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1
Outage Probability of Cognitive Relay Networks
with Interference Constraints
Jemin Lee, Hano Wang, Jeffrey G. Andrews, Senior Member,IEEE,
and Daesik Hong, Senior Member,IEEE
Abstract—This paper evaluates the outage probability of
cognitive relay networks with cooperation between secondary
users based on the underlay approach, while adhering to the
interference constraint on the primary user, i.e., the limited
amount of interference which the primary user can tolerate. A
relay selection criterion, suitable for cognitive relay networks, is
provided, and using it, we derive the outage probability. It is
shown that the outage probability of cognitive relay networks
is higher than that of conventional relay networks due to the
interference constraint, and we quantify the increase. In addition,
the outage probability is affected by the distance ratio of the
interference link (between the secondary transmitter and the
primary receiver) to the relaying link (between the secondary
transmitter and the secondary receiver). We also prove that
cognitive relay networks achieve the same full selection diversity
order as conventional relay networks, and that the decrease in
outage probability achieved by increasing the selection diversity
(the number of relays) is not less than that in conventional relay
networks.
Index Terms—cognitive relay networks, outage probability,
selection diversity.
I. INT ROD UC TI ON
In cognitive radio networks, unlicensed users (secondary
users) are permitted to use the licensed band so long as they
protect the data transmission of the licensed user (primary
user) using spectrum underlay, overlay and interweave ap-
proaches [1]. In the underlay approach, the secondary user
is allowed to use the spectrum of the primary user only
when the interference from the secondary user is less than the
interference level which the primary user can tolerate. Hence,
the transmission power of the secondary user is constrained not
to exceed the interference level. In the overlay approach, the
secondary user uses the same spectrum concurrently with the
primary user while maintaining or improving the transmission
of the primary user by applying sophisticated signal processing
and coding [1]. Otherwise, using the interweave approach,
the secondary user utilizes the spectrum not currently being
used by the primary user, known as a spectrum hole, after
performing detection on the spectrum.
Relay networks have been proposed as a way to enhance
the total throughput and coverage of wireless networks [2].
The advantage of relay networks lies in reducing the overall
path loss achieved by using a relay between a source and a
destination. Inspired by cognitive radio and relay networks,
cognitive relay networks (CRN) have recently been investi-
gated as a potential way to improve secondary user throughput
using one of two approaches: cooperation between primary
and secondary users [3], and cooperation between secondary
users [4]-[7].
For cooperation between secondary users, approximate [4]
and exact [5] outage probabilities of cognitive relay networks
have been presented considering the impact of the spectrum-
sensing accuracy in overlay coexistence. Also, it is shown that
full diversity cannot be achieved under imperfect spectrum
sensing [4]. Decentralized schemes for transmit power alloca-
tion for secondary relays have been proposed to minimize the
overall transmit power or to maximize the received signal to
noise-interference ratio (SINR) in [6]. In addition, the perfor-
mance of cognitive relay networks in licensed and unlicensed
bands is compared to that of conventional relay networks
[7]. Although the location of the relay and appropriate relay
selection are important [8], no prior work has considered
an appropriate relay selection procedure for cognitive relay
networks.
Our goal in this paper is to evaluate the performance of
cognitive relay networks using cooperation between secondary
users based on the underlay approach while adhering to the
interference constraint on the primary user. We first provide a
relay selection criterion suitable for cognitive relay networks
and then derive the outage probability of cognitive relay
networks. Our main contributions are to show that: 1) the
outage performance of cognitive relay networks is affected by
the distance ratio of the interference link (from the secondary
transmitter to the primary receiver) to the relaying link (be-
tween the secondary transmitter and the secondary receiver);
2) the outage probability of cognitive relay networks consists
of (or can be divided into) the conventional relay network
outage probability and the increase in outage probability
resulting from the interference constraint; and 3) cognitive
relay networks achieve the same relay selection diversity order
as conventional relay networks, but the decrease in outage
probability of cognitive relay networks achieved by increasing
the selection diversity is equal to or greater than that in
conventional relay networks.
