![@ IJTSRD | Available Online @ www.ijtsrd.com
ISSN No: 2456
International
Research
Performance Analysis of Bayesian methods to for the spectrum
utilization in cognitive radio
Abdul Hameed Ansari
Pravara Rural Engineering College, Loni
ABSTRACT
Cognitive radio is an exciting wireless technology that
has been introduced for the efficient used of spectrum.
Using cognitive radios (CRs), the secondary users
(unlicensed users) are allowed to use the spectrum
which is originally allocated to primary users (PUs) as
far as the active primary users are not using it
temporarily. In order to prevent harmful interference
to primary users, the SUs need to perform spectrum
sensing before transmitting signal over the spectrum.
In this paper we use an optimal Bayesian detector for
digitally modulated primary user to improve the
spectrum utilization, without prior knowledge of
transmitted sequence of the primary signals. And
further suboptimal detectors in low and high SNR
regime. We provide the performance analysis in terms
of Detection probability and False alarm probability.
Keywords: Cognitive radio, Spectrum sensing,
spectrum utilization, Energy Detector, Bayesian
Detector
I. Introduction
The huge demand for wireless communication raises
the need to efficient use of the available spectrum
resources. A recent survey made by federal
communication commission (FCC) of spectrum
utilization has indicated that the actual licensed
spectrum is largely unutilized in vast temporal and
geographic dimensions. So the Spectrum scarcity is
due to the inefficient spectrum management rather
than spectrum shortage. To address this problem,
cognitive radio has emerged as a desirable technology
that has ability to deal with the stringent requirement
@ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 1 | Issue – 5 | July-Aug 2017
ISSN No: 2456 - 6470 | www.ijtsrd.com | Volume
International Journal of Trend in Scientific
Research and Development (IJTSRD)
International Open Access Journal
Performance Analysis of Bayesian methods to for the spectrum
utilization in cognitive radio
Pravara Rural Engineering College, Loni
Narode Sweety S
Pravara Rural Engineering College, Loni
wireless technology that
has been introduced for the efficient used of spectrum.
Using cognitive radios (CRs), the secondary users
(unlicensed users) are allowed to use the spectrum
which is originally allocated to primary users (PUs) as
primary users are not using it
temporarily. In order to prevent harmful interference
to primary users, the SUs need to perform spectrum
sensing before transmitting signal over the spectrum.
In this paper we use an optimal Bayesian detector for
dulated primary user to improve the
spectrum utilization, without prior knowledge of
transmitted sequence of the primary signals. And
further suboptimal detectors in low and high SNR
regime. We provide the performance analysis in terms
lity and False alarm probability.
Cognitive radio, Spectrum sensing,
spectrum utilization, Energy Detector, Bayesian
The huge demand for wireless communication raises
need to efficient use of the available spectrum
urces. A recent survey made by federal
communication commission (FCC) of spectrum
utilization has indicated that the actual licensed
spectrum is largely unutilized in vast temporal and
geographic dimensions. So the Spectrum scarcity is
nt spectrum management rather
than spectrum shortage. To address this problem,
cognitive radio has emerged as a desirable technology
that has ability to deal with the stringent requirement
and scarcity of the radio spectrum and thereby
increases the spectral efficiency.
In cognitive radios, the secondary users are allowed to
use the spectrum which is originally allocated to
primary users as far as primary users are not using it
temporarily. It is known as opportunistic spectrum
access (OSA). To avoid harmful interference to the
primary users, the Secondary unlicensed users have to
perform spectrum sensing before transmission over
the spectrum. Spectrum sensing is a process in which
secondary unlicensed users keep sensing the spectrum
to determine whether the PU is transmitting or not.
While detecting if PU is absent than the SUs can use
those frequencies for transmission. This will help to
increase overall spectrum utilization and also in turn
increase the spectrum efficiency [6].
