International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 2 - November 2015
Secrecy Outage Analysis of Underlay Cognitive Radio Over
Nakagami-Q (Hoyt) Fading Channels
P Harish*, S Sri Gowri**
*M.Tech student, ECE Department, SRK Institute of Technology, Enikepadu, Vijayawada, India
**Prof& Head, ECE Department, SRK Institute of Technology, Enikepadu, Vijayawada, India
Abstract:
An underlay cognitive radio unit over the
Nakagami - q fading channel which consists of a source
S, a secondary user (SU) and an eavesdropper who
wants to eavesdrop the information between S and SU,
is studied. The broadcast power of S is simultaneously
adjusted according to the channel state information of
S-PU link and a given threshold interference of that
primary user can permit. A closed form analytical
expressions of Secrecy Outage Probability has been
derived. The robustness of our analysis models are
verified by simulation results.
Index terms: Secrecy Outage Probability, Nakagami-q
(Hoyt), Underlay Cognitive radio networks(CRNs)
I. Introduction
Spectrum scarcity and poor spectrum
utilization are two contradictory statements that makes
to focus public on cognitive radio network, which
makes secondary users (SUs) enable to share the
frequency band of primary users(PUs). The three
different models of cognitive radio networks (CRNs)
enable users to share their frequency bands are
underlay, overlay, interweave etc. [10]. Among the
models that we have discussed the underlay type of
strategy is easy to realize, as SUs are needed to just
adjust the power of them within the threshold level that
PUs can tolerate without experiencing a complex
calculation.
studies about the Nakagami-m fading channels, which
include special cases like one-sided Gaussian
distribution (m=0.5), Rayleigh(m=1) but they didn't
mention about the security problems in CRNs. [11]
studies the secrecy outage probability (SOP) and the
probability of non-zero secrecy capacity (PNSC) of
underlay cognitive radio has been derived by using the
closed form expressions of both SOP and PNSC.
According to the best of my knowledge, SOP over Hoyt
distribution has not been investigated.
In this paper, we study the SOP of the
underlay cognitive radio unit as shown in fig.1 over
Nakagami-q fading channel (Hoyt distribution) and the
closed form expression of the Secrecy Outage
Probability (SOP) is derived.
II. System Model
We consider the system model same as the [1]
but the fading that channel experience is Nakagami-q
fading. PU_Tx and PU_Rx are primary user's
transmitter and receiver of the underlay cognitive radio
networks unit as shown in Fig 1.
PU_Tx
h2
h1
S
SU
The security of CRNs discussed by [2] to [11].
In [2] secrecy capacity for a multi-antenna SU
transmitter in the presence of eavesdropper is studied.
Reference [3] discusses the secure resource allocation
in CRNs for guaranteeing a secrecy rate for PUs. A
secure medium access control (MAC) is proposed in [4]
for CRNs. Some secure broadcasting in non-CRNs over
independent/correlated Rayleigh [5], [6] /log-normal
[7], Gaussian fading channels [8]. Reference [9], [10]
ISSN: 2231-5381
PU_RX
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h3
Eav
Fig. 1 System model
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International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 2 - November 2015
In the secondary system, a Source (S) sends
confidential information to destination SU, while
eavesdroppers want to eavesdrop the confidential
information. All the channels (hi, i∈ {1,2,3}) shown in
Fig. 1 are assumed to experience independent
Nakagami-q fading with parameters mi, Ωi ,i∈ {1,2,3})
and Additive White Gaussian Noise with power
density, N0. The channel state information (hi,
,i∈{1,2,3}) is assumed to be available at S. Though h3
is unavailable when Eav keeps in silence and just
listens, we assume h3 is available at S to set up analysis
models to study the secrecy outage performance for
every realization of h3. The peak interference power
from S which PU Rx can tolerate is Pth. P denotes the
maximum transmit power at S. In the underlay scheme,
the interference power received at PU_Rx must be
within Pth, such that P = Pth=|h2|2. In this work, we
assume that SU is located far from PU_Tx. Then, the
received signals at SU will not be influenced by PU
system. Thus, the signal to noise ratio at SU and Eav
can be written as SU = P|h1|2/N0 = Pth|h1|2/N0|h2|2), E =
P|h3|2/ N0 = Pth|h3|2/N0|h2|2), respectively.
