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Das Menghwar et al. EURASIP Journal on Wireless Communication s and
Networking 2012, 2012:205
http://jwcn.eurasipjournals.com/content/2012/1/205
RESEARCH Open Access
Cooperative space-time codes with
network coding
Gordhan Das Menghwar1*, Akhtar Ali Jalbani1,MukhtiarMemon
1, Mansoor Hyder1
and Christoph F Mecklenbr ¨
auker2
Abstract
Because of the gains like diversity, throughput, and the coverage extension provided by the multiple-input multiple-
out (MIMO) systems, it has been part of the various wireless communications standards. However, to reap the benefits
offered by MIMO systems in size-constrained nodes, used in wireless communications, has been a challenging issue.
To address this challenge, cooperative communications has been introduced as an implementable way to exploit the
multi-antenna (MIMO) gains in small size nodes. Various schemes or protocols have been devised to address the way
by which cooperative communications actually takes place. In this article, we propose and investigate a novel scheme
which provides a way to combine the benefits of space-time codes and network coding for cooperative
communications. In this scheme, the cooperating users using space-time codes are assisted by the availability of a fixed
relay node proposed for the future wireless networks. We compare our scheme with cooperative communications
using Alamouti scheme and non-cooperative communications. With analytical results, we prove that the proposed
scheme offers diversity gain of order three while cooperative communications using Alamouti scheme offers two and
non-cooperative communications offers diversity order of one only. Moreover, the proposed relay assisted scheme
outperforms by 15% in terms of multiplexing gain, the cooperative communications scheme being compared.
Introduction
Cooperative communications has been a hot topic for
research since its introduction by Sendonaris et al. [1-3]
in 1998. The reason for the popularity of the idea is that
it gives a way to exploit the multiple-input multiple-out
(MIMO) benefits in size-constrained nodes, like used in
Ad hoc, sensor or a cellular network. It is well known
that the wireless channel, while giving us independence
of movement, also introduces an unreliability in the mes-
sage being transmitted [4]. This unreliability is due to the
inherent characteristics of the wireless channel like scat-
tering, reflection, refraction, and diffraction. To overcome
this problem, MIMO was introduced to use the spatial
dimension, another degree of freedom, available in the
wireless channel. MIMO uses multiple transmit and mul-
tiple receive antennas for transmission of the message and
introduces independent fading paths between each trans-
mit and receive antenna of the MIMO systems. In this way,
*Correspondence: gdas@sau.edu.pk
1Information Technology Centre, Sindh Agriculture University, Tandojam,
Pakistan
Full list of author information is available at the end of the article
the receiver is provided with multiple copies of the same
message from various statistically independent paths; this
introduces spatial diversity gain in the wireless channel.
As for as point to point communications is concerned,
this technique of MIMO system worked and has been part
of many standards like UMTS [5], WiMAX [6], WLAN
[7], and LTE-Advanced [8]. But due to the space prob-
lem, same happened to be challenging in size-constrained
nodes. Cooperative communications is a concept to
implement MIMO in the situation where it is not feasible
to install multiple antennas on the nodes due to their size
and the cost incurred per node.
Cooperative communications is a communications
strategy where transmitting users use each others’ anten-
nas to realize MIMO gains. In cooperative communica-
tions when the transmitters send their messages to the
destination, the free users present in their surrounding
also receive that message. The users after detecting those
messages, forward some additional information on behalf
of the transmitting users to the destination. In this way,
the receiver is provided with multiple copies of the same
© 2012 Das Menghwar et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
Das Menghwar et al. EURASIP Journal on Wireless Communications and Networking 2012, 2012:205 Page 2 of 8
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message transmitted and the spatial diversity gain is intro-
duced in the channel [2,3,9]. On the other hand, in a relay
channel [10], a dedicated node is present between the
transmitter and the receiver which is used to forward the
second copy of the message transmitted by the user to the
destination.
