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International Journal of Engineering and Advanced Technology (IJEAT)
ISSN: 2249-8958 (Online), Volume-9 Issue-2, December, 2019
2655
Published By:
Blue Eyes Intelligence Engineering
& Sciences Publication
Retrieval Number: F8703088619/2019©BEIESP
DOI: 10.35940/ijeat.F8703.129219
Journal Website: www.ijeat.org
P. Venkatapathi, Habibulla Khan, S. SrinivasaRao
Abstract: Cognitive radio (CR) is a new technology that is
proposed to improve spectrum efficiency by allowing unlicensed
secondary users to access the licensed frequency bands without
interfering with the licensed primary users. As there are several
methods available for spectrum sensing, the energy detection (ED)
is more popular due to its simple implementation. However, ED is
more vulnerable to the noise uncertainty so for that reason, we
present a robust detector using signal to noise ratio (SNR) with
dynamic threshold energy detection technique is combined with
the kernel principal component analysis (KPCA) in Cognitive
Radio Networks (CRN). The primary purpose of kernel function is
to ensure that its dependency relies on inner-product of data
without the feature space data requirement. In this paper, with the
aid of kernel function the spectrum sensing with the leading
eigenvector approach is modified to a feature space of higher
dimensionality. By introducing of efficient detection system with
dynamic threshold facility helps the better detection levels even
low SNR values with quite a lot of noise uncertainty levels. The
simulation results of the proposed system reveal that KPCA
outperforms with that of traditional PCA in terms of false alarm
rate, detector performance when tested under various
uncertainties for orthogonal frequency division multiplexing
signal.
Index Terms: Cognitive Radio; Energy Detection; kernel
Principal Component Analysis; Spectrum sensing; Principal
Component Analysis
I. INTRODUCTION
With the advances of information and communication
technologies and the development of the world economy,
there has been an explosive demand for wireless
communication services. Specifically, wireless internet
access through smart-phones, tablets, and laptops has become
the primary means of personal communication. The wireless
communication applications go beyond the personal
communication services to perform sensing, monitoring
system, patient monitoring, and vehicle network and so on.
Revised Manuscript Received on December 30, 2019.
* Correspondence Author
P. Venkatapathi*, Research Scholar, Department of ECE, KLEF,
Vijayawada, Andhra Pradesh, India.
Dr. Habibulla Khan, Professor, Department of ECE, KLEF, Andhra
Pradesh, India.
Dr. S. Srinivasa Rao, Professor & HOD, Department of ECE, MRCET,
Hyderabad, Telangana, India.
© The Authors. Published by Blue Eyes Intelligence Engineering and
Sciences Publication (BEIESP). This is an open access article under the CC
BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
This proliferation of broad contact through the association
of the network has become an integral part of various types of
wireless communication devices, which already enable users
to communicate with different services from remote
operating areas of the available (and useful) radio spectrum.
The need for wireless services in the communications
industry has led engineers and professionals to focus a great
deal on the rapid development of reliable wireless
communications technologies. According to the views of [2],
the spectrum distribution utilization variation is more useful
to give the chance to users based on this regulatory
committee. Referring to the Fig.1, most of the portion of
bands are underutilized in certain cases and over-utilized in
other cases. So, to fix this problem of scarcity in the
allocation of frequency bands to the secondary users (SUs)
which are not preoccupied with the primary users (PUs)
without any interference. To alleviate the above issue of
detection of channel occupancy, several authors worked on
this theory as well implemented experimental testbeds, some
of them are: In [3], the authors proposed a low complexity
Energy detection (ED) scheme to detect the PU occupancy
with low cost. Although the ED is a simpler mechanism fails
to address the detection at lower signal-to-noise-ratios
(SNR). In [4], the authors proposed a new framework for
detecting the spectrum availability data and adopted
intelligent-decision making method for sensing spectrum.
Fig.1. Signal strength distribution over the wireless
spectrum [3]
Later in [5], the authors contributed to modify the multi-band
spectrum sensing scheme with the aid of search heuristics to
some extent. In [6], the authors investigated the problem of
maximization that can solve the spectrum sensing duration
over the complete period of the sensing cycle.
Performance Analysis of Spectrum Sensing in
Cognitive Radio under Low SNR and Noise
Floor

