In this paper, we investigate physical layer security for multiple decodeandforward (DF) relaying underlay cognitive radio networks (CRNs) with fixed transmit power at the secondary network against passive eavesdropping attacks. We propose a simple relay selection scheme to improve wireless transmission security based on the instantaneous channel information of all legitimate users and the statistical information about the eavesdropper channels. The closedform expressions of the probability of nonzero secrecy capacity and the secrecy outage probability (SOP) are derived over independent and nonidentically distributed Rayleigh fading environments. Furthermore, we conduct the asymptotic analysis to evaluate the secrecy diversity order performance and prove that full diversity is achieved by using the proposed relay selection. Finally, numerical results are presented to verify the theoretical analysis and depict that primary interference constrain has a significant impact on the secure performance and a proper transmit power for the second transmitters is preferred to be energyefficient and improve the secure performance.
1. Introduction
C
ognitive radio (CR) has emerged as a promising solution to optimize spectrum resources exploitation
[1]
[2]
. The improvement is achieved by allowing the secondary users (SUs) to exploit the originally spectrum of the licensed primary users (PUs). One of the cognitive modes defining this coexistence between PUs and SUs is the “underlay” approach. In which, the SUs and PUs can exist in the same frequency band simultaneously as long as the SUs strictly satisfies the interference constraint at the primary receiver. To fulfill this constraint limit, SUs generally use relatively low transmit power which eventually limits the reliable and coverage performance of the secondary system.
In order to enhance the performance of secondary systems, cooperative relaying, as a way to achieve the space diversity, has been further exploited in cognitive ratio networks (CRNs). The performance of decodeandforward (DF) and amplifyandforward (AF) relaying in underlay cooperative CRNs (CCRNs) has been widely investigated in
[3

9]
. Different from the noncooperative CRNs, both the SUs and the relays should maintain the interference constraint to fulfill the requirement of PUs in underlay CCRNs. In general, there are two transmit power control strategies to keep the induced interference always below a given allowable threshold
[10]
. One is adaptive transmit power (ATP) control, by which the secondary transmitters can adjust their transmit power to satisfy the interference constraint. The other is fixed transmit power (FTP) control, by which the secondary transmitters use their maximum available power when the primary interference constraint is verified, and remain silent otherwise. Although the use of FTP slightly deteriorates the system performance, it significantly alleviates the signaling requirements and implement complexity compared to ATP
[10]
.
On the other hand, due to the broadcasting nature of wireless channel and the openness of cognitive radio architecture, security against overhearing of the eavesdroppers is one of the important issues
[11]
. Traditionally, the cryptographic techniques relying on secret keys have been employed to protect the communication confidentiality against eavesdropping attacks, however, which increases the computational and communication overheads and introduces additional system complexity for the secret key distribution and management
[12]
. Recently, physical layer security (PLS) is drawing a lot of attentions as a promising technique to achieve secure communication by exploiting the physical characteristics of wireless channels
[13]
.
More recently, PLS has been considered for underlay CRNs in
[14

21]
. Different from noncognitive wireless networks, there are some unique challenges to be addressed for physical layer security in cognitive radio networks, e.g., the PU’s QoS protection issue and the mitigation of mutual interference between PUs and SUs. The first attempt to address the secure transmission for underlay CRNs from the information theoretic perspective has been made in
[14]

[16]
. In
[17]
, Zou
et al
. investigate the multiuser scheduling issues in CRNs for physical layer security transmission against eavesdropping attacks. Secure resource allocation problems for underlay CRNs are investigated in
[18]
. The authors in
[19]
indicated that user cooperation not only improves the reliability and coverage performance of cognitive radio networks, but also has great potential to enhance physical layer security against eavesdropping
[19]
. In
[20]
, the authors introduce cooperative secure resource allocation to maximize the secondary secrecy rate subject to maintaining a certain level quality of service for PUs via the interference threshed constraint. In
[21]
, the secure transmission issue for a cognitive radio network has investigated over the slow fading channel, which aims to maximize the secrecy throughput of the primary transmission. Recently, the authors attempt to enhance wireless transmission security in underlay CCRNs by relay selection in
[22]
, where the secondary source sends confidential information to a secondary destination with the assist of multiple DF relays, and the adaptive transmit power (ATP) control strategy is used to fulfill the interference power constraints. The proposed relay selection scheme in
[22]
selects a trusted relay to assist the secondary transmitter and maximize the achievable secrecy rate under the availability of perfect channel state information (CSI) of all channels. However, it is often difficult or impossible for the transmitter to know the accuracy of the eavesdropper’s channel, especially for the passive eavesdropping scenario.
