Admissible Evidence: Trustworthy Cooperative

Spectrum Sensing Based on Dempster-Shafer

Theory in Cognitive Radio Networks Shuo Feng1, Xueqiang Zheng1, Ran Liu2, Juan Chen1, Suqin Xu1, Linyuan Zhang1

1College of Communications Engineering, PLA University of Science and Technology, Nanjing, China 2Maintenance Department of Transformer Substation, Hangzhou Power Supply Company of State Grid, Hangzhou, China

E-mail: fengshuo1010@gmail.com. zxqq302@163.com. xusqnine@gmail.com. zhanglinyuan5@163.com.

Abstract--Cognitive radio (CR) is a promising technology which improves the spectrum utilization. Cooperative spectrum sensing (CSS) has been adopted to exploit spatial diversity in cognitive radio networks (CRNs). Since CSS is subject to attacks from malicious users, several secure schemes have been proposed recently. But, they only utilize current information to estimate the reliability of secondary users. In this paper, we propose a trustworthy CSS scheme based on Dempster-Shafer theory. It evaluates the trustworthiness degree of each user with two indicators, which are the current reliability and the historical reputation. Besides, it takes advantage of Dempster-Shafer theory’s ability to reflect uncertainty in the evaluation as well. Simulation results have shown that the proposed scheme is effective to counter with different attacks patterns.

Index Terms--Cognitive Radio; Cooperative Spectrum Sensing; Security; Dempster-Shafer Theory; Trustworthiness Degree.

I. INTRODUCTION

Current spectrum regulation has resulted in extreme scarcity of available spectrum due to the static allocation strategy, while plenty of spectrum resources are actually unused temporally/geographically [1]. Cognitive radio (CR) is regarded as a promising technology to address this problem. CR enables secondary users (SUs) to access a spectrum band while it is not occupied by the primary user (PU). Different from traditional wireless networks, cognitive radio network (CRN) is able to perceive the environment, make informed decisions, and reconfigure the network accordingly. As one of the most fundamental components in CR technology, reliable and efficient spectrum sensing is very important for the realization of CRN [2].

Since single SU may be shadowed or experience multi-path fading, extensive researches have been done to

study cooperative spectrum sensing (CSS) recently [3]. In CSS, each SU performs the local spectrum sensing individually at first, and then forwards its measurements to the fusion center (FC), at where those measurements are used to make the decision about whether PU is present [4].

Unfortunately, CSS is subject to the attacks from malicious SUs [5-6]. The falsified measurements reported by malicious SUs will mislead FC to make incorrect decisions. Therefore, several CSS schemes based on Dempster-Shafer theory have been proposed [7-9]. In [7], Dempster-Shafer theory is firstly adopted to combine the sensing reports from each SU. This scheme does not need prior knowledge about PU, and can work quite well if there is no attack. In [8], an enhanced CSS scheme is proposed. It evaluates the reliability of SUs before making the decision, but requires the SNR of PU’s signal at each SU to accomplish the evaluation. Another enhanced CSS scheme proposed in [9] focuses on countering the spectrum sensing data falsification (SSDF) attack. By calculating the similarity degree of evidences, those evidences with low similarity degree are removed from the combination.

However, most of the existing CSS schemes based on Dempster-Shafer theory only utilize current information to estimate the trustworthiness of each SU’s measurements. Due to the open, dynamic, and uncertain character of wireless environment, even honest SUs may have inaccurate measurements sometime. In such circumstances, it is likely for those schemes to confuse honest SUs with malicious SUs and result in poor performance.

Therefore, we propose a trustworthy CSS scheme based on Dempster-Shafer theory in this paper. Instead of evaluating the SUs only with their current measurements, the proposed scheme calculates the trustworthiness degree of each SU by considering two indicators, which are the current reliability and the historical reputation. Furthermore, in the historical reputation calculation, the ability of reflecting uncertainty of Dempster-Shafer theory is properly utilized to update the reputation value as well.

The rest of this paper is organized as follows. Section II describes the system model briefly. The proposed trustworthy CSS scheme based on Dempster-Shafer theory is discussed in Section III. In Section IV, simulation results are presented. Conclusion is drawn in Section V.