The common algorithms that enable spectrum sensing
are energy detection, matched filtering,
cyclostationary detection, covariance based detector
and wavelet-based sensing method. A matched filter
is obtained by correlating a known signal with
unknown signal to detect the presence
in the unknown signal. But the matched filter based
detection requires the entire knowledge of the primary
signals, which is not feasible for practical
applications. In energy detection method, the energy
of input signal is compared with so
energy value. The signal is said to be present at a
specified frequency if the energy of the signal is
beyond the energy level of the threshold. But, the
execution of energy detection extremely degrades in
presence of noise and interference po
and the detector fails to differentiate primary signal
Aug 2017 Page: 912
6470 | www.ijtsrd.com | Volume - 1 | Issue – 5
Scientific
(IJTSRD)
International Open Access Journal
Performance Analysis of Bayesian methods to for the spectrum
Narode Sweety S
Pravara Rural Engineering College, Loni
and scarcity of the radio spectrum and thereby
ctral efficiency.
In cognitive radios, the secondary users are allowed to
use the spectrum which is originally allocated to
primary users as far as primary users are not using it
temporarily. It is known as opportunistic spectrum
mful interference to the
primary users, the Secondary unlicensed users have to
perform spectrum sensing before transmission over
the spectrum. Spectrum sensing is a process in which
secondary unlicensed users keep sensing the spectrum
the PU is transmitting or not.
While detecting if PU is absent than the SUs can use
those frequencies for transmission. This will help to
increase overall spectrum utilization and also in turn
increase the spectrum efficiency [6].
t enable spectrum sensing
are energy detection, matched filtering,
cyclostationary detection, covariance based detector
based sensing method. A matched filter
is obtained by correlating a known signal with
unknown signal to detect the presence of the template
in the unknown signal. But the matched filter based
detection requires the entire knowledge of the primary
signals, which is not feasible for practical
applications. In energy detection method, the energy
of input signal is compared with some threshold
energy value. The signal is said to be present at a
specified frequency if the energy of the signal is
beyond the energy level of the threshold. But, the
execution of energy detection extremely degrades in
presence of noise and interference power uncertainty
and the detector fails to differentiate primary signal](https://image.slidesharecdn.com/113performanceanalysisofbayesianmethodstoforthespectrumutilizationincognitiveradio-180811114245/85/Performance-Analysis-of-Bayesian-Methods-to-for-the-Spectrum-Utilization-in-Cognitive-Radio-1-320.jpg)
![International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470
@ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 1 | Issue – 5 | July-Aug 2017 Page: 913
from the harmful interference. Cyclostationarity
feature detection is a method for detecting primary
user transmissions by utilizing the cyclostationarity
features of the received signals but it doesn’t make
complete use of the characteristics of the modulated
signals. In this paper, we proposed a spectrum sensing
for digitally modulated primary signals using
Bayesian detector (BD) to the utilization of spectrum,
without the prior knowledge of the transmitted
sequence of the primary signals. This method makes
use of the prior observations of PU activity as well as
the signaling information of the PU such as
modulation order and symbol rate to improve the SU
throughput and the overall spectrum utilization of
both PUs and SUs.
II. System Design
In Spectrum sensing there are two hypotheses: the
hypothesis that the PU is not present is ℋ0 and the
hypothesis that the PU is available or present is ℋ1 .
In spectrum sensing, there are two important design
parameters: the probability of SU to correctly detects
the presence of primary signals known as probability
of detection (PD), and the probability of SU to falsely
detects primary signals when PU is actually not
present known as probability of false alarm (PF ). So
we determine spectrum utilization as
𝑃(𝐻0)(1 − 𝑃𝐹) + 𝑃(𝐻1)𝑃𝐷 (1)
and normalized SU throughput1 as
𝑃(𝐻0)(1 − 𝑃𝐹) (2)
Note that P(ℋ1)PD is PU throughput when there are
active primary signals and the SUs finds the presence
of these primary signals.
In order to find whether the available spectrum is
being used by the primary user or not, the detection
statistic TD is being compared with a predetermined
threshold ϵ.
