1
Secure Transmission Design for Cognitive Radio
Networks with Poisson Distributed Eavesdroppers
Xiaoming Xu, Student Member, IEEE, Biao He, Student Member, IEEE, Weiwei Yang, Member, IEEE,
Xiangyun Zhou, Member, IEEE, and Yueming Cai, Senior Member, IEEE
Abstract—In this paper, we study physical layer security
in an underlay cognitive radio (CR) network. We consider
the problem of secure communication between a secondary
transmitter-receiver pair in the presence of randomly distributed
eavesdroppers under an interference constraint set by the pri-
mary user. For different channel knowledge assumptions at the
transmitter, we design four transmission protocols to achieve the
secure transmission in the CR network. We give a comprehensive
performance analysis for each protocol in terms of transmission
delay, security, reliability, and the overall secrecy throughput.
Furthermore, we determine the optimal design parameter for
each transmission protocol by solving the optimization problem
of maximizing the secrecy throughput subject to both security
and reliability constraints. Numerical results illustrate the per-
formance comparison between different transmission protocols.
Index Terms—Physical layer security, cognitive radio networks,
on-off transmission, secrecy guard zone.
I. INTRODUCTION
A. Background and Motivation
With the rapid adoption of wireless devices, there is an
unprecedented growth in the demand for radio spectrum. To
address the conflict between spectrum scarcity and spectrum
underutilization, cognitive radio (CR) [1–3] has been regarded
as a promising technology to solve the problem of inefficient
spectrum usage. In CR networks, unlicensed secondary users
(SUs) are allowed to access the spectrum of licensed primary
users (PUs) with the requirement of not interfering the PUs.
Generally, there exist two paradigms of CR networks classified
by the spectrum access strategy: i) overlay CR [4, 5] and ii)
underlay CR [6, 7]. For the overlay CR, the SUs first adopt
spectrum sensing techniques to identify the licensed spectrum
hole, and then transmit data over the detected spectrum holes.
For the underlay CR, the SUs simultaneously utilize the
licensed spectrum while guaranteeing the interference at the
PU not beyond the acceptable threshold.
Allowing the spectrum sharing in the CR network is not
without drawbacks. The coexistence of licensed and unli-
censed users in the same network makes the data transmissions
vulnerable to security attacks [8]. To address this concern,
This work was supported by the Natural Science Foundation of China under
Project 61371122, Project 61471393, and the Australian Research Council
under Discovery Project Grant DP150103905.
X. Xu, W. Yang and Y. Cai are with College of Communications
Engineering, PLA University of Science and Technology, Nanjing 210007,
China (e-mail: xiaomingxu.plaust@gmail.com, wwyang1981@163.com,
caiym@vip.sina.com).
B. He and X. Zhou are with the Research School of Engineering,
Australian National University, Canberra, ACT 0200, Australia (e-mail:
biao.he@anu.edu.au, xiangyun.zhou@anu.edu.au).
innovative security technologies have been proposed for CR
networks [8]. As a complement to the traditional cryptographic
techniques [9], physical layer security (PLS) has been widely
studied [10] [11] to secure the wireless transmissions by
exploiting the fading characteristics of wireless channels.
To the best of authors’ knowledge, the current research
on PLS in CR networks assumed that either the channel
state information (CSI) of eavesdropping channel is perfectly
known or there are a small number of eavesdroppers at known
locations. In practical scenarios, a passive eavesdropper would
not reveal its CSI or location information to the legitimate
communication nodes, and hence such assumptions are not
always valid. Taking into account potentially a large number
of eavesdroppers inside the network at random and possibly
changing locations (due to mobility), a common analytical
approach is to model the location set of eavesdroppers to be a
stochastic process following some distribution [12–14]. For the
secure communication in CR networks, the consideration of
randomly distributed eavesdroppers has been rarely discussed
in CR networks.
B. Our Approach and Contribution
In this paper, we study the problem of achieving PLS in an
underlay CR network where a secondary transmitter (SU-Tx)
sends confidential information to a secondary receiver (SU-Rx)
over a quasi-static Rayleigh fading channel in the present of
multiple eavesdroppers. The location set of the eavesdroppers
is modeled as a homogeneous Poisson point process (HPPP).
1
We consider different transmission protocols for the SU-
Tx to achieve secure communication while guaranteeing the
instantaneous interference to the primary receiver (PU-Rx) not
beyond a given threshold. To satisfy the interference constraint,
the transmit power at the SU-Tx is carefully adjusted, which
is determined by the instantaneous channel condition from the
SU-Tx to the PU-Rx.