This work is supported by the National Basic Research Program ofChina under Grant No.2009CB320400, the National Natural ScienceFoundation of China under Grant No.60932002, No.61172062, and No.61301160, and in part by Jiangsu Province Natural ScienceFoundation under Grant No.BK2011116.

978-1-4799-4860-4/14/$31.00 copyright 2014 IEEE ICIS 2014, June 4-6, 2014, Taiyuan, China

Figure 1. Cooperative spectrum sensing in cognitive radio networks.

II. SYSTEM MODEL

In this section, we describe the CSS scenario in CRNs, and introduce three attack patterns considered in this paper.

A. Cooperative Spectrum Sensing

As illustrated in Fig. 1, the network is composed by one PU, n SUs, and one FC. Each SU individually performs local spectrum sensing, which is essentially a binary hypothesis testing [3]:

0

1

( ),( )

( ) ( ) ( ),i

ii i

n t Hx t

h t s t n t H⎧

= ⎨ +⎩ (1)

where ( )ix t is the received signal at iSU , ( )in t is the additive white Gaussian noise (AWGN), ( )ih t is the amplitude gain of the sensing channel, and ( )s t is the signal transmitted from PU. 0H represents PU is absent, and 1H represents PU is present. Without loss of generality, ( )s t and ( )in t are assumed to be independent in this paper.

We also assume that simple energy detection method is employed by each SU in the local spectrum sensing. With a band-pass filter, the received signal power can be measured by:

2

1i

N

E ijj

x x=

=∑ (2)

where ijx is the thj sample of the received signal at iSU . Besides, 2N TW= , and TW is the time-bandwidth product. When N is large enough (say, 10N > ),

iEx can be approximated as a Gaussian random variable under both hypotheses 0H and 1H , with mean 0iμ , 1iμ and variance 2

0iσ , 21iσ , respectively [10]. That is,

20 0 0

21 1 1

~ ( , ),

~ ( , ),i

i

E i i

E i i

x N H

x N H

μ σ

μ σ

⎧⎪⎨⎪⎩

(3)

20 0

21 1

, 2

( 1), 2 (2 1)i i

i i i i

N N

N N

μ σμ γ σ γ

⎧ = =⎪⎨

= + = +⎪⎩ (4)

where iγ is the average SNR at iSU . To perform CSS, SUs are required to report their own measurements, which can be either the received energy

iEx or a function of it, such as the one-bit hard decision (i.e., 0 or 1). The measurement of iSU at thL sensing slot is denoted by L

iu , thus the reports received at FC can be denoted as

1 2[ , , , ]L L L Lnu u u u= (5)

Based on Lu , the final decision about PU’s activity 0Lu is

made at FC. In addition, the reporting channel between SUs and FC is assumed to be error-free.

B. Attack Patterns

In this paper, the SSDF attack model is adopted. In SSDF attack, a malicious SU falsifies its measurements to mislead FC for the purpose of obtaining more spectrum opportunities or deteriorating the performance of CSS. Three different patterns of SSDF attack are considered in this paper: always busy (AB), always free (AF), and always opposite (AO).

Specifically, AB attack is conducted by sending falsified measurements which indicate PU is present, when the real measurements actually indicate that PU is absent. This attack pattern mainly aims at increasing the false alarm probability. On the contrary, AF attack is conducted by indicating PU is absent while it is not. This attack pattern will increase the missed detection probability. AO attack is a stronger (but less stealthy) malicious behavior, since it indicates incorrect state about PU’s activity all the time, and will lead to the increase of both false alarm probability and missed detection probability.

III. TRUSTWORTHY COOPERATIVE SPECTRUM SENSING

BASED ON DEMPSTER-SHAFER THEORY

In this section, the proposed trustworthy CSS scheme based on Dempster-Shafer theory is discussed in detail. As shown in Fig. 2, it is carried out in three successive steps, which are basic probability assignment (BPA), trustworthiness degree calculation, and combination of admissible evidence. With these steps, the evidences that support hypotheses 0H and 1H are extracted from SUs, adjusted to be admissible by considering both current reliability and historical reputation of each SU, and then aggregated to obtain the combined evidence and make the final decision.