Probability of false alarm PF is the probability of SU
that chooses ℋ1 while actually it is in fact ℋ0:
𝑃𝐹 = 𝑃(𝑇𝐷 > 𝜖|𝐻0 ) (3)
Probability of detection PD is the probability of SU
that correctly decides ℋ0 when it is ℋ1:
𝑃𝐹 = 𝑃(𝑇𝐷 > 𝜖|𝐻1 ) (4)
III. Signal model
Through the signal model, we have considered time-
slotted primary signals in which N primary signal
samples are used to analyze the existence of PU
signals. Similarly the PU symbol duration is T which
is known to the SU and at the secondary receiver, the
received signal r(t) is sampled at a rate of 1/T . For
MPSK signals, the received signal of k-th symbol at
the CR detector, r(k)
𝑟(𝑘) =
𝑛(𝑘) 𝐻
ℎ𝑒 ( )
+ 𝑛(𝑘) 𝐻
(5)
Where 𝑛(𝑘) = 𝑛 (𝑘) + 𝑗𝑛 (𝑘) is a complex AWGN
signal with variance N0 𝑛 (𝑘)and𝑛 (𝑘) are
respectively the real and imaginary part of
n(k),φn(k) = 2πn M⁄ , n =0, 1, …..M-1 with equi-
probability, and the propagation channel h is assumed
to be constant within the sensing period. Let
r = [r(0) r(1) ……. r(N − 1)] such that the SU
receiver has no information with regards to the
transmitted signals by the PU and φn(k), k =
0, 1, … … N − 1 independent and identically
distributed (i.i.d.) and independent of the Gaussian
noise.
Detection statistics of energy detector (ED) is defined
as the average energy of detected samples as
𝑇 = ∑ |𝑟(𝑘)| (6)
As the energy detector does not require the prior
knowledge of the symbol rate, so we assume that the
sample rate and symbol rate are similar. It is known
that the optimal detector based on Bayesian rule or
Neyman-Pearson theorem for binary hypothesis
testing is to calculate the likelihood ratio and then
make its choice by comparing the ratio with the
threshold ϵ. The likelihood ratio test (LRT) of the
values ℋ1 and ℋ0 can be defined as
𝑇 (𝑟) =
( | )
( | )
(7)
IV. Optimal Detector Structure
The probability density function (PDF) of received
signals over N symbol duration for hypothesis of H0
is indicated as p(r|H0), and can be written as
𝑝(𝑟|𝐻 ) = ∏
| ( )| /
(8)](https://image.slidesharecdn.com/113performanceanalysisofbayesianmethodstoforthespectrumutilizationincognitiveradio-180811114245/85/Performance-Analysis-of-Bayesian-Methods-to-for-the-Spectrum-Utilization-in-Cognitive-Radio-2-320.jpg)
![International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470
@ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 1 | Issue – 5 | July-Aug 2017 Page: 914
Since the noise signals n(k), k=0,1.…..N-1 are
independent.
The PDF of received signals over N symbol duration
under hypothesis H1 is denoted as p (r|H1). With
equiprobability of φn(k) = 2nπ/M , n = 0, 1, . . .,M −
1, can be obtain as follows:
𝑝(𝑟|𝐻 ) = ∏ ∑ 𝑝(𝑟(𝑘)|𝐻 , 𝜑 (𝑘)𝑝𝜑 (𝑘)( ) (9)
Hence, the log-likelihood ratio (LLR), ln TLRT(r), is
∑ 𝐼𝑛 ∑ 𝑒
[ ( )ℎ∗ ( )]
− γ − In M
(10)
Where 𝛾 is the SNR of the received signal sample i.e
𝛾 =
|ℎ|
Let
𝑉 (𝑘) = 𝑅[𝑟(𝑘)ℎ∗
𝑒 ( )
] (11)
It is easy to derive the structure of the optimal
detector (BD) for MPSK signals as:
T = ∑ 𝐼𝑛 ∑ cosh (𝑣 (𝑘))! >
<
𝛾 +
𝐼𝑛 + (12)
Even though the detector is optimal, it is very
complicated to use in practice. So we will simplify the
detector when the SNR is very low or very high as
follows.
V. Bayesian detector (ABD) structure through the
Approximations in the Low and High SNR
regimes
In this paper we have given the theoretical analysis
(detection performance and threshold) in low SNR
regime for the suboptimal detector to analyze
complex MPSK signals (M = 2 and M > 2) and
compare with the results for real BPSK primary
signals [4].
i. Approximation in the Low SNR regime
We study the approximation of our proposed detector
in the low SNR regime for the complex MPSK
modulated primary signals. When 𝑥 → 0, cosh(x) ≈
1 + 𝑎𝑛𝑑 (1 + 𝑥) ≈ 𝑥 we can obtain
∑ 𝐼𝑛 ∑ 𝑐𝑜𝑠ℎ 𝑣 (𝑘) (13)
Through approximation, the detector structure
becomes:
𝑇 = ∑ |𝑟(𝑘)|
<
>
𝛾 + (14)
ii. Approximation in the High SNR regime
In this section we consider the high SNR regime.