Thewaybywhicharelaynodeinarelaychannel
and the partner user in cooperative communications for-
ward information to the destination is known as protocol.
Some of the basic relaying protocols introduced so far
are Decode-and-Forward, Compress-and-Forward, and
Amplify-and-Forward [11,12]. In Decode-and-Forward
relaying protocol, the relay node decodes and then re-
encodes the message received from the transmitting
user and forwards it to the destination. In Amplify-and-
Forward protocol, the relay node amplifies and forwards
the signal received from the transmitting user to the
destination. Finally, in Compress-and-Forward protocol,
the relay node forwards the compressed version of the
message received from the transmitting user to the desti-
nation.
We propose a scheme which is based on Decode-and-
Forward protocol. Here the transmitting users, also called
the partner users, act as relay nodes for each other. In
addition, these cooperating users also exploit the avail-
ability of a dedicated relay node to cope with various
adverse effects of the wireless channel and achieve the
MIMO gains. Information theoretic outage probability
and diversity multiplexing tradeoff are used as perfor-
mance measures and the proposed scheme is compared
with Alamouti scheme based cooperative communica-
tions and non-cooperative communications. The results
achieved show that the proposed scheme offers higher
diversitygainthannon-cooperativeaswellascooperative
communications using Alamouti scheme.
The rest of the article is structured as follows. In
Section System model, we describe our system model.
Section Mutual information and the outage probability
deals with the mutual information and the resulting out-
age probability of the proposed scheme. On the basis of
the outage probability results in Section Mutual informa-
tion and the outage probability, the diversity-multiplexing
tradeoff perspective of the proposed scheme is pre-
sented in Section Diversity-multiplexing tradeoff. Finally,
in Section Conclusion we conclude our article.
System model
To better explain our scheme, we take a cellular scenario
with two mobile users u1and u2transmitting to a com-
mon destination, that is base station in this case. These
transmitting users are considered to use space-time cod-
ing based Alamouti scheme for cooperation. In addition
to that, we also introduce a dedicated relay node in the
surrounding of the transmitting users and the scenario
is depicted in Figure 1. The dedicated relay node is used
to send network coded bits of the information received
from the cooperating users to the destination. The net-
work coded bits are formed by taking Exclusive-OR of the
information bits received from the transmitting users.a
For better understanding, first we briefly discuss here
the cooperative communications setup using Alamouti
scheme only, this is depicted in Figure 2. The transmis-
sion of the message is accomplished in two phases. The
first phase is the broadcast phase where mobile station
users transmit their messages s1and s2,respectivelytothe
destination. Due to the broadcast nature of the wireless
channel, these messages, in addition to the intended des-
tination, are also received by each other and the scenario
is illustrated in Figure 2a. The second phase is called the
multiple-access phase. In this phase, the mobile station
users, after detecting the messages from each other, send
−s∗
2and s∗
1, respectively to the destination. The messages
sent in the multiple-access phase are formed by following
well known space-time coding based Alamouti scheme
[13]. The second phase of the transmission is shown in
Figure 2b.
After having discussed this, now we explain our pro-
posed scheme which we call as cooperative communica-
tions using Alamouti scheme with network coding. Again
the whole process of communication spans two phases,
i.e., the broadcast phase and the multiple access phase.
This time in the first phase, the transmitted messages are
not only received by the cooperating mobile station users
and the intended destination but at a dedicated relay node,
UBase Station
1
Relay
U2
UBase Station
1
Relay
U2
Figure 1 Alamouti scheme based cooperative communications
with network coding. (a) Broadcas t phase. (b) Multiple access phase.
Das Menghwar et al. EURASIP Journal on Wireless Communications and Networking 2012, 2012:205 Page 3 of 8
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UBase Station
1
U2
UBase Station
1
U2
Figure 2 Alamouti scheme based cooperative communications.
present in the surrounding of the transmitting users, as
well. This scenario is illustrated in Figure 1a. As shown,
the transmitted messages are represented as s1and s2.