A. Basic Probability Assignment

Since the detection of PU is a binary hypothesis testing in CSS, the framework of discernment is naturally defined as { }1 0,H HΩ = . The BPA of Dempster-Shafer theory refers to a function m , which maps the power set of Ω (i.e., ( )ℜ Ω ) to the interval of [ ]0,1 and can be denoted as [11]

[ ]: ( ) 0,1m ℜ Ω → (6)

such that ( ) 0m ∅ = (7)

( )

1( ) 1k

km A

ℜ Ω

==∑ (8)

where ( )kA ∈ℜ Ω , { }0 1( ) , , ,H Hℜ Ω = ∅ Ω , and ( )ℜ Ω is the cardinality of ( )ℜ Ω .

Therefore, iSU can estimate its own BPA at thL sensing slot according to the following formulation [10]

iEx

0( )Lim H 1( )L

im H

0( )Lim H∗

1( )Lim H∗

( )( )

1

0

L

L

m Hm H

λ>

1H0H

( )1Lm H( )0

Lm H

1 0( )Lm H 1 1( )Lm H 0( )Lnm H 1( )L

nm H

1 0( )Lm H∗1 1( )Lm H∗

0( )Lnm H∗

1( )Lnm H∗

Figure 2. Schematic illustration of trustworthy cooperative spectrum

sensing based on Dempster-Shafer theory.

20

0 200

( )1( ) exp22Ei

L ii x

ii

xm H dxμσπσ

+∞ ⎛ ⎞−= −⎜ ⎟⎜ ⎟⎝ ⎠

∫ (9)

21

1 211

( )1( ) exp22

EixL i

iii

xm H dxμσπσ−∞

⎛ ⎞−= −⎜ ⎟⎜ ⎟⎝ ⎠

∫ (10)

and then reports them to FC, that is, 0 1[ ( ), ( )]L L Li i iu m H m H= .

B. Trustworthiness Degree Calculation

Due to the fact that some of the SUs may be malicious in CSS, the reports from different SUs should be treated discriminatingly. In the proposed scheme, the trustworthiness degree of iSU is calculated and assessed by FC properly. It not only reflects the credibility of BPAs from iSU at thL sensing slot, but also reflects the credibility of previous reports from iSU . The former indicator is referred as current reliability, and the latter indicator is referred as historical reputation.

1) Current Reliability: Since the reports from malicious SUs are falsified, they may not be consistent with the reports from other SUs to some extent. Therefore, we can primarily evaluate the credibility of iSU based on its report’s similarity with other SUs. Specifically, the similarity degree of reported BPAs between iSU and jSU can be expressed by the following formula [9]

( )

1( )

1

min( ( ), ( ))

max( ( ), ( ))

L Li k j k

L kij

L Li k j k

k

m A m Asim

m A m A

ℜ Ω

=ℜ Ω

=

=∑

∑ (11)

Then the similarity degree matrix can be expressed as

1 1

1

1

1

1

11

1

L Lj n

L L Li in

L Ln nj

sim sim

Sim sim sim

sim sim

⎡ ⎤⎢ ⎥⎢ ⎥⎢ ⎥= ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦

(12)

By adding up the total similarity degree of iSU with respect to other SUs, the support to the BPAs from iSU at thL sensing slot is denoted as

1, , , 1,2, ,

nL Li ij

jSup sim j i i j n

== ≠ =∑ (13)

So the current reliability of iSU can be normalized as

max( )

LL ii L

i

SupRelSup

= (14)

However, a SU with low current reliability may not be a malicious one due to the uncertainty of environment, and vice-versa. Moreover, at some particular times when several honest SUs have poor performance, their reports may have higher similarity degree with malicious SUs rather than with the well functioning honest ones. To tackle this problem, the reputation mechanism is introduced into the proposed scheme.

2) Historical Reputation: Unlike most of the existing reputation mechanisms which calculate reputation values by counting the times of each SU’s historical correctness, in the proposed scheme, the ability of reflecting uncertainty of Dempster-Shafer theory is properly utilized. That is, the reputation value of iSU is calculated and updated based on its historical BPAs.