Performance Analysis of Spectrum Sensing in Cognitive Radio under Low SNR and Noise Floor
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Blue Eyes Intelligence Engineering
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Retrieval Number: F8703088619/2019©BEIESP
DOI: 10.35940/ijeat.F8703.129219
Journal Website: www.ijeat.org
Also the work recommended the scheme for unknown
constant signals for CR network, the cooperative sensing
scheme, compared the various hard and soft energy-efficient
schemes. Another important work on the cyclostationary
feature detection approach was investigated by the authors in
[7]. In this paper, PCA, KPCA is of particular relevance to
efficient spectrum sensing and is examined along with the
combination of the ED mechanism.
The main contributions and organization of this paper are
summarized as follows: In section 2 we describe background
details of different cognitive radio networks. The section 3
system model. The section 4 discusses about proposed
system. The section 5 deliberates results and discussions.
Finally, in section 6 we concluded the paper.
II. BACKGROUND WORKS
Cognitive radio technology allow the primary and secondary
users to share the same spectrum by either Overlay technique,
i.e., when white space is sensed, SU starts its transmission in
that white space, or Underlay technique, i.e., SU share the
spectrum by transmitting at the same time as the PU but at
low power so as not to interfere with the PU. Cognitive radios
have the following general model known as cognitive cycle
shown in Fig.2 wherein it has the ability to sense spectrum
with smart technology.
Fig.2. Cognitive Cycle
The primary understanding of the cognitive radio cycle is
necessary because of its abrupt channel variations under
noise uncertainties [11-13], as illustrated in figure.2 clearly,
so one can address the decision of suitable algorithm for
decision mechanism in the CR network.
III. SYSTEM MODEL
Let us consider the detection problem in this study can be
characterized as a binary postulate as
   
:
0
H Y n W n=
(1)
     
:
1
H Y n W n hS n=+
(2)
τ > λ primary user present,
τ < λ primary user absent (3)
where S treated as primary user signal, Y be the secondary
user signal, W treated to AWGN and h is the channel gain.
The decision threshold representation (λ) is useful largely
because it allows the test statistic (τ) as
Fig. 3. Energy detector block diagram [9]
Referring to the Fig. 3 the simple Energy detector mechanism
with two hypothesis can be put in mathematical form as [10].
( )
12
( ( ))
1
N
n Y n
n

−
=
=
(4)
Where Y(n) treated to be received signal, N is the sample size,
𝜏(𝑛) considered as test statistic of energy.
According to the key concept of central limit theorem, the test
data can be put in the form as
( )
24
~ , 2
0
H T Normal N N
ww

=
( )
( )
2 2 2 2 2
~ , 2 ( )
1
H T Normal N N
w x w x
   
= + +
(5)
T> γ signal is present
T< γ signal is absent
Then Pd and Pf can be calculated as:
( )
( )
22
Υ
|
12 2 2
2 ( )
Nwx
p p T H Q
dNwx



−+
=  =
+




(6)
( )
2
|04
2
Nw
p p T H Q
fa Nw


−
=  = 


(7)
( )
1
2
2 exp 2
Qx ydy
x

=−




(8)
We get the detection probability Pd by suitably substituting
the threshold value in the eq. (7). Another parameter
minimum observation window Nmin can be obtained by
( )
( ) ( )
1 1 1 1 2
2[( ] N Q P Q P SNR Q P
min fa d d
− − − −
= − −
(9)
Where
x
SNR
w


=
It was clearly shown from eq. (9), if the SNR value is
minimum, then the signal will not be detected. Although the
fixed threshold schemes are widely used in spectrum sensing
for CR networks, they are inflexible with inaccurate decision
making and their fluctuating environment.

