Communications and Network, 2013, 5, 42-47
http://dx.doi.org/10.4236/cn.2013.53B2009 Published Online September 2013 (http://www.scirp.org/journal/cn)
Secure Communications for Two-Way Relay Networks
Via Relay Chatt i ng
Jun Xiong1, Dongtang M a1, Chunguo Liu2, Xin Wang1
1School of Electronic Science and Engineering, National University of Defense Technology, Changsha, China
2National Key Laboratory of Blind Signals Processing, Chengdu, China
Received May, 2013
ABSTRACT
In this paper, we investigate a two-way relay network consisting of two sources, multiple coo perative relays and an ea-
vesdropper. To enhance secure communications, a new relay chatting based on transmission scheme is proposed. Spe-
cifically, the proposed scheme selects a best relay that maximize the sum mutual information among the sources to for-
ward the sources’ signals using an amplify-and-for ward protocol, an d the remaining r elays transmit interf erence signals
to confuse the eavesdropper via distributed beam forming. It can be found that the proposed scheme with relay chatting
does not require the knowledge of the eavesdropper’s channel, and outperforms the joint relay and jammer selection
scheme, which introduces the interference into the sources. Numerical results show that the secrecy outage probability
of the proposed scheme converg es to zero as the transmit power increases.
Keywords: Two-way Relay Networks; Physical Layer Security; Relay Chatting
1. Introduction
Recently, there has been considerable interest in physical
layer security, which exploits randomness properties of
wireless channels. It was pioneered in the 1970s by
Wyner [1], who introduced the wiretap channel and
demonstrated that when the wiretap channel is a de-
graded version of the main channel, the source and the
legitimate receiver can exchange secure messages at a
non-zero rate. The result was later extended to the scalar
Gaussian channels [2] and broadcast channels [3]. With
the additional spatial degrees of freedom (DoF) provided
by multi-antenna systems, the limitation that the main
channel could be worse than the eavesdropper channel
can be overcome. In particular, the secrecy capacity in
Gaussian multiple-input multiple-output (MIMO) wire-
tap channel was studied in [4,5].
However, due to cost and size limitations, multiple
antennas may not be available at network nodes. In these
scenarios, cooperation is an effective way to enable sin-
gle-antenna nodes to enjoy the benefits of multi-antenna
systems. And some recent works have been proposed to
obtain security using cooperative relays [6-11]. In these
works, proper relay or jammer selection schemes seem to
be interesting approaches, which provide a good trade-
off between secrecy performance and system complexity
[9-11].
Opportunistic relay selection in one-way relay net-
works with secrecy constraints was addressed in [9],
where the proposed scheme involved the joint selection
of a relay and a jamming node to enhance the security.
Following a similar idea, a joint relay and jammer selec-
tion were investigated for two-way cooperative networks
in [10]. Different from [9], the proposed algorithms in
[10] selected three relay nodes to enhance security,
where the first selected node operated in the conventional
relay mode and forwarded the sources’ signals, and the
second and third nodes acted as jammers to confuse the
eavesdropper in the first and second phase, respectively.
However, the secrecy outage probability wou ld converge
to a fixed value as the transmit power increases since the
selected single-antenna jammer nodes introduced inter-
ference into the legitimate receiver [9,10]. Most recently,
a relay chatting based on transmission scheme was pro-
posed to enhance secure communications for one-way
relay networks in [11], where a b est relay was selected to
forward the source’s signal using an am-
plify-and-forward (AF) protocol, and the remaining re-
lays transmitted a jamming signal to confuse the eaves-
dropper via distributed beam forming. It was shown that
the use of opportunistic relay chatting gu aranteed that th e
outage probability converged to zero at high transmit
power.
Motivated by [11], we extend relay chatting based
transmission scheme to two-way relay networks in this
paper. Specially, a best relay that maximize the sum mu-
tual information among the two sources is selected to
C
opyright © 2013 SciRes. CN

