Communications and Network, 2013, 5, 166-170
http://dx.doi.org/10.4236/cn.2013.53B2032 Published Online September 2013 (http://www.scirp.org/journal/cn)
Outage Performance of Cognitive Relay Networks with
Best Relay Selection in Nakagami-m Channels
Zongsheng Zhang, Qihui Wu, Jinlong Wang, Xueqiang Zheng, Xinhong Shao, Cheng Tan
Affiliation: College of Communications Engineering, PLA University of Science and Technology,
No. 2, YuDao Street, Nanjing China
Received May, 2013
ABSTRACT
This paper investigates the outage performance of a cognitive relay network considering best relay selection in Naka-
gami-m fading environment. The secondary user is allowed to use the spectrum when it meets the interference con-
straints predefined by primary user. Due to deep fading, cogn itive source is u nable to co mmunicate directly with cogni -
tive destination. As such , multiple relays are ready to deliver the signal from the cognitive source to cognitive destina-
tion. We select a single best relay and the selected relay uses decode-and-forward protocol. Specifically, we derive the
exact outage probability expression, which provides an efficient means to evaluate the effects of several parameters.
Finally, numerical simulation results are presented, which validate the correctness of the analytical analysis.
Keywords: Cognitive Realy Networks (CRNs); Nakagami-m Fading; Outage Probability
1. Introduction
In the past decades, the demand for wireless spectrum
use has been growing dramatically with the rapidly de-
velopment of the mobile telecommunication industry.
Conventional spectrum management policies use static
spectrum assignment to prevent interference. Recently,
this policy has led to the well-known artificial spectrum
scarcity. Lots of surveys have told us that the licensed
spectrum are critically under-utilized, often as low as
2%-15% [1]. This motivates the concept of spectrum
reuse that allows secondary users (SUs) to re-use the
spectrum. The key technology behind spectrum re-use is
cognitive radio (CR) [2-5 ]. The CR technolog y is defined
as a technology that can guide the co mmunication system
to adjust its power, frequency, modulation, coding, and
other parameters to efficiently utilize the licensed spec-
trum.
Cooperative technology, emerging as a new spatial
diversity technique, can effectively combat fading and
improve the throughput. However, the advantages of
such system achieve at the expense of a reduction in
spectral efficiency. As such, relay selection has been
investigated [6,7] to overcome this shortcoming. Re-
cently, cooperation also has great potential to be used in
cognitive radio networks, known as cognitive relay net-
works (CRNs) [8-14]. In [11], the exact outage probabil-
ity of an underlay CRNs us ing DF relaying with multiple
PUs in Rayleigh fading channels has been derived. Most
recently, the exact outage probability of an underlay
cognitive relay networks over Nakagami-m fading was
derived in [12]. In [13], the outage probability of cogni-
tive amplify-and-forward (AF) relay networks in inde-
pendent non-identically distributed (i. n. i. d) Naka-
gami-m fading was investigated. The outage probability
of dual-hop CRNs considering the direct link and inter-
ference from primary user has been derived in [14]. In
[15], the outage performance of CRNs considering both
direct link and relay selection was investigated in
Rayleigh fading environment. The outage analysis of
amplify-and-forward with partial relay selection under
spectrum-sharing constraints was analyzed in [16].
While those previous work have improved our under-
standing on the outage performance of CRNs. However,
the previous work [11-14] ignored the relay selection,
and [15,16] considered the Rayleigh fading environment.
To the best of our knowledge, the outage performance of
CRNs considering relay selection in Nakagami-m fading
environment is almost unexplored from the analytical
point view. As such, the main focus of this paper is to fill
this important gap.
The remainder of this paper is organized as follows.
Section II presents a brief description of system model.
In Section III, the exact outage probability expression of
the considered system is derived. Some numerical results
are presented to validate the correctness of theoretical
analysis in Section IV. Finally, some concluding remarks
are provided in Section V.
C
opyright © 2013 SciRes. CN

Z. S. ZHANG ET AL. 167
2. System Model
We consider a spectrum-sharing system with one pair of
primary user1, a cognitive source (S), M cognitive relays2,
and a cognitive destination (D), as depicted in Figure 1.
The communication in cognitive system takes place in
two phases. In the first phase, the cognitive source bro a d-
casts the signal to cognitive relays. In the second phase,
the best relay decodes the signal and forwards the de-
coded signal to the cogn itive destination. Specifically, all
the channel gains between any two nodes are Naka-
gami-m fading.
Specifically, for the transmission of cognitive system,
the cognitive source and cognitive relay should limit
their transmit powers so that the interference on the pri-
mary network will not ex ceed a threshold Q, which is the
peak interference that the primary network can tolerate.
As such, the transmit power of the cognitive source and
cognitive relay can be expressed as
2
3
||
SQ
Ph  (1)
and
2
4
||
i
R
i
Q
Ph  (2)
where and denote the channel gains of
and , respectively. Specifically, the
channel gains 1
||
i, , and follow
a Nakagami-m distribution with fading parameters i
and i, . Therefore, the probability density
function (PDF) and cumulative distributed function
(CDF) of a gamma random variable with parameters m
and can be denoted as
2
3
||h
PU
i
2
4
||
i
h
RP
22
h
, 4
S