Specifically, we define two parameters, self-assessed confidence and center-assessed confidence, to differentiate the particular cases in making the final decision. Self-assessed confidence represents how sure is iSU about its own reports, and center-assessed confidence represents how sure is FC about its final decision. Both self-assessed confidence and center-assessed confidence at ( 1)thL − sensing slot are calculated at FC, and can be written as

1 1 11 0( ) ( )L L L

i i ic m H m H− − −= − (15)

1 1 11 0( ) ( )L L Lc m H m H− − −= − (16)

respectively. 11( )Lm H− and 1

0( )Lm H− refer to the combined evidences at ( 1)thL − sensing slot and will be explained later. Therefore, the reputation of iSU at thL sensing slot can be updated as

1 101 1 1( 1) , 2,3,L L

iu vL L L Li i ir r c c L

− −+− − −= + − ⋅ ⋅ = (17)

where 1Lir

− is its reputation value at ( 1)thL − sensing slot, 10Lu −

is the final decision, and 1Liv − is the inferred local decision,

which can be reasoned from the reported BPAs of iSU using the same decision rule. Initially, 1 , 1,2, ,ir i n= Δ = . After normalization, the historical reputation of iSU can be expressed as

, 0max( ) 1,2, ,

0, 0

LLi

iLLii

Li

r rrRep i n

r

⎧>⎪

= =⎨⎪ ≤⎩

(18)

Then the trustworthiness degree of iSU at thL sensing slot can finally be obtained by integrating its current reliability and historical reputation

, 1,2, ,L L Li i iTru Rel Rep i n= ⋅ = (19)

C. Combination of Admissible Evidence

Basically, admissible evidence refers to the evidence that is relevant, acceptable, and creditable to be introduced to the court [12]. In this paper, we use this term to deliver the idea that evidences collected from different SUs should be well processed before brought into the combination or decision-making.

For each iSU , if 0LiTru ≤ , then it is discarded from the

combination step at thL sensing slot; otherwise, the admissible evidences of iSU are obtained by adjusting its BPAs with the corresponding trustworthiness degree

0 0( ) ( )L L Li i im H Tru m H∗ = ⋅ (20)

1 1( ) ( )L L Li i im H Tru m H∗ = ⋅ (21)

and

0 1( ) 1 ( ) ( )L L Li i im m H m H∗ ∗ ∗Ω = − − (22)

Then all of the admissible evidences are combined according to the combination rule of Dempster-Shafer theory

( ) ( )( )

( )0 1

0 1 2 0

11

i

i

pLi i

A H iL L L Lp p

Li i

A i

m Am H m m m H

m A

∗

= =∗ ∗ ∗

∗

=∅ =

= ⊕ ⊕ ⊕ =−

∑ ∏

∑ ∏∩

∩

(23)

( ) ( )( )

( )1 1

1 1 2 1

11

i

i

pLi i

A H iL L L Lp p

Li i

A i

m Am H m m m H

m A

∗

= =∗ ∗ ∗

∗

=∅ =

= ⊕ ⊕ ⊕ =−

∑ ∏

∑ ∏∩

∩

(24) where ( )iA ∈ℜ Ω , and p is the number of SUs whose evidences are qualified to participate in the combination. At last, the combined evidences ( )0

Lm H and ( )1Lm H are used

to make the final decision according to the following decision rule

( )( )( )( )

10

00

11

0

0,

1,

L

LL

L

L

m HDecide H if

m Hu

m HDecide H if

m H

λ

λ

⎧≤⎪

⎪= ⎨⎪ >⎪⎩

(25)

where λ is the decision threshold chosen by FC to meet different performance requirements. After the final decision

is made, the historical reputation can be updated according to (17) for the detection of next sensing slot.

IV. SIMULATION RESULTS

In this section, simulation results are presented to compare the performances of proposed trustworthy CSS scheme with several existing schemes, as shown in Fig. 3 and Fig. 4. Specifically, the curve of “LRT” represents the LRT-based optimal fusion rule in [13], “SIG” represents the single SU spectrum sensing, “RSE D-S” represents the enhanced scheme with reliability source evaluation in [8], “SIM D-S” represents the enhanced scheme with similarity degree calculation in [9], and the proposed scheme is denoted as “TRU D-S”.

The probabilities of presence and absence of PU are both 0.5. The time-bandwidth product is 10TW = . The number of SU is 6n = . Initial reputation value is set to be 5Δ = .