J. XIONG ET AL. 43
forward the sources’ signals, and two chatting groups
formed from the remaining relays transmit artificial in-
terference to degrade the eavesdropper in the first and
second phase, respectively. It can be found that the pro-
posed relay chatting scheme does not require the knowl-
edge of the eavesdropper’s channel state information
(CSI), and obtains better secrecy performance than the
joint relay and jammer selection scheme proposed in
[10].
The reminder of this paper is organized as follows. We
present the system model and signal model in Section 2.
In Section 3, the relay chatting based transmission
scheme is presented. Numerical results are provided in
Section 4, and the conclusion s are drawn in Section 5.
Notations: Vectors and matrices are typed in boldface
letters, and variables are italic letters; the transpose,
complex conjugate, Hermitian, and inverse of
A
are
, ,
T
A A
H
A and , respectively;
1
A
N
I denotes a
identity matrix; denotes statistical ex-
pectation while denotes the probability of an
input event;
NN

Ε

,


max 0
Pr

x
x
.
2. System Model and Signal Model
2.1. System Model
We assume a network configuration consisting of two
sources S1 and S2, one eavesdropper E, and a relay node
set


1, 2,,
in
SK with K nodes. Each node is equipped
with a single omni-directional antenna and operates in a
half-duplex mode. In Figure 1, it schematically shows
the system model. As the relay nodes cannot transmit and
receive simultaneously, the total communication process
is performed by two phases. In the first phase, S1 and S2
broadcast their messages 1
s
and 2
s
, and the best relay
node listens, where the criterion for the best relay
selection will be discussed later. At the same time, a chat-
tin g group with size , denoted by
*
R
1
N

1
112
,,,
N
RR R ,
is formed from the remaining relays and trans-
mits a random messages 1K
1
x
via distributed beamform-
*
R
*
R
*
1
,SR
h
*
2
,SR
h
2
,SE
h
*1
,
R
S
h
1
R
1
N
R
1
,SE
h
*2
,
R
S
h
1
R
2
N
R
Figure 1. System model with two sources S1 and S2, a relay
node set, and one eave sdropper E.
ing. In the second phase, the best relay node forwards the
source messages to the corresponding destinations based
on AF protocol while a new chatting group of size 2,
denoted as N


,,,
N
RR R 2
212 , transmits a random
message 2
x
using a new beam forming vector. We as-
sume that the eavesdropper E can overhear the signals
from the two phases.
The channel gain from node i to node j is denoted by
,ij
, which is modeled as a zero-mean, independent, cir-
cularly-symmetric complex Gaussian random variable
with the variance
h
2
,ij

, where 2
,,ij ij
d



, ,ij denotes
the Euclidean distance between node i and node j, and
d

represents the p ath-loss exponen t. Furthermor e, addi-
tive white Gaussian noise (AWGN) with zero mean and
unit variance is assumed at each receiver.
2.2. Signal Model
In the first phase, the two sources send information
symbols 1
s
and 2
s
, respectively, which are mapped to
a PSK set. The received signals at the best relay node
and eavesdropper E can be, respectively, expressed
as
*
R
** **
12 1
12
112 21 1
1211
,,
1,1,2 11
,
,
T
SS R
RSR SRR
T
ESSE SSERE
E
yPhsPhsPxn
yPhsPhsPxn
 
 
hf
hf
*
1
R
(1)
where


21,1, 2
i
siΕ, *
R
n and 1
E
n denote the
noise at and the eavesdropper E, respectively.
*
R
1121
,, ,
,,,
N
T
ERERERE
hh h





h
with ,
i
R
E
h
i
R denoting the channel gain from the relay node of the chatting group to the eavesdropper
E. And 1

*** *
12 1
,,,
N
T
RRRRRRR
hh h





h
with ,
i
R
R
h

denoting the channel gain from the relay
node of the chatting group 1
 to the best relay
node . is the beamforming vector and
i
R
*
R1 f1
x
is the
interference signal with

2
11xΕ. In order to make
the interference signal invisible to the best relay node
while only degrading the eavesdropper’s reception, 1
should be constructed to satisfy *1
f
0
T
R

hf and
111
H

ff . 1
R
P denotes the transmit power of the relay
chatting group 1

.
In the second phase, is selected to amplify its re-
ceived signal, and forwards it to S1 and S2. At the same
time, a new chatting group of size , denoted by 2
*
R
2
N