Moreover, in underlay CCRNs, PUs and SUs can transmit signals simultaneously by sharing the same spectrum recourses. As a result, the relays and secondary destination inevitable suffer interference from PUs, which comes in the form of cochannel interference (CCI). However, most of previous work have not taken the interference from PUs into consideration or just have translated PUs’ interference into the noise term of SUs.
Motivated by the above discussions, in this paper, we investigate physical layer security in underlay CCRNs consisting of one primary transmitter, one primary receiver, one secondary source, multiple secondary relays, and one secondary destination, where one eavesdropper are ready to intercept the transmissions from the secondary relays to the secondary destination. The FTP strategy is adopted at the secondary transmitters, including the secondary source and multiple secondary relays, which significantly depress signal burden and implement complexity. As compared with the existing works, the main contributions of this paper are exhibited as follows:
1) To the best of author’s knowledge, this paper is the first attempt to investigate physical layer security for underlay CCRNs employing FTP control strategy under passive eavesdropping attacks. Furthermore, different from previous works, the impact of PU’s interference on the relays and secondary destination also is considered.
2) Different from
[22]
, we propose a new relay selection scheme in underlay CCRNs to achieving tradeoff between complexity and secure performance, where a secondary relay that satisfies the primary interference constraint and successfully decodes the source message will be selected based on the instantaneous knowledge of all legitimate links and the statistical knowledge of the eavesdropper channels. Thus, our proposed relay selection scheme does not require the estimation of the instantaneous eavesdropper link and thus seems to be an efficient solution with practical interest.
3) We derive the closedform expressions for the probability of nonzero secrecy capacity and the secrecy outage probability (SOP) over independent and nonidentically distributed Rayleigh channels. Moreover, we also conduct the asymptotic analysis for the SOP to provide insights on the impact of some critical parameters, such as the transmit power of the secondary users, the interference constraint, and the number of relays, on the secrecy diversity order performance. Simulation results verify the theoretical analysis, and illustrate that the secure diversity order is same as the number of secondary relays which depicts the fact that full secure diversity is achieved by the proposed relay selection scheme.
4) Furthermore, simulation and theoretical results show that, due to FTP strategy and interference constraint considered, the secure performance in underlay CCRNs is not a monotonically decreasing/increasing function of the transmit signaltonoise ratio (SNR) anymore. After the SNR approaches a certain level, further increasing SNR may sharply degrade the secrecy performance. Therefore, a proper transmit SNR for secondary transmitter is preferred to be energyefficient and improve the secure performance.
5) In addition, the interference constraint significantly affects the relay selection process. A strict interference constraint will drop the secondary relays from the active set and thereby reduce the secure performance. As the interference constraint approach infinity, the secure performance is limited by the second hop, and then converges to constant values as the performance floors.
Throughout this paper, the following notations will be used. The channel fading gain of link
x
→
y
is denoted by 
h_{xy}

^{2}
, with mean of
x
∈ {
s
,
r
_{1}
,⋯,
r_{M}
,
u
} and
y
∈ {
s
,
r
_{1}
,⋯,
r_{M}
,
d
,
e
,
v
}.
E_{x}
is the transmit power of node
x
and
N
_{0}
is variance of the zeromean additive white Gaussian (AWGN) at each node.
γ_{xy}
=
E_{x}

h_{xy}

^{2}
/
N
_{0}
and
stand for the instantaneous SNR and the average SNR of link
x
→
y
, respectively.
f_{x}
(·) and
F_{X}
(·) represent the probability density function (PDF) and the cumulative distribution function (CDF) of random variable (RV)
X
, respectively.
2. System Model and Relay Selection Scheme
 2.1 System Model
We consider a secrecy communication scenario in underlay CCRNs shown as
Fig. 1
. In the primary network, a primary source
u
sends data to a primary destination
v
. In the secondary network, a secondary source
s
sends confidential information to a secondary destination
d
by employing the assistance of
M
secondary relays (
r_{i}
,
i
=1,2,⋯,
M
). An eavesdropper
e
is located around the secondary destination overhearing the transmission from the relays. All the nodes are equipped with single antenna and work in the halfduplexing mode. For notational convenience,
M
relays are denoted by R={
r_{i}

i
=1,2,⋯,
M
} , where the DF relay protocol is employed. Different from
[23]
and
[24]
, we assume that the direct links from
s
to
d
and
e
are not available, e.g.,
d
and
e
both are out of the coverage area, which avoids considering the twohop leakages and simplifies the system model. At each secondary transmitter, including
s
and
r_{i}
,
i
=1,2,⋯,
M
, the FTP strategy
[10]
is adapted instead of ATP control to depress the system complexity. Each link in the underlay CCRN is subjected to an AWGN with zero mean and variance
N
_{0}
. More specially, the mutual interference exists between primary and cognitive transmissions in underlay CCRNs.