iU
hi
2, 3
2
|| 2
3
||h2
4
||
i
hm
1,
21
|| () ()
mm
h
m
f
tte
m



 (3)
and
2
||
(, )
() ()
h
mt
Ft m


 (4)
where /m

, (,)mt

represents the incomplete
gamma function [17]. Consequently, the received sig-
nal-to-interference ratio (SIR) at the ith relay and cogni-
tive destination can be expressed as
2
1
20
3
||
||
i
i
SR
h Q
N
h
  (5)
1i
h
2i
h
3
h
4i
h
Figure 1. System model.
and
2
2
20
4
||
||
i
i
RD
i
h Q
N
h
  (6)
where 0 denotes the variance of add itive white Gaus-
sian noise (AWGN). For simplicity of analysis, we set
0
N
1N

. Because we select the best decode-and-forward
protocol in this paper. As such, the end-to-end SIR can
be denoted as
1,...,
max {min(,)}
ii
SDF SRR D
iM



  (7)
3. Outage Probability
In this section, we will derive the outage probability of
the considered system. The outage probability, i.e., the
end-to-end SIR falls below the threshold th

, is ex-
pressed as
Pr{}( )
BDF
BDF
out
PF





  (8)
Accordingly, the main focus is to derive the CDF of
B
DF

. Based on (5) and (6), we conclude that the i
SR

and i
R
D

are not independent due to common variable
. For simplicity of representation, we set
2
3
||h2
3
||
X
h,
2
1
||
i
A
h, ,
2
2
||
i
Bh2
4
||
i
Ch
a
nd min( ,)
ii
SRR D
U



.
Therefore, the CDF of U conditioned on
X
can be
expressed as
(|)Pr{min(,)|}
1Pr{min(,)|}
1(1(|))(1(|))
ii
ii
SRR D
ii
SRR D
SRR D
FU XX
X
F
XF X

 
 


 
 
(9)
1In this paper, we only consider a single primary user, for simplicity o
f
analysis. The obtained results can be extended to multiple primary
user.
2In this paper, multiple relays are assumed closely located to be a clus-
ter. Therefore, we assume that the distance between any relay are small
compared to the distance between cognitive source and relay or be-
tween relay and cognitive destination. As such, for simplicity of analy-
sis, the pathloss is same for any relays, and is not taken into considera-
tion in this paper.
As such, the main focus is to derive the (| )
SRi
F
X


and (|)
RD
i
F
X


. In this way, the (| )
SRi
F
X


and
(| )
RD
i
F
X


can be expressed as

Z. S. ZHANG ET AL.
168
2
1
0
1
1
1
||
(|)Pr{| }
Pr{|}
(, )
()
SRi
i
Qh
F
XX
NX
X
AX
Q
X
mQ
m







(10)
and
444
2
22
4
00
0
2
2
1 4
042
||
(|)Pr{| }
||
Pr{|}
()()
()()
(, )
() ()
RD
i
i
i
c
Q
CB
CB
mmc
Qh
FX X
h
C
BX
Q
fcfbdbdc
c
fcFdc
Q
c
mQ
ce dc
mm




















1
1I
(11)
where
41
2
141
1
1
4241
1()
2 0
414
() (1)!
() !()
mk
m
kmk
k
mk
ImQk Q








 (12)
As such, the (| )
U
F
X

can be denoted as
1
1
1
1
1
( |)1 (1( |))(1(|))
1(1(|))
(, )
1(1)
()
SRR D
ii
SRi
U
FXFX FX
FXI
X
mQI
m







 
 
 
(13)
Due to independent distribution and random variable
B
DF

 is the maximum of M random variables. There-
fore, the CDF of
B
DF

 conditioned on
X
can be
expressed as
1
1
1
1
(, )
(| ) (1(1))
()
BDF
M
X
mQ
F
X
m

I




  (14)
Based on (14), the unconditional cumulative distrib-
uted function of
B
DF

 marginalized out with respect to
X
can be calculated as
0
()( |)()
SDFBDF X
F
FXfx




dx (15)
Substituting (3) and (14 ) into (15), the ()
BDF
F


 can
be calculated as
333
333
0
1
11
3
1
013
1
11
3
1
0013
()
(| )()
(, )
(1 (1) )
() ()
(, )
()(1)
() ()
SDF
BDF X
mmx
M
m
Mmx
mm m
M
m
F
FXfxdx
x
mQI xedx
mm
x
mQ
C Ixedx
mm

























