Security aware relaying scheme for cooperative networks with untrusted relay nodes

IEEE COMMUNICATIONS LETTERS, VOL. 19, NO. 3, MARCH 2015 463
Security-Aware Relaying Scheme for Cooperative Networks
With Untrusted Relay Nodes
Li Sun, Pinyi Ren, Qinghe Du, Yichen Wang, and Zhenzhen Gao
Abstract—This paper studies the problem of secure transmis-
sion in dual-hop cooperative networks with untrusted relays,
where each relay acts as both a potential helper and an eavesdrop-
per. A security-aware relaying scheme is proposed, which employs
the alternate jamming and secrecy-enhanced relay selection to
prevent the confidential message from being eavesdropped by the
untrusted relays. To evaluate the performance of the proposed
strategies, we derive the lower bound of the achievable ergodic se-
crecy rate (ESR), and conduct the asymptotic analysis to examine
how the ESR scales as the number of relays increases.
Index Terms—Cooperative communications, untrusted relays,
relay selection, secrecy rate.
I. INTRODUCTION
RECENTLY, the applications of Physical-Layer Security
(PLS) techniques in cooperative networks have attracted
considerable attention. Among the candidate PLS solutions,
cooperative jamming (CJ), which exploits the cooperating users
to transmit the artificial noise, is a promising tool to combat
eavesdropping [1], [2]. To harvest the diversity gain while
guaranteeing the security requirement, great efforts have also
been devoted to combine CJ and relay selection [3]–[5].
Common to [1]–[5] is that all of them assume the relays are
trusted, and the eavesdroppers are external entities in addition
to legitimate parties. However, in some applications, the relays
themselves are untrusted, from which the transmitted messages
must be kept secret. For example, in heterogeneous networks,
the relays may have a lower security clearance (and thus a
lower level of information access) than the source-destination
pair. The research on untrusted relay systems was pioneered
by He and Yener in [6], where the non-zero secrecy rate is
proven to be achievable by enlisting the help of the destination
who performs jamming. In [7], the joint beamforming design
at the source and the relay was proposed for MIMO untrusted
Manuscript received July 27, 2014; accepted December 10, 2014. Date of
publication December 22, 2014; date of current version March 6, 2015. This
work was partially supported by the National Natural Science Foundation of
China (NSFC) under Grant No. 61102078, the open research fund of National
Mobile Communications Research Laboratory, Southeast University under
Grant No. 2012D04, and the Fundamental Research Funds for the Central
Universities of China. The associate editor coordinating the review of this paper
and approving it for publication was K. Tourki.
L. Sun is with the Department of Information and Communications Engi-
neering, Xi’an Jiaotong University, Xi’an 710049, China, and also with the
National Mobile Communications Research Laboratory, Southeast University,
Nanjing 210096, China (e-mail: lisun@mail.xjtu.edu.cn).
P. Ren, Q. Du, and Z. Gao are with the Department of Information and
Communications Engineering, Xi’an Jiaotong University, Xi’an 710049, China
(e-mail: pyren@mail.xjtu.edu.cn; duqinghe@mail.xjtu.edu.cn; zhenzhen.gao@
mail.xjtu.edu.cn).
Y. Wang is with the Department of Information and Communications
Engineering, Xi’an Jiaotong University, Xi’an 710049, China, and also
with the University of Maryland, College Park, MD 20742 USA (e-mail:
wangyichen0819@mail.xjtu.edu.cn).
Digital Object Identifier 10.1109/LCOMM.2014.2385095
relay systems. In [8], the secrecy outage probabilities of several
relaying schemes were analyzed. In [9], the power allocation
policy was developed for amplify-and-forward (AF) untrusted
relay systems.
Although diverse results on untrusted relay systems have
been reported, the majority of existing works deal with the sim-
ple model with only one relay node. For multi-relay networks,
[10] analyzed the relationship between the system secrecy
capacity and the number of untrusted relays. Reference [11]
proposed to use relay assignment and link adaptation to realize
both secure and spectral-efficient communications. However,
[10] and [11] only considered the information leakage prob-
lem during the first phase of any two-hop transmission. This
simplifies the protocol design, but may not hold in practice.
