IRJET- Rapid Spectrum Sensing Algorithm in Cooperative Spectrum Sensing for a Large Network

International Research Journal of Engineering and Technology (IRJET) e-ISSN: 2395-0056
Volume: 06 Issue: 06 | June 2019 www.irjet.net p-ISSN: 2395-0072
© 2019, IRJET | Impact Factor value: 7.211 | ISO 9001:2008 Certified Journal | Page 3331
Rapid Spectrum Sensing Algorithm in Cooperative Spectrum Sensing
for a Large Network
S.B. Gaikwad1, V.V. Dixit 2, A.R. More3
1(PG Student)Department of Electronics & Telecommunication, RMD SSOE, Pune, 411058 India
2(Principal), RMD SSOE, Pune, 411058 India
3(Assistant Professor), Department of Electronics & Telecommunication, RMD SSOE, Pune, 411058 India
---------------------------------------------------------------------***----------------------------------------------------------------------
Abstract - Cognitive radio is an emerging technology that
enhances the utilization of available spectrum through
dynamic access allocation. It autonomously identifies the
unutilized portions, white spaces (spectrum holes) , in the
licensed band and thus efficiently improving its usage. In co-
operative spectrum sensing, decision of spectrum
availability is taken based on collective decision by multiple
cognitive users. For any detector applied to cooperative
spectrum sensing, the ideal voting rule is obtained. The
detection threshold was optimized when using energy
detection .Finally, a rapid spectrum sensing algorithm is
suggested for a big network that needs fewer cognitive
radios in cooperative spectrum sensing is obtained
Key Words: Cognitive radio, energy detection,
optimization, spectrum sensing, throughput
1. INTRODUCTION
With advancement in wireless technology, spectrum as
the major resource for wireless communication systems
has now become much a scarcer resource.. Static spectrum
allocation of licensed band by Government has resulted in
spectrum scarcity in particular spectrum bands. Moreover,
reports by Federal Communications Commission (FCC)
show that 70% of the allocated spectrum bands in US are
not fully utilized [1]. Hence, dynamic access to spectrum
was proposed to solve these spectrum inefficiency
problems. Dynamic spectrum allocation enables cognitive
radio (CR) users to opportunistically utilize the vacant
licensed spectrum bands in either temporal or spatial
domain. CR networks, however, impose unique challenges
due to the high fluctuations in the available spectrum, as
well as the diverse quality of service (QoS) requirements of
various applications. Here, we consider optimizing
cooperative spectrum sensing with energy detection. The
article includes cooperative spectrum sensing, cooperative
spectrum sensing optimization, optimal voting rule, ideal
threshold and rapid spectrum sensing techniques
1.1 System Modeling
A] Spectrum Sensing
We consider the cognitive network with K quantity of
CRs, one primary user and one fusion centre (i.e.
famous receiver).The spectrum sensing is separately
performed by each CR.CR's choices are sent to the
fusion centre and then the fusion centre decides
whether the main user is present or absent. Two
hypotheses are considered [1].
H0: The primary user is absent.
H1: The primary user is in operation.
When each ith CR receives the signal, two hypotheses
follow as above. Then the signal will be obtained as
{ (1.1)
where, ( )ix t is the received signal at the
th
i CR in time
slot t , ( )is t is the PU signal. The ( )ih t shows the complex
channel gain between PU and ith CR with the node. ( )iw t
is the AWGN (Additive White Gaussian Noise).
Assume that the sensing time is smaller than the coherence
time of the channel. Then, the sensing channel can be
viewed as time-invariant during the sensing process.
Assume that the sensing time is smaller than the coherence
time of the channel. Then, the sensing channel can be
viewed as time-invariant during the sensing process.
Moreover, we consider that the status of the PU remains
unchanged during the period of spectrum sensing .If prior
knowledge of the PU signal is unknown, the energy
detection

