-
Counteracting Malicious Users in Cognitive Radio Networks over
Imperfect Reporting Channels
Jun Du1,2, Chaocan Xiang1, Daoxing Guo1, Bangning Zhang1, and
Hailiang Zhang2
1College of Communications Engineering, PLA University of
Science & Technology, Nanjing 210007, China 2Unit 72959 of PLA,
Jinan 250031, China
Email: {dujun607, xiang.chaocan}@gmail.com; {xyzgfg,
ofdm3000}@163.com; [email protected]
AbstractSpectrum sensing data falsification (SSDF) attack are
serious threats to collaborative spectrum sensing (CSS) of
cognitive radio networks (CRNs). In this paper, inspired by EM
(Expectation Maximization) method, we propose a scheme to estimate
the presences of primary user (PU) and the SUs operating point
parameters (false alarm and detection probabilities) iteratively.
The key features of the proposed scheme is that, by using the
estimated SUs operating point parameters, the fusion center can
estimate the presences of the PU, while the PU's state information
is feedback to enhance the estimation accuracy of SUs operating
point parameters. Furthermore, our scheme can achieve a powerful
capability of eliminating incorrect sensing reports, which can
avoid over penalize the honest users who have random errors in
reporting channels. The numerical result shows that, the proposed
method can achieve higher malicious user detection accuracy than
the existing reputation-based schemes, and can thus improve the CSS
performance significantly.
KeywordsCognitive radio network, collaborative spectrum sensing,
expectation maximization algorithm, malicious secondary users
detection, security;
I. INTRODUCTION More and more powerful smartphones and tablet
computer
are becoming popular nowadays, demanding high-rate mobile
multimedia transmission services. This has resulted in the scarcity
of spectrum allocated for cellular communications. Cognitive radio
has been proposed as the way to alleviate the spectrum shortage,
and is considered to be a potential candidate technology in next
generation intelligent transportation systems [1] . The basic idea
of cognitive radio is that secondary (unlicensed) users (SUs) can
share spectrum bands with the primary (licensed) users (PUs)
without causing harmful interference to PUs. A major challenge in
cognitive radio networks (CRNs) is to detect the presence of PUs
with high accuracy. The performance of spectrum sensing degrades
significantly when wireless channel experiences fading or
shadowing. Collaborative spectrum sensing (CSS) has been proposed
to improve detection accuracy by exploiting SUs spatial diversity.
However, collaborative spectrum sensing also induces security
vulnerabilities [2], such as spectrum sensing data falsification
(SSDF) attack. In an SSDF attack, a malicious user intentionally
send falsified local spectrum sensing reports to a fusion center
(FC) in an attempt to confuse the FC. From the FCs point of view,
these malicious user have significantly different false alarm rate
or/and detection alarm than the honest SUs.
SSDF attacks in CSS of CRNs have attracted considerable
attention recently. Many solutions have been proposed to resist
SSDF attack in literature, where the essential idea is to identify
the attackers according to its behavior and then ignore its
reports. The authors in [3] have proposed a reputation-based scheme
to identify the attackers. Basically, when a SUs report deviates
from the global decision beyond a certain threshold, its reputation
value is degraded. When the attackers are identified, their
negative impact on the CSS will be weakened or eliminated. In [4],
the authors proposed a malicious user detection scheme based on
outlier detection techniques. The SU, which does not exhibit
similar behavior as rest of the SUs, is assigned a high outlier
factor. These outlier factors are used to identify malicious users.
By exploring the spatial and temporal correlations among the
reported information of the SUs, the authors in [5] assigned a
trust value to each SUs. The trust value serves as the measurement
of the reliability of a SU, and mitigates its harmful effect on the
final decision. The main characteristic of all these solutions is
that lower weight will be assigned to the SUs whose reports are
inconsistent with the majoritys decisions. Obviously, these
solutions rely on the correctness of global decision. When
malicious sensors dominate the network, the prior information aided
solutions are proposed. In [6], with the assistance of one trusted
SU, the proposed malicious user detection solutions can achieve
high malicious user detection accuracy for arbitrary percentage of
malicious users. In [7], the authors propose a Bayesian framework
to perform spectrum sensing and detection of malicious users. In
order to reduce the computational complexity, belief propagation
algorithm is applied. Note that, the solution is also assumed that
there is a subset of trusted SUs, whose identities are known to the
FC.