III. Secrecy outage Probability Analysis
The probability that secrecy capacity is smaller
than that of threshold secrecy capacity Cth is defined as
SOP. SOP can be expressed as [12]
The pdf of the channel power gain over
Nakagami-q or Hoyt fading channel can be given by
[12]
1 qi 2
1 qi 2
exp(
2qi i
f ( i)
where
i
Let a1
| hi |2 ,
4qi 2
i
) I0 (
ai
4qi 2
i
)
(4)
i
1, a3
0(i
Pth / N 0 . It is
1, 2,3 ), such that
a1 | h1 |2
. The pdf of X
a2 | h 2 |2 a3 | h 3 |2
Z
i
E[ i ]
Pth / N 0 , a2
obvious that
1 qi 4
ai | h i |2
can be computed as follows:
1 1 qi 2
(1 q 2 )2 x
(1 q 4 ) x
.
.exp(
).I
(
)
0
| a i | 2qi i
4qi 2 i ai
4qi 2 i ai
f x ( x)
1 qi 2
(1 qi 2 )2 x
(1 qi 4 ) x
.exp(
).I
(
) (5)
0
2qi i ai
4qi 2 i ai
4qi 2 i ai
a2 | h 2 |2 a3 | h 3 |2 as
We can write the pdf of Z1
z1
f Z1 (z1 )
f a |h |2 ( x). f a |h |2 (z1 x) dx
2
2
3
3
0
z1
k exp(ax).I o (bx).I0 (c(z1 x)) dx
(6)
0
SOP(Cth )
P
P(CSU
1
log 2 (1
2
Cth )
SU)
1
1 SU
P{ log 2
2
1 E
Substituting
SOP(Cth )
SU and
P{1
(
Where
1
log 2 (1
2
k
Cth }
Pth
| h1 |2
N 0|
Pth
1) | h 2 |2
| h 3 |2
N0
z} (2)
aa
2
a
(1 q32 )2
4q32 3a3
c
1 q34
4q32 3a3
(1)
E into Eq. (1), we have
(1 q 22 )2
,b
4q22 2 a2
0
pdf z ( z )dz 1
pdf z ( z )dz.
(3)
k
z1
eax ebx .
2
0
1
(1 q32 )2 z1
),
4q32 3a3
(1 q 2 4 )
,
4q2 2 2 a2
By expanding Io terms
f z1 ( z1 ) k exp(ax).
1
.exp(
3 2 3
z1
2
Where
Thus, SOP can be computed as
0
4q2 q3
E ) Cth
2*Cth
SOP(Cth )
1 q2 2 1 q32
1
e
bx cos
1
dx
0
1
bx.ebx .
6
e
c (z1 x)cos
3
ec ( z1
x)
.
1
c( z1 x).ec ( z1
6
Thus, as shown in Eq (3), to obtain the closed-form
expression of SOP, we should characterize the pdf of
the positive random variable, Z.
ISSN: 2231-5381
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dx dx
0
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x)
.
3
dx
International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 2 - November 2015
z1
f z1 ( z1 ) k.
eax bx c (z1 x) (
2
0
For q1
1 bx c( z1 x) 1
bx(c(z1 x) 2 )dx (7)
2
6
6
36
After Integration we get
e(a
b)z1
ecz1
b
e(a
6(a b c)2
2
(a b c) z1 1 e
6(a b c)2
bc 2
(e(a
36(a b c)3
e
2
f z1 ( Z1 ) K
(a b)z1
ce
e
e(a
f Z (Z )
K
e
cz1
(a b)z1
e
2
0
e(a
1 q12
.exp
2q1 1a1
b)z1
ecz1
SOP(Cth ) 1
x
)
1a1
a
a
a
f z ( z)
.
a
1
K
2
b)z1
1
ecz1
2
SOP(Cth ) 1
cecz1 be(a
b)z1
0
SOP(Cth ) 1
1
e
.
(a b)z1
1 q12
.exp
2q1 1a1
e
cz1
2bc 2
36(a b c)3
(10a)
(
.