II. SYSTEM MO DE L
The cognitive relay network model of interest to us is
described in this section. In this model, a primary user coexists
with secondary users as shown in Fig. 1. In the figure, P URX ,
SUS, and SUDrepresent a primary receiver, a secondary
source, and a secondary destination, respectively. In addition,
there are Kpotential secondary user relays which are denoted
by SUk(k= 1,· · ·, K ). The relay mode is regenerative mode,
2
SU
S
SU
D
SU
k
PU
RX
h
S
k
P
h
kD
h
kP
Inte rference links
Relaying links
Fig. 1. System model of cognitive relay networks; P URX,S US,SUD, and
SUkrepresent a primary receiver, a secondary source, a secondary destination,
and the kth potential relay, respectively.
so a relay decodes the received data and then forwards it to
a secondary destination. Let M={S, D, 1,2,· · · , K}be
the set of secondary user indexes. We assume that a primary
receiver occupies multiple primary spectra (frequency chan-
nels) spaced with greater frequency separation than coherence
bandwidth2, and each relay uses different frequency channel
among the primary spectra. On the ith frequency channel used
by SUi, the instantaneous channel of the link between SUi
and SUj, the relaying link in Fig. 1, is represented by hij .
The channels of the links from SUSand SUito P URX , the
interference links in Fig. 1, are denoted by hSiPand hiP ,
respectively. The channels are assumed to consist of path loss
and an independent fading effect as hij =χijd−α/2
ij (i, j ∈M)
where αand dij denote the pathloss exponent and the distance
between two users, respectively. The fading coefficient, χij,
is a complex Gaussian random variable with unit variance.
Hence, the channel gain |hij |2(i, j ∈M)is an exponential
distributed random variable with the mean value 1/λij, and
the average channel power is defined as 1/λij =E|hij|2=
d−α
ij where E[·]denotes expectation. Since the link distance
of hSiPis dSP for all i∈M,λSiPis the same as λSP . The
perfect channel information such as |hiP |2at the secondary
users is also assumed1.
In the underlay approach of this paper, the secondary
user can utilize the primary user’s spectrum so long as the
interference it generates on the primary receiver remains below
the interference threshold ( ¯
I), which is the maximum tolerable
interference level at which the primary user can still maintain
reliable communication [1]. For this reason, the secondary
user’s transmission power is constrained as Pk≤¯
I/|hkP |2,
where Pkis the transmission power of SUk; this constraint
1The channel information of |hiP |2can be obtained at secondary users by
direct reception from a primary receiver using some pilot signals [9], [10]
or by using the band manager, which can exchange the channel information
between primary and secondary users [10]. The channel information estimator
without feedback could be also used by the methodology in [11].
2This can be compatible with the assumption that multiple primary receivers
use different frequency channels, and each channel is occupied by a primary
receiver [12].
is called the interference constraint. In addition, there is also
the maximum transmission power constraint,Pk≤¯
Pwhere
¯
Pis the maximum transmission power [6]. By those two
constraints, the transmission power constraint of SUkbecomes
as follows [6], [9]:
Pk≤min ¯
I
|hkP |2,¯
P.(1)
If the secondary source transmits data with the help of the
kth potential relay in dual-hop, known to be the most efficient
multi-hop transmission with respect to system capacity [8],
the capacity of the secondary user based on a unit bandwidth
becomes as follows [8]:
Ck=1
2min log21 + PSk|hSk|2
No,log21 + Pk|hkD|2
No.
(2)
In (2), 1/2 is from the dual-hop transmission in two time slots
and Nois the noise variance. In addition, any interference from
the primary transmitter is assumed to be neglected3.
III. OUTAG E ANALYSIS OF COGNITIVE RELAY NETWORKS
This section present an appropriate relay selection criterion
for cognitive relay networks. Also, we analyze the relay
transmission performance in terms of the outage probability,
and compare it to that of conventional relay networks.
A. Cognitive Relay Networks
We begin this subsection by reviewing an existing relay
selection criterion and conventional relay network outage
performance. A variety of criteria for relay selection have
been proposed as a way of maximizing capacity or minimizing
outage probability in conventional relay networks [15]-[17].
The max-min criterion, which maximizes the minimum of
signal-to-noise ratios (SNRs) of the source-relay link and
relay-destination link, has proven optimal for this purpose
[16]. Hence, a relay selection criterion in conventional relay
networks is defined as follows [16], [17]:
l∗= arg max
kmin |hSk |2,|hkD |2,(3)
where l∗is the selected relay index in conventional relay
networks. Thus, the relay is chosen based on the channel
gains of the relaying links. Hence, under the assumption that
all users use the maximum transmission power, the outage
probability based on the kth relay is defined as Po
Conv,k =
1−e−(λSk +λkD )·UT/¯
Pwhere UT=No22CT−1and CT
is the target bandwidth efficiency [16]. Hence, the outage
probability in conventional relay networks when the relay
selection is applied becomes the following:
Po
Conv =
K
k=1 1−e−(λSk +λkD )·UT/¯
P.(4)
3This can be possible if the primary transmitter is located far away from
the secondary users [13], or the interference is represented by the noise term
under an assumption that the primary transmitter’s signal is generated by
random Gaussian codebooks [14].