Unlike [10] and [11], we in this paper try to secure the
transmissions of both the first and the second phases, and our
contributions are threefold: First, an alternate jamming method
is introduced to prevent information leakage. Second, both opti-
mal and sub-optimal secrecy-enhanced relay selection policies
are proposed. Third, the lower bound of the achievable ergodic
secrecy rate (ESR) is derived, and the asymptotic analysis of
the ESR is given as well.
II. SYSTEM MODEL
We consider a dual-hop AF network consisting of a source
(S), a destination (D) and K untrusted relays (Rk,k = 1,...,K).
The direct link between S and D does not exist. Each node
is employed with a single antenna and operates in a half-
duplex mode. S transmits its signals frame by frame, and the
transmission of each frame is composed of two phases, namely
the broadcast phase (1st phase) and the relaying phase (2nd
phase). The channel between any node pair (i, j), denoted by
hi j, is modeled by a complex Gaussian variable with mean
zero and variance µi j. All channel coefficients remain constant
within one frame and vary independently from frame to frame.
The channels are assumed to be reciprocal, i.e., hi j = hji. The
total transmit power of each phase is constrained by P, and
the additive noise at each receiver is characterized by a zero-
mean, complex Gaussian variable with variance N0. We denote
the average signal-to-noise-ratio (SNR) per phase by ρ = P/N0.
For the considered channel model, γi j
Δ
= ρ|hi j|2 follows an
exponential distribution with the rate parameter λi j = (ρµi j)−1.
Throughout this paper, log(·) denotes the base-2 logarithm, E[·]
represents the expectation operator, and [x]+ = max{0,x}.
To prevent the source message from being eavesdropped at
the untrusted relays, we propose to use an alternate jamming
method, whose details are given as follows.
During the 1st phase, S transmits xS with power αP and D
sends the artificial noise nD with power (1 − α)P, where α ∈
(0,1) represents the power allocation factor. Thus, the received
signal at any relay Rl during this phase is given by
y
(1)
l = hsl
√
αPxS +hdl (1−α)PnD +w
(1)
l . (1)
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464 IEEE COMMUNICATIONS LETTERS, VOL. 19, NO. 3, MARCH 2015
Throughout this paper, w
(n)
m is the additive noise at node m(m ∈
{Rl,D}) within the nth phase (n ∈ {1,2}).
During the 2nd phase, a single selected relay Rk normalizes
its received signal y
(1)
k and forwards it with power βP(0 < β <
1). Note that all the non-selected relays can hear from Rk and act
only as eavesdroppers. Therefore, we let S transmit the artificial
noise nS, with power (1 − β)P, to jam these relays. Thus, at
the end of the 2nd phase, the received signals at D and Rl(l =
1,...,K,l = k) can be expressed respectively as
yd = hkdηky
(1)
k +w
(2)
d (2)
and
y
(2)
l = hklηky
(1)
k +hsl (1−β)PnS +w
(2)
l (3)
where ηk = βP
αP|hsk|2+(1−α)P|hdk|2+N0
.
Since nD is the transmitted signal from the destina-
tion during the previous phase, D can subtract the term
(1−α)PηkhkdhdknD from yd and then decode the source in-
formation based on the remainder. Consequently, the achievable
rate at the destination can be calculated by
R D =
1
2
log(1+γD)=
1
2
log 1+
αβγskγkd
1+αγsk+(1+β−α)γkd
. (4)
Due to the half-duplex constraint, the selected relay Rk receives
the source signal in the broadcast phase only, and thus its
achievable rate is given by
R k =
1
2
log 1+γ
(1)
k =
1
2
log 1+
αγsk
1+(1−α)γkd
. (5)
The non-selected relays Rl’s (l = k), on the other hand, can
receive signals during both the 1st and 2nd phases, and combine
y
(1)
l and y
(2)
l to extract the source information. For simplicity,
we assume selection combining (SC) is adopted at these relay
nodes. After some derivations, we can express the achievable
rate at any non-selected relay Rl by
R l =
1
2
log 1+max γ
(1)
l ,γ
(2)
l (6)
where γ
(1)
l = αγsl
1+(1−α)γld
and γ
(2)
l =
αβγskγkl
αγsk+(1−β)γsl(1+αγsk+(1−α)γkd)+(1+(1−α)γkd)(1+βγkl) .