C
R
C
RP
U Common
ReceiverC
R
C
R
Fig-1: System Model
method is optimal for detecting zero-mean
constellation signals [13]. We are going for the method of
energy detection as the PU signal is unknown. We
discover average detection probability, probability of
missed detection and probability of false alarm over the
AWGN channel with the following equations for each CR
by energy detection [1];
( )
(1.2)
√ √ (1.3)
(1.4)
Where, i is the energy detection threshold and i is the
instantaneous signal to noise ratio (SNR) at the
th
i CR.
Also u is the energy detector's time bandwidth product,
( )a is the gamma function and ( , )a x is the
incomplete gamma function isequal to
∫
(1.5)
The generalised Marcum Q-function i.e. ( , )uQ a b is given
by [1];
∫ (1.6)
Where 1(.)uI  is the first kind and order 1u  modified
Bessel function.
Cooperative spectrum sensing, where number of CRs
make binary decisions Di based on local observation and
forward a bit of decision to the common recipients. These
choices are summarized at the common recipient and will
determine whether the PU is present or in operation [1].
∑ { (1.7)
Y is the threshold representing the rule "n-out - of-K." If
the amount of CR is one, i.e. n=1 it corresponds to the rule
of OR and if n = K it relates to the rule of AND.
We find the distance between any two cognitive radios to
be lower than the range between one CR and PU in the
radio frequency setting around CR's. The signal obtained
at each CR therefore follows the same path loss. For AWGN
channel, 1 2 ....... k       and for Rayleigh fading
channel 1 2, ....... k   because we suppose it is
autonomous and distributed identically (i.i.d) with instant
SNRs. These SNR's are also i.i.d. random variables with the
same mean distributed exponentially. We take another
hypothesis that each CR threshold is the same and that it is
the same 1 1 2 3 ........ .        
As threshold is
constant for all CR, ,f iP will be independent of i , therefore
,f iP = fP . For AWGN channel, ,d iP is independent of i and
we denoted as dP . In Rayleigh fading channel, dP is ,d iP
averaged over the different values of 1 [1-3].
Using the average probability of each CR, the prevalent
receiver calculates false alarm probability and missed
detection probability. The probability of false alarm is
provided by[1],
( ) { } (1.8)
Also, the missed detection probability is given by;
( ) { } (1.9)
2. OPTIMIZATION OF COOPERATIVE SPECTRUM
SENSING
We evaluate ideal voting rule, optimization of CR number
and detection threshold with cooperative spectrum
sensing in this section.
2.1 Optimal Voting Rule
Let, K is then set the ideal value of n so we get the
minimum error rate, this is the ideal voting rule and the
ideal value of n is called as o p t n. We've plotted n=1 to
n=10 chart. For each n, we calculated the error rate for
distinct threshold values. We get more error rate and ideal
rule AND rule for tiny threshold value (i.e. n=10). Optimal
rule for big threshold value is OR rule. But if n = 5 for
medium threshold values, we get more mistake rate [1].

Statement 1: To find nopt the minimum error rate value
that we suggested as follows;
( ) (1.10)
Where,
(1.11)
Proof:
From equation 7 and 8, we get, ( ) 1 ( ).f mQ Q G n  
For optimal value of n, error rate should be minimum, [1]
i.e.
(1.12)
Therefore, the difference is given by ( 1) ( )G n G n 
(1.13)
∑ ( )[ ]
∑ ( )[
]
(1.14)
( ) [ ] (1.15)
i.e. only l = n term remains
(1.16)
(1.17)
On simplifying, we get
* +
(1.18)
Where,
(1.19)
We get certain values for n from equation 9;
a) If Pf and Pm are of same order then α ≈ 1 and n=K/2
b) If Pf ≤ Pm k-1 results in Pf<<Pm for large K then α ≥ K-1
and n=1 i.e. OR rule.
c) If Pm << Pf then α tends to zero and n=K i.e. AND rule.
2.2 Optimal Energy Detection Threshold
Here we find that K, n and SNR are then known what the
optimum threshold π * will be to minimize the complete
error rate. We have plotted distinct limit values for the
complete error rate curve in Figure 1.Figure has the small
error rate for specified n for only one threshold value.
That is to say, there is one and only value λ for which
( )f mQ Q is minimum [1]
{ } (1.20)
For optimal energy threshold;
(1.21)
∑ ( )
∑ ( )
(1.22)
( )
∑ ( )
(1.23)
2.3 Optimal Number of Cognitive Radios
In a single time slot, only one CR should send its local
decision to the common receiver so as to easily separate
decisions easily at the receiver end. Hence, for a cognitive
radio network with a large number of CRs, cooperative
spectrum sensing may become impractical.. As a result the
sensing time can become intolerably long. This issue can be
addressed by allowing the CRs to send the decisions
concurrently. But it may complicate the receiver design
when separating the decisions from different CRs. Another
potential solution is to send the decisions on orthogonal
frequency bands, but this requires a large portion of
available bandwidth. To address these issues, So we
suggested an effective sensing algorithm, defining some
error bound and calculating the optimum amount of CR's.
Each CR also sends a choice in one slot of time. By this
technique we get the necessary error rate using only a few
CRs. If SNR and threshold values are known, then we
calculate the smallest number of CRs in cooperative
spectrum sensing to attain target error limitations. i.e.