We consider four transmission protocols to achieve the se-
cure transmission in the CR network: the full activity protocol,
the secrecy guard zone protocol, the threshold-based protocol
and the hybrid protocol. These four different protocols are
suitable for the scenarios with different assumptions on the
channel knowledge of the SU-Tx and the location knowledge
about the eavesdroppers. Specifically, the full activity protocol
is for the scenario where the SU-Tx does not have any
knowledge about the CSI of its receiver and the location
1
HPPP has been widely adopted to model the eavesdropper locations in the
existing literature, e.g., [12, 13, 15].
2
information of the eavesdroppers. The secrecy guard zone
protocol is for the scenario where the SU-Tx can detect
the existence of eavesdroppers in its vicinity, i.e., a circular
guard zone of radius r. The SU-Tx suspends the transmissions
when eavesdropper(s) are detected inside the guard zone. The
threshold-based protocol is for the scenario where the SU-Tx
can obtain a one-bit feedback about the SU-Tx’s instantaneous
channel gain. The SU-Tx suspends the transmissions when
the channel gain is worse than some threshold µ. Finally, the
hybrid protocol includes both the secrecy guard zone and the
threshold-based transmissions, hence, is expected to have the
best performance.
For each transmission protocol, we evaluate various quality-
of-service measures by studying performance metrics related
to transmission delay, security and reliability. Specifically, we
use outage-based metrics which are suitable for quasi-static
fading channels. Instead of adopting a widely-used outage
probability of secrecy capacity [16] which does not distinguish
between outages due to suspended transmission (i.e., delay),
information leakage to eavesdroppers (i.e., security) and un-
reliable reception at the intended receiver (i.e., reliability), we
use separate outage metrics for each type of quality of service.
We also define an outage metric called transmission secrecy
outage probability (TSOP) that comprehensively evaluates
the security and reliability performance in order to tell the
probability of having a secure and reliable transmission. The
tradeoff between security and reliability is also captured by
the TSOP. Finally, the overall performance of each protocol is
measured by the secrecy throughput defined as the achievable
average rate of secure and reliable transmissions.
We further optimize the design of transmission proto-
cols based on the derived outage probabilities and secrecy
throughput expressions. To this end, we study the optimization
problem of achieving the maximal secrecy throughput with
given security and reliability outage constraints. We first study
the feasible security and reliability constraints for each trans-
mission protocol, under which a non-zero secrecy throughput
is achievable. We then obtain the closed-form solutions of
the optimal guard zone’s radius r and/or the optimal SNR-
threshold µ that maximize the secrecy throughput for the
corresponding transmission protocols. Our results show that
the secrecy guard zone protocol is preferred when the security
constraint is stringent while the threshold-based protocol is
preferred when the reliability constraint is stringent.
The remainder of this paper is organized as follows. Sec-
tion II discusses the related work. Section III gives the channel
model and performance metrics. Section IV introduces the
four transmission protocols. Sections V and VI evaluate and
optimize the transmission protocols, respectively. Section VII
presents the numerical results. Finally, Section VIII concludes
the paper.
II. RELATED WORK
Underlay CR communications [6, 7] has received a lot of
attention as a promising paradigm to improve spectrum usage
efficiency, e.g., [17–19] focusing on the performance analysis
and [20–24] investigating the network design. In recent years,
there has been increasing interest in the security issue of
CR networks, due to the rapid growing amount of private
and sensitive data transmitted in wireless networks. From an
information-theoretic perspective, the performance of PLS in
CR networks was studied in, e.g., [25–29]. The ergodic secrecy
capacity for the CR network was evaluated in [25, 26] with
the consideration of fast fading channels where the encoded
messages are assumed to span sufficient channel realizations to
capture the ergodic features of the fading channel. Considering
the slow fading channels, the secrecy performance of the CR
network was evaluated in [27] by the outage-based formula-
tion. The secrecy throughput scaling laws were investigated in
[28, 29]. More recently, various signal processing techniques
and system design protocols were proposed to improve the
secrecy performance of the CR networks. For the multi-
antenna CR network, beamforming designs and cooperative
jamming techniques were studied in [30–32]. For the CR
network with multiple SUs, the user scheduling scheme for
improving the security level of cognitive transmissions was
proposed in [33]. Furthermore, the CR network with decode
and forward relays was studied in [34] where the optimal relay
selection scheme to minimize the secrecy outage probability
was proposed.