For untrusted relay systems, any relay node acts as an
eavesdropper, no matter whether it is the selected helper or not.
According to [1, eq. (11)], the secrecy rate of the system, with
Rk being the selected relay, can be calculated as
R (k)
s = R D −max R k, max
1≤l≤K,l=k
R l
+
=
1
2
log(1+γD)−
1
2
log(1+γE)
+
, (7)
where γE = max γ
(1)
k , max
1≤l≤K,l=k
{max{γ
(1)
l ,γ
(2)
l }} .
III. SECRECY-ENHANCED RELAY SELECTION
A. Optimal Selection Scheme
The secrecy-enhanced relay selection aims at maximizing the
secrecy rate given by (7). To achieve this goal, the selected relay
needs to satisfy
k∗
= argmax
1≤k≤K
R (k)
s . (8)
It can be seen from (4)–(7) that, to select the optimal relay,
the instantaneous channel state information (CSI) of all relaying
links as well as that of all inter-relay links have to be acquired.
Therefore, it is rather difficult to realize the optimal relay
selection in practical systems, especially when the number of
relays is large. This motivates us to design the sub-optimal relay
selection strategy with a lower complexity.
B. Suboptimal Selection Scheme
The suboptimal relay selection scheme can be developed by
examining the lower bound of the secrecy rate expression. To
fulfil this, we first derive the lower bound of γD as follows:
γD =
β
1+β−α
αγsk(1+β−α)γkd
1+αγsk +(1+β−α)γkd
(a)
≥
β
1+β−α
αγsk(1+β−α)γkd
αγsk +(1+β−α)γkd
−
1
4
≥
βmin(αγsk,(1+β−α)γkd)
2(1+β−α)
−
β
4(1+β−α)
, (9)
where (a) is obtained by using [12, eq. (21)].
On the other hand, γE can be re-written as
γE = max γ
(1)
k , max
1≤l≤K,l=k
max γ
(1)
l ,γ
(2)
l
= max max
1≤l≤K
γ
(1)
l , max
1≤l≤K,l=k
γ
(2)
l . (10)
Since γ
(2)
l (l = k) can be upper bounded by
γ
(2)
l <
αβγskγkl
((1−β)γsl +1+βγkl)(1+(1−α)γkd)
<
αβγskγkl
βγkl (1+(1−α)γkd)
=
αγsk
1+(1−α)γkd
=γ
(1)
k , (11)
γE can be further simplified as
γE = max
1≤l≤K
γ
(1)
l = max
1≤l≤K
αγsl
1+(1−α)γld
. (12)
By substituting (9) and (12) into (7), we can obtain the lower
bound of the instantaneous secrecy rate under the assumption
that Rk is the selected relay. Now, instead of maximizing the
secrecy rate in (7), we try to maximize this lower bound, and
develop the sub-optimal relay selection strategy as
k∗
= argmax
1≤k≤K
min(αγsk,(1+β−α)γkd). (13)
The proposed scheme in (13) only requires the instantaneous
CSIs of the source-relay and relay-destination links, and does
not depend on the availability of the inter-relay channel coef-
ficients. Thus, it can be realized in a distributed manner [3],
which enjoys a low complexity.
IV. ERGODIC SECRECY RATE ANALYSIS
In this section, the lower bound of the ESR achieved by
the proposed sub-optimal strategy is derived. For mathematical
convenience, we assume all λsk’s are identical and denote them
by λsr. The same assumption holds as well for all λkd’s, i.e.,
λkd = λrd for all k’s. By plugging (9) and (12) into (7) and
letting k = k∗, we can lower bound the ESR by (14), which
is shown at the bottom of the next page.

SUN et al.: SECURITY-AWARE RELAYING SCHEME FOR COOPERATIVE NETWORKS 465
For the considered channel model, αγsk and (1 + β − α)γkd
are exponentially distributed with rate parameters λsr
α and
λrd
(1+β−α) , respectively. Let Z = min(αγsk∗ ,(1+β−α)γk∗d). Ac-
cording to the probability density function (PDF) of exponential
variables and order statistics, the PDF of Z can be expressed
as fZ(z) = Kλe−λz(1 − e−λz)K−1, where λ = λsr
α + λrd
(1+β−α) .