,
creates a new beamforming vector 2
f
to transmit inter-
ference signal. Similarly, we should make the interfer-
ence signal invisible to the two sources. Hence, 2
f
should be located at its null space of the two sources’

J. XIONG ET AL.
44
channels, i.e.,

12 2
,Thh
f
0

*
R
and 22 , where
1 and 2
h denote the channels from the relay node of
the chatting group 2 to the sources S1 and S2, respec-
tively. As such, the signals transmitted from the best re-
lay node can be expressed as
1
Hff
h
*
R
*
R
,
x
y

 (2)
where ***
12
12
22
,,
SS
RS
RSR
hPh 1PP  and
*
R
P denotes the transmit power of the node *
R
.
Since each source knows the own transmit signal
i, it can cancel the self-interference [10]. Thus,
each source can extract the message from the other
source. As such, the residual signals at S1 and S2 can be
respectively expressed as

i

1, 2s
** **
212 1
** **
121 2
12
,, ,
21
,, ,
,
,
SRS SRRSR
SRS SRRSR
yPhhshn
yPhhshn




1
2
n
n


(3)
where 1 and 2 denote the noise at the sources S1
and S2, respectively.
n n
On the other hand, the received signal at the eaves-
dropper can be expressed as
*** *
12
1
**
22
21
,, ,,
22 2
,,
ES S
RESR RESR
T
RE ERER
2
2
PhhsPhh s
Pxhnn



hf
y
h
(4)
where with
212 2
,,,
N
T
ERERERE
hh h




,
i

R
E
h denot-
ing the channel gain from the relay node of the cha t-
ting group 2 to the eavesdropper E. 2
i
R

R
P denotes the
transmit power of the relay chatting group .
2
2
x
is
the interference signal with

2
21xΕ, and 2
E
n de-
notes the noise at the eavesdropper E.
3. Secure Communications with Relay Chatting
In this section, we discuss the relay selection for the
proposed secure scheme with relay chatting. Then, we
provide the secrecy outage probability as the metric of
the secrecy performance.
3.1. Relay Selection
We define
j

i
as the signal to interference-plus-noise
ratio (SINR) of the virtual channel i (for
). They can be calculated as j
SS
,ij 1,2,j
*
212
*1
22
2,,
12
2,
,
1
SRS SR
RS
Phh
h




*
(5a)
**
121
*2
22
2,,
22
2,
.
1
SRS SR
RS
Ph h
h



 (5b)
Thus, the sum mutual information among the sources
can be expressed as


12 21
212
11
;;
22
1
2log 11,
S
y
sys





II I
where
(6)


2
1
;log1
2
ij i
ys

I
scalar factor with ,1,2,iji j and the12 is due to the f
units are required in two phases.
Equation (6) can be used as the criterion for the best
lection, i.e.,
act that two time
relay se


*argmax
in S
RS
RI



12
argmax 11.
(7)
in
RS

We can find that the relay selection strategy based on
Equation (7) is no t dependent on the eavesdro ppe
In addition, the relay selection can be implemented in a
distributed way [12], since each node only requires its
lo
secrecy outage
es the outage prob-
ed destinations are
r’s CSI.
cal CSI to calculate Equation (7).
3.2. Secrecy Outage Probability
We use the secrecy outage probability as the metric of
secrecy performance. The meaning of the
probability is twofold. First, it provid
ability for the case where the intend
unable to decode the messages from the sources reliably.
It also gives the metric for the case where the message
transmission is not perfectly secure, i.e., there exists
some information leakage to the eavesdropper E [13].
In order to calculate the secrecy outage probability, we
firstly have to get the SINR of the links i SE for
1, 2i

. We assume a simple case in which the eaves-
dropper applies maximal ratio combining (MRC), so as
to
ceived
examine the efficiency of the proposed scheme. Ac-
cording to MRC, the eavesdropper E comb re-
signals by multiplying 1
ines the
E
y and 2
E
y with proper
weighting factors.
11 22
,
ii i
EE E
yyy