As mentioned in Section I-A, the consideration of randomly
distributed eavesdroppers has been rarely discussed in CR
networks. However, the randomly distributed eavesdroppers
are often considered in the study on PLS in large-scale wireless
networks using tools from stochastic geometry [35]. The
network model based upon stochastic geometry allows us to
study the probabilistic network behaviors and corresponding
performance metrics [36–38]. In particular, the location set
of the randomly distributed eavesdroppers is often modeled
by the HPPP, e.g., [12, 14, 15, 39–41]. The HPPP-based model
not only provides tractable closed-form results but also de-
scribes the randomness of eavesdropper locations in practical
scenarios [41]. Specifically, Goel et al. [14] introduced a
secrecy graph model based on the HPPP to capture the
uncertainty in eavesdropper locations at the network level.
Pinto et al. [12] proposed the Poisson iS-graph to study the
secrecy connectivity of large scale network. Zhou et al. [15]
investigated the secrecy transmission capacity of the wireless
network. Furthermore, the scaling laws for secrecy capacity
were investigated in [39–41]. For the secure communication
in CR networks, the consideration of randomly distributed
eavesdroppers has been studied in [42, 43], in which Shu
et al. considered that the message to the PU is confidential
and derived the secrecy capacity in the presence of randomly
distributed eavesdroppers whose location set is modeled as
a HPPP. However, the work in [42, 43] only considered a
simplified channel model consisting of the pass loss effect
only, while the fading effect is not considered. It is important
to note that the performance of secure communication is
very different between a fading and a non-fading scenario.
Furthermore, the presence of fading can be smartly utilized to
achieve a better security performance.
It is worth mentioning that the literature review in this
section focuses on only the most closely related work in the
areas of CR networks, PLS in CR networks, and PLS in
3
PU-Rx
SU-Tx
SU-Rx
j
E
PU-Tx
Data link
Interference link
Eavesdropper link
Fig. 1. Illustration of a cognitive radio network with a Poisson field of
eavesdroppers.
large-scale wireless networks. Due to the rapid development of
wireless technology and the increasing demand of secure com-
munications, there also exists many other interesting studies
on the current and next generation of wireless networks and
communication security, e.g., [44–56].
III. SYSTEM MODEL
A. Channel Model
As shown in Figure 1, we consider an underlay CR network
that consists of a primary transmitter-receiver pair and a sec-
ondary transmitter-receiver pair. The SU-Tx sends confidential
messages to the SU-Rx in the present of multiple movable
eavesdroppers, which are denoted by {E
j
|j = 1, 2, · · ·}. The
primary network allows the secondary network to share the
spectrum by underlay method, and requires that the instanta-
neous interference power at PU-Rx from SU-Tx is lower than
a threshold, denoted by I
0
.
We assume that the eavesdroppers are randomly distributed
in the network. The location set of the eavesdroppers, denoted
by Φ
E
, is modeled as a HPPP with density λ
E
. Different
from the deterministic model, the spatial HPPP introduces
total randomness for the node deployment, and only the node
density variable is required to characterize this stochastic
process. In addition, the randomness introduced by the HPPP-
based model has the advantage of being tractable in perfor-
mance analysis, since it often leads to closed-form results
on statistical analysis for signal attenuation laws [57]. By
adopting the PPP-based topology for wireless networks with
randomly distributed nodes, important results on connectivity,
coverage, and throughput have been successfully derived in
[36, 58, 59].
In this work, we assume that all communication nodes
have a single antenna and the wireless communication channel
is modeled as a path-loss plus quasi-static Rayleigh fading
channel. Denote the transmitter power at SU-Tx as P . Then,
the received signal to noise ratios (SNRs) at the SU-Rx and
eavesdropper E
j
are given by
γ
D
=
P
σ
2
D
|h
SD
|
2
d
−α
SD
(1)
and
γ
E
j
=
P
σ
2
E
j
h
SE
j
2
d
−α
SE
j
, (2)
respectively, where α ≥ 2 denotes the path loss exponent,
d
SD
and d
SE
j
denote the distance from SU-Tx to SU-Rx
and the distance from SU-Tx to E
j
, respectively, σ
2
D
and
σ
2
E
j
denote additive white Gaussian noise (AWGN) variances
at SU-Rx and E
j
, respectively, with σ
2
D
= σ
2
E
j
= σ
2
. In
addition, h
SD
and h
SE
j
denote the channel coefficients for the
channel from SU-Tx to SU-Rx and the channel from SU-Tx
to E
j
, respectively, which are modeled as complex Gaussian
variables with zero mean and unit variance, i.e., CN (0, 1). We
further assume that the interferences from PU-Tx at the SU-
Rx and the eavesdroppers are neglectable. We highlight that
such an assumption is widely adopted in the literature studying
CR networks, e.g., [27, 33, 60–62]. A practical example that
approximates this occurrence is the scenario where the PU-
Tx is located far away from the terminals in the secondary
network [61].