In the next phase called the multiple access phase,
the cooperating users u1and u2, following Alamouti
scheme, forward −s∗
2and s∗
1, respectively to the des-
tination. In addition to that in the multiple access
mode, the available relay node sends the network coded
bits of the information received from the cooperat-
ing users to the destination. This scenario is illustrated
in Figure 1b.
In addition to the operational details of the scheme
mentioned above, we assume that all the nodes operate
in half duplex mode and all the transmitting terminal are
assigned orthogonal channels by allocating separate time
slots to the mobile station users and the relay node to
transmit. The detailed description of the protocol showing
the transmitting nodes, their channel assignments (time
slots), and the respective transmitted messages are shown
in Table 1.
In addition to that, every transmitting node is assumed
to obey a fixed transmission power constraint of Pjfor
Table 1 Protocol description
Time slot Transmitter Message Receiver
1u1s1u2,BS,r
2u2s2u1,BS,r
3u1−s∗
2BS
4u2s∗
1BS
5rs
1⊕s2BS
theirmessagestobetransmitted.Signaltonoiseratiois
defined as
SNR =|hj,d|2,(1)
where =Pj
ηand j=1, 2 represents the transmit-
ting mobile station index. ηshows the noise introduced
at the receiving end which is assumed to follow complex
Gaussian distribution with zero mean and unit variance.
Mutual information and the outage probability
As detailed in Section System model, we consider a block-
fading channel model. In this case, the channel is assumed
to change its state from on channel realization to another.
Since the mutual information is dependent on the channel
gain between the transmitter and the receiver, the mutual
information by itself is a random variable and does not
support a constant rate requirement of certain application
and the system is said to be in outage.
This section deals with the outage analysis of our pro-
posed scheme and to calculate outage probability, we
follow the definition from [14,15] which is given as
P[]=P[I<]. (2)
That is, the outage probability P[], defines an event
when the information theoretic mutual information I,is
less than the required spectral efficiency, of the sys-
tem. Therefore, to calculate the outage probability, first we
need to find out the mutual information of the proposed
scheme, which in our case becomes.b
I=2
5log 1+SNR
2
2
i=1
|hi,d|2+2
5log(1+SNR|hr,d|2)
(3)
where hi,dis used to represent the channel gain from
mobile station ito the destination d,andhr,dis the chan-
nel gain from the relay node to the destination d.For
simplification, the channel between the mobile station
usersisassumedtobeerrorfree.Equation(3)isthe
mutual information between user uiand the destination
and as seen, the given expression is composed of two
terms. The first term is because of the Alamouti scheme
[16], where the transmitting and the partner user trans-
mit using Alamouti scheme, and the second term shows
here because of the relay node forwarding network coded
bits to the destination [17]. We have introduced a factor
of 2
5in front of mutual information to count the fact that
fivetimeslotsareusedbytwocooperatingusersforthe
transmission of their messages to the destination [17,18].
Das Menghwar et al. EURASIP Journal on Wireless Communications and Networking 2012, 2012:205 Page 4 of 8
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Now by putting the value of mutual information (3)
into (2), the outage probability of the proposed scheme is
found as follows.
P[]=P[I<]
=P⎡
⎣
2
5log ⎛
⎝1+SNR
2
2
j=1
|hj,d|2⎞
⎠
+2
5log 1+SNR|hr,d|2<
⎤
⎦
=P⎡
⎣
2
5log ⎛
⎝1+SNR
2
2
j=1
|hj,d|2⎞
⎠
×1+SNR|hr,d|2<
⎤
⎦
=P⎡
⎣⎛
⎝|hr,d|2+1
2
2
j=1
|hj,d|2
+SNR
2|hr,d|2
2
j=1
|hj,d|2⎞
⎠<25
2−1
SNR ⎤
⎦
Let |hr,d|2=y,2
j=1|hj,d|2=z,and 25
2−1
SNR =δ.