3
From (4), we can see that Po
Conv is solely a function of the
distances of relaying links. Moreover, minimizing the outage
probability is equal to minimizing λSk +λkD , and the outage
probability has a symmetric form per λSk and λkD . Since the
selection criterion in (3) is to minimize the outage probability,
we can deduce from (4) that the relay located at exactly the
midpoint between the source and destination would be the one
most likely to be selected in average.
In contrast to conventional relay networks, an additional
transmission power constraint, the interference constraint,
exists in cognitive relay networks, making the conventional
relay selection criterion inappropriate. For instance, a relay
which has good channel conditions on its source-relay and
relay-destination links is likely to be selected in conventional
relay networks, but may be an inappropriate relay in cognitive
relay networks if the relay generates a lot of interference
at the primary receiver. Hence, as a max-min criterion for
maximizing relay transmission performance, the relay selec-
tion criterion must be redefined while considering both the
interference constraint and the maximum power constraint as
follows:
k∗= arg max
kmin min ¯
I
|hSkP|2,¯
P· |hSk |2,
min ¯
I
|hkP |2,¯
P· |hkD |2
= arg max
kmin {u1,k, u2,k }= arg max
kUk,
(5)
where k∗is the relay index selected for cognitive relay
networks.
Lemma 1. Using the outage probability of conventional relay
networks, Po
Conv,k = 1 −e−(λSk +λkD )UT/¯
P, the outage
probability for cognitive relay networks after applying the
relay selection described in (5) can be defined as follows:
Po
CR =
K
k=1 Po
Conv,k +βk,(6)
where βkis an increase in outage probability due to the
interference constraint, defined as (7), shown at the bottom of
the page, where n=¯
I/ ¯
P,γ1,k =λSP /λSk = (dSP /dSk )α,
and γ2,k =λkP /λkD = (dkP /dkD )α.
Proof: In (5), due to the interference constraint, Uk=
min {u1,k, u2,k }is no longer an exponential random vari-
able. Hence, the first step is to define the distribution of
u= min ¯
I|hx|2,¯
P· |hy|2so as to derive the outage
probability, as follows:
Pr {u≤UT}=∞
x=¯
I/¯
Px·UT/¯
I
y=0
fxy(x, y)dydx
+¯
I/¯
P
x=0 UT/¯
P
y=0
fxy(x, y)dydx
=e−γ·λy·¯
I/ ¯
P
γ¯
IUT+ 1 −1e−λyUT/¯
P+ 1
=gu(λx, λy),
(8)
where fxy(x, y ) = λx·λy·e−(λx·x+λy·y)and γ=λx/λy.
Using (8), the outage probability based on the kth relay,
Po
CR,k = Pr {Ck≤CT}= Pr {Uk≤UT}, can be de-
fined as Po
CR,k = 1 −Pr {u1,k ≥UT}Pr {u2,k ≥UT}=
1−(1 −gu(λSP , λSk)) ·(1 −gu(λkP , λkD)). Hence, the
outage probability in cognitive relay networks is defined as
Po
CR = Pr {Uk∗≤UT}, and presented as
Po
CR =
K
k=1 1−1−e−λSk γ1,k ¯
I/ ¯
P
γ1,k ¯
I/UT+ 1
×1−e−λkDγ2,k ¯
I/ ¯
P
γ2,k ¯
I/UT+ 1e−(λSk +λkD )UT/¯
P.
(9)
From Lemma 1, we can see that the outage probability
when the kth relay is used in cognitive relay networks consists
of the outage probability in conventional relay networks,
Po
Conv,k , and an increase due to the interference constraint,
βk.βkbecomes zero as ¯
Pgoes to zero. Moreover, if ¯
P
goes to infinity, then βkbecomes {(γ1,k +γ2,k)¯
I/UT+
1}/{γ1,k ¯
I/UT+ 1γ2,k ¯
I/UT+ 1}so that βkbecomes
zero as ¯
Igoes to infinity, and one as ¯
Igoes to zero. Hence,
βkhas a range of 0≤βk≤1. Therefore, it can be said that
the outage probability in cognitive relay networks is always
equal to or greater than that in conventional relay networks.