International Journal of Engineering and Advanced Technology (IJEAT)
ISSN: 2249-8958 (Online), Volume-9 Issue-2, December, 2019
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Published By:
Blue Eyes Intelligence Engineering
& Sciences Publication
Retrieval Number: F8703088619/2019©BEIESP
DOI: 10.35940/ijeat.F8703.129219
Journal Website: www.ijeat.org
So, it results in higher miss detection and false alarm rates
shows that its inefficiency to use for sensing spectrum. So,
therefore, there is a requirement of focusing on mitigation
sensing failure problem [8] by introducing a combined
spectrum sensing method concentrated on the estimated SNR
with an adaptive threshold in the combination of kernel PCA.
Probability of false alarm (
Pfa
): When the signal is from the
primary user, it is defined as the process of probability
declaration of existence of PU signal during the period of
spectrum vacancy(free) by the SUstated as,
( )
\
10 P P H H
r
fa =
(10)
The lower the 𝑃𝑓𝑎, the additional the spectrum access the
SUs will acquire.
Probability of misdetection (
𝑷𝒎𝒅
): It is defined as the process
of probability declaration of non-existence of PU signal
during the period of spectrum occupancy by the SU. It is
defined as [15],
( )
\
01
P P H H
r
md =
(11)
Probability of detection (
𝑷𝒅
): Another widely metrics is the
probability of detection (PD) [14],
1PP
d fa
=−
( )
\
11
P P H H
r
d=
(12)
Where 𝐻0 and 𝐻1 supposed to be the nonexistence and the
existence of the PU signal. If there is 𝑃𝑑 value to be high that
indicates, the better the PU security is. For finding out the
efficiency of the particular spectrum sensing methods, the
three evaluation parameters are considered as
1P P P
d fa md
+ + =
There have been confused region between the primary signal
and noise variance. To detect the probability of false and miss
detection parameters of the detector with the respect to
various noise levels for spectrum sensing process as depicted
in Fig.4.
Fig.4. Energy Distribution Curve of PU Signal and
noise
IV. PROPOSED FRAMEWORK
The primary requirement for our model is Energy Detector
(ED) with dynamic threshold, instead of fixed threshold with
the kernel principal component analysis approach that it
helps keep the probability detection higher for different SNR.
Generally, PCA is used to reduce the dimensionality of data
which will make spectrum sensing easier.
The received vector for d-dimensional is augmented as
.( ( ), ( .1), ,( ( 1)). T
Y y n y n y n d= + + −
(13)
:
0
H y w=
:
1
H y x w=+
(14)
The training set contains
( ) ( ) ( )
( , 1 , , ( 1 )
1T
X x n x n x n d= +  + −
( ) ( ) ( ) ( )
( 1 , ( 1 1, , ( 1 1)T
X x n M i x n M i x n M i d
M= + − − +  + − + −
(15)
\
Where M denote the number of vectors in the training set and
i is the sampling interval. T represents transpose.
A. Proposed Kernel PCA with leading eigenvector
Technique:
The key concept of this technique is that it uses eigenvector
1f
v
as template for spectrum sensing without need of
principal components of feature space. As mentioned earlier
the incorporation of kernel function in the feature space,
works better as compared to the normal PCA which takes
much lesser computations. Let the training set of KPCA is
φ(x1), φ(x2),…., φ(xM) has zero mean, so can be written as
1( ) 0
1
M
xi
Mi

=

=
(16)
In the similar way, the sample covariance matrix of φ(xi) is
Hence the leading vector
1f
v
of Rφ(x) corresponding to the
largest eigenvalue
1f

fulfils
( )
1( ) ( )
1
MT
R x x
ii
xMi


=
=
(17)
( )
1 1 1
f f f
R v v
x


=
1( ) ( )
1 1 1
1
Mf f f
T
x x v v
ii
Mi
  
==

=
1( ), ( )
1 1 1
1
Mf f f
x v x v
ii
Mi
  
=   =

=
(18)
According to eq. (18)
1f
v
is the linear combination of the
feature space data φ(x1), φ(x2),…., φ(xM),
()
11
M
f
vx
ii
i