When x >> 0, cosh(x) ≈ or when x << 0, cosh(x) ≈
The detector structure becomes
TH ABD =
∑ In ∑ e
2
N0
R r(k)h∗
e jφn(k)
M 2⁄ 1
n 0
N 1
k 0 γ + InM
(15)
In such a special case of MPSK signals, we consider a
real signal model for the BPSK modulated primary
signals. In the high SNR regime, the suboptimal
Bayesian detector employs the addition of received
signal magnitudes to detect the presence of primary
signals which indicates that in this regime energy
detector is not optimal.
VI. RESULTS
We plot a result for Secondary users’ throughput of
H-ABD vs. SNR (dB) for BPSK signal at high SNR
in fig. 1 it is observed that as SNR increases the
secondary user’s throughput also increases.](https://image.slidesharecdn.com/113performanceanalysisofbayesianmethodstoforthespectrumutilizationincognitiveradio-180811114245/85/Performance-Analysis-of-Bayesian-Methods-to-for-the-Spectrum-Utilization-in-Cognitive-Radio-3-320.jpg)
Performance Analysis of Bayesian Methods to for the Spectrum Utilization in Cognitive Radio
- 1. @ IJTSRD | Available Online @ www.ijtsrd.com ISSN No: 2456 International Research Performance Analysis of Bayesian methods to for the spectrum utilization in cognitive radio Abdul Hameed Ansari Pravara Rural Engineering College, Loni ABSTRACT Cognitive radio is an exciting wireless technology that has been introduced for the efficient used of spectrum. Using cognitive radios (CRs), the secondary users (unlicensed users) are allowed to use the spectrum which is originally allocated to primary users (PUs) as far as the active primary users are not using it temporarily. In order to prevent harmful interference to primary users, the SUs need to perform spectrum sensing before transmitting signal over the spectrum. In this paper we use an optimal Bayesian detector for digitally modulated primary user to improve the spectrum utilization, without prior knowledge of transmitted sequence of the primary signals. And further suboptimal detectors in low and high SNR regime. We provide the performance analysis in terms of Detection probability and False alarm probability. Keywords: Cognitive radio, Spectrum sensing, spectrum utilization, Energy Detector, Bayesian Detector I. Introduction The huge demand for wireless communication raises the need to efficient use of the available spectrum resources. A recent survey made by federal communication commission (FCC) of spectrum utilization has indicated that the actual licensed spectrum is largely unutilized in vast temporal and geographic dimensions. So the Spectrum scarcity is due to the inefficient spectrum management rather than spectrum shortage. To address this problem, cognitive radio has emerged as a desirable technology that has ability to deal with the stringent requirement @ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 1 | Issue – 5 | July-Aug 2017 ISSN No: 2456 - 6470 | www.ijtsrd.com | Volume International Journal of Trend in Scientific Research and Development (IJTSRD) International Open Access Journal Performance Analysis of Bayesian methods to for the spectrum utilization in cognitive radio Pravara Rural Engineering College, Loni Narode Sweety S Pravara Rural Engineering College, Loni wireless technology that has been introduced for the efficient used of spectrum. Using cognitive radios (CRs), the secondary users (unlicensed users) are allowed to use the spectrum which is originally allocated to primary users (PUs) as primary users are not using it temporarily. In order to prevent harmful interference to primary users, the SUs need to perform spectrum sensing before transmitting signal over the spectrum. In this paper we use an optimal Bayesian detector for dulated primary user to improve the spectrum utilization, without prior knowledge of transmitted sequence of the primary signals. And further suboptimal detectors in low and high SNR regime. We provide the performance analysis in terms lity and False alarm probability. Cognitive radio, Spectrum sensing, spectrum utilization, Energy Detector, Bayesian The huge demand for wireless communication raises need to efficient use of the available spectrum urces. A recent survey made by federal communication commission (FCC) of spectrum utilization has indicated that the