Most of existing solutions to resist SSDF attacks are separate
the detection of malicious user from the detection of PUs state,
which will result in the loss of performance. Recently, some
valuable works have revealed that joint malicious user detection
and PUs state detection is more efficient than the isolated
designs. In [8], a fast detection solution is proposed by
considering jointly the classification of SUs and the detection the
presence of the SU, which optimizes the system performance. The
authors assumed that all the SUs in a class have the same detection
and false alarm probabilities.
On the shoulder of the previous valuable works, in this paper,
we consider an infrastructure-based CRN in which sensing results
are collected from all SUs, where the identity (i.e., honest or
malicious) of SUs, and hence the reliability of the sensing reports
made by them, is not known a priori.
2014 Sixth International Conference on Wireless Communications
and Signal Processing (WCSP)978-1-4799-7339-2/14/$31.00 2014
IEEE
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Moreover, due to the existence of error in reporting channel,
the sensing reports from the honest SUs may have some mistakes. No
prior information about the network is assumed to be known except
the honest SUs are in majority. We present a malicious user
detection algorithm that calculates SUs operating point parameters
(i.e., false alarm and detection probabilities) and then utilizes
the operating point parameters to eliminate the malicious users'
influence on PU's state detection results. Since PU's state
estimation and SUs operating point parameters estimation are
tightly coupled with each other, we tackle the problem using the
iterative method. First, in the PU's state estimation step, we use
the estimated SUs operating point parameters, which is come from
the SUs operating point parameters estimation step, to estimate the
presence of PU, while the PU's state information is feedback to the
next step to enhance the estimation accuracy of SUs operating point
parameters. Second, in the SUs operating point parameters
estimation step, inspired by EM (Expectation Maximization) method
[9], we can incrementally enhance the estimations of SUs operating
point parameters in each iterative with the inexact PU's presence
information.
The remainder of this paper is organized as follows. The system
model is introduced in Section 2 followed by the problem statement.
In Section 3, we transform the complex problem into a simple one.
In Section 4, we propose an iterative algorithm which joint design
PU's state estimation and SUs operating point parameters
estimation. The performance Evaluations Metrics are introduced in
Section 5 and the numerical results are presented in Section 6.
Finally, conclusions are drawn in Section 7.
II. SYSTEM MODEL AND PROBLEM STATEMENT
A. System Model We consider an infrastructure based cognitive
radio network
(CRN) where a group of N secondary (unlicensed) user (SU), 1su ,
..., Nsu , make individual observations about the presence
or absence of a PU signal in a spectral band. The CRN includes a
secondary fusion center (FC) which coordinates CSS and SUs access
to a PU channel. The CRN operates on a frame-by-frame basis. At the
beginning of each frame {1,2,..., }t T , each SU carries out
spectrum sensing and decides whether the PU signal is present or
not. A one bit local decision made by
nsu at frame t is denoted by ,n td , 1, 2,...,n N= . If the nsu
decides on PU signal present, then , 1n td = , and , 0n td =
otherwise. Then each SU transmits its binary report to the FC
through the reporting channels. The binary reports received from
all SUs are denoted by ,{ , 1, 2,..., , 1, 2,..., }n tr n N t T= =
. Due to imperfect reporting channels or malicious users
misbehaviors, ,n tr is not always equal to ,n td . Let
0, , ,Pr( 1 | 0)n n t n tr d = = = and 1, , ,Pr( 0 | 1)n n t n
tr d = = = denote the probability that the received report from nsu
is different from its local decision at frame t . The FC collects T
frames of reports from each SU to form a binary report matrix
,[ ]n tr=R , 1, 2,...,n N= , 1, 2,...,t T= . Based on R , the FC
makes a decision regarding the presence or absence of the PU
signal at each frame using a data fusion and detection scheme.
Denote by , 1,2,{ }...,th t T= =H , {0,1}th the actual state of the
PU signal at each frame and 1th = denote PU signal present at ,
,=Pr( 1 | 1)d n n t tP d h= = and false alarm probability
, ,=Pr( 1 | 0)f n n t tP d h= = , respectively. From the FCs
perspective, the detection probability ,d nP
and false alarm probability ,f nP of the SU nsu can be
represented as,
, , 1, , 0, ,=Pr( 1 | 1) (1 ) (1 )d n n t t n d n n d nP r h P P
= = = + (1)
, , 1, , 0, ,=Pr( 1| 0) (1 ) (1 )f n n t t n f n n f nP r h P P
= = = + (2) We define the pair , ,( , )f n d nP P to be the
operating point
parameter [10] of the SU nsu . Accordingly, we refer to , ,={( ,
), 1, 2,..., }f n d nP P n N=P as the parameter matrix of all
SUs, which denote the false alarm and detection probability
perceived by the FC for all SUs.