1
.e
1a1
.
z 2
1
) (
1a1
3 a3
a
1a1
dy (11)
(12)
z 2
)
1a1
1
1
3 a3 ) (
2 a2
1 1
yz
1
1
3 a3 ) (
2 a2
1
1a1 ( 2 a2
1
e(a
3a3
e
1
.
dy
f z ( Z )dz
2 a2
. e
3 3
1
1a1 ( 2 a2
SOP(Cth ) 1
3a3
e
y
y
2 2
z1
2 a2
. e
3 3
y
f z ( z)
(9a)
z1
1
2 2
(9)
( z x)
x
1
).
exp( 1
)dx (10)
2 a2
3 a3
3 a3
1
.exp(
2 a2
f z1 ( z1 )
bc 2 z1
36(a b c)2
(1 q12 )2 z
(1 q14 ) z
.
I
0
4q12 1a1
4q12 1a1
1
exp(
1a1
0
z1
1
6(a b c) 6(a b c) 2
b)z1
f x ( x)
z1
2bc 2
36(a b c)3
1
ecz1
x
) I 0 (0)
1a1
f z1 (Z1 )
bc 2 z1
36(a b c) 2
1 Equation (5) becomes
1
exp(
1a1
ecz1
z1
1
6(a b c) 6(a b c) 2
(a b)z1
cz1
b)z1
2bc 2
36(a b c)3
2
cecz1 be(a
2
ecz1 ) Z1 (a b c) 2 e(a
1
cz1
be
b)z1
b)z1
q3
f x ( x)
cz1
1 (a b c) z1 ecz1 .c
2
f z1 ( Z1 ) K
b)z1
q2
1
z 2
1
) (
1a1
3 a3
( 1a1 )2
2 a2 )( 1a1
z 2
)
1a1
dz
(14)
a)
3 3
IV. Results and Discussions
z1
1
6(a b c) 6(a b c)2
dz
bc 2 z1
36(a b c)2
(1 q12 ) 2 z
(1 q14 ) z
.I 0
dy
2
4q1 1a1
4q12 1a1
(8)
Special Case:
We know Io(0)=1, so we get q=1 as a Special case
ISSN: 2231-5381
Fig. 2 SOP Vs Pth/No (for q=0.5)
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(13)
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International Journal of Engineering Trends and Technology (IJETT) – Volume 29 Number 2 - November 2015
[8] X. Sun, J. Wang, W. Xu, and C. Zhao, “Performance of secure
communications over correlated fading channels,” IEEE Sig. Process.
Lett., vol. 19, no. 8, pp. 479-482, Aug. 2012.
[9] N. Yang, P. L. Yeoh, M. Elkashlan, et al., “Transmit antenna
selection for security enhancement in MIMO wiretap channels,”
IEEE Trans. Commu., vol. 61, no. 1, pp. 144-154, Jan. 2013.
[10] J. Lee, H. Wang, J. G. Andrews and D. Hong, “Outage
probability of cognitive relay networks with interference constraints,”
IEEE Trans. Wireless Commun., vol. 10, no. 2, pp. 390-395, Feb.
2011.
[11] C. Tang, G. Pan, T. Li, "Secrecy outage analysis of underlay
cognitive radio networks over nakagami-m fading channels," IEEE
Wireless Commmun.., vol.3. no.6. December 2014
[12] M.-S. Alouni, M.K.Simon "A unified approach to the
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1998.
Fig. 3 SOP Vs Pth/No (for q=1)
Fig 2, Fig. 3 shows the SOP vs Signal to Noise Ratio,
where the unit of Cth is bits/s/Hz. Generally Nakagamiq span rangers from q=0 to1. Where it exhibits one
sided Gaussian noise at 0 and Rayleigh at 1. fig 2.
exhibits the values for q1=q2=q3=0.5. According the
definition and meaning of secrecy outage probability
with the strengthening of the signal i.e., increasing
signal to noise ratio (SNR) values the outage
probability will be reduced. We S- SU link is better
than that of S-Eav link. Similarly fig 3 exhibits the
values for q1=q2=q3=1. By adjusting the Cth values
from 0.794 to 1 to 1.254 we achieved good results.
V. Conclusion
In this paper, the analytical model for the SOP of a
basic underlay cognitive radio networks unit over
Nakagami-q channel is presented, verified by
simulation.
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