Performance of cooperative spectrum sensing for different number of cr users in cognitive radio

International Journal of Science and Research (IJSR), India Online ISSN: 2319-7064
Volume 1 Issue 3, December 2012
www.ijsr.net
Performance of Cooperative Spectrum Sensing for Different
Number of CR users in Cognitive Radio
Mohammad Alamgir Hossain1
, Shahoreare Ahmed2
, Md. Shamim Hossain3
, Md. Ibrahim Abdullah4
1
B.sc (Hons) & M.sc in CSE, Islamic University, Bangladesh
alamgirlovely@yahoo.com
2
B.sc (Engineer) in EEE, International Islamic University Chittagong, Bangladesh
nshahoreare@gmail.com
3
Department of CSE, Islamic University, Bangladesh
shamimmalitha@yahoo.com
4
Department of CSE, Islamic University, Bangladesh
ibrahim25si@yahoo.com
Abstract: We have studied the performance of cooperative spectrum sensing for different number of CR users in cognitive radio over
non-fading channel AWGN and fading channels such as Rayleigh and Nakagami. This paper presents a simulation comparison of these
fading channels based on fusion OR-rule. We observe that spectrum sensing for different number of CR users is harder in presence of
Rayleigh and Nakagami fading than non-fading AWGN channel. It also shows that spectrum sensing gives better performance when
more number of CR users is cooperated.
Keywords: cognitive radio, cooperative spectrum sensing, fading channels, energy detection
1. Introduction
Cognitive radio is defined as software defined radio
which is aware of its environment, learns from and has the
ability to change its parameters according to these changes in
its environment and the networks requirements [1]. The
concept of cognitive radio has been introduced to alleviate
the spectrum under-utilization problem of wireless
communications. One of the most challenging tasks in
cognitive radio networks is spectrum sensing, which is
required to opportunistically access the idle radio spectrum.
Existing spectrum sensing techniques can be divided into
three types [2]: energy detection, matched filter detection
and cyclostationary detection. Among them, energy
detection has been widely applied since it does not require
any a priori knowledge of primary signals and has much
lower complexity than the other two schemes. The radio
channel is characterized by two types of fading effects: large
scale fading and small scale fading [3], [4]. Small scale
fading models include the well-known Rayleigh, Rice, and
Nakagami-m [5]-[6] distributions. For large scale fading
conditions, it is widely accepted that the probability density
function (PDF) of the fading envelopes can be modeled by
the well-known Log-normal distribution [7], [8]. Due to the
several multipath fading, a cognitive radio may fail to notice
the presence of the PU and then will access the licensed
channel and cause interference to the PU. To combat these
impacts, cooperative spectrum sensing schemes have been
proposed to obtain the spatial diversity in multiuser CR
networks [9-11]. The performance of single CR user based
spectrum sensing in fading channels such as Rayleigh,
Nakagami, Weibull has been studied in [12]. The
performance of cooperative spectrum sensing with censoring
of cognitive radios in Rayleigh fading channel has been
evaluated in [13-15]. Cooperative spectrum sensing
improves the detection performance. All CR users sense the
PU individually and send their sensing information in the
form of 1-bit binary decisions (1 or 0) to Fusion center (FC).
The hard decision combining rule (OR, AND, and
MAJORITY rule) is performed at FC using a counting rule
to make the final decision regarding whether the primary
user present or not [16]-[18]. Cooperative spectrum sensing
has been addressed in [19-22]. However, the existed works
examined the additive white Gaussian noise (AWGN)
channel and the Rayleigh fading channel. In this paper, we
study performance of cooperative spectrum sensing for
different number of CR users in cognitive radio.
The rest of this paper is organized as follows. In Section
II, the system model is introduced. In Section III, detection
and false alarm probabilities of non-fading AWGN and
fading channel such as Rayleigh and Nakagami are
described. Cooperative spectrum sensing over various fading
channels is derived in Section IV. The simulation result and
discussion are presented in section V. Finally, we draw our
conclusions in Section VI.
2. System Model
The local spectrum sensing is to decide between the
following two hypotheses,
 
