig. 5(a)] without power con-
trol is considered here.
The error performance of the proposed two-user DCSK-CC
and CDMA-CC have been simulated by the Monte Carlo
method over three-path multipath quasi-static block-faded
channels. The path gains of the channels are the same with those
assumed in Section III, and the delays are ,
where is the sampling period of the chaotic signal.
Figs. 7 and 8 show the BEP performance of the DCSK-CC
system and the CDMA-CC system in various scenarios with
different user-distance ratios and with
spread-spectrum factors of 32 and 64, respectively. From these
figures, one can see that the BEP curves of the DCSK-CC
system become lower than that of the CDMA-CC system
Fig. 7. BEP performance comparisons of the DCSK-CC system and the
CDMA-CC system, .
Fig. 8. BEP performance comparisons of the DCSK-CC system and the
CDMA-CC system, .
in high-SNR range, except for the case with distance ratios
1:1:1. The slopes of the BEP curves of the DCSK-CC system
become steeper than that of the CDMA-CC system at BEP
levels below for the scenarios with near-far effects. The
difference of the slopes aforementioned indicates that the
performance of the DCSK-CC system with a steeper slope is
more sensitive to noise than the CDMA-CC system at high
values of SNR. The DCSK-CC system is more effective at high
SNR for the reason given below. Autocorrelation receiver of
DCSK obtains the gain of multipath diversity as well as the
user-cooperative diversity gain in the proposed scheme. On the
contrary, the conventional single path correlation receiver of
CDMA cannot get multipath diversity gain unless the RAKE
receiver is applied. However, compared with AcR of DCSK,
the RAKE receiver requires complete knowledge about the
channel state information, which is usually obtained by the
complex channel estimation algorithm. So, it is unsuitable for
low-power and low-complexity applications, for example the
WSN. Consequently, the DCSK-CC system has performance
advantages at the BEP of to meet the low-cost
202 IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: REGULAR PAPERS, VOL. 58, NO. 1, JANUARY 2011
Fig. 9. BEP performance comparisons of the DCSK-CC system and the
CDMA-CC system over COST 207 RA channel, .
data transmission demands. In particular, it achieves greater
performance advantages in near-far effect scenarios. Thus,
compared with the CDMA-CC network, the energy consump-
tion and complexity of the proposed network are reduced,
without using the power control techniques at the transmitter.
To further justify the advantages of the proposed scheme, its
performances on COST 207 Rural Area multipath channel [36],
whose power delay profile is , are eval-
uated and compared. Assume that the path gains have Rayleigh
distributions, and the delay vector is .
Fig. 9 shows the BEP curves of the DCSK-CC system and
CDMA-CC system in various scenes of user-distance ratios,
with a spread-spectrum factor of 64. One can see that the ad-
vantages of DCSK-CC system are held in the far-near scenarios
as well.
C. Comparison With the Space-Time Cooperative System
Tofurther improve the error performance of the user-coopera-
tive systems, space-time cooperation was proposed in [37]. The
cooperation framework is illustrated in Fig. 5(b) where it could
be noticed that cooperative users transmit their partner’s data as
well as their own bits in “even” frame compared with the con-
ventional cooperative pattern shown in Fig. 5(a). Figs. 10 and 11
show the BEP performances of the conventional cooperative and
space-time cooperative systems with spread-spectrum factors
32 and 64, respectively. It is worth noting that the performance
of the space-time cooperative system is not better than that of
the conventional cooperative system in the DCSK-CC system at
all times. On the contrary, the performance of the conventional
cooperative system outperforms that of the space-time cooper-
ative system at higher SNR with spread-spectrum factor 32, ex-
cept for the case with 1:1:1. Unlike the user-cooperative com-
munication systems based on traditional digital modulations, it
implies that the conventional cooperation is a better cooperation
protocol than the space-time cooperation in DCSK-CC system.
D. Performances of Multiple Relays
In this section, the performance of multiuser DCSK-CC
system is evaluated in a more general situation. The four-user
Fig. 10. BEP performance of conventional cooperative system and space-time
cooperative system, .
Fig. 11. BEP performance of conventional cooperative system and space-time
cooperative system, .
DCSK-CC systems, with two relays and three relays, respec-
tively, are considered and compared with that of the situation
with only one relay. Assume that the link distances between
relay users are negligible; thereby, the same distance ratio
criterion of the two-user cooperation system is adopted. Fig. 12
shows the BEP performances of the DCSK-CC with one relay,
two relays, and three relays in the scene where the distance
ratios of source to destination, source to relays, and relays to
destination are of 1:0.8:0.4. It shows that the performance gain
is remarkable when the number of relays is increasing from one
to two. However, this gain decreases greatly when the number
of relays increases from two to three. Thus, it can be concluded
that the performance contribution of increasing the number of
relays is negligible when it is greater than two in a multiuser
DCSK-CC system.