( ) .f mQ Q  where  is the target error bound. As
previously indicated for optimum voting rule[1],
( * +) (1.24)
Here, K* (1≤K*≤K) is the least number of CR’s to satisfy
target error bound ( ) .f mQ Q  and  is calculated
from, Pf, Pm, and known SNR and  values. We define the
function,
(1.25)
Where k is the amount of collaborative spectrum sensors
and
opt
kn Is calculated from above. The probability fQ and
mQ are functions of k and
opt
kn . Therefore we get;
(1.26)
We can use the above equations k* = [k0], Where k0 is the
function's first zero crossing point F( k,
opt
kn ) in terms of
k. Hence, it is possible to implement quick sensing
algorithms by considering only k* CR's instead of K. This
decreases the time slot from K to k * to keep the target
error bound for the prevalent receiver.
3. System Modelling With Energy Detection of Signal
Here, the signal energy is calculated and false alarm and
detection probability is calculated. [92-94]. First, we
define separate AWGN channel threshold values and
calculate the energy obtained from the signal. If energy of
received signal is 1( ) ( ) ( ),x t s t w t  then the energy of
1( )x t is calculated, also if received signal is 2 ( ) ( ),x t w t
then energy of 2 ( )x t is calculated. If energy of 1( )x t is
higher than the limit value then the likelihood of detection
and if the energy of the 2 ( )x t is higher than the limit value
then the likelihood of false alarm [2].
∑ (1.27)
And
∑
(1.28)
where N02is the two sided noise power spectral density [2]
and is given by;
∑
(1.29)
The SNR values are allocated exponentially for the
Rayleigh Fading Channel. We consider SNR values with the
same mean to be an exponential random number. We used
Rayleigh to determine the fading channel gain [3]
√
(1.30)
Then we discover the authority of two sides of the noise
[3]
{ ∑ }
(1.31)
Then using this value of 02 N and equation (31) we
calculated the energy of the received signal and find
probability of false alarm and detection using threshold
values.
The energy becomes in Rayleigh Fading Channel;
∑
(1.32)
3 ROC of AND under AWGN
A. Energy Detector
The ED is the simpler method in CRN for spectrum
sensing. In a determined spectrum bandwidth, it merely
estimates the energy content. The statistical test
connected with this is formulated as
| |
(1.33)
Such statistical tests are likened to a threshold level
(
√
√ )
(1.34)
Where the statistical test is lower than the limit λ, the SU
selects an idle channel, otherwise the channel will be busy
and the SU will not broadcast.
Sensing-time vs. Throughput problem formulation
The likelihood of fake alarm
(.)fp
and detection
likelihood
(.)dp using the Central Limit Theorem (CLT)

approach, associated with the ED can be formulated as a
function of the sensing time parameter τ.
√ √
(1.35)
(
√
√ )
(1.36)
where dp and fp The likelihood of detection target
and false alarm target, respectively, and the essential
function of the Gussian probability density is described
as
√
∫ ( )
(1.37)
The π threshold value can be associated with the
detection probability as [5].
( √ ) (1.38)
When there are distinct channel occupancy probability
values, then eq. (1.17) Available to:
( √ )
(1.39)
where
1
( )r pP H SNR  . The value of pSNR is
weighted to
1
( )rP H , Which is the channel's likely to be
busy.
As a consequence, in the lack and in the presence of the
PU, the throughput of the SU is provided.
(1.40)
( ) (1.41)
Where C0 is the SU's output when operating in the absence
of the PU and C1 is the SU's output when operating in the
presence of the PU. Obviously, the value of C0 is always
larger than the value of the C1, i.e The PU signal interferes
with the throughput when the channel is busy. The first
and third scenarios therefore contribute to the
relationship between sensing and performance [5]
(1.41)
(1.42)
In the first case, the PU is not present then SU not generate
false alarm. For the second case PU signal is active. Hence,
0 ( )B  and 1( )B  represent the SU throughput dependent
on the sensing-time duration (τ < T) when PU is absent
and present, respectively. The probabilities for occurrence
of the first and third scenarios are given by [5]
Pr(correct detection) = [1 − Pf (τ )] · Pr(H0) (1.43)
Pr(miss detection) = [1 − Pd(τ )] · Pr(H1) (1.44)
where
0
( )rP H and
1
( )rP H The channel is likely to be
idle and busy (linked to first and third situations). The
probability (1 ( ))dP  is called the likelihood of miss
detection. So, the throughput 0 ( )R  and 1( )R  they are
respectively for the first and third situations.
(1.45)
(1.46)
Finally, the complete SU network output is provided by
(1.47)
The throughput is provided by eq for the ED spectrum
sensing case. (1.26) [5], next page at the top. To simplify,
we find the channel's probability to be small, i.e
1
( )rP H ≤
0.2 And the second word of the performance feature in
(4.27) becomes meaningless and can be simplified as
√
√
(1.48)
Finally, the issue of streamlined optimization of sensing-
throughput (STO) can be articulated as
(1.49)
(1.50)
(1.51)
Where Pd = 0.9 is the IEEE 802.22 WRAN detection target
probability. The convexity of the issue of optimization (21)
is shown in the appendix. The above issue of optimization
can be viewed as a sensing-throughput tradeoff aimed at
identifying the ideal sensing duration τ for each frame
time in the MAC layer, such that the achievable throughput
of the SU is guaranteed, while ensure the PU protection,
that is related with the value of the Pd.

