2011 Third International Conference on Computational Intelligence, Communication Systems and Networks
Detection of SSDF Attack using SVDD Algorithm in Cognitive Radio Networks
F. Farmani
M. Abbasi Jannat-Abad
R. Berangi
Electrical Engineering Department Iran University of Science and Industry Tehran, Iran
[email protected]
Electrical Engineering Department Ferdowsi University of Mashhad Mashhad, Iran
[email protected]
Computer Engineering Department Iran University of Science and Industry Tehran, Iran
[email protected]
counter SSDF attacks in cognitive radio mobile ad hoc networks (CR-MANETs) based on particle swarm optimization (PSO). In [8], the authors propose a cooperative spectrum sensing with trusted nodes assistance by introducing a reputation-based mechanism to identify malicious nodes. In this paper, we propose a new robust algorithm to mitigate malicious nodes (“always yes” or “always no”) based on omitting outliers. Sensing data from malicious nodes are outliers. So we can use classification techniques to mitigate SSDF attacks. The one-class classification problem is an interesting field in pattern recognition and machine learning researches. In this kind of classification, we assume the one class of data as the target class and the rest of data are classified as the outlier. One-class classification is particularly significant in applications where only a single class of data objects is applicable and easy to obtain. Objects from the other classes could be too difficult or expensive to be made available. So we would only describe the target class to separate it from the outlier class. The SVDD is a kind of one-class classification method based on Support Vector Machine which proposed by Tax & Duin [8]. It tries to construct a boundary around the target data by enclosing the target data within a minimum hypersphere. Inspired by the support vector machines (SVMs), the SVDD decision boundary is described by a few target objects, known as support vectors (SVs). The paper is organized as follows. In the next section, we review the support vector data description (SVDD). The proposed method is explained in Section 3. In section 4, the simulation results are presented and finally, we conclude the paper.
Abstract—In this paper, a new robust algorithm is proposed for spectrum sensing in cognitive radio networks. The goal of spectrum sensing is to identify holes. Malicious nodes are degraded the performance of spectrum sensing. To mitigate spectrum sensing data falsification attack, we employ support vector data description in sensing procedure. The SVDD algorithm distinguishes malicious nodes from trusted ones and omits them from decision phase. In other words, the proposed algorithm omits outliers from decision phase. It tries to construct the boundary around the target data by enclosing the target data within a minimum hyper-sphere. Inspired by the support vector machine the SVDD decision boundary is described by a few target objects, known as support vectors. Then the algorithm votes between trusted nodes to decide whether the spectrum is empty. The performance of the proposed algorithm is evaluated by computer simulations. Keywords-component; Malicious nodes; Cognitive radio network; Support Vector Data Description; Spectrum Sensing Data Falsification
I.
INTRODUCTION
Cognitive radio (CR) is a promising technology to solve spectrum scarcity. To improve spectrum usage efficiency, primary users (PU) and secondary users (SU) are serviced in CR. Although the bandwidth originally licensed to the PU, when the PU does not occupy the bandwidth, it can be allocated to the SUs. One of the most important tasks in CR is spectrum sensing in which So SUs sense the frequency band to detect spectrum holes. There are many methods for spectrum sensing such as energy detection, matched filter detection [1], cyclostationary feature detection [2, 3], wavelet detection [4] and covariance detection [5]. Due to presence of malicious nodes, some sensing data may be false. For example, “always yes” malicious node reports presence of PU, when the PU is absent. This behavior leads to increase false alarm probability (Pf). Also “always no” malicious node report absence of PU, when the PU is present that decrease detection probability. In recent years, different sensing algorithms have been proposed to mitigate this challenge. In [6], a secure cooperative spectrum sensing algorithm is proposed to mitigate spectrum sensing data falsification (SSDF). The proposed algorithm identifies the malicious users based on outlier detection techniques employing energy detection at the SUs. In [7], a consensusbased cooperative spectrum sensing scheme is presented to 978-0-7695-4482-3/11 $26.00 © 2011 IEEE DOI 10.1109/CICSyN.2011.51
II.
SUPPORT VECTOR DATA DESCRIPTION
Let xi , i = 1,..., n be p-dimensional training samples belonging to one class. We consider approximating the class region by the minimum hyper-sphere with center
e = ( e1 , e2 ,..., e p ) and radius R in high dimensional feature T
space (HDS), excluding the outliers. Then the problem is
201
and from (7) if α i > 0 , we have
n
min R 2 + C ∑ ξi R , e ,ξ
n
i =1
R 2 + ξi = K ( xi , xi ) − 2∑α j K ( xi , x j )
(1)
⎧⎪ g ( x ) − e ≤ R 2 + ξ , i = 1,..., n i i s