E. Performances of Different Chaotic Maps
Finally, the performances of various DCSK-CC systems are
investigated with the following chaotic maps: logistic map,
cubic map and Bernoulli-shift map, defined respectively by
XU et al.: PERFORMANCE OF DCSK COOPERATIVE COMMUNICATION SYSTEMS OVER MULTIPATH FADING CHANNELS 203
Fig. 12. BEP performance of the DCSK-CC system with different relays in a
multiuser environment, .
Fig. 13. BEP performances of DCSK-CC system when logistic map, cubic
map, and Bernoulli-shift map are used, respectively, .
when
when .
The BEP curves for the two-user DCSK-CC system, corre-
sponding to different chaotic maps with distance ratio 1:0.8:0.4,
are plotted in Fig. 13. It is found that the chaotic sequences gen-
erated by the Bernoulli-shift map produce higher BEP, while the
BEPs for the system using the cubic map and the logistic map
are the same. There are similar results in conventional multiuser
DCSK systems [6]. This observation can be explained in terms
of the variances of chaotic sequences; that is, the variance of
Bernoulli-shift map sequence is larger than that of the logistic
map and the cubic map sequences [6].
V. C ONCLUSION
In this paper, the performance of a user-cooperative system
has been investigated based on DCSK modulation, which em-
ploys the orthogonal Walsh code to achieve orthogonal subchan-
nels for cooperation. Over multipath Rayleigh fading channels,
the performance comparisons between the DCSK-CC systems
and the CDMA-CC systems subject to the same bandwidth ef-
ficiency have been evaluated, which show that the former out-
performs the latter at the BEP of . The advantages
are prominent in near-far scenes. Thus, the common power con-
trol device which mitigates near-far effects is not needed in the
proposed system comparing to CDMA-CC systems. Therefore,
the DCSK-CC has great potential for improving link perfor-
mances by only increasing overheads of the relay protocol while
keeping all terminal conditions unchanged. This implies that
the former has a simpler algorithmic design with lower trans-
ceiver cost than the latter. It has also been found that space-time
cooperation in the proposed system cannot improve the per-
formance, different from the traditional cooperative communi-
cation systems. In other words, conventional cooperation is a
good choice for the proposed system. As a performance bench-
mark, the BEP performance lower bound of the proposed system
with a conventional cooperation protocol has been derived over
three-path Rayleigh fading channels, which well agree with its
counterparts in simulations. Thus, the proposed system can be
expected applicable to energy-constrained and low-cost wire-
less networks with simple cooperation protocols.
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Weikai Xu (S’10) received the B.S. degree in
electronic engineering from the Three Gorges
College, Chongqing, China, in 2000 and the M.Sc.
degree in communication engineering from the
Chongqing University of Posts & Telecommunica-
tions, Chongqing, in 2003. He is currently working
toward the Ph.D. degree in the Department of
Electronic Engineering, Xiamen University, Fujian,
China.
His research interests include cooperative
communications, chaotic communications, and
ultrawideband.
Lin Wang (S’99–M’03–SM’09) received the B.Sc.
degree in mathematics (with first class honors)
from the Chongqing Normal University, Chongqing,
China, in 1984, the M.Sc. degree in applied mathe-
matics from the Kunming University of Technology,
Kunming, China, in 1988, and the Ph.D. degree in
electronics engineering from the University of Elec-
tronic Science and Technology of China, Chengdu,
China, in 2001.
From 1984 to 1986, he was a Teaching Assistant in
the Mathematics Department of Chongqing Normal
University. From 1989 to 2002, he was Teaching Assistant, Lecturer, and then
Associate Professor in Applied Mathematics and Communication Engineering
in the Chongqing University of Post & Telecommunications, Chongqing. From
1995 to 1996, he spent one year with the Mathematics Department at the Uni-
versity of New England, Australia. In 2003, he spent three months as visiting
researcher in the Center for Chaos and Complexity Networks at the City Uni-
versity of Hong Kong. Since 2002, he has been Full Professor and Associate
Dean in the School of Information Science and Technology, Xiamen Univer-
sity, Xiamen, China. He holds five patents in the field of physical-layer digital
communications and published over 60 journal and conference papers. His cur-
rent research interests are in the areas of channel coding and chaos modulation,
and their applications to wireless communications and storage systems.
Guanrong (Ron) Chen (M’89–SM’92–F’97)
received the M.Sc. degree in computer science
from the Sun Yat-sen (Zhongshan) University,
Guangzhou, China, in 1981 and the Ph.D. degree in
applied mathematics from Texas A&M University,
College Station, in 1987.
Currently he is a Chair Professor and the Director
of the Center for Chaos and Complex Networks at the
City University of Hong Kong, Hong Kong, China.
Prof. Chen serves as Editor at different ranks for
several IEEE Transactions and international journals.
He is an ISI highly cited researcher in engineering, and has received four best
journal paper awards in 1998, 2001, 2002, and 2005, and the 2008 State Natural
Science Award of China. He is Honorary Professor at different ranks at more
than 30 universities worldwide.