B. Problem Statement Due to imperfect reporting channels,
performance
difference and misbehaviors of SUs, reports in the report matrix
R are inaccurate and unreliable. As a result, it is vitally
important but challenging for the FC to acquire the accurate
information from these reports, e.g. whether the PU signal exist or
not at each frame {1,2,..., }t T . We denote the probabilities of
the presence of PU at each frame by [ ]t= ,
{1,2,..., }t T , where Pr( 1)t th = = is the probability that
the PU is present at frame t . Note that are not prior
probabilities of the PU being presence at each frame and are used
as the detection statistics to help us decide on the state of PU in
the following iterative algorithm. Therefore, given the report
matrix R , our goal is to compute i) the best estimation on the
presence of the PU signals H , and ii) the best estimation on the
SUs parameter matrix P , when the prior probabilities of the PU's
activity are previously unknown. Formally,
, ,
, arg max Pr( | , )< >=H P
H P R P
, where , 1, 2 { ,..., }th t T= =H denote the optimal estimation
of H .
, , {( , ), 1, 2,.. ., }f n d nP P n N= =P denote the optimal
estimation
of P .
III. PROBLEM TRANSFORMATION It is worth noting that, maximizing
the probability of
reports Pr( | , )R P is very difficult due to the unknown data,
i.e., H , P and . To address this problem, we first choose the PU
presence vector H as latent variables. Then, adding the latent
variables, we evaluate Pr( , | , )R H P and from which obtains the
log-likelihood function, denoted by
, |( ),L R H P in (3), then we transform the maximum
log-likelihood estimation problem , ,maxlog[Pr( | , )]H P R P into
the
-
simple problem of maximizing log-likelihood expected problem ,
,max ( , , )H P R,H P .
, , , ,1 1
, , , ,1 1
( , | , ) log[Pr( , | , )]1(1 )[ log( ) (1 ) log(1 ) log(1
)]
1[ log( ) (1 ) log(1 ) log( )]
N T
t n t f n n t f n tn tN T
t n t d n n t d n tn t
L
h r P r PN
h r P r PN
= =
= =
=
= + +
+ + +
R H P R H P
(3)
Let us denote the expected log-likelihood function as ( , , , )
R H P , which is the expected value of the log-
likelihood function ( , | , )L R H P with respect to the
distribution of the PU existences.
Theorem 1: ( | , ) ( , , , )L R P R H P , where ( | , ) log[Pr(
| , )]L =R P R P and the equality holds if and
only if Pr( ) Pr( | , )=H H R,P .
Proof: The log-likelihood function ( | , )L R P can be written
as (4)
( | , ) log[Pr( | , )]
Pr( | , ) Pr( , | , )logPr( | , , ) Pr( | , )
Pr( | , , ) Pr( )logPr( | , , )
Pr( )log(Pr( | , , )) logPr( | , , )
L =
=
=
= +
R P R P
R P R H PH R P R P
R H P HH R P
HR H PH R P
(4)
Taking the expectation with respect to H on both sides of (4)
note that ( | , )L R P is independent of H , we get (5),
where Pr( )(Pr( ) || Pr( | , , )) log
Pr( | , , )D E
= H
HH H R PH R P
is the
Kullback-Leibler (K-L) divergence between Pr( )H and Pr( | , ,
)H R P .According to Information Inequality [11],
(Pr( ) || Pr( | , , )) 0D H H R P with equality if and only if
Pr( ) Pr( | , , )=H H R P . Therefore,
( | , ) ( , , , )L R P R H P and the equality holds if and only
if Pr( ) Pr( | , , )=H H R P .
Theorem 1 tell us that the lower bound of the log-likelihood
function ( | , )L R P is the expected log-likelihood function
( , , , ) R H P . Lemma 1: If there exist the optimal values *P
, * and *H , which maximize ( , , , )* * * R H P , then
( | , ) arg max ( | , )* *L L=R P R P P, .
Lemma 1 can be easily proved by contradiction. Therefore we
transformed the complex maximization problem with unknown
parameters into the maximizing expected log-
likelihood problem. Formally, the problem can be rewritten as
follows (6).