Therefore, after some mathematical manipulations, we have
E
1
2
log 1+
β[2min(αγsk∗ ,(1+β−α)γk∗d)−1]
4(1+β−α)
=
K
2ln2
K−1
∑
k=0
K −1
k
(−1)k
k +1
ln 1−
β
4(1+β−α)
−e
(k+1)λ(4+3β−4α)
2β Ei −
(k +1)λ(4+3β−4α)
2β
, (15)
where we have utilized [13, eq. (4.337.1)], and Ei(x) is the
exponential integral function defined in [13, eq. (8.21)].
Now attention is shifted to the calculation of E[1
2 log(1 +
max
1≤l≤K
αγsl
1+(1−α)γld
)] = E[1
2 log(1+γE)]. By resorting to the order
statistics, we can obtain the cumulative distribution function
(CDF) of γE as
FγE (x) = 1−
λrd
λrd + λsr(1−α)
α x
e− λsr
α x
K
. (16)
Using the above CDF expression and doing some tedious
derivations, we have
E
1
2
log 1+ max
1≤l≤K
αγsl
1+(1−α)γld
=
−1
2ln2
K
∑
k=1
K
k
−αλrd
λsr(1−α)
k ∞
0
G(x)e− λsrkx
α dx
I1
, (17)
where G(x) = (1 + x)−1(x + λrdα
λsr(1−α) )−k. Exploiting
[13, eq. (3.352.4)], [13, eq. (3.353.2)], and the partial
fraction expansion technique, we can simplify I1 as
I1 = −A11e
λsrk
α Ei −
λsrk
α
−A21e
λrdk
1−α Ei −
λrdk
1−α
+
k
∑
p=2
A2p
⎡
⎢
⎣
p−1
∑
t=1
(t−1)!
(p−1)!
−
λsrk
α
p−t−1
αλrd
λsr(1−α)
−t
−
−λsrk
α
p−1
(p−1)!
e
λrdk
1−α Ei −
λrdk
1−α
⎤
⎥
⎦, (18)
where Aip (i = 1, 2 and 1 ≤ p ≤ k) is given by Aip =
1
(σi−p)!
dσi−p
dxσi−p [(x−ρi)σi G(x)]
x=ρi
with σ1 = 1, σ2 = k, ρ1 =
−1, and ρ2 = − λrdα
λsr(1−α) .
Substituting (15), (17), and (18) into (14), we can obtain the
closed-form expression for the ESR lower bound. However, we
omit its explicit expression due to page limit. The tightness of
this bound will be verified via simulations in Section VI.
V. ASYMPTOTIC ANALYSIS OF ERGODIC SECRECY RATE
Now we focus on the large-K case and study how the ESR
scales as the number of relays increases. Here, the extreme-
value theory (EVT) will be used to facilitate the analysis. The
main results of EVT can be found in [14, Sec. III].
The lower bound of ESR is shown in (14). To perform the
asymptotic analysis, we define γ
(k)
D = β[2min(αγsk,(1+β−α)γkd)−1]
4(1+β−α) .
It can be easily verified that γ
(k)
D belongs to Type I domain of
attraction (See [14] for its definition.). Consequently, max
1≤k≤K
γ
(k)
D
converges in distribution to aD
Kµ + bD
K as K → ∞, where µ is a
Gumbel-distributed random variable [14], and aD
K and bD
K are
respectively given by
aD
K =
β
2λ(1+β−α)
(19)
and
bD
K = aD
K ln Ke− 1
2 λ
=
βln Ke− λ
2
2λ(1+β−α)
. (20)
Based on Lemma in [14], there exist sequences of constants
cD
K =
log(e)aD
K
1+bD
K
and dD
K = log(1+bD
K) such that log(1+ max
1≤k≤K
γ
(k)
D )
can be well approximated by cD
KδD +dD
K for large K, where δD
obeys the Gumbel distribution.
Following similar steps we can derive that, as K tends to
infinity, log(1 + max
1≤l≤K
αγsl
1+(1−α)γld
) converges in distribution to
cR
KδR +dR
K, where δR is a random variable following the Gumbel
distribution, and cR
K and dR
K are given as cR
K =
log(e)aR
K
1+bR
K
and
dR
K = log(1+bR
K), with aR
K and bR
K being calculated by
aR
K =
α
λsr
⎛
⎝1+
1−α
λrd +
(1−α)λsrbR
K
α
⎞
⎠
−1
(21)
and
bR
K =
α
λsr
W
Kλrd
1−α
e
λrd
1−α −
λrd
1−α
(22)
respectively. In (22), W(x) is the Lambert-W function.