 
    1
0
H
H
tnths
tn
tx




 (1)
where x(t) is the signal received by secondary user and
s(t) is primary user’s transmitted signal, n(t) is the additive
white Gaussian noise (AWGN) and h is the amplitude gain
of the channel.
The energy collected in the frequency domain is denoted
by Y which serves as a decision statistic. Following the work
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of Urkowitz [23], Y may be shown to have the following
distribution,
  1
0
,2
2
2
2
2 H
H
Y
TW
TW







(2)
where TW2
2
 and   22
2
TW denote central and non-
central chi-square distributions respectively, each with 2TW
degrees of freedom and a non-centrality parameter of 2γ for
the latter distribution. For simplicity we assume that time-
bandwidth product, TW, is an integer number which we
denote by u.
3. Detection and False Alarm Probabilities
In this section, we give the average detection probability
over Rayleigh and Nakagami fading channels and in closed
form [24]. In communications theory, Nakagami
distributions and Rayleigh distributions are used to model
scattered signals that reach a receiver by multiple paths.
Depending on the density of the scatter, the signal will
display different fading characteristics. Rayleigh and
Nakagami distributions are used to model dense scatters.
Nakagami distributions can be reduced to Rayleigh
distributions, but give more control over the extent of the
fading.
3.1 Non-fading environment (AWGN channel)
In non-fading environment the average probability of
false alarm, the average probability of detection, and the
average probability of missed detection are given,
respectively, by [24]
    ,2| 1 ud QHYPP  (3)
   
 u
u
HYPPf



2/,
| 0

 (4)
and
dm PP 1 (5)
where λ denotes the energy threshold. Γ(.) and Γ(.,.) are
complete and incomplete gamma functions respectively [25]
and  .,.uQ is the generalized Marcum Q-function defined
as follows,
   dxaxIe
a
x
baQ u
ax
u
u
u 1
0
2
1
22
, 
 


where .1uI is the modified Bessel function of (u−1)th
order. If the signal power is unknown, we can first set the
false alarm probability fP to a specific constant. By equation
(4), the detection threshold λ can be determined. Then, for
the fixed number of samples 2TW the detection probability
dP can be evaluated by substituting the λ in (3). As
expected, fP is independent of γ since under 0
H there is no
primary signal present. When h is varying due to fading,
equation (3) gives the probability of detection as a function
of the instantaneous SNR, γ. In this case, the average
probability of detection dP may be derived by averaging (3)
over fading statistics [19],
   dxxfQP
x
ud   ,2 (6)
where fγ(x) is the probability distribution function (PDF)
of SNR under fading.
3.2 Rayleigh Fading Channels
When the composite received signal consists of a large
number of plane waves, for some types of scattering
environments, the received signal has a Rayleigh distribution
[26]. If the signal amplitude follows a Rayleigh distribution,
then the SNR γ follows an exponential PDF given by
  









 exp
1
f , 0 (7)
In this case, a closed-form formula for dP may be
obtained (after some manipulation) by substituting  xf in
(6),
1
2
0
2
1
2!
1




 




 







u
u
k
k
dRay
k
eP


   







 















2
0 12!
1
212
u
k
k
ee




(8)
3.3 Nakagami Fading Channel
Although Rayleigh and Ricean distributions are the most
popular distributions to model fading channels, some
experimental data does not fit well into neither of these
distributions. Thus, a more general fading distribution was
developed whose parameters can be adjusted to fit a variety
of empirical measurements [25]. This distribution is called
the Nakagami fading distribution. The Nakagami distribution
was introduced by Nakagami in the early 1940’s to
characterize rapid fading in long distance HF channels [27].
It is possible to describe both Rayleigh and Rician fading
with the help of a single model using the Nakagami
distribution. The Nakagami m-distribution is used in
communication systems characterize the statistics of signal
transmitted through multipath fading channels.
The Nakagami distribution is often used for the
following reasons. First, the Nakagami distribution can
model fading conditions that are either more or less severe
than Rayleigh fading. When m=1, the Nakagami distribution
becomes the Rayleigh distribution, when m=1/2, it becomes
a one-sided Gaussian distribution, and when m=∞ the
distribution becomes an impulse (no fading). Second, the
Rice distribution can be closely approximated by using the
following relation between the Rice factor K and the
Nakagami shape factor m [27];
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mmm
mm
K