Pr( )( | , ) [log(Pr( | , , ))] logPr( | , , )
( , , , ) (Pr( ) || Pr( | , , ))
L E E
D
= +
= +
H HHR P R H P
H R PR H P H H R P
(5)
, ,
, arg max ( , , , )< >=H P
H P R H P
(6)
IV. ITERATIVE COLLABORATIVE SPECTRUM SENSING AND SU PARAMETER
ESTIMATION ALGORITHM
To estimate the SUs sensing performance, in this section, we
propose RESISTANT, a iterative collaborative spectrum sensing and
SU parameter estimation algorithm. Through the iterative, the
expected log-likelihood function of the report matrix can gradually
reach the maximum and the optimal estimation of SUs parameters will
be got. Specifically, as shown in Fig. 1, RESISTANT is mainly
comprised of two iterations process: the estimation of the PUs
existences process and the estimation of the SUs parameter matrix
process.
( 1)iP ( )kP( )i
( 1)i
( 1)k
( )k
R
Fig. 1. The framework of RESISTANT, a iterative collaborative
spectrum sensing and SU parameter estimation algorithm.
A. The Estimation of the PUs Existences Process: According to
Theorem 1, we know that ( , , , ) R H P can
reach its maximum ( | , )L R P when Pr( ) Pr( | , )=H H R,P . It
is noted that Pr( | , )H R,P denotes the posterior probability of
the PUs presence. Heuristically, we take Pr( | , )H R,P as the
estimation of the PUs presence Pr( )H in the iterations. According
to Bayes theorem [12], the estimation of ( )it in the thi iteration
is:
( ) ( 1) (i 1):,
( 1) (i 1):,
1( 1) (i 1)
:,0
Pr( 1 | , , )
Pr( , , | 1) Pr( 1)
Pr( , , | ) Pr( )
i it t t t
it t t t
it t t t
j
h r
r h h
r h j h j
=
= =
= =
=
= =
P
P
P (7)
, ,
, ,
11( 1) ( 1) ( 1)
, ,( ) 1
1( 1) ( 1) ( 1), ,
1
(1 ) ( ) (1 )1
( ) (1 )
n t n t
n t n t
Nr ri i i
t f n f ni n
t Nr ri i i
t d n d nn
P P
P P
=
=
= +
(8)
-
B. The Estimation of the SUs Parameter Matrix Process For
presentation convenience, we take the thk iteration as an
example. In this process, we need to estimate the SUs parameter
matrix ( )kP and the probability of the PUs presence
( )k in the thk iteration, given ( 1)k in the ( 1)thk
iteration.
According to (6), we need to maximize the expectation likelihood
function ( , , , ) R H P with respect to the ( 1)k . Formally,
( ) ( ) ( ) ( ) ( 1)
, ,
, arg max ( , , )k k k k k < >= |H P
H P R P
(9)
Then, the estimation of ( )kP and ( )kt can be found by solving
(9) as,
( ) ( ) ( 1) ( ),( , , ) 0
k k k kf nd dP
| =R P (10) ( ) ( ) ( 1) ( )
,( , , ) 0k k k k
d nd dP| =R P (11)
( ) ( ) ( 1) ( )( , , ) 0k k k ktd d | =R P (12) After some
manipulations, the estimations for ( )kP and ( )kt
are derived as:
( ) ( 1) ( 1), ,
1 1(1 ) (1 )
T Tk k k
f n t n t tt t
P r = =
= (13)
( ) ( 1) ( 1), ,
1 1
T Tk k k
d n t n t tt t
P r = =
= (14)
( ) ( 1)k kt t = (15)
To estimate the existences of the PU signals th , we use the
estimated t which maximizes the expectation likelihood function ( ,
, , ) R H P . Therefore, we let
1,0,
0.5otherwise.
tth
=
> (16)
C. Summary of RESISTANT
Based on the derivations in the previous two processes, the
entire procedure of RESISTANT is summarized in Algorithm 1.