System model
The channels between nodes
x
∈ {
s
,
r
_{1}
,⋯,
r_{M}
,
u
} and
y
∈ {
r
_{1}
,⋯,
r_{M}
,
d
,
e
,
v
} are modeled as independent and nonidentically distributed Rayleigh fading random variable. Thus, the channel fading gains, denoted by 
h_{xy}

^{2}
, are independent and exponential random variables with means of
δ
^{2}
_{xy}
.
The interference level at primary destination caused by the secondary transmitters (source and relays) must be below an interference constraint, noted I
_{0}
. Using a FTP
E_{x}
(
x
∈ {
s
,
r
_{1}
,⋯,
r_{M}
}), the interference caused by a secondary transmitter
x
(
s
or
r_{i}
), noted I
_{x}
is written as I
_{x}
=
E_{x}

h_{xy}

^{2}
. Without loss of generality, we assume that all relays have the same transmit power, e. g.,
E_{ri}
=
E_{r},
∀
r_{i}
∈ R . Thereby, each secondary transmitter may be activated with the probability of
P_{x}
_{,I0}
= Pr(I
_{x}
˂ I
_{0}
) , otherwise, keep silent with the probability of
It is implied that the whole transmission starts only if
s
satisfies the interference constraint with the probability of
P_{s}
_{,I0}
. Meanwhile, some secondary relays in R fall short of the interference constraint and thus they remain silent. The other relays, which meet the interference constraint, are activated and compose a new set A . Given
M
relays in secondary network, there are 2
^{M}
possible combinations from the full set R . Thus, the active relay set is given by
where
ϕ
represents the empty set, while A
_{m}
is a nonempty subset from R . If the active set A is empty, the confidential message is unable to reach the destination.
The scenario of A =
ϕ
is described as
Similarly, the event A = A
_{m}
is formulated as
Given a nonempty A
_{m}
, the relays in this set will try to decode its received signal. When
s
broadcasts it’s confidential message, the relays in A
_{m}
receive both the useful data from s and the interference from
u
. The instantaneous channel capacity of
s
→
r_{i}
link can be given by
where
E_{u}
is the transmission power at the primary transmitter. The capacity is halved because two time slots are required for completing the whole transmission.
When the capacity is large than a predetermined transmission rate threshold
R_{S}
, i.e.,
C_{sri}
˃
R_{S}
,
r_{i}
is able to decode
x
successfully. Those relays that successfully decode the secondary source signal are represented as the decoding set D . Given an active set A
_{m}
with the cardinality of A
_{m}
, the decoding set is given by
If the decoding set D is empty, the confidential message is also unable to reach the destination and the transmission outage occurs; otherwise a best relay will be chosen to forward the decoded signal. The scenario of D =
ϕ
is described as
Similarly, the event D = D
_{n}
is formulated as
Given that D = D
_{n}
and the selected relay according to the next subsection is
r
_{D}
∈ D ,
r
_{D}
encodes the decoding confidential message by the widelyadopted wiretap code
[25]
. The corresponding instantaneous channel capacity of link
r
_{D}
→
d
and link
r
_{D}
→
e
are given by respectively
where
Hence, combining (8) and (9), the instantaneous secrecy capacity condition on D = D
_{n}
and the selected relay
r
_{D}
is given by
[26]
where [
x
]
^{+}
denotes max(0,
x
) .
 2.2 Proposed Suboptimal Relay Selection Scheme
According to (8), (9), and (10), the relay selection scheme with best secrecy capacity performance condition on D = D
_{n}
should be implemented as
However, this optimal relay selection has not only to consider the instantaneous CSI of the legitimate link, but also needs to take the instantaneous CSI of eavesdropper link into consideration. Although this is a common assumption in the physical layer security literature, it is not practical in most passive eavesdropping attack scenarios. Furthermore, the instantaneous CSI of
u
→
d
and
u
→
e
interference links is not available for cognitive networks.
Although the tacking of the instantaneous
r_{i}
→
e
link seems to be impossible for practical applications, knowledge of the average channels can be estimated and obtained by longterm monitoring the eavesdropper’s transmission. Thus, we consider a suboptimal relay selection scheme, which selects the relay based on the instantaneous CSI of
r_{i}
→
d
link and the statistical CSI of
r_{i}
→
e
link. In this paper, the relay selection rule can be formulated as
Specially, if assuming
which correspond to the scenario where the relays are close to each other and forming a cluster, our proposed relay selection scheme would be totally independent of CSI of the eavesdropper links, and can be implemented as the traditional relay selection scheme in
[27]
, e.g.
3. Secrecy Performance for Underlay CCRNs
In this section, we characterize the secrecy performance of our proposed relay selection scheme for underlay CCRNs with FTP in term of probability of nonzero secrecy capacity, exact secrecy outage probability, and asymptotic secrecy outage probability over independent and nonidentically distributed Rayleigh fading channels.