2
2
1m
 
 12
1
2



K
K
m
Since the Rice distribution contains a Bessel function
while the Nakagami distribution does not, the Nakagami
distribution often leads to convenient closed form analytical
expressions that are otherwise unattainable. Using the
alternative representation of Marcum-Q function given in
[28, eq. (4.74), pp. 104], (1) can be written as,
 
kun
kn
n
u
k
e
n
e
Q 





 






2!!
,2
1
0
2
0




(9)
If the signal amplitude follows a Nakagami distribution,
then the PDF of γ follows a gamma PDF given by
 
  












 





mm
m
f m
m
exp
1 1
, 0 (10)
where m is the Nakagami parameter. The average dP in
the case of Nakagami channels dNakP can now be obtained
by averaging (3) over (10) and then using again the change
of variable 2x yielding
 dxxQ
mx
xP u
m
dNak 

 ,
2
exp
0
2
12









 (11)
where
 
m
m
m
m 






 

 1
2
1
(12)
In this case, a closed-form formula of Nakagami
channels can be given by
 
  
















 


1
1 1
11
2
;1;
!2
2/u
n
dNak
m
nmF
n
GP


 (13)
where  .;.;.11 F is the confluent hypergeometric
function [18].
  2/2 


 







 e
m
m
m
(14)
and
 dxxQ
mx
xG u
m










0
2
12
1 ,
2
exp 

(15)
Where Q(.,.)=Q(.,.) is the first-order Marcum Q-function.
G1 can be evaluated for inter m with the aid of [25, Eq.(25)]
 
1
2
1
1 1
!12

























m
m
m
m
m
m
mm
e
mm
m
G






























 







m
L
m
m
m
L
m
n
n
n
m
22
2
0
1
(16)
where is the Laguerre polynomial of degree n [25,
8.970].
4. Cooperative Spectrum Sensing over various
Fading Channels
In real communication environments, the hidden terminal
problem, deep fading and shadowing, etc., would deteriorate
the signal detection performance of cognitive users. To
address this issue, multiple cognitive radios can be
coordinated to perform spectrum sensing. Several recent
works have shown that cooperative spectrum sensing can
greatly increase the probability of detection in fading
channels [19], [29].
Let N denote the number of users sensing the PU. Each
CR user makes its own decision regarding whether the
primary user present or not, and forwards the binary decision
(1 or 0) to fusion center (FC) for data fusion. The PU is
located far away from all CRs. All the CR users receive the
primary signal with same local mean signal power, i.e. all
CRs form a cluster with distance between any two CRs
negligible compared to the distance from the PU to a CR.
For simplicity we have assumed that the noise, fading
statistics and average SNR are the same for each CR user.
We consider that the channels between CRs and FC are ideal
channels (noiseless).
Assuming independent decisions, the fusion problem
where k out of N CR users are needed for decision can be
described by binomial distribution based on Bernoulli trials
where each trial represents the decision process of each CR
user. With a hard decision counting rule, the fusion center
implements an n–out-of-M rule that decides on the signal
present hypothesis whenever at least k out of the N CR user
decisions indicate 1H . Assuming uncorrelated decisions, the
probability of detection at the fusion center [30] is given by
 