Among six SUs, one is malicious and initiates SSDF attack. To be specific, AB attack is conducted by measuring

iEx at first, and then using an increased energy 1iEx η⋅ to derive BPAs if

iEx δ< . AF attack uses a decreased energy 2iEx η to derive BPAs if

iEx δ≥ , and AO attack essentially uses a falsified energy ( 1iEx η⋅ if

iEx δ< , or 2iEx η if

iEx δ≥ ) to derive BPAs all the time. In the simulation results presented in this paper, 0 1( + ) 2i iδ μ μ= , and 1 2 2η η= = .

In Fig. 3, all SUs are assumed to have the same average SNR 3dBγ = − . From Fig. 3(a) and Fig. 3(b), we can see that both RSE D-S scheme and proposed TRU D-S scheme can achieve a desirable performance under AB and AF attack. Meanwhile, LRT scheme is vulnerable to AB attack as there is no security mechanism. Since RSE D-S and LRT scheme require the SNR of each SU as prior knowledge in the detection, our proposed scheme is more feasible in practice. Besides, SIM D-S scheme outperforms single SU spectrum sensing but is worse than other schemes. The reason is that honest SUs may also have poor performance sometime, so the similarity degree is not always accurate to reflect reliability. In Fig. 3(c), it is seen that the performance of RSE D-S, LRT, and SIM D-S scheme degrade severely under AO attack, while the proposed scheme remains relatively robust. The performance gain is achieved due to the consideration of both current reliability and historical reputation, as discussed in Section III.B.

In Fig. 4, to evaluate the effectiveness of our proposed scheme in a more practical scenario, we consider the average SNR of six SUs are -7dB, -6dB, -5dB, -4dB, -3dB, -2dB, respectively. Without loss of generality, performance of the worst case where the sixth SU (with the highest average SNR 6 2dBγ = − ) is malicious is shown in this paper. SIG shows the sensing performance of the second SU (i.e., the one with SNR 2 6dBγ = − ) as reference. Comparing Fig. 4 with Fig. 3, we can see that the overall performance of each scheme would degrade if the channel conditions get worse. Besides, Fig. 4(a) substantiates that the proposed TRU D-S scheme is more robust than other schemes under AB attack. Fig. 4(b) shows that under AF attack pattern, SIM D-S scheme suffers heavy performance degradation,

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Qf

Qd

SIGLRTRSE D-SSIM D-STRU D-S (proposed)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Qf

Qd

SIGLRTRSE D-SSIM D-STRU D-S (proposed)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Qf

Qd

SIGLRTRSE D-SSIM D-STRU D-S (proposed)

(a) AB attack pattern (b) AF attack pattern (c) AO attack pattern

Figure 3. Performance comparison under different attack patterns when the same average SNR is -3dB.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Qf

Qd

SIGLRTRSE D-SSIM D-STRU D-S (proposed)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Qf

Qd

SIGLRTRSE D-SSIM D-STRU D-S (proposed)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Qf

Qd

SIGLRTRSE D-SSIM D-STRU D-S (proposed)

(a) AB attack pattern (b) AF attack pattern (c) AO attack pattern

Figure 4. Performance comparison under different attack patterns when six SUs’ average SNR are -7dB, -6dB, -5dB, -4dB, -3dB, -2dB, respectively.

while LRT, RSE D-S, and TRU D-S schemes still work quite well. However, as illustrated in Fig. 4(c), such schemes as LRT, SIM D-S, especially RSE D-S are almost disabled under AO attack. The proposed TRU D-S scheme outperforms other schemes significantly. By taking current reliability and historical reputation of each SU into account, and exploiting the potential of Dempster-Shafer theory to represent uncertainty, the proposed scheme differentiates SUs more effectively, treats their evidences more properly, and thus achieves a better performance.

V. CONCLUSION

In this paper, we have proposed a trustworthy CSS scheme based on Dempster-Shafer theory in CRNs. It is carried out in three successive steps, which are basic probability assignment, trustworthiness degree calculation, and combination of admissible evidence. When evaluating the trustworthiness degree of each SU, we not only utilize the current information to estimate its reliability, but also take its previous reports into consideration. Besides, this trustworthy CSS scheme takes advantage of Dempster-Shafer theory’s ability to reflect uncertainty in the evaluation as well. Simulation results have shown that the proposed scheme is effective to counter with attacks.

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