We assume that the receiver side (including PU-Rx, SU-
Rx and the eavesdroppers) has the perfect CSI, while the
availability of CSI at the transmitter-side is different between
PU-Rx and SU-Rx due to the different capabilities of the com-
munication terminals. We consider a scenario where the PU-
Rx is a cellular base station which is capable of instantaneous
CSI feedback to both PT-Tx and SU-Tx, while the SU-Rx
is not capable of full CSI feedback. Specifically, the PU-Rx
feeds back to the SU-Tx with the instantaneous channel gain,
denoted by |h
SP
|
2
, to enable the SU-Tx to adjust its transmit
power to satisfy the interference constraint [17–19].
2
Although
the SU-Rx is not capable of full CSI feedback, we consider
the possibility of a low-complexity feedback scheme in which
the SU-Rx uses one bit to inform SU-Tx about its channel
condition. The eavesdroppers are totally passive, and hence
their CSI is not revealed to SU-Tx.
To satisfy the instantaneous interference constraint, I
0
, the
SU-Tx adjusts the transmit power to
P =
I
0
|h
SP
|
2
d
−α
SP
1
(condition)
, (3)
where d
SP
denotes the distance from SU-Tx to PU-Rx, and
h
SP
∼ CN (0, 1). The 1
(condition)
in (3) denotes an indicator
function for whether the transmission is “on” or “off” at SU-
Tx, which is given by
1
(condition)
=
1, if the condition holds
0, otherwise,
(4)
where the condition depends on the specifical transmission
protocol, and will be detailed later in Sections IV. Note that
having such an “on-off” transmission strategy can effectively
improve the security and/or reliability performance, as will be
shown in Sections V.
2
This can be achieved through a spectrum-band manager that mediates
between the licensed and unlicensed users [63]. However, it is worth noting
that, for certain scenarios, obtaining the interference channel power gains
may be challenging. For these cases, our results serve as the bounds for the
performance of the considered network.
4
For a robust analysis, we consider that all eavesdroppers
can collude and exchange information. Thus, the multiple
eavesdroppers can be regarded as a single eavesdropper, E
joint
,
with multiple distributed antennas, and the equivalent received
SNR at the E
joint
is given by
γ
E
=
P
σ
2
X
E
j
∈Φ
E
h
SE
j
2
d
−α
SE
j
. (5)
From (1) and (5), we note that γ
D
and γ
E
have the same power
variable P , which makes them correlated with each other. For
convenience, we define Z
Φ
E
=
P
E
j
∈Φ
E
h
SE
j
2
d
−α
SE
j
in the
following analysis.
B. Secure Encoding
The SU-Tx uses the widely-adopted wiretap code [64] to
encode the confidential messages. Let C (R
B
, R
S
) denote the
set of all possible Wyner codes, where R
B
is the codeword
transmission rate and R
S
is the confidential information rate
with R
B
> R
S
. The rate difference R
B
− R
S
reflects the cost
of securing the message against eavesdropping. We assume
that the encoding rates have already been designed, and hence
R
B
and R
S
are fixed.
3
Such a fixed-rate transmission scheme
is suitable for practical applications requiring low complexity,
e.g., video streams in multimedia.
C. Outage Probability Metrics
In the following, we detail the outage definitions for char-
acterizing the transmission delay, the security performance
and the reliability performance of the network. Moreover, we
propose a new probability metric to comprehensively evaluate
the joint performance of security and reliability.
1) TP: Since the transmission may not always happen at
SU-Tx depending on the transmission protocol, there exists a
probability of transmission referred to as TP, which is given
by
p
tx
= P
1
(condition)
= 1
, (6)
where P(·) denotes the probability measure. We adopt the
probability of transmission as a measure of the performance
of transmission delay [65].