actual licensed spectrum is largely unutilized in vast temporal and geographic dimensions. So the Spectrum scarcity is nt spectrum management rather than spectrum shortage. To address this problem, cognitive radio has emerged as a desirable technology that has ability to deal with the stringent requirement and scarcity of the radio spectrum and thereby increases the spectral efficiency. In cognitive radios, the secondary users are allowed to use the spectrum which is originally allocated to primary users as far as primary users are not using it temporarily. It is known as opportunistic spectrum access (OSA). To avoid harmful interference to the primary users, the Secondary unlicensed users have to perform spectrum sensing before transmission over the spectrum. Spectrum sensing is a process in which secondary unlicensed users keep sensing the spectrum to determine whether the PU is transmitting or not. While detecting if PU is absent than the SUs can use those frequencies for transmission. This will help to increase overall spectrum utilization and also in turn increase the spectrum efficiency [6]. The common algorithms that enable spectrum sensing are energy detection, matched filtering, cyclostationary detection, covariance based detector and wavelet-based sensing method. A matched filter is obtained by correlating a known signal with unknown signal to detect the presence in the unknown signal. But the matched filter based detection requires the entire knowledge of the primary signals, which is not feasible for practical applications. In energy detection method, the energy of input signal is compared with so energy value. The signal is said to be present at a specified frequency if the energy of the signal is beyond the energy level of the threshold. But, the execution of energy detection extremely degrades in presence of noise and interference po and the detector fails to differentiate primary signal Aug 2017 Page: 912 6470 | www.ijtsrd.com | Volume - 1 | Issue – 5 Scientific (IJTSRD) International Open Access Journal Performance Analysis of Bayesian methods to for the spectrum Narode Sweety S Pravara Rural Engineering College, Loni and scarcity of the radio spectrum and thereby ctral efficiency. In cognitive radios, the secondary users are allowed to use the spectrum which is originally allocated to primary users as far as primary users are not using it temporarily. It is known as opportunistic spectrum mful interference to the primary users, the Secondary unlicensed users have to perform spectrum sensing before transmission over the spectrum. Spectrum sensing is a process in which secondary unlicensed users keep sensing the spectrum the PU is transmitting or not. While detecting if PU is absent than the SUs can use those frequencies for transmission. This will help to increase overall spectrum utilization and also in turn increase the spectrum efficiency [6]. t enable spectrum sensing are energy detection, matched filtering, cyclostationary detection, covariance based detector based sensing method. A matched filter is obtained by correlating a known signal with unknown signal to detect the presence of the template in the unknown signal. But the matched filter based detection requires the entire knowledge of the primary signals, which is not feasible for practical applications. In energy detection method, the energy of input signal is compared with some threshold energy value. The signal is said to be present at a specified frequency if the energy of the signal is beyond the energy level of the threshold. But, the execution of energy detection extremely degrades in presence of noise and interference power uncertainty and the detector fails to differentiate primary signal