 3.1 Preliminaries
Firstly, we present the probabilities of the occurrence of active relay set A and the decoding set D , respectively, to facilitate the following secrecy performance analysis.
Since the channel gain
, ∀
r_{i}
∈ R of different relays are independent of each other and obey exponential distribution with parameter
the probability of the event A =
ϕ
is obtained from (2) as
Similarly, the probability of the occurrence A = A
_{m}
is obtained from (3) as
Meanwhile, given a nonempty A
_{m}
, the probability of the event D =
ϕ
is obtained from (7) as
where
θ
_{1}
= 2
^{2Rs}
1.
Similarly, the conditional probability of the occurrence D = D
_{n}
given the nonempty A
_{m}
is given by
Next, given a nonempty D
_{n}
, we will provide the conditional CDF of
according to our proposed relay selection scheme in (11).
Lemma 1:
Given a nonempty D
_{n}
, the conditional CDF of
is given by
where
When B= 0 , we define
Proof
: Given decoding set D = D
_{n}
, if the relay
r
_{D}
is selected according to (11), it must satisfy the fact that
from which we derive the probability as
Thus, the conditional CDF of
can be derived as
Following the multinomial identity and simple integral, we can obtain (16).
 3.2 Probability of NonZero Secrecy Capacity
In this subsection, we examine the condition for the existence of nonzero secrecy capacity, which depicts the possibility of achievable secure communication.
By imposing the fact that the secrecy capacity is zero when
s
keep silent, or the active relay set A is empty, or the decoding relay setD is empty, or the signaltointerferenceplusnoise ratio (SINR) from the chosen relay to the destination is lower than that to the eavesdropper. Thus, the probability of nonzero secrecy capacity is given by
where
According to (10), the conditional probability Pr{
C_{s}
(D = D
_{n}
)˃0,
r
_{D}
=
r_{i}
D = D
_{n}
} can be further expressed as
where
denote the SINR of the link
r_{i}
→
d
and link
r_{i}
→
e
, respectively. Since
and
can be expressed as
respectively, the conditional probability is totally independently with the transmit power
E_{r}
of the secondary relays in (20). And the impact of
E_{r}
on the probability of nonzero secrecy capacity embodies in limiting the candidates of active relays by (12) and (13).
Since
γ_{ud}
is an exponential RV, we can obtain the conditional CDF of
U
_{1,i}
using
Lemma 1
as
From
e
’s point of view, the optimum relay selection for
d
is a random relay selection, as the link
r_{i}
→
d
and link
r_{i}
→
e
are uncorrelated. Thus, we can obtain the conditional PDF of
U
_{2,i}
as
Thereby, using (20), (21) and (22), and applying [28, 3.352.4] and [28, 3.353.3], the conditional probability Pr{
C_{s}
(D = D
_{n}
)˃0,
r
_{D}
=
r_{i}
D = D
_{n}
} can be given by
where
and Ei(·) is the exponential integral function
[28]
.
Finally, the closedform expression for the probability of nonzero secrecy capacity can be obtained by substituting (13), (15) and (23) into (19).
 3.3 Exact Secrecy Outage Probability
The secrecy outage probability is defined as the probability that the achievable secrecy rate is less than a given secrecy transmission rate
R_{S}
[29]
. Based on the data transmission and our proposed relay selection scheme in previous section, we can find that the secure transmission outage occurs if
s
keep silent, or the active relay set A is empty, or the decoding relay set D is empty, or the SINR from the chosen relay to the destination is lower than the eavesdropper SINR. Hence, using the law of total probability, the SOP can be formulated as
Using (20), (21) and (22), and applying [28, 3.352.4] and [28, 3.353.3], the conditional probability Pr{
C_{s}
(D = D
_{n}
)˂
R_{S}
,
r
_{D}
=
r_{i}
D = D
_{n}
} can be given by
where
θ
_{2}
=2
^{2Rs}
,
Thereby, the exact closedform expression for the SOP is derived by substituting (12), (13), (14), (15) and (25) into (24). It is worth pointing out that the closedform expression for the SOP in (24) is useful to evaluate the impacts of the transmit power of the secondary users, the interference constraint, and the number of relays on the secure performance of underlay CCRNs with fixed transmit power control.
 3.4 Asymptotic Behavior of Secrecy Outage Probability
Since the exact SOP analysis results are too complicated to render insight on the impact of system parameters, we will investigate the asymptotic behavior of the SOP by some special cases in this subsection.