Then
P[]=Py+1
2z+1
2SNRyz <δ
=Py1+1
2SNRz<δ−1
2z
=Py<δ−1
2z
1+1
2SNRz
=2δ
0
Py<δ−1
2z
1+1
2SNRz|zPZ(z)dz
=2δ
01−exp −λδ−1
2z
1+1
2SNRzPZ(z)dz
(4)
The expression just before Equation (4) is because of the
total probability theorem. That is [19]
FX(x)=P[X≤x]
=
n
i
P[X≤x|Bi]P(Bi)
Birepresent the mutually exclusive events. Moreover,
in the last line, yhas been replaced by its probability
distribution which actually is the cumulative distribution
function (cdf) of a single exponential random variable. As
mentioned before, the variable zis the sum of two expo-
nential random variable and PZ(z)is the pdf for the sum
of two exponential random variables. For completeness, a
general form for PZ(z)is given by [19].
PZ(z)=λ
(m−1)!(λz)m−1exp(−λz)for z>0
0forz≤0(5)
where λ>0 represents the parameter of an exponential
distribution. Moreover, Equation (5) is a special form of
Gamma distribution when the shape parameter is taken to
be an integer.
Results and discussion
Figure 3 displays various outage probability curvesc
obtained by using the outage probability expression (4)
evaluated using different SNR values and the SNR itself
is defined by Equation (1). Moreover, to achieve these
curves, without loss of generality, is fixed at 1 b/s/Hz
and λis taken to be one.
In Figure 3, the slopes of various communication
schemes show the diversity order of that particu-
lar scheme [20]. To give a comparative overview, we
also show in Figure 3, the outage probability curves
for non-cooperative and cooperative communications
using Alamouti sheme only. As seen, the slopes of
0 5 10 15 20 25 30 35 40
10−6
10−5
10−4
10−3
10−2
10−1
100
SNR (dB)
P[R]
Non−Cooperative Communications
CCAS
CCAS−with−NWC 1
Figure 3 Outage probability for cooperative communications
using Alamouti scheme with network coding when is fixed at
1b/s/Hz and λis taken to be one.
Das Menghwar et al. EURASIP Journal on Wireless Communications and Networking 2012, 2012:205 Page 5 of 8
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the outage probability curves indicate that the diver-
sity order of non-cooperative and cooperative commu-
nications based on Alamouti scheme is one and two
respectively. However, the diversity order of our pro-
posed scheme, that is, cooperative communication using
Alamouti scheme with network coding is three. This
shows that the proposed scheme, in terms of the out-
age probability, outperforms both of the schemes being
compared.
In addition to that, while most of the protocols do not
offer gain in the low SNR regime, even they lose their per-
formance in that region, the proposed scheme, as seen,
offers better performance in that region as well. Normally
low SNR term is used when the analytical expression are
approximated in asymptotic sense. The remarkable work,
in this direction, is done by Avestimehr and Tse [21]. How-
ever, in this article, by low SNR we imply the SNR in dB
where the cooperative communications using Alamouit
scheme has low performance than non-cooperative com-
munications. As seen in the figure, the proposed scheme
offersnolossinthisregimeaswell,wheremostof
the protocols lose their performance. This happens
between zero to 5 dB, where the proposed scheme
offers better performance than other cooperative com-
munications scheme being compared, i.e, only Alamouti
scheme based cooperative communications, as presented
in Figure 2.
There is considerable work where people have tried to
improve performance in the low SNR regime, but some
of the notable work done in this direction is presented in
[22,23].
Diversity-multiplexing tradeoff
After having presented the outage behavior in the pre-
vious section, in this section we derive another perfor-
mance measure called the diversity-multiplexing tradeoff
perspective of our proposed scheme.
For this, we use the standard definition used by Zheng
and Tse [24,25] and Menghwar [26] given as.
If a code family with a fixed block length for each SNR
satisfies
r=lim
SNR→∞
R(SNR)
log(SNR)(6)
then ris known to be the multiplexing gain.