- 2. International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470 @ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 1 | Issue – 5 | July-Aug 2017 Page: 913 from the harmful interference. Cyclostationarity feature detection is a method for detecting primary user transmissions by utilizing the cyclostationarity features of the received signals but it doesn’t make complete use of the characteristics of the modulated signals. In this paper, we proposed a spectrum sensing for digitally modulated primary signals using Bayesian detector (BD) to the utilization of spectrum, without the prior knowledge of the transmitted sequence of the primary signals. This method makes use of the prior observations of PU activity as well as the signaling information of the PU such as modulation order and symbol rate to improve the SU throughput and the overall spectrum utilization of both PUs and SUs. II. System Design In Spectrum sensing there are two hypotheses: the hypothesis that the PU is not present is ℋ0 and the hypothesis that the PU is available or present is ℋ1 . In spectrum sensing, there are two important design parameters: the probability of SU to correctly detects the presence of primary signals known as probability of detection (PD), and the probability of SU to falsely detects primary signals when PU is actually not present known as probability of false alarm (PF ). So we determine spectrum utilization as 𝑃(𝐻0)(1 − 𝑃𝐹) + 𝑃(𝐻1)𝑃𝐷 (1) and normalized SU throughput1 as 𝑃(𝐻0)(1 − 𝑃𝐹) (2) Note that P(ℋ1)PD is PU throughput when there are active primary signals and the SUs finds the presence of these primary signals. In order to find whether the available spectrum is being used by the primary user or not, the detection statistic TD is being compared with a predetermined threshold ϵ. Probability of false alarm PF is the probability of SU that chooses ℋ1 while actually it is in fact ℋ0: 𝑃𝐹 = 𝑃(𝑇𝐷 > 𝜖|𝐻0 ) (3) Probability of detection PD is the probability of SU that correctly decides ℋ0 when it is ℋ1: 𝑃𝐹 = 𝑃(𝑇𝐷 > 𝜖|𝐻1 ) (4) III. Signal model Through the signal model, we have considered time- slotted primary signals in which N primary signal samples are used to analyze the existence of PU signals. Similarly the PU symbol duration is T which is known to the SU and at the secondary receiver, the received signal r(t) is sampled at a rate of 1/T . For MPSK signals, the received signal of k-th symbol at the CR detector, r(k) 𝑟(𝑘) = 𝑛(𝑘) 𝐻 ℎ𝑒 ( ) + 𝑛(𝑘) 𝐻 (5) Where 𝑛(𝑘) = 𝑛 (𝑘) + 𝑗𝑛 (𝑘) is a complex AWGN signal with variance N0 𝑛 (𝑘)and𝑛 (𝑘) are respectively the real and imaginary part of n(k),φn(k) = 2πn M⁄ , n =0, 1, …..M-1 with equi- probability, and the propagation channel h is assumed to be constant within the sensing period. Let r = [r(0) r(1) ……. r(N − 1)] such that the SU receiver has no information with regards to the transmitted signals by the PU and φn(k), k = 0, 1, … … N − 1 independent and identically distributed (i.i.d.) and independent of the Gaussian noise. Detection statistics of energy detector (ED) is defined as the average energy of detected samples as 𝑇 = ∑ |𝑟(𝑘)| (6) As the energy detector does not require the prior knowledge of the symbol rate, so we assume that the sample rate and symbol rate are similar. It is known that the optimal detector based on Bayesian rule or Neyman-Pearson theorem for binary hypothesis testing is to calculate the likelihood ratio and then make its choice by comparing the ratio with the threshold ϵ. The likelihood ratio test (LRT) of the values ℋ1 and ℋ0 can be defined as 𝑇 (𝑟) = ( | ) ( | ) (7) IV. Optimal Detector Structure The probability density function (PDF) of received signals over N symbol duration for hypothesis of H0 is indicated as p(r|H0), and can be written as 𝑝(𝑟|𝐻 ) = ∏ | ( )| / (8)
- 3. International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456-6470 @ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 1 | Issue – 5 | July-Aug 2017 Page: 914 Since the noise signals n(k), k=0,1.…..N-1 are independent. The PDF of received signals over N symbol duration under hypothesis H1 is denoted as p (r|H1). With equiprobability of φn(k) = 2nπ/M , n = 0, 1, . . .,M − 1, can be obtain as follows: 𝑝(𝑟|𝐻 ) = ∏ ∑ 𝑝(𝑟(𝑘)|𝐻 , 𝜑 (𝑘)𝑝𝜑 (𝑘)( ) (9) Hence, the log-likelihood ratio (LLR), ln TLRT(r), is ∑ 𝐼𝑛 ∑ 𝑒 [ ( )ℎ∗ ( )] − γ − In M (10) Where 𝛾 is the SNR of the received signal sample i.e 𝛾 = |ℎ| Let 𝑉 (𝑘) = 𝑅[𝑟(𝑘)ℎ∗ 𝑒 ( ) ] (11) It is easy to derive the structure of the optimal detector (BD) for MPSK signals as: T = ∑ 𝐼𝑛 ∑ cosh (𝑣 (𝑘))! > < 𝛾 + 𝐼𝑛 + (12) Even though the detector is optimal, it is very complicated to use in practice. So we will simplify the detector when the SNR is very low or very high as follows. V. Bayesian