1) Case of
I
_{0}
→ 0 or
E_{s}
=
E_{r}
→ ∞ : From (24), we directly obtain P
_{so}
(
R_{S}
) → 1 as I
_{0}
→ 0 or
E_{s}
=
E_{r}
→ ∞, which illustrates the huge impact of the interference constraint on the underlay CCRNs with FPT strategy. Given a limited I
_{0}
, increase of transmit power will not always lead to the improvement of secure performance, which is significantly different from the traditional wireless communication systems. Therefore, a proper transmit power is preferred for secondary relays to be energyefficient and improve the secure performance.
2) Case of
I
_{0}
→ ∞
and
→ ∞, ∀
r_{i}
∈ R : This case corresponds to the scenario where the primary destination can tolerate an unlimited interference and the relays is close to the secondary source. Notice that when
→ 0 , the probability of successful decoding will go to one, thus P
_{so}
(
R_{S}
) → 1. As such, we omit this case in this paper.
When I
_{0}
→ ∞ and
→ ∞, ∀
r_{i}
∈ R, from (13) and (15), we have Pr(I
_{s}
≤ I
_{0}
)=1,
and
Therefore, the SOP in (24) can be simplified as
where Pr{
C_{s}
(D = R)˂
R_{S}
,
r
_{D}
=
r_{i}
D = R} can be derived by substituting D
_{n}
= R into (25). Thus,
Remark:
Traditionally, the diversity order is used to evaluate the wireless transmission reliability performance in
[30]
, which characterizes the slope of bit error rate (BER) curve as SNR tends to infinity. However, in the presence of eavesdropping attack, the SOP is used to evaluate the secure performance. Moreover, it is observed from (24) the SOP is independent of the transmit power in the high SNR. Thus, the traditional diversity order is not applicable to measure the secure performance. To provide an insight into the impact of the number of the relays on the secrecy performance, we investigate the generalized secure diversity order introduced in
[27]
.
3) Case of
I
_{0}
→ ∞,
→ ∞, ∀
r_{i}
∈ R, and
λ_{me}
→ ∞ : where
represent the reference channel gains of the legitimate links and the eavesdropper links, respectively, and the maintoeavesdropper ratio (MER)
[22]
. Here, me
λ_{me}
→ ∞ corresponds to the scenario where the secondary destination is located much closer to the relays than the eavesdropper, which is a practical scenario of interest
[29]
.
In
[27]
, a generalized secure diversity order can be expressed as
where
P
_{int}
denotes the intercept probability, which is the occuring probability of an intercept event when the secrecy capacity becomes negative in
[27]
.
As such, when I
_{0}
→ ∞ and
→ ∞, ∀
r_{i}
∈ R, by setting
R_{S}
= 0, mathematically, the value of probability P
_{so}
(
R_{S}
) is equal to
P
_{int}
, e.g.
To derive the secure diversity order of this case, we first derive the approximate analysis of the SOP as
λ_{me}
→ ∞.
Lemma 2:
For I
_{0}
→ ∞ and
→ ∞, ∀
r_{i}
∈ R, and
λ_{me}
→ ∞, we can obtain
as
Proof :
Letting
λ_{me}
→ ∞, we have
Accordingly, the conditional CDF of
in (16) with D
_{n}
= R can be approximated as
where (
a
) follows from the fact that
γ
(
n
,
x
) ≈
x^{n}
/
n
as
x
→ 0.
Then, the conditional CDF of
U_{i}
_{,1}
is approximated as
Therefore, using (34) and (22), we can derive
Using [28, 3.352.4], the approximated probability
can be given by (31).
From (31), we can observe that the SOP
behaves as (1/
λ_{me}
)
^{M}
as
λ_{me}
→ ∞. Substituting (31) into (30), we can obtain the secure diversity order of our proposed relay selection scheme same as
[27]
which shows the secure diversity order is same as the number of secondary relays, revealing the fact that full secure diversity is achieved by the proposed relay selection scheme. It also indicates that although the PU’s interference definitely degrades the SOP, it does not affect the speed at which the SOP decreases as
λ_{me}
→ ∞ when I
_{0}
→ ∞, and
→ ∞, ∀
r_{i}
∈ R. In contrast, increasing the number of secondary relay, the SOP will decrease at a faster speed. Therefore, exploiting multiple relay with relay selection can effectively improve the secrecy performance.
4. Numerical Results and Discussions
This section presents the numerical results to exam the impacts of the transmit power of the secondary users, the interference constraint, and the number of relays on the secure performance of CCRNs with fixed transmit power control. In all cases,
R_{S}
= 0.5 bits/s/Hz ,
E_{u}
/
N
_{0}
= 5dB ,
∀
r_{i}
∈ R . All the nodes are equipped with single antenna and work in the halfduplexing mode. Each link in the underlay CCRN is subjected to an AWGN with zero mean and variance
N
_{0}
. All the channels are modeled as independent and nonidentically distributed Rayleigh fading random variables. We see from the figures that the exact curves precisely agree with the simulations, which validate the accuracy of our analytical results. We further plot asymptotic curves to predict the secure diversity order. Most importantly, we compare the secrecy performance of our proposed relay selection scheme (PRS) with the traditional relay selection scheme (TRS) in
[27]
and the optimal relay selection scheme (ORS) in
[22]
.