N
kl
lN
id
l
idd PP
l
N
P ,, 1 (17)
where idP , is the probability of detection for each
individual CR user as defined by (3) and (6).
OR-rule : In this rule, if any one of the local decisions
sent to the decision maker is a logical one, the final decision
made by the decision maker is one. Cooperative detection
performance with this fusion rule can be evaluated by setting
k=1 in eq. (17).
 N
idORd PP ,, 11  (18)
5. Simulation Result and Discussion
All simulation was done on MATLAB version R2011a
over two different fading under Rayleigh and Nakagami
channel and a non-fading channel AWGN. We described the
receiver through its complementary ROC curves for different
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values of probability of false alarm and Cognitive Radio
user.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
10
-4
10
-3
10
-2
10
-1
10
0
Cooperative Spectrum Sensing over non-Fading AWGN Channel
Probability of False alarm (Pfa)
ProbabilityofMissedDetection(Pmd)
CR User=2
CR User=3
CR User=4
Figure 1: Complementary ROC of OR-rule over non-fading
AWGN channel ( =10dB, u=5).
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
10
-4
10
-3
10
-2
10
-1
10
0
Cooperative Spectrum Sensing over Rayleigh Fading Channel
CR User=2
CR User=3
CR User=4
Figure 2: Complementary ROC of OR-rule over Rayleigh
fading channel ( =10dB, u=5).
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
10
-4
10
-3
10
-2
10
-1
10
0
Cooperative Spectrum Sensing over Nakagami m=3 Fading Channel
CR User=2
CR User=3
CR User=4
Figure 3: Complementary ROC of OR-rule over Nakagami
fading channel ( =10dB, u=5, m=3).
Fig. 1, 2, and 3 show the complementary ROC of fusion
OR rule for different number of cooperative users. CR users
are taken 2, 4 and 6 for simulation. Simulation is done for
cooperative spectrum sensing over non-fading AWGN
channel, Rayleigh and Nakagami fading channel
respectively. Average SNR and u are assumed to be 10 dB
and 5 respectively. Nakagami parameter m are set to be 3.
Simulation result shows that spectrum sensing is better when
more number of users are cooperated. It also shows that in
non-fading AWGN channel the sensing performance is
better than in other channels.
6. Conclusion
We have studied the performance of cooperative
spectrum sensing for different number of Cognitive Radio
users in Cognitive Radio. Performance of cooperative
spectrum sensing over Rayleigh and Nakagami fading are
presented and compared. It has been found that probability
of missed detection is decreased by using different number
of CR users.
We used OR rule as this has better performance than
AND and MAJORITY rule in various channels. We also
observe that spectrum sensing for different number of CR
users is harder in presence of Rayleigh and Nakagami fading
and performance of energy detection degrades more in
Nakagami channels than Rayleigh channel.
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Oriented Wireless Networks and Communications
(CrownCom’07), pp. 428-432, June 2008.
Author Profile
Mohammad Alamgir Hossain received the B.Sc
and M.Sc degrees in Computer Science and
Engineering (CSE) from Islamic University (IU),
Kushtia-7003, Bangladesh in 2010 and 2012
respectively. His current research interest is in the
area of OFDM and Cognitive Radio.
Shahoreare Ahmed is studying B.SC degree with
engineering in Electrical and Electronics
Engineering in International Islamic University
Chittagong, Bangladesh. His current research interest
is in the area of Cognitive Radio, Renewable Energy
and Power System.
Md. Shamim Hossain has been received Bachelor’s
and Master’s degree in CSE from Islamic University,
Kushtia. Courrently he is a Lecturer of the
Department of Computer Science and Engineering
(CSE), Islamic University (IU) His areas of interest
include mobile communication & Cognitive Radio.
Md. Ibrahim Abdullah has been received the
Bachelor’s, Master’s and M.Phil degree in Applied
Physics & Electronics from Rajshahi University,
Rajshahi. Courrently he is an Associate Professor of
the department of CSE, Islamic University, Kushtia-
7003, Bangladesh. His areas of interest include
Network security, Wireless Sensor Network, mobile
communication & Cognitive Radio.
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