In the same way, if
d=− lim
SNR→∞
log Pe(SNR)
log(SNR)(7)
where Peis the probability of error, then dis called the
diversity gain.
Using the fact that the outage probability is the lower
bound on the probability of error, Equation (7) is replaced
by
d=− lim
SNR→∞
log[ P(I<)]
log(SNR).(8)
The same approach has also been used in [14,27]. As
seen, to use the above definition, we need the high SNR
approximation of the outage probability. Therefore, we
further simplify the outage probability results (4) of our
scheme and get its high SNR approximation as follows.
P[]=2δ
01−exp −λδ−1
2z
1+1
2SNRzPZ(z)dz
=2δ
01−exp −λδ−1
2z
1+1
2SNRzλλzexp(−λz)dz
≤2δ
0λδ−1
2z
1+1
2SNRzλ2zdz
(9)
In the above simplification, the second equality of the
expression (9) is obtained by using the actual form of
PZ(z), i.e., the pdf for the sum of two exponential random
variables. Finally, for the last inequality, the well known
bounds 1 −exp(−z)≤z,∀z≥0andλexp(−λz)≤λ
have been used.
To proceed further, we use a mathematical technique
called the change of variable is used to get the more sim-
plified version of (9), specifically, putting z=wδin (9)
gives us.
P[]≤λ21
0δ−δw
1+SNRδw2δw2δdw
=4λ2δ31
01−w
1+twwdw
=4λ2δ31
01−w
1+twwdw
=4λ225
2−1
SNR 31
01−w
1+twwdw
=4λ225
2−1
SNR 3
A(t)(10)
where
A(t)=1
01−w
1+twwdw and t=25
2−1.
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The above approximation (10) can further be simplified
with the help of the bounds on A(t) from [14] given as.
1
6+6t≤A(t)≤1
2(11)
Now by substituting bound (11) into (10) we get follow-
ing asymptotic upper and lower bounds on (10) for outage
probability which can be shown to be
P[]≥25
2−1
SNR 3
2−5
22λ2
3, (12)
P[]≤25
2−1
SNR 3
2λ2. (13)
Finally these bounds can readily be used in (8) to eval-
uate the required diversity-multiplexing tradeoff of the
proposed scheme, i.e., cooperative communications using
Alamouti scheme with network coding as follows.
The upper bound on diversity-multiplexing tradeoff
The achieved bounds (12) and (13) make it easy to use
definition to (8) derive our second performance mea-
sure, i.e., diversity-multiplexing tradeoff of the proposed
scheme. Specifically the lower bound (12) on the outage
probability (4) will lead us to the upper bound on the
diversity-multiplexing tradeoff as follows.
d≤− lim
SNR→∞
log 25
2−1
SNR 3
2−5
22λ2
3
log(SNR)
=− lim
SNR→∞
log 25
2−1
SNR 3
−log 25
2+log(2λ2
3)
log(SNR)
≤− lim
SNR→∞
3log25
2rlog SNR −1−3log(SNR)−log 25
2rlog SNR
log(SNR)
=− lim
SNR→∞
3log2logSNR 5
2r−1−3log(SNR)−log 2log SNR 5
2r
log(SNR)
≤−logSNR (SNR)5r−3
=3−5r(14)
The lower bound on diversity-multiplexing tradeoff
In the same way, the upper bound (13) on the outage
probability (4) is used to derive the lower bound on the
diversity-multiplexing tradeoff which is given as
d≥− lim
SNR→∞
log 25
2−1
SNR 3
2λ3
log(SNR)
=− lim
SNR→∞ 3log25
2−1−3log(SNR)+log(2λ3)
log(SNR)
≤− lim
SNR→∞ 3log25
2rlog SNR −1−3log(SNR)
log(SNR)
=− lim
SNR→∞ 3log 2log SNR 5
2r−1−3log(SNR)
log(SNR)
≥−3logSNR (SNR)5
2r−1
=3−15
2r. (15)
For simplification, from the second to the fifth line of
expressions (14) and (15), we have used the basic log rules
for multiplication and division. In addition to that, to
arrive at the final expressions (14) and (15), we exploited
the well known change of base formula.