2) SOP and COP: With the fixed-rate wiretap code, there
exist two kinds of outage events [65, 66]: secrecy outage
event and connection outage event. The secrecy outage event
happens when the perfect secrecy of the message cannot be
guaranteed, and the probability of the secrecy outage referred
to as SOP is given by [65]
p
so
= P
C
E
> R
B
− R
S
| 1
(condition)
= 1
, (7)
where C
E
= log (1 + γ
E
) denotes the channel capacity of
E
joint
. The connection outage event happens when the message
cannot be decoded at the intended receiver without error, and
the probability of the connection outage referred to as COP is
given by
p
co
= P
C
B
< R
B
| 1
(condition)
= 1
, (8)
3
The design of rate parameters is beyond the scope of this work.
where C
B
= log (1 + γ
D
) denotes the channel capacity of the
secondary link. In this work, we adopt the SOP as a measure
of the security performance and the COP as a measure of the
reliability performance.
3) TSOP: From (7) and (8), we note that the security and
reliability become correlated in the considered CR network
due to the correlation between γ
D
and γ
E
. This is actually
different from the case in most of the non-cognitive scenarios,
e.g., [15, 66, 67]. Therefore, it is necessary to comprehensively
study the joint performance of the security and the reliability.
To this end, we propose a new outage performance metric,
namely transmission secrecy outage probability (TSOP). The
TSOP characterizes the probability that either secrecy outage
or connection outage happens, which is given by
p
tso
=1−P
C
E
≤R
B
−R
S
, C
B
≥R
B
| 1
(condition)
= 1
. (9)
Remark 1: Comparing the expressions of p
so
, p
co
and p
tso
in (7), (8) and (9), we note that the TSOP takes the mutual
correlation between the SOP and the COP into account. For the
special case that SOP and COP are independent,
4
the TSOP
can be further derived as
p
tso
= 1 − (1 − p
co
) (1 − p
so
) . (10)
Remark 2: The proposed TSOP characterizes the joint se-
curity and reliability performance. In fact, a similar concept of
jointly measuring security and reliability performance can be
found in another widely-adopted outage probability definition,
i.e., p
out
= P (C
S
< R
S
) [16], where C
S
denotes the secrecy
capacity. Compared with the expression of p
out
, the proposed
TSOP takes into account the system design parameters, such as
the rate of the transmitted codewords as well as the condition
under which message transmission happens.
D. Secrecy Throughput
The overall performance of the system is measured by
the secrecy throughput taking into account the transmission
delay, the security performance and the reliability performance
together. The secrecy throughput is given by
η = p
tx
(1 − p
tso
) R
S
, (11)
where p
tx
is the TP in (6) and p
tso
is the TSOP in (9).
As mentioned before, p
tx
quantizes the transmission delay
performance and p
tso
quantizes the joint security and reliability
performance. As such, the secrecy throughput in (11) quantizes
the average secrecy rate at which the messages are securely
and reliably transmitted to SU-Rx.
It is worth mentioning that the secrecy throughput in (11)
is different from the throughput definition in [65] and [66].
In [65] and [66], the throughput is formulated as
η = p
tx
(1 − p
co
) R
S
, (12)
which quantizes the average secrecy rate at which the mes-
sages are reliably transmitted to SU-Rx. We find that the
throughput expression in (12) does not reflect whether the
4
When the transmit power is fixed in cognitive or non-cognitive networks,
the SOP and COP usually are independent [15, 66, 67].
5
transmission is secure, and hence it is proper to use the secrecy
throughput expression in (11) for characterizing the overall
performance of the transmission.
IV. SECURE TRANSMISSION PROTOCOLS
For the considered CR network as described in Section III,
there are four possible cases of channel knowledge assump-
tions at the SU-Tx, which are detailed as follows: 1) SU-Tx
does not know any information about the channel condition
to the SU-Rx and does not know any information about
the eavesdropper locations; 2) SU-Tx does not know any
information about the channel condition to the SU-Rx but
can detect the existence of eavesdroppers in its vicinity; 3)
SU-Rx has the one-bit feedback about the channel condition
to the SU-Rx but does not know any information about the
eavesdropper locations; 4) SU-Rx has the one-bit feedback
about the channel condition to the SU-Rx and can detect
the existence of eavesdroppers in its vicinity. These four
cases complete the possible channel knowledge assumptions
at the SU-Tx for the considered CR network. Accordingly,
we design four secure transmission protocols which are full
activity protocol, secrecy guard zone protocol, threshold-based
protocol and hybrid protocol. The details of each protocol are
given in the following subsections.
A. Full Activity Protocol
For the full activity protocol, the SU-Tx can neither obtain
the one-bit feedback from the SU-Rx nor detect the existence
of eavesdroppers in its vicinity. Therefore, the SU-Tx keeps
sending the confidential information to the SU-Rx all the time
while satisfying the power constraints. This protocol is the
simplest protocol amongst the four transmission protocols.