4. Result and Discussion
In figure.1, by maintaining SNR=10 db, we discovered
error rate for various threshold values and amount of CR's.
The error rate in the figure is small for n=5 and high for
n=10 and n=1.i.e. We can achieve a small error rate with 5
CRs out of 10. This figure explains the optimal rule. The
error rate is nothing but . That is the likelihood
of missed detection and if very few or high amount CR's
are used, the false alarm probability is high.Thus the
number of CRs used should be half of the total CR's, i.e. for
n=5 the likelihood of missed detection and false alarm
probability is low, so cooperative spectrum sensing
allocation is done correctly. We also compare the
outcomes of modeling and modeling by modeling the
system. We compare outcomes obtained from n = 5
modeling and formulae. The two outcomes are the same.
We use the equations described in section 3 for modeling.
As of MATLAB Optimization Toolbox. The numerical
solutions discussed in this system confirm that the
maximum is a global optimum and the objective function
is a concave function.
Figure 1: Complementary ROC curves for local spectrum
sensing under AWGN and Rayleigh channel with m = 10
Comparing the values of Pd with values of threshold one
can see that different values of threshold implies in values
of Pd ≥ 0.9, which respects the constraints. Comparing
values of Pd with values of Ns and values of sensing time, it
is possible to conclude that for values of Ns ≥ 15600
samples, implies in values of Pd above 0.9, with no
violation of the constraints limits. Hence, we concluded
that the obtained solution respect the constraint of the
optimization problem, in addition to maximize the
throughput of the SU
Figure 2: Energy Detection Graph
Figure 3: Complementary ROC curves for cooperative
spectrum sensing using AND-rule under Rayleigh channel
with m = 10 and SNR = -10 dB.
In the figure.1, we found error rate for different threshold
values and number of CR’s by keeping SNR=10 db. In
figure, the error rate is low for n =5 and it is high n =10 and
n =1.i.e. with use of 5 CR’s out of 10 we can achieve low
error rate. This figure explains the optimal rule. The error
rate is nothing but ( )f mQ Q . That is probability of
missed detection and false alarm probability is high if very
few or high number CR’s are used. So the number of CR’s
used should be half of total CR’s, i.e. for n=5 the probability
of missed detection and false alarm probability is low, so
cooperative spectrum sensing allocation is done in correct
way. Also, by modeling the system, we compare results get
from modeling and formulae for n =5. The both results are
same. For modeling, we use equations explained in section
4.We discovered optimum value of ' n ' i.e. ' n from K ' CR's
in figure.2.We differ limit values from 10 to 40 and we
discovered ideal value of ' n ' from equation 9 for distinct
SNR values (0dB, 5dB, 10dB).From the graph we conclude
that the necessary amount of CR's is more for low
threshold value with low SNR.As we raise the limit value
with low or equal SNR, we need very less CR. The ideal
value of n also rises as SN rises. E.g. If SNR= 0dB and = 33,
the ideal value of n is 1.We can attain a small error rate
with 1 CR.
For high threshold value, the ideal value of n is small, so
we get low likelihood of missed detection and false alarm

likelihood for elevated threshold value with fewer CRs.
This probability also decreases in AWGN channel by
reducing SNR values for a tiny amount of ' n '
Chart 4: Total error rate of cooperative spectrum sensing
in AWGN channel with 10dB SNR. Optimal voting rule for
n=1,2,.........,10 and K=10.
5. CONCLUSION
The cooperative energy detection spectrum sensing using
formula and system modeling was researched. Analysis of
the scheme has been performed with optimum voting rule
for minimum error rate and K/2 is the optimum value. In
addition, threshold optimization was performed with
minimum probability values for missed detection and false
alarm probability. System analysis has been performed for
the less likelihood of missed detection and false alarm
probability, so the spectrum has been properly allocated
to secondary consumer. The quick sensing algorithm was
suggested and the smallest number of CR's calculated for a
specified error bound. With quick sensing algorithm, the
intolerably lengthy sensing time has been eliminated.
REFERENCES
[1] Wei Zhang, Member, IEEE, Ranjan K. Mallik, Senior
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