=
=
(19)
Substituting (19) into (18)
1( ) ( ) ( ) ( )
1
1 1 1
M M M
f
T
x x x x
i i i j j j
Mi i j
      
=
  
= = =
(20)

Performance Analysis of Spectrum Sensing in Cognitive Radio under Low SNR and Noise Floor
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DOI: 10.35940/ijeat.F8703.129219
Journal Website: www.ijeat.org
And left multiplying
()
T
xi

, t= 1.2… M to the both sides of
eq. (20), results in
1( ), ( ) ( ), ( )
11
MM
x x x x
i i j i j
Mij
    
   

==
( ), ( )
11
M
fxx
j i j
j
   
=  

=
(21)
By bring together the kernel matrix in to the feature space
( )
,)K k x x
i j ij
=
eq. (21), can be rewritten as
2
1 1 1 1 1 1
ff
K M K K M K
     
= = =
(22)
It can be realized that β is the leading eigenvector of the
kernel matrix K. The normalization of can be derived by
1 ,
11
ff
vv=
( ), ( )
11
MM
xx
i i i i
ii
   
=
==
( ), ( )
,1
M
xx
i j i j
ij
   
=  

=
11
T

=K
1 1 1
T
  
=
,
1 1 1
  
=
(23)
in which μ1 is the eigenvalue corresponding to the
eigenvector β11 of K. In the method [15], the primary
principal component of a random point φ(x) in the feature
space can be take out by
( ) ( )
, , ( )
11
M
f
x v x x
ii
i
   
=  

=
( )
,
1
M
k x x
ii
i

=
=
(24)
Without knowing
1f
v
explicitly.
So in this paper, we used the efficient detection scheme
explicitly with unknown
1f
v
simply relies on the leading
eigenvector with applied covariance matrix for different
feature space. The proposed algorithm can be explained with
the help of flow diagram as illustrated in Fig. 5, shows that
how it can detect the presence of primary user.
Fig. 5.Proposed kernel PCA flow diagram for spectrum
sensing
V. RESULTS AND DISCUSSION
The simulation was done on MATLAB version R2013a
through which the capability of Kernel PCA based energy
detector is evaluated. Besides, the proposed system is tested
by considering the parameters under various noise
uncertainties for the BPSK modulation technique is used and
input is the OFDM signal. Also, we express the problem of
signal detection in the presence of additive noise and
elucidate the spectrum detection scheme which includes
Kernel PCA with the leading eigenvector-based energy
detector. The first section of the OFDM signal with samples
with length L= 500 is taken as the samples of the primary
user's signal x(n) have taken the probability of false alarm
rate supposed are (0, 1), and sample points of count N=500.

International Journal of Engineering and Advanced Technology (IJEAT)
ISSN: 2249-8958 (Online), Volume-9 Issue-2, December, 2019
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Published By:
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Retrieval Number: F8703088619/2019©BEIESP
DOI: 10.35940/ijeat.F8703.129219
Journal Website: www.ijeat.org
Fig.6. ROC curves for different SNR values at N=500
Fig. 6 clearly shows the ROC curves of PCA+ED at three
different values -20dB, -15dB, -10dB to show the
performance of probability of false alarm on X-axis and
probability of detection on Y-axis. It is obvious that detection
performance of the PCA based energy detector improved by
increasing SNR value.
Fig.7. ROC curves for different N values at SNR = -15dB
Fig.7 clearly shows the ROC curves of PCA+ED at sample
points taken are N=500, 1000, 1500 at fixed SNR= -15dB to
show the performance of probability of false alarm on X-axis
and probability of detection on Y-axis. In addition, to test, the
detection performance of PCA based energy detector is
possible by taking the observations for different values of
false alarm values range of 0 to 1 at regular intervals to find
out the probability of detection. It is obvious that the
detection performance of the KPCA based energy detector
enhanced for growth of N (sample points) values irrespective
of low SNR values.
Fig. 8. ROC curves of Kernel PCA with different noise
uncertainty at N=1500
Fig.9. ROC curves of PCA+ED with different noise
uncertainty at N=1000
Fig. 10. ROC curves of traditional PCA+ED under
various noise uncertainty at N=500