0
0.5
1
00.20.40.6
0.810
0.2
0.4
0.6
0.8
1
pdpf
Trust
Fig. 2. The trust value verse the operating point
Algorithm 1 RESISTANT: iterative collaborative spectrum sensing
and SU parameter estimation algorithm Input: SUs report matrix R ;
Output: the estimation of the PU's state vector H ; the estimation
of the SUs' parameter matrix P ;
1. Initialize P and by (0)P and (0) , respectively. i=1;k=1; 2.
While ( 1) ( 1)( , , )i i R H,P does not converge do 3. Compute (
)i based on ( 1)it and (i 1)P according to (8) 4. Compute ( )kP
based on ( )i according to (13) and (14) 5. Update ( )kt ( 1,
2,...,t T= ) according to (15); 6. 1i i= + ; 7. Let ( 1)it and (i
1)P be the value of ( )kt ( 1, 2,...,t T= ) and ( )kP ,
respectively; 1k k= + ; 8. end while 9. Let P be the converged
values of ( )kP ; 10. Compute H based on the converged values of (
)k according to (16).
V. PERFORMANCE EVALUATIONS METRICS
A. The Discriminability Metrics To show the discriminability of
the PUs state, we define the
PU discriminability rate by [8].
1
1 | |T
H t tt
h hT
=
= (17) To evaluate the accuracy of RESISTANT in estimating
the
SUs' parameter matrix P , we define the average estimation error
of SUs' parameter matrix P based on the normalized
Euclidean distance between the estimated SUs' parameter matrix
and actual parameter matrix [13], i.e.,
2 2, , , ,
1
1 ( ) ( )2
N
P f n f n d n d nn
P P P PN =
= + (18)
B. The Trust Metrics To detect the malicious behaviors of the
SUs, we define the
trust metrics based on the estimated SUs operating point
parameter, i.e.,
2 2, ,n
1( ) (1 )2 f n d
Trust n P P= + (19)
The trust metrics are in the range [0,1], where value '0' mean
that the corresponding SU is malicious with the highest attack
intensity. The trust metrics are equal to 1 when the corresponding
SU is honest with the perfect detection performance. It is
generally known that the receiver operating characteristic (ROC)
curve should always be above the 45 line (shown dashed in Fig. 2)
[10]. In Fig. 2, We observed that when the ROC curve is below the
45 line, the trust value is less than 1/ 2 . Furthermore, the
minimum trust value for the SUs operating point parameter on the 45
line is 0.5. The trust value 0.5 corresponds to the operating point
parameter (0.5,
-
0.5), which like guessing the PUs state based on a coin toss. So
we set the identification threshold to 1/ 2 . When a SUs trust
value is less than 1/ 2 , the SU is identified as malicious user.
Specifically, when a SUs trust value is less than 0.5, the SU is
identified as the malicious user who always flipping his
decision.
VI. NUMERICAL RESULTS We consider a centralized cooperative
sensing system with
N=20 SUs (including honest SUs and malicious users) detect the
status of a PU collaboratively. Two types of SSDF attacks [14]
might exist in the CRNs. The first type is selfish attack where the
aim of this type of attacker is to get exclusive spectrum access.
Generally, this type of attackers have higher false-alarm rate than
the honest SUs. The second type is vandalism attack where the
intention of this type of attacker is to both cause interference to
PU and inhibit the communication of other SUs. Attackers of this
type have higher false-alarm rate and missing-detection rate than
honest SUs. Note that, the effect of imperfect reporting channels
is also to increase false-alarm rate and missing-detection rate. In
practice, all SUs have different operating point parameters. To
facilitate comparison between different solutions, in the
simulations, we consider four different attack scenarios as shown
in Table 1, where n denoting the fraction of SUs in the population.
The attack strength increase with the scenario sequence number. In
the scenario S1, the attackers launch selfish attack and the
vandalism attack with the operating point parameter (0.7, 0.2)
which represent flipping decision. In the scenario S2, the
attackers launch vandalism attack only, including almost-always-no
almost-always-yes and flipping decision. In the scenario S3 and S4,
the attacker launch mixed vandalism attack and selfish attack with
different composition and proportion.