Results and discussion
Figure 4 shows the diversity-multiplexing tradeoff curve
for our proposed scheme along with the curves for coop-
erative communications using Alamouti scheme and non-
cooperative or direct transmission.
In the figure, on the horizontal axis, we show the mul-
tiplexing gain, rand on the vertical axis, we show the
diversity gain d.
As seen in Figure 4, both of the calculated upper and
the lower bounds on the diversity-multiplexing trade-
off curves show that our proposed scheme offers the
diversity gain of order three. In contrast, the maximum
2.5
3
Lower Bound for CCAS-with-NWC
1.5
2
0.5
1
Diversity Gain: dt
Upper Bound for CCAS-with-NWC
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
Multiplexing Gain: r
CCAS
Figure 4 Diversity-multiplexing tradeoff for cooperative
communications using Alamo uti scheme with network coding.
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diversity gain achieved by Alamouti scheme based coop-
erative communications is two and with non-cooperative
communications in one only.
Another perspective, that is of multiplexing gain r,
shows that we get bounds, i.e., the upper and the lower
bounds on the multiplexing gain. The Figure 4 shows that
the upper bound on the multiplexing gain for our pro-
posed scheme is 3
5and the lower bound is 2
5, whereas, the
maximum multiplexing gain for Alamouti scheme based
cooperative communications is 1
4and for direct transmis-
sion is one. This shows that the proposed scheme output
performs by %15 Alamouti scheme based cooperative
communications.
Conclusion
In this article, we propose a novel scheme which exploits
the availability of a relay node to aid a cooperative com-
munications setup in a wireless network. To present the
idea, we take two users Alamouti scheme based cooper-
ative communication and a dedicated relay node in the
network. With analytical results on the outage proba-
bility and the diversity-multiplexing tradeoff of the pro-
posed scheme, we show that the proposed scheme out-
performs Alamouti scheme based cooperative communi-
cations as well as non-cooperative or direct transmission.
The results show that our proposed scheme offers diver-
sity gain of order three in comparison with the diversity
order of two and one offered by cooperative commu-
nications using Alamouti scheme and non-cooperative
transmission respectively. The proposed scheme offers
multiplexing gain of 3
5against 1
4offered by cooperative
communications using Alamouti scheme only. In addition
to that, while most of the existing schemes lose their per-
formance in the low SNR regime, the proposed scheme
offers no loss in the low SNR regime as well.
Endnotes
aIn this article, the symbol of ⊕is used to denote
Exclusive-OR operationn.
bIn this article, all logarithms are taken to base 2, unless
indicated explicitly.
cIn the figure, CCAS stands for cooperative communi-
cations using Alamouti scheme and CCAS-with-NWC
stands for cooperative communications using Alamouti
scheme with network coding.
Competing interests
The authors declare that they have no competing interests.
Acknowledgements
The authors would like to thank Prof. Dr. Gerald Matz, Institute of
Telecommunications, Vienna University of Technology, Austria for his valuable
discussions on information theoretic perspective of cooperative
communications. They would also like to thank anonymous reviewers for their
valuable comments to improve the technicality and readability of this
manuscript.
Author details
1Information Technology Centre, Sindh Agriculture University, Tandojam,
Pakistan. 2Institute of Telecommunications, Vienna University of Technology,
Vienna, Austria.
Received: 3 October 2011 Accepted: 22 May 2012
Published: 2 July 2012
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doi:10.1186/1687-1499-2012-205
Cite this articl e as: Das Menghwar et al.:Cooperative space-time codes with
network coding. EURASIP Jou rnal on Wireless Communications and Ne tworking
2012 2012:205.
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