 4.1 Impact of Transmit Power of Secondary Users
The impact of the transmit power of the secondary users on secure performance in term of the probability of nonzero secure capacity and the secrecy outage probability is illustrated in
Fig. 2
and
Fig. 3
, respectively. We consider an equal average energy strategy at the secondary source and relays (i.e.
E_{s}
=
E_{r}
=
E_{T}
), and the equal SNR is defined as
E_{T}
/
N
_{0}
. And we set
M
= 3 , I
_{0}
/
N
_{0}
=15dB,
∀
r_{i}
∈ R .
Probability of nonzero secure capacity versus E_{T} / N_{0}.
Secrecy outage probability versus E_{T} / N_{0}.
Observe that as
E_{T}
/
N
_{0}
→ 0 , the probability of nonzero achievable secrecy rate approaches 0 and the secrecy outage probability approaches 1, due to all the
s
→
r_{i}
links are under outage and no confidential message can be delivered to the destination. We can also see that the secure performance keeps improving as
E_{T}
/
N
_{0}
increases to about 10dB while an unexpected decrease occures when
E_{T}
/
N
_{0}
keeps rising. Specially, as
E_{T}
/
N
_{0}
→ ∞ , the probability of nonzero achievable secrecy rate approaches 0 and the secrecy outage probability approaches 1. This is because that at the lowtomedium SNR region secure performance is dominated by outage probibility of the
s
→
r_{i}
links while at the high SNR region the finite interference constraint (I
_{0}
= 15dB) drops all the relays from the candidate pool. Obviously, due to FTP strategy and interference constraint considered, the secure performance in underlay CCRNs is not a monotonically decreasing/increasing function of the transmit signaltonoise ratio (SNR) anymore. After the SNR approaches a certain level, further increasing SNR may sharply degrade the secrecy performance. As shown in
Fig. 2
and
Fig. 3
, the best secure performance has been achieved when
E_{T}
/
N
_{0}
≈ 7dB, and further increasing the transmit power can not improve the secrecy performance. Thus, a fixed and proper
E_{T}
/
N
_{0}
is preferred for secondary relays to be energyefficient and significantly improve the secure performance.
As can be seen, TRS is not efficient for configurations with the eavesdropper and perform the worst secure performance. On the other hand, ORS achieves the best secrecy performance owing to the availability of the eavesdropper’s instantaneous CSI. However, for most of passive eavesdropping attacks, assuming perfect knowledge of the eavesdropper’s CSI is often difficult and impossible. PRS has a complexity overhead similar to TRS as it does not require the estimation of the instantaneous eavesdropper link and thus seems to be an efficient solution with practical interest.
 4.2 Impact of Interference Constraint
In
Fig. 4
and
Fig. 5
, the probability of nonzero secure capacity and secrecy outage probability curves for the relay selection schemes versus interference constraint I
_{0}
are plotted respectively. We set that
M
= 3 ,
E_{s}
/
N
_{0}
=
E_{r}
/
N
_{0}
= 10 dB ,
∀
r_{i}
∈ R .
Probability of nonzero secure capacity versus I_{0}.
Secrecy outage probability versus I_{0}.
The figures show that as I
_{0}
→ 0, the probability of nonzero secure capacity approaches 0 and the secrecy outage probability approaches 1 since in this case all the relays are dropped from the active selection pool and keep silent during the transmission. Along with the increase of I to about 15dB, the secure performance improves sloely. This improvement lies mainly in the fact that with a rise or an absolute relax of the interference constraint, there are more secondary relays satisfying the interference constrains and participating in the selection during the second time slot, which obviously results in better performance. As I
_{0}
→ ∞, the secure performance is limited by the second hop, and then converges to the constant value as the performance floor.
 4.3 Impact of the number of relays M
The impact of
M
on the secrecy outage probability and the secure diversity order is illustrated in
Fig. 6
. In order to give prominence to the parameter
M
, we focus on the special case where the primary destination can tolerate an unlimited interference from the secondary transmitters and all the relay nodes successfully decode the source transmission, e.g. I
_{0}
→ ∞,
→ ∞, ∀
r_{i}
∈ R . We set that
E_{s}
/
N
_{0}
=
E_{r}
/
N
_{0}
= 10 dB,
∀
r_{i}
∈ R .
Fig. 6
plots the exact and asymptotic secrecy outage probability versus MER
for various
M
. We see a pronounced SNR advantage with increasing
M
. This can be explained by the fact that
M
exerts an increasing effect on the secure diversity order via its proportional contribution.
Secrecy outage probability versus MER λ_{me} with E_{r} / N_{0} = 10 dB.
5. Conclusion
In this paper, we have evaluated physical layer security of multiple DF relaying underlay CCRNs with fixed transmit power control in the presence of one eavesdropper. Considered the interference power constraint at PU and modeled CCIs from PU to the secondary system, we proposed a new and simple relay selection scheme, where the relay that satisfies the primary interference constraint and successfully decodes the source message will be selected based on the instantaneous knowledge of all legitimate links and the statistical knowledge of the eavesdropper channels. The exact closedform expressions for the probability of nonzero secure capacity and the secrecy outage probability have been derived. In order to predict the secure diversity order, moreover, the asymptotic secrecy outage probability analysis is also given. Simulation results are presented to confirm the validity of our theoretical analysis, and illustrate that due to FTP strategy and interference constraint considered, the secure performance in underlay CCRNs is not a monotonically decreasing/increasing function of the transmit signaltonoise ratio (SNR) anymore. After the SNR approaches a certain level, further increasing SNR may sharply degrade the secrecy performance.
While this paper considered the case when the direct links form the secondary source to the destination and the eavesdropper are ignorable, only one eavesdropper overhear the transmission form the relays, and all nodes are equipped with single antenna, secure communication for the general cases with multiple eavesdroppers, multiple antenna node, and the direct links to the eavesdropper is a challenging problem, which is remained for future work.
BIO
Songqing Wang is currently working toward the Ph. D. degree at PLA University of Science and Technology. His research interests include physical layer security, cooperative communications, and cognitive radio.
Xiaoming Xu is currently studying at PLA University of Science and Technology for his Ph. D. degree. He focuses on researching in physical layer security, simultaneous wireless information and power transfer, and cooperative cognitive networks.
Weiwei Yang received his ph. D. degree in 2011 at PLA University of Science and Technology. He is currently an associate professor in PLA University of Science and Technology. His research focuses on OFDM, channel estimation, in physical layer security, simultaneous wireless information and power transfer, cooperative communications, and cognitive radio.
Xu Z.
,
Qin W.
,
Tang Q.
,
Jiang D.
2014
“Energyefficient cognitive access approach to convergence communications,”
SCIENCE CHINA Information Sciences
http://www.cnki.com.cn/Article/CJFDTotalJFXG201404006.htm
2014, 57(4): 112.
57
(4)
1 
12
DOI : 10.1007/s1143201450810
Tourki K.
,
Qaraqe Khalid. A.
,
Alouini M. S.
2013
“Outage analysis for underlay cognitive networks using incremental regenerative relaying,”
IEEE Trans. Veh. Technol.
62
(2)
721 
734
DOI : 10.1109/TVT.2012.2222947
Zou Y.
,
Zhu J.
,
Zheng B.
,
Yao Y.D.
2010
“An adaptive cooperation diversity scheme with bestrelay selection in cognitive radio networks,”
IEEE Trans. Sig. Pross.
58
(10)
5438 
5445
DOI : 10.1109/TSP.2010.2053708
Duong T. Q.
,
Bao V. N. Q.
,
Tran H.
,
Alexandropoulos. G. C.
,
Zepernick H.J.
2012
“Effect of primary network on performance of spectrum sharing AF relaying,”
Electron, Lett.
48
(1)
25 
27
DOI : 10.1049/el.2011.3151
Xu W.
,
Zhang J.
,
Zhang P.
,
Tellambure C.
2012
“Outage probability os denodeandforword cognitive relay in presence of primary user’s interference,”
IEEE Commun. Lett.
16
(8)
1252 
1255
DOI : 10.1109/LCOMM.2012.061912.120770
Hussain S. I.
,
Abdallah M. M.
,
Alouini M.S.
,
Hasna M. O.
,
Qaraqe K.
“Performance analysis of selective cooperation in underlay cognitive networks over Rayleigh channels,”
in Proc. of IEEE SPAWC
2011
Hussain S. I.
,
Alouini M.–S.
,
Qaraqe K.
,
Hasna M.
“Reactive relay selection in underlay cognitive networks with fixed gain relays,”
in Proc. of IEEE ICC
2012
Hussain S. I.
,
Alouini M.–S.
,
Qaraqe K.
,
Hasna M.
“Outage Analysis of Selective Cooperation in Underlay Cognitive Networks with Fixed Gain Relays and Primary Interference Modeling,”
in Proc. of IEEE PIMRC
2012
Hakim H.
,
Boujemmaa H.
,
Ajib W.
2013
“Performance comparison between adaptive and fixed transmit power in underlay cognitive radio networks,”
IEEE Trans. Commun.
61
(12)
4836 
4846
DOI : 10.1109/TCOMM.2013.110413.120578
Shu Z.
,
Qian Y.
,
Ci S.
2013
“On physical layer security for cognitive radio networks,”
IEEE Network
12
(5)
28 
33
Delfs H.
,
Knebl H.
2007
Introduction to cryptography: principles and applications
2nd edn.
Springer
Mukherjee A
,
Fakoorian S. A.
,
Huang J.
,
Swindlehurst A. L.
2014
“Principles of physical layer security in multiuser wireless network: a survey,”
IEEE Commun. Survey & Tutorials
16
(3)
1550 
1573
DOI : 10.1109/SURV.2014.012314.00178
Makki B.
,
Eriksson T.
“Secure spectrum sharing via rate adaptation,”
in Proc. of ICNC
2013
Pei Y.
,
Liang Y.C.
,
The K. C.
,
Li K. H.
“Achieving cognitive and secure transmissions using multiple antennas,”
in Proc. of IEEE PIMRC
2009
Pei Y.
,
Liang Y.C.
,
The K. C.
,
Li K. H.
2010
“Secure communication over MISO cognitive ratio channels,”
IEEE Trans. Wireless Commun.
9
(4)
1494 
1502
DOI : 10.1109/TWC.2010.04.090746
Zou Y.
,
Wang X.
,
Shen W.
2013
“Physicallayer security with multiuser scheduling in cognitve radio networks,”
IEEE Trans. Commun.
61
(12)
5103 
5113
DOI : 10.1109/TCOMM.2013.111213.130235
Wu Y.
,
Liu K.
2011
“An information secrecy game in cognitive radio networks,”
IEEE Trans. Inf. Forensics Security
6
(3)
831 
842
DOI : 10.1109/TIFS.2011.2144585
Son P. N.
,
Kong H. Y.
“The underlay cooperative cognitive network with secure transmission,”
Communications (QBSC), 27th Biennial Symposium on
June 2014
164 
167
Mokari N.
,
Parsaeefard S.
,
Saeedi H.
,
Azmi P.
2013
“Cooperative secure resource allocation in cognitive radio networks with guaranteed secrecy rate for primary users,”
IEEE Trans.Wireless Commun.
13
(2)
1058 
1073
DOI : 10.1109/TWC.2013.010214.130929
Wang C.
,
Wang H. –M.
2014
“On the secrecy throughput maximization for MISO cognitive radio network in slow fading channels,”
IEEE Trans. Inf. Forensics Security
9
(11)
1814 
1827
DOI : 10.1109/TIFS.2014.2356339
Sakran H.
,
Shokair M.
,
Nasr O.
,
ElRabaie S.
,
ElAzm A. A.
2012
“Proposed relay selection scheme for physical layer security in cognitive ratio networks,”
IET Commun.
6
(16)
2676 
2687
DOI : 10.1049/ietcom.2011.0638
Huang J.
,
Swindlehurst A. L.
2011
“Cooperative jamming for secure communications in MIMO relay networks,”
IEEE Trans. Signal Process.
59
(10)
4871 
4884
DOI : 10.1109/TSP.2011.2161295
Wang H. –M.
,
Luo M.
,
Xia X. –G.
,
Yin Q.
2013
“Joint cooperative beamforming and jamming to secure AF relay systems with individual power constraint and no eavesdropper’s CSI,”
IEEE signal process. Lett.
20
(1)
39 
42
DOI : 10.1109/LSP.2012.2227725
Oggier F.
,
Hassibi B.
2011
“The secrecy capacity of the MIMO wiretap channel,”
IEEE Trans. Inf. Theory
57
(8)
4961 
4972
DOI : 10.1109/TIT.2011.2158487
Zou Y.
,
Wang X.
,
Shen W.
2013
“Optimal relay selection for physicallayer security in cooperative wireless networks,”
IEEE J. Sel. Areas Commun.
31
(10)
2099 
2111
DOI : 10.1109/JSAC.2013.131011
Gradshteyn I. S.
,
Ryzhik I. M.
2007
Table of Integrals, Series, and Products
7th edition
Academic Press
San Diego
http://www.scirp.org/reference/ReferencesPapers.aspx?ReferenceID=697112
Yang N.
,
Yeoh P. L.
,
Elkashlan M.
,
Schober R.
,
Collings I. B.
2013
“Transmit antenna selection for security enhancement in MIMO wiretap channels,”
IEEE Trans. Commun.
61
(1)
144 
154
DOI : 10.1109/TCOMM.2012.12.110670
Zheng L.
,
Tse D.
2003
“Diversity and multiplexing: a fundamental tradeoff in multipleantenna channels,”
IEEE Trans. Inf. Theory
49
(5)
1073 
1096
DOI : 10.1109/TIT.2003.810646