 (8)
where i
E
y represents the cbining signal for the
source i S and om
1,
12
ES
j
N

*,,
ii
SSE
iPh
  (9)
**
2,
22,
ii
ES
j
SRE SR
i
N
Ph h 


 (10)
,1,2,iji j

. 1,
2
E
S
j
N

and 2,
2
E
S
j
N

with represent
wer the total interference and noise po terms in1
E
y and
2
E
y, denoted by respectively ,

J. XIONG ET AL. 45
1 1, 1
22
2,1
1,
jj ES
j
T
SSER NE
Ph P  hf  (11)
**
2 2, 2
*
2
2
2,
1.
jj
SR
RE
h  
(12)
2
22
22,,
ES
j
T
SR
NE
RE
Ph hP  hf
Thus, the SINR of th e link can
as i
SEbe calculated
11
**
2
.
i
SRE
Ph 

** *
22
2
,
22
,1
2
2
2
22 2
22
2
,, ,
1
1
ii
i
jj
i
jj
SSE
ET
SSE RE
SR
T
SR
E
RE SRRE
Ph
Ph P
h
Ph hPh




hf
hf
(13)
The instantaneous secrecy rate with the relay node set
for the source can be expressed as [10]
in
Si S

 22
11
log 1log 1,
22
i
Si
Rj
E




 
(14)
where
ne
sec
,1,2,iji j.
The overall secrecy performance of the two-way relay
twork is characterized by the sum of the two sources’
recy rate, i.e.,


12
21
22
21 21
11
1log
EE

 



 


21
12
12
2
11 11
log log
.
211
SSS
EE
RRR








 

(15)
For a target secrecy rate , the secrecy outage
probability can be expressed as fows [13,1
0
Rllo4]
 



0
21
00
12
2
Pr
11
Pr2 .
11
so SS
R
EE
PR RR R 

 



 






(16)
it
Power
In this subsection, we do some quantitative analy
the asymptotic performance for the proposed schem
high transmit power range.
Following the similar idea from [10], we assume that
rces,
e
samer words, as the source’s transmit power
3.3. Performance Analysis at High Transm
sis on
e in
the transmit power for all nodes including two sou
the selected best relay and the relay chatting set is th
. In othe
S
P, i
S
P, *
R
P and i
R
P also go to infinity. In this
case, we can obtain
**
***
,,
2
22
,, ,
lim ,
ij
S
ii j
SRS SR
i
P
RS SRSR
Ph h
hhh
 

(17)
2
2
1
**
****
2
2
2
,1
lim i
SE
PT
SE
h
h
 
h
,
2
2
2
22
2 2
2
,, , ,
,
i
j
i
jij
SE
E
RE SR
T
E
RESRSRSR
hh
hh h h




f
hf
(18)
where
2
,1,2,iji j


n see that . We cai

grows rapidly as increases,
while S
P
i
E

rresp
(16), th
transm
convergo a fixed value then
the coonding cnnels. Therefore, baon
tion e secrecy outage probability can go to zero at
highit pow
erical Resu
In rots
a 2D square toy withi
es t
ha
er, i.e.,
at dep
sed
0 as
ds on
Equa-

0so S
PR R S P.
4. Numlts
this section, we pvide numerical resul in order to
validate the effectiveness of the proposed scheme. The
simulation environment consists of two sources S1 and S2,
one eavesdropper E, and a relay node cluster. We assume
that all nodes are located inpologn
a 11

unit square. We co
S2, and E are located at nsider this scenario where S1,



11
,0,1
SS
XY,


22
,1,1
SS
XY,
and




,0.5,0
EE
XY,
respectively. The K relay nodes spread randomly within
theare space. For example, Figure 2 gives the simu-
lation scenario with K
squ 8

relays.
00.1 0.20.3 0.40.5 0.6 0.70.8 0.91
0
0.1
0.2
0.3
0.4
0.5
1
0.6
0.7
0.8
0.9
X
Y
S1
S2
E
Rel a y
S2
E
S1
Figure 2. The 1 × 1 simulation scenario with K = 8 relays.