detector (ABD) structure through the Approximations in the Low and High SNR regimes In this paper we have given the theoretical analysis (detection performance and threshold) in low SNR regime for the suboptimal detector to analyze complex MPSK signals (M = 2 and M > 2) and compare with the results for real BPSK primary signals [4]. i. Approximation in the Low SNR regime We study the approximation of our proposed detector in the low SNR regime for the complex MPSK modulated primary signals. When 𝑥 → 0, cosh(x) ≈ 1 + 𝑎𝑛𝑑 (1 + 𝑥) ≈ 𝑥 we can obtain ∑ 𝐼𝑛 ∑ 𝑐𝑜𝑠ℎ 𝑣 (𝑘) (13) Through approximation, the detector structure becomes: 𝑇 = ∑ |𝑟(𝑘)| < > 𝛾 + (14) ii. Approximation in the High SNR regime In this section we consider the high SNR regime. When x >> 0, cosh(x) ≈ or when x << 0, cosh(x) ≈ The detector structure becomes TH ABD = ∑ In ∑ e 2 N0 R r(k)h∗ e jφn(k) M 2⁄ 1 n 0 N 1 k 0 γ + InM (15) In such a special case of MPSK signals, we consider a real signal model for the BPSK modulated primary signals. In the high SNR regime, the suboptimal Bayesian detector employs the addition of received signal magnitudes to detect the presence of primary signals which indicates that in this regime energy detector is not optimal. VI. RESULTS We plot a result for Secondary users’ throughput of H-ABD vs. SNR (dB) for BPSK signal at high SNR in fig. 1 it is observed that as SNR increases the secondary user’s throughput also increases.
- 4. International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456 @ IJTSRD | Available Online @ www.ijtsrd.com Fig. 1: Secondary users throughput of SNR ABD for BPSK signal at H SNR Fig. 2: Spectrum utilization of SNR (dB) vs. H for BPSK signal at high SNR. In the simulation for BPSK signals it is shown that both BD and H-ABD has higher Pd and lower Pf than ED. so that BD/H-ABD has a better performance in terms of secondary users’ throughput and spectrum utilization. Also it is shown fig. 2 that as SNR increases the spectrum utilization of H increases for Bpsk signals. The results confirm that energy detector is not optimal in high SNR regime. VII. Conclusion In this paper, we surveyed on optimal Bayesian detector in order to detect known order of MPSK modulated primary signals over AWGN channels, which is based on Bayesian decision rule. Through approximations, we have found that at Low SNR regime the Bayesian detector has similar structure as energy detection. But at High SNR energy is the sum of signal magnitude, where the Bayesian detector performs better in terms of spectrum utilization as well as secondary user’s throughput than energy International Journal of Trend in Scientific Research and Development (IJTSRD) ISSN: 2456 @ IJTSRD | Available Online @ www.ijtsrd.com | Volume – 1 | Issue – 5 | July-Aug 2017 Fig. 1: Secondary users throughput of SNR vs. H- ABD for BPSK signal at H SNR Fig. 2: Spectrum utilization of SNR (dB) vs. H-ABD for BPSK signal at high SNR. In the simulation for BPSK signals it is shown that ABD has higher Pd and lower Pf than has a better performance in terms of secondary users’ throughput and spectrum Also it is shown fig. 2 that as SNR increases the spectrum utilization of H-ABD also The results confirm that mal in high SNR regime. In this paper, we surveyed on optimal Bayesian detector in order to detect known order of MPSK modulated primary signals over AWGN channels, which is based on Bayesian decision rule. Through that at Low SNR regime the Bayesian detector has similar structure as energy detection. But at High SNR energy is the sum of signal magnitude, where the Bayesian detector performs better in terms of spectrum utilization as ut than energy detector. And hence this improves the detection probability for given false alarm probability. References 1. Shoukang Zheng, Pooi-Yuen Kam, Ying Liang, and Yonghong Zheng, “Spectrum sensing for digital primary signals in cognitive radio: A Bayesian approach for maximizing spectrum utilization,” wireless communications, vol. 12, no. 4, April 2013, pp. 1774-1782. 2. T. Y¨ucek and H. Arslan, “A survey of spectrum sensing algorithms for cog applications,” IEEE Communication Surveys & Tutorials, vol. 11, no. 1, 2009 pp. 116 3. 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