TABLE I. THE SUS' PARAMETER MATRIX IN DIFFERENT SCENARIOS
Scenario , ,( , )f n d nP P
n
S1
(0.7, 0.2) (0.4, 0.7) (0.5, 0.7) (0.2, 0.7)
20% 10% 10% 60%
S2
(0.7, 0.2) (0.05, 0.05) (0.95, 0.95) (0.2, 0.7)
20% 10% 10% 60%
S3
(0.7, 0.2) (0.4, 0.7) (0.5, 0.7) (0.6, 0.7) (0.2, 0.7)
20% 10% 10% 10% 50%
S4
(0.7,0.2) (0.4, 0.7) (0.5, 0.7) (0.6, 0.7) (0.2, 0.7)
30% 10% 10% 10% 40%
In Fig. 3, we analyze the performance of RESISTANT verse
iteration, in terms of the estimated operating point parameter of
1su and PU discriminability rate. We set the
number of SUs to be 20, and the scenario in this example is S1
shown in Table 1. 1su is attackers with the operating point
parameter (0.7, 0.2). As shown in Fig. 3,
5 10 15 20 25 30 35 40 45 500
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Number of iterations
P f,1
Pd,1
h
^
^
Fig. 3. Performance rate verse iteration steps, in terms of the
estimated operating point parameter of 1su and PU discriminability
rate for T=60 and N=20.
15 20 25 30 35 40
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Number of Received Frames T
H
RBA, S1RESISTANT, S1RBA, S2RESISTANT, S2RBA, S3RESISTANT, S3RBA,
S4RESISTANT, S4
Fig. 4. PU discriminability rate verse T
30 40 50 60 70 80 90 100
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.26
Number of Received Frames T
P
RBA, S1RESISTANT, S1RBA, S2RESISTANT, S2RBA, S3RESISTANT, S3RBA,
S4RESISTANT, S4
Fig. 5. The Average estimation error of SUs' parameter matrix
verse T for N=20.
H decreases with the iteration of the loop until they remain
unchanged. Likewise, the estimated operating point parameter of 1su
gradually converge to the correct operating point of
1su (0.7, 0.2). From Fig. 3, we observe that, the estimation
-
precision of the PU state and 1su s operating point parameter
increases with iterations, and RESISTANT converges after 40
iterations of the loop.
20 40 60 80 100 120 140 160 180 2000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Number of Received Frames T
Tru
st
malicous SUsHonest SUs
Selfish SUs
Vandalism SUs
Fig. 6. The Trust value of the SUs verse T.
Using the metrics defined in Section 5, the performance of the
RESISTANT is compared with reputation-based algorithm (RBA) [3].
The PU discriminability rate H with respect to the number of
received frames, T, is shown in Fig. 4. As shown in Fig. 4, the
RESISTANT has smaller H than the RBA in all scenarios, which means
the accuracy of the RESISTANT in estimating PUs state is better
than the RBA. With the attack strength increase, the performances
of both algorithms deteriorate. We also find, as the number of
received frames increase, the H of RESISTANT converge to zero.
However for RBA, as the number of received frames increase, the H
does not converge to zero. The reason behind this is that, for RBA
when the FC is not aware of the SU's parameter matrix as is the
case here, majority rule will be used [3], which did not make full
use of the previously received data. Whereas for RESISTANT,
previously received data is well utilized through iterative
computing, and the accuracy of the algorithm tend to increase as
the number of received frames increase.
Figure 5 demonstrates the effects of different number of
received frames on the estimation error P . It can be seen that the
RESISTANT achieving better performance than RBA in all scenarios,
especially in the scenarios of stronger attack strength. When the
attack strength is weak, the performance of both algorithms
improves with T. When the attack strength is strong, the
performance of RBA improves as the number of received frames T
increases up to a certain value, and then, it becomes roughly
constant. However, as for the RESISTANT, the performance improves
with T regardless of the attack strength.
In Fig.6, we then show an example of the evolution of Trust
values as a function of the number of received frames for all SUs.
The scenario in this example is S1 shown in Table 1. It is shown
that the accuracy of detection improves with T. The Trust values of
selfish SUs are higher than vandalism SUs but lower than the
identification threshold. From Fig.6, it can be confirmed that our
proposed RESISTANT can correctly identify the malicious SUs among
all SUs
VII. CONCLUSION In this paper, we aim at addressing how to
identify the
malicious SUs only based on unreliable reports in CSS. The FC
collects all SUs reports through an erroneous reporting channel,
and consequently the honest SUs operating point parameters are
different. We formulated a joint SUs operating point parameters
estimation and PUs state detection model and defined the related
trust metrics to identify malicious SUs. The iterative algorithm is
developed based on an EM method that using the estimated SUs
operating point parameters to computes the PU's state, and
incrementally enhance the estimations of SUs operating point
parameters with the inexact PU's state information in each
iterative. Compared against conventional reputation-based algorithm
(RBA), we have shown through numerical simulations that the
proposed solution significantly outperforms it in PU's state
estimation and malicious SUs detection.
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