Performance Analysis of Spectrum Sensing in Cognitive Radio under Low SNR and Noise Floor
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It is observed from Fig.8-10, there is a poor performance of
the detector when traditional PCA is applied for increasing
levels of noise uncertainties. Also due to the fixed threshold,
there is a drastic change in the functionality of the energy
detector.
Fig.11. ROC curves of Kernel PCA+ED with different
noise uncertainty at N=1500
Fig .11 shows the performance of our proposed Kernel PCA
based energy detection scheme, in which the Pfa on X-axis
and Pd on Y-axis. So, therefore, introducing the dynamic
threshold in place of fixed threshold for KPCA, brings about
improved performance in terms of probability of detection,
false alarm rates for various noise uncertainties.
VI. CONCLUSION
The expansion of the cognitive radio network brought about
remarkable changes in the industry, wireless gadgets, and
other engineering applications. In this paper, to obtain the
detector performance with the eigenvector ensure that an
efficient model is implemented for kernel PCA. The concept
associated with the inner-product between leading
eigenvectors is taken as the similarity measure for the kernel
PCA approach. The proposed algorithm makes the detection
in an arbitrary dimensional feature space possible. In the
initial stage, it is shown that to improve the performance of
energy detector even at lower SNR values, the PCA scheme
is applied and substantial increment in SNR values and rise in
the data samples. Secondly, the performance of the proposed
algorithm is evaluated under ROC curves for noise
uncertainty, dynamic threshold, and both effects together.
Finally, the dynamic threshold energy detection technique is
combined with the kernel principal component analysis
(KPCA) which given rising to improved performance as
related to that of the fixed threshold mechanism.
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AUTHORS PROFILE
Venkatapathi Pallam, received M. Tech Degree
from JNTU Hyderabad, Telangana, India in
2009.He is currently working toward the Ph.D.
degree in electronics and communication
engineering, KL University, Vijayawada, AP,
India. Also
working as an Assistant Professor at Malla Reddy
College of Engineering, Secunderabad, Telangana,
India. He has 14 years of experience inthe field of
teaching. His area of research Interest includes Wirelesscommunication &
signal processing.
Dr. Habibulla Khan, received Ph. D degree from
Andhra University in the year of 2007. Presently
working as Professor and dean students affaire
inthe KL University. He published various nationa
land international journals & conferences. He is a
member of professional bodies like IEEE, ISTE
and IETE. His area of research Interest includes
wireless communications & signal processing. He
published more number of papers in various
national and international journals & conferences. His area of research
Interest includes wireless communications, signal processing and antennas.

International Journal of Engineering and Advanced Technology (IJEAT)
ISSN: 2249-8958 (Online), Volume-9 Issue-2, December, 2019
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Published By:
Blue Eyes Intelligence Engineering
& Sciences Publication
Retrieval Number: F8703088619/2019©BEIESP
DOI: 10.35940/ijeat.F8703.129219
Journal Website: www.ijeat.org
Dr. S. Srinivasa Rao, received the B.Tech degree
from Madras Institute of Technology, Anna
University, and the M. Tech and Ph.D fromJNTU
Hyderabad, Telangana, India. Presently working
as Professor and Head of the Department at Malla
Reddy College of Engineering and Technology,
Secunderabad. He has 26 years of
experience in the field of teaching. He is a
member of professional bodies like IEEE, ISTE
and IETE and also reviewer for springer’s
international journal on wireless personal communication. He
published more number of papers in various national and international
journals & conferences. His area of research Interest includes wireless
communications & signal processing.