Moreover, from (9), we can see that the outage probability
depends not on the distances of the interference links, but on
the distance ratio of the interference link to the relaying link.
This means that the relative distance of the interference link
based on the relaying link distance has more of an impact
on the outage probability than the absolute distance of the
interference link.
B. Comparison of Relay Selection Diversity
This subsection compares the relay selection diversity in
cognitive relay networks to that in conventional relay net-
works. For simplicity, it is assumed that each link has an
equal mean of channel gain, λSk =λSR ,λkD =λRD ,
and λkP =λRP for all k[17], [18], since this assumption
provides a simple form for the analysis without changing the
βk=e−(λSk +λkD )UT/¯
P−e−(λSk γ1,k +λkD γ2,k )n+γ2,k ¯
I/UT+ 1e−λSkγ1,k n+γ1,k ¯
I/UT+ 1e−λkDγ2,k n
γ1,k ¯
I/UT+ 1γ2,k ¯
I/UT+ 1.(7)
4
diversity order. With this assumption, Po
Conv,k and βkbecome
equal for all kas ¯
PConv and ¯
β. Thus, the outage probabilities
in conventional relay networks and cognitive relay networks
become Po
Conv =¯
PConv Kand Po
CR =¯
PConv +¯
βK=
¯
PCR K. Using binomial theorem [19], Po
CR can be redefined
as follows:
Po
CR =¯
PConv K+gI C (K),(10)
where
gIC (K) =
K
i=1 K
i¯
PK−i
Conv ·¯
βi,
0≤¯
β≤1,0≤¯
PConv +¯
β≤1.
(11)
Hence, we can see that the outage probability of cognitive
relay networks with relay selection is divided into the outage
probability in conventional relay networks, Po
Conv , and the
increased outage probability arising from the interference
constraint, gIC (K).
If the outage probability is proportional to ρ−mas ρ
approaches infinity, the selection diversity order is mwhere ρ
is the SNR [20]. Then, the following lemma can be obtained.
Lemma 2. Cognitive relay networks achieve the full relay
selection diversity order of K.
Proof: In cognitive relay networks, we need to consider
two cases of SNR from the transmission power constraint in
(1). First, when Pk=¯
P(i.e., ¯
I/|hkP |2>¯
P), SNR is ρ1=
¯
P /No. In (6), ¯
PCR is proportional to ρ−1
1as ρ1goes to infinity
since UT/¯
P= (22CT−1)ρ−1
1. So, Po
CR scales no slower than
O(ρ−K
1). Second, when Pk=¯
I/|hkP |2(i.e., ¯
I/|hkP |2≤¯
P),
the average SNR is ρ2=λkP ¯
I/No. From βkin Lemma 1,
we can see that ¯
PCR is proportional to ¯
I/No−1as ¯
I/No
approaches infinity since ¯
I/UT= (22CT−1)−1¯
I/No. So,
Po
CR also scales no slower than O(ρ−K
2). Hence, the selection
diversity order is Kfor all cases of transmission power.
Note that this is the same as the selection diversity order in
conventional relay networks [18]. Hence, with full selection
diversity order, the outage probabilities for both cognitive and
conventional relay networks decrease as the number of relays
increases. However, the reduction in the amount of outage
probability achieved by adding a relay in cognitive relay
networks is different from what occurs in conventional relay
networks. We designate this the diversity gain. In the generally
considered range of the outage probability (i.e., ¯
PCR ≤0.5),
the following lemma on the diversity gain can be obtained.
Lemma 3. The diversity gain in cognitive relay networks is
always equal to or greater than that in conventional relay
networks when ¯
PCR ≤0.5.
Proof: The diversity gains achieved by increasing the
total number of relays from K−1to Kin cognitive
and conventional relay networks are defined as GCR(K−
1, K) = ¯
PCR K−1−¯
PCR Kand GConv (K−1, K ) =
¯
PConv K−1−¯
PConv K, respectively. From (10), GCR (K−
x
y
0.0 0.1 0.2 0. 3 0.4 0.5 0.6 0.7 0.8 0. 9 1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.6
0.2
0.4
0.3
0.5
1.6
0.4
0.8
1.2
1.8
Cognitive Relay
Networks Conventional Relay
Networks
Relays
SU
S
PU
RX
SU
D
Fig. 2. Percentages of relay selection in conventional relay networks (dotted
line), and in cognitive relay networks (solid line) (400 candidate relays are
distributed equidistantly over a square area and the secondary source, the
secondary destination and the primary receiver are located at the coordinates
(0,1), (1,0) and (1,1), respectively).