(16)
The
1
1
1
(, )
(1 )
()
m
x
mQ
m



 can be expanded as follows
1
111
1
..
11
111
0
11
(,)( )
(1 )..
() !...!
m
m
ll
mx mm
mQ
ll m
xx
mQQ
e
ml

l










(17)
Plugging (17) into (16), the exact outage expression
can be expressed as
1
13
11 33
1
1
11
13
1
..
1
11 1
3
1
000
13
..
1
11 13
1(.. )
1
00
13
()
()
().. !... !()
() (.. 1)!
() ..!...!()
SDF
m
m
m
m
m
ll
mx m
mm
Mmx
mm Q
M
mll
m
ll
mm
Mmm m
Mllm
mll
m
F
x
Q
CIe xed
ll m
llm
Q
CI m
ll Q

















 

 
 





x
(18)
4. Numerical Results
In this section, we confirm the analytical results derived
in Section III via comparisons using Monte Carlo simu-
lations. We mainly focus on the impacts of interference
links, transmit links and the maxi mum allowable transmit
power of primary user on the outage performance of the
considered system. Specifically, all the simulatio n results
are obtained th ro u gh independent trials.
8
10
Firstly, we evaluate the impact of the number of relays
on the outage performance of the cognitive relay net-
works. The parameters for simulation are set as follows:
11m

, 21m

, 31m

and 4. Specifically, we
consider three schemes in the simulation: Scheme 1:
1m
1
M

, Scheme 2: 3M

, Scheme 3: 5M

. Obvi-
ously, Figure 2 shows that the outage performance of the
considered system will improve when we increase .
Similarly, the same conclusion can be obtained from the
parameters
Q
M
and the
M
affects the diversity of the
considered system. Moreover, the Monte Carlo simula-
tion results keep tight with the analytical results which
validate the analytical analysis.
Secondly, we evaluate the impact of channel gains of

Z. S. ZHANG ET AL. 169
the secondary system on the outage performance of the
cognitive relay networks. As such, the channels gains
between the secondary user and the primary user keep
fixed. We consider two schemes in the simulation:
Scheme 1:, Scheme 2: ,
. Figure 3 clearly shows that the outage per-
formance will improve greatly when we increase the
quality of channel gains of the secondary system. spe-
cifically, the channel gains of the secondary system will
not affect the diversity of the considered system.
(1,1,1,1)
i
m(2,2,1,1)
i
m
1, 2,3, 4 i
Lastly, we evaluate the impact of the channel gains
from the primary user on the outage performance of the
cognitive relay networks. As such, the channel gains be-
tween secondary system keep fixed. Similarly, we also
consider two schemes in the simulation: Scheme 1:
, Scheme 2: , (2,2,2,2)
i
m(2,2,1,1)
i
m1, 2,3, 4i

.
We can directly observe from Figure 4 that the outage
probability will increase when the quality of primary
links becomes better. Moreover, the channel gains be-
tween secondary user and primary user do not affect the
diversity of the considered system.
05 10 15 20 25 30
10
-7
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Maximum Interference Power (Q) (dB)
Outage Probability of CRNs
Anal ytical R esul t s M = 1
Simulation Resul t s M=1
Anal ytical R esul t s M = 3
Simulation Resul t s M=3
Anal ytical R esul t s M = 5
Simulation Resul t s M=5
Sche m e 1
Scheme 2
Scheme 3
Figure 2. Impacts of number of relays on the outage perfor-
mance of cognitive relay networks.
05 10 15 20 25
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Maximum In t erference Power (Q) (dB)
Out a ge Pr obability of CRNs
An al ytical r esults ( Scheme 1)
Simulat ion R esult s ( Schem e1)
An al ytical r esults ( Scheme 2)
Simulat ion R esult s ( Schem e2)
Figure 3. Impacts of channel gains of the secondary system
on the outage performance of cognitive relay networks.
05 10 15 20 25
10
-6
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
Maximum I n t erference Power (Q) (dB)
Out age Probability of CRNs
An al ytical r esults ( Schem e 1)
Simu l ation R esu l t s ( Scheme1)
An al ytical r esults ( Schem e 2)
Simu l ation R esu l t s ( Scheme2)
Figure 4. Impacts of channel gains of primary network on
the outage performance of cognitive relay networks.
5. Conclusion
In this paper, the outage performance of cognitive relay
networks with multiple relays was derived in Nakagami-
m fading environment. We consider a spectrum-sharing
system with a primary user as long as the secondary us er
meets the power interference requirements predefined by
the primary user. Specifically, the best decode-and-for-
ward relay selection protocol is adopted in this paper.
Moreover, we derived the exact outage probability ex-
pression, which provides an efficient means to evaluate
the effects of several parameters. Last, numerical results
are provided, and the Monte Carlo simulations results
match well with the analysis results.
6. Acknowledgements
This work was supported by the national basic research
program (973) of China under grant no. 2009CB320400,
the National Science Foundation of China under grant no.
60932002 and no. 61172062, and in part by the Jiangsu
Province Natural Science Foundation of China under
grant no. BK2011116.
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