J. XIONG ET AL.
46
We assume that the sources, the best relay , and
the chatting group transmit with the same
2
. The path-los
*
R
power, i.e.,
s exponent is
*,1,
ii
SRS
R
PPPPi 
set to 3

. All the remain
used as chatting relays, i.e.,
In Figure 3, the secrecy ou
ing relay nodes are
s hbeen
shown as functions of the transmit power The tar get
secrecy rate is set asbits/s/Hz. It can be seen
that the relay chattingme canize zero-ap-
poaching outage probe tranower in-
creases. Meanwhile, as tnumber of t relay nodes
increases, the secrecy ourobability poundly de-
creases. A similar obcan be foFigure 4,
which presents thtage probility with dif-
ferent target secrecy rate. The transmwer is
set to 10 dB. The secrormamed
by inviting more relays into cooperation due to the op
portun
1K
12
NN
probab1K.
tageilitieave
S
P.
real
smit p
he
rof
und in
ab
it po
nce can be i
03R
sche
ability as th
he
tage p
servation
e secrecy ou
0
R
ecy perf S
P
prov -
istic use of the multiple relays.
02 46 810 12 14 16 1820
10
-4
10
-3
10
-2
10
-1
10
0
Ps[dB]
S ec rec y Outage P roba
bility
Rel ay Cha ttin g K= 4
Rel ay Cha ttin g K= 6
Rel ay Cha ttin g K= 8
Figure 3. Secrecy outage probability versus the transmit
power PS with different number of relays K.
01234567
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
R0[b i ts /s/Hz]
Secrecy Outage Probability
Relay Chat ting K = 4
Relay Chat ting K = 6
Relay Chat ting K = 8
Figure 4. Secrecy outage probability versus the target se-
crecy rate R with different number of relays K.
05 1015 20 2530
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Ps[dB]
Secrecy Out age P robabilit y
Rel ay Chat tin g
OS-MSISR
Figure 5. Secrecy outage probability versus the transmit
Next, wempare the proposed relay chattng scheme
with the joint relay and jammer selection scheme pro-
posed in [10]. It is assumed in [10] that the jammers
transmit with a power subject to the relay-jammer power
ratio
power PS..
coi
, i.e., JR
PPL


10L

where
J
P
de.
denotes the
transmr of the selected jammer noWe give the
simulation results of the optimal selectio n with maximum
sum instantaneous secrecy rate (OS-MSISR) in Section
III-A of [10]. It can be found that the OS-MSISR scheme
requires the precise knowledge of the eavesdropper’s
channel, which is hard to obtain, e.g., a passive eaves-
dropper [14]. However, the proposed relay chatting in the
previous section avoids the use of the eavesdropper’s
CSI.
Figure 5 presents the secrecy outage probability of
both schemes, where the target secrecy rate is set to
it powe
03.5R

bits/s/Hz and the number of relay nodes is
8K

. As 03.5R

shown in , the secrecy outage prob-
OS-MSISR wounverge to a fixed value as
to
heme. Performance analysis and simulation results
sh
ability of
the tran
rge
ld co
the transm
smit power S P increases since the selected sin-
gle-antenna jammer nodes introd uce the interference into
the sources. It can be also seen that the secrecy outage
probability of our proposed relay chatting scheme can
convezero as it power S goes to in-
finity.
5. Conclusions
In this paper, a new relay chatting transmission scheme is
proposed to enhance secure communications for two-way
relay networks. The proposed scheme does not require
the knowledge of the eavesdropper’s channel and achieves
better performance than the joint relay and jammer selec-
tion sc
P
ow that the secrecy outage probability of the proposed
scheme goes to zero as the transmit power increases.
0

J. XIONG ET AL.
47
6. Ackn
al Journal, Vol. 54, No. 8, 1975, pp. 1355-1367.
538-7305.1975.tb 02040.x
owledgements
This work was supported in part by the NSFC under
Grants 61101096 and 61002032, and the NSF of Hunan
Province under Grant 11jj4055.
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