1, K)and GC onv (K−1, K)have the following relation:
GCR (K−1, K)−GC onv (K−1, K) = gI C (K−1)−gIC (K).
(12)
Assuming gIC (t),t∈R+, is a continuous
function, then the gradient is defined as gIC (t)′=
ln ¯
PConv +¯
β¯
PConv th(t)where h(t) =
¯
P−1
Conv ¯
PConv +¯
βt−ln ¯
PConv ln ¯
PConv +¯
β−1.
Since ln ¯
PConv +¯
β≤0and h(t)≥0when
¯
PConv +¯
β≤0.5for t > 0,gIC (t)′≤0. Hence,
gIC (k)is a monotonically decreasing function of k∈R+.1
Accordingly, gIC (K−1) −gIC (K)is not less than zero,
which implies GCR (K−1, K)−GConv (K−1, K)≥0in
(12).
From Lemma 2 and Lemma 3, it can be seen that cog-
nitive relay networks have the same relay selection diversity
order as conventional relay networks, but that the decrease
in outage probability achieved by increasing the selection
diversity is larger. Hence, the outage probability of cognitive
relay networks, generally larger than that of conventional relay
networks, approaches that of conventional relay networks as
the number of relays increases.
IV. NUMERICAL RES ULT S
In this section, we examine the performance of cognitive
relay networks based on the outage probability. Simulations
were conducted to verify the derived outage probabilities in
(9) and (10), and the results closely match the analysis, as
shown in Figs. 3-5.
1gIC (t)′≤0means gI C (t)is monotonically decreasing at any point
t∈R+, so gIC (k)is also a monotonically decreasing function with respect
to k,k∈N, since N⊂R+.
5
10-1 100
10-2
10-1
100
Ratio of interference threshold to maximum transmission power
Outage Probability of Sec ondary User
Cog-Direct (Simulation)
Cog-Relay (Analy sis)
Cog-Relay (Si mualtion)
Conv-Relay (Analysis)
Conv-Relay (Simualtion)
Cognitive Relay
Networks:
PU
RX
=(1.5,1.5)
Cognitive Relay
Networks:
PU
RX
=(1.0,1.0)
Conventional Relay
Networks
/I P
Fig. 3. Comparison of outage probabilities of cognitive relay networks (Cog-
Relay), conventional relay networks (Conv-Relay), and direct transmission in
cognitive radio networks (Cog-Direct) according to the interference threshold
compared to the maximum transmission power, ¯
I/ ¯
P(In this simulation, ρ=
¯
P /No= 30dB, CT= 5 bps/Hz, and 20 potential relays are distributed
uniformly within a rectangular area described by the coordinates (0,0), (0,
1), (1,0), and (1,1)).
As discussed above, the relay selection criterion in cognitive
relay networks considers the interference constraint as well as
the maximum power constraint. Hence, the relay selected is
different from the one selected in conventional relay networks,
even in the same environment. Fig. 2 shows the distribution of
probabilities that a relay in a specific location will be selected
in cognitive relay and conventional relay networks. To obtain
more precise distributions, 400 potential relays are located
equidistantly (marked with ‘x’ in Fig. 2). The numbers on
the contour lines represent the probability that a specific relay
will be selected, and the relay that is most likely to be selected
is indicated by a square. In conventional relay networks, the
relay located exactly at the midpoint between source and
destination (near the coordinates (0.5,0.5)) is the one most
likely to be selected. However, in cognitive relay networks,
the relay located farthest from the primary receiver (near the
coordinates (0.35,0.35)), is the one most apt to be selected.
Accordingly, the conventional relay selection criterion is not
suitable in cognitive relay networks.