By combining the above results with (14) and performing the
statistical average, we have (for large K)
R (LB)
s ≈
1
2
κ cD
K −cR
K + dD
K −dR
K
+
(23)
where κ ≈ 0.577 is the Euler constant.
R s ≥E
⎧
⎨
⎩
⎡
⎣1
2
log
1+
4(1+β−α)
1+ max
1≤l≤K
αγsl
1+(1−α)γld
⎤
⎦
+⎫
⎬
⎭
≥
⎧
⎨
⎩
E
⎛
⎝1
2
log
1+
4(1+β−α)
1+ max
1≤l≤K
αγsl
1+(1−α)γld
⎞
⎠
⎫
⎬
⎭
+
= E
1
2
log 1+
4(1+β−α)
−E
1
2
log 1+ max
1≤l≤K
αγsl
1+(1−α)γld
+
Δ
= R (LB)
s . (14)

466 IEEE COMMUNICATIONS LETTERS, VOL. 19, NO. 3, MARCH 2015
Fig. 1. Ergodic secrecy rate versus the average SNR per phase, where K = 4,
µsr = 3, µrd = 5, and µrr = E[|hRiRj |2] = 10 for all i’s and j’s.
It is not hard to verify that, as K → ∞, cD
K dD
K and cR
K dR
K.
Therefore, the asymptotic expression for the lower bound of the
ESR can be further approximated as
R (LB)
s ≈
1
2
dD
K −dR
K
+
=
1
2
log
1+bD
K
1+bR
K
+
. (24)
By plugging (20) and (22) into (24) and exploiting the fact
W(x) ≈ lnx−lnlnx for large x, we can re-write (24) as
R (LB)
s ≈
⎡
⎢
⎢
⎣
1
2
log
1+aD
K lnK−1
2 λaD
K
1+ α
λsr
ln Kλrd
1−α −lnln Kλrd
1−α e
λrd
1−α
⎤
⎥
⎥
⎦
+
.
(25)
It can be proven that the right-hand side of (25) is a decreas-
ing function of K. This implies that, although the untrusted
relays can assist the S → D transmission, the achievable ESR
will degrade when deploying more relays.
VI. SIMULATION RESULTS AND DISCUSSIONS
In this section, simulations are carried out to validate the
proposed schemes. For simplicity, we set α = β = 0.5. In the
following figures, the notation “SNR” represents the ratio of P
to N0, i.e., ρ in Section II.
Fig. 1 exhibits the ESR performances for the proposed
optimal and suboptimal relay selection schemes, where two
combining methods (i.e., MRC and SC) are assumed to be
adopted at the relay nodes. The ESR of the AF system with
trusted relays, which is the Shannon capacity of the system,
is provided to show the performance loss incurred by the
untrustworthy behaviors of the relays. In addition, we compare
the ESR achieved by our design with that of the selection policy
in [5, eq. (10)]. It is observed from Fig. 1 that, the proposed
sub-optimal relay selection scheme can achieve near-optimal
performance, and the ESR differences between the sub-optimal
and the optimal schemes are negligible. When MRC is adopted,
the proposed policy in (13) works as well, and its achieved
ESR performance is also very satisfactory. Further, the derived
lower bound is tight for medium to high SNRs, verifying our
theoretical analysis. A final observation is that, our scheme can
yield a significant performance gain compared to the existing
counterpart in [5].
The achievable ESR versus the number of relays (K) for
the suboptimal relay selection scheme is depicted in Fig. 2,
where the results in (14) and (25) are also plotted. Fig. 2 shows
Fig. 2. Ergodic secrecy rate versus the number of relay nodes (K), where
µsr = µrd = µrr = 10.
that, the ESR decreases as K increases, which is in accordance
with the analysis in Section V. An intuitive explanation to
this phenomenon is that, although the existence of more relays
provides a higher probability to select a better helper, it also
increases the amount of information leakage, where the latter is
the dominant factor.
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