Since the BS is always active, the indicator function in (4)
is always equal to one, and the SNRs at the SU-Rx and the
eavesdropper E
joint
are given by
γ
D
=
I
0
|h
SD
|
2
d
−α
SD
σ
2
|h
SP
|
2
d
−α
SP
(13)
and
γ
E
=
I
0
σ
2
|h
SP
|
2
d
−α
SP
Z
Φ
E
, (14)
respectively.
B. Secrecy Guard Zone Protocol
For the secrecy guard protocol, we consider the scenario
where the SU-Tx is able to detect the existence of eavesdrop-
pers within a finite range. As per the mechanism of secrecy
guard zone [15, 68], we model the finite range around the SU-
Tx as a secrecy guard circle B with radius r. The SU-Tx sends
messages only when there is no eavesdropper detected inside
the guard circle. Consequently, the SNRs at the SU-Rx and
the eavesdropper E
joint
under the secrecy guard zone protocol
are given by
γ
D
=
I
0
|h
SD
|
2
d
−α
SD
σ
2
|h
SP
|
2
d
−α
SP
1
(C
1
)
(15)
and
γ
E
=
I
0
σ
2
|h
SP
|
2
d
−α
SP
Z
Φ
E
1
(C
1
)
, (16)
respectively, where C
1
denotes the event that no eaves-
dropper is detected inside the secrecy guard zone, i.e.,
C
1
: ∀E
j
∈ Φ
E
, d
SE
j
> r
.
C. Threshold-Based Protocol
In the threshold-based protocol, we assume that the SU-Tx
can obtain a one-bit feedback from the SU-Rx to enable a
threshold-based on-off transmission. Specifically, the SU-Tx
transmits only when the received SNR at SU-Rx is larger
than a predetermined threshold µ. Otherwise, the SU-Tx
suspends the transmission. To this end, the SU-Rx sends an
instantaneous one-bit feedback to the SU-Tx for indicating
whether the received SNR is larger the threshold µ. In such a
protocol, the SNRs at the SU-Rx and the eavesdropper E
joint
are given by
γ
D
=
I
0
|h
SD
|
2
d
−α
SD
σ
2
|h
SP
|
2
d
−α
SP
1
(C
2
)
(17)
and
γ
E
=
I
0
σ
2
|h
SP
|
2
d
−α
SP
Z
Φ
E
1
(C
2
)
(18)
respectively, where C
2
denotes the event that the SNR at the
SU-Rx is larger than µ, i.e.,
n
C
2
:
I
0
|h
SD
|
2
d
−α
SD
σ
2
|h
SP
|
2
d
−α
SP
> µ
o
.
D. Hybrid Protocol
In this protocol, we assume that the SU-Tx can not only
detect the existence of eavesdroppers within the secrecy guard
zone but also obtain the one-bit feedback from the SU-
Rx, and hence, the SU-Tx adopts a joint secrecy guard
zone and SNR threshold based transmission strategy. As
the same to Section IV-B, we denote the secrecy guard
zone as a circle B with radius r around the SU-Tx. As
the same to Section IV-C, we denote the received SNR
threshold as µ. The SU-Tx transmits only when both of
the following two conditions are satisfied: 1) there is no
eavesdropper in the secrecy guard zone around the SU-Tx;
2) the received SNR at SU-Rx is larger than the threshold
µ. The AND rule is applied at the SU-Tx for determining
whether to transmit, and the condition for transmission is given
by
n
C
1
&C
2
: ∀E
j
∈ Φ
E
, d
SE
j
> r and
I
0
|h
SD
|
2
d
−α
SD
σ
2
|h
SP
|
2
d
−α
SP
> µ
o
.
Then, the SNRs at the SU-Rx and the eavesdropper E
joint
are
given by
γ
D
=
I
0
|h
SD
|
2
d
−α
SD
σ
2
|h
SP
|
2
d
−α
SP
1
(C
1
&C
2
)
(19)
and
γ
E
=
I
0
σ
2
|h
SP
|
2
d
−α
SP
Z
Φ
E
1
(C
1
&C
2
)
, (20)
respectively.
V. PERFORMANCE ANALYSIS
In this section, we derive the TP, the COP, the SOP and the
TSOP for different transmission protocols, to characterize the
transmission delay, the reliability, the security and the joint
security and reliability performance, respectively.