Fig. 3 depicts the outage performances versus ¯
I/ ¯
P. For
this simulation, we vary the interference threshold while ¯
P
is fixed, so that the outage performance of the conventional
relay network is not affected by the variation of ¯
I/ ¯
P. In
Fig. 3, if we compare the results when the primary receiver’s
locations are (1,1) (dotted lines) and (1.5,1.5) (solid lines), we
see that the outage performance of cognitive relay networks
improves when the primary receiver is located farther away
from the secondary users. In addition, the outage probability
of cognitive relay networks approaches that of conventional
relay networks as the interference threshold increases. In
general, we can see that the relaying transmission achieves
better outage performance than direct transmission. However,
2 4 6 8 10 12 14 16 18 20
10
-4
10
-3
10
-2
10
-1
10
0
Ratio of maximum transmis sion power to noise
Outage Probability of Sec ondary User
Cog-Relay (Analys is)
Cog-Relay (Simulati on)
Conv-Relay (Analysis)
Conv-Relay (Simulation)
K=4
K=2
/ (dB)
o
P N
( )
/
K
o
P N
−
A
A
Fig. 4. Comparison of outage probabilities of cognitive relay networks (Cog-
Relay) and conventional relay networks (Conv-Relay) according to the ratio
of the maximum transmission power to the noise, ¯
P /No(¯
I/No= 12dB,
and CT= 1.5bps/Hz).
direct transmission can outperform relay transmission when
the primary receiver is located close to the secondary users
or the interference threshold is low, as shown in Fig. 3. This
results from the fact that, in those cases, the loss from using
twice the resources (e.g., 1/2term in (2)) is more dominant
than the improved capacity achieved via relay transmission. In
addition, we note that the relay transmission is more sensitive
to any variation in the interference threshold or the location
of the primary receiver than direct transmission.
Figs. 4-6 are to show the diversity order and the gain when
the primary receiver is located at the coordinates (1.5,1.5),
and each channel’s mean is assumed to be equal, λSk =
λSR = 2−α/2,λkD =λRD = 2−α/2, and λkP =λRP = 2α/2
for all k, as described in Section III.B.
In Fig. 4, the curves obtained by ¯
P /No−Kare included as
references to explicitly verify the diversity order. Comparing
the slopes of the results confirms that cognitive relay networks
indeed achieve full diversity order equivalent to conventional
relay networks. However, due to the transmission power
constraint in (1), the outage probability of cognitive relay
networks converges to a constant when ¯
Pis high, e.g., in
the area Ain Fig. 4. In this case, the transmission power is
¯
I/|hkP |2with high probability. So, the diversity order needs
to be verified according to ¯
I/Noas Fig. 5, which shows the
outage probability when ¯
Pis high, i.e., ¯
P /No= 40dB. In Fig.
5, the same slopes of the results also confirm the full diversity
order of cognitive relay networks. We can thus see that the
interference constraint in cognitive relay networks does not
change the diversity order.
In Fig. 6, both the outage probabilities of cognitive relay
networks and conventional relay networks decrease and be-
come similar to each other as the number of relays increases.
On comparing GCR (K−1, K)and GConv (K−1, K), we
can see that the diversity gain achieved by increasing the
number of relays is greater in cognitive relay networks than in
6
4 6 8 10 12 14 16 18
10
-4
10
-3
10
-2
10
-1
10
0
Ratio of interference threshold to noise
Outage Probability of Secondary User
Cog-Relay (Analys is)
Cog-Relay (Simulat ion)
K=4
K=2
K=1
/ (dB)
o
I N
( )
/
K
o
I N
−
Fig. 5. Outage probability of cognitive relay networks (Cog-Relay) according
to the ratio of the interference threshold to the noise, ¯
I/No(¯
P /No= 40dB,
and CT= 2 bps/Hz).
conventional relay networks, as is discussed in Section III.B.
For instance, if the number of relays is increased from 3to 4,
the outage probability reduction amounts are 0.05 in cognitive
relay networks and 0.01 in conventional relay networks. We
can therefore achieve a greater reduction in outage probability
in cognitive relay networks than in conventional relay net-
works by providing additional relays.
V. CONCLUSIONS
The overall contribution of this paper is the evaluation of the
outage probability of cognitive relay networks when a suitable
relay selection criterion is applied. As opposed to conventional
relay networks, the outage probability in cognitive relay net-
works is affected by the distance-ratio of the interference link
to the relaying link, and not the absolute distances. Moreover,
it is always higher than that of conventional relay networks due
to the interference constraint, and the difference between them,
depending on the interference threshold and the maximum
transmission power, is quantified. The outage probability of
cognitive relay networks decreases with full selection diversity
order the same as conventional relay networks, but the de-
crease in outage probability achieved by increasing the number
of relays is greater than that of conventional relay networks.
These observations give quantitative insight into the effect of
the interference constraint and the number of potential relays
on the outage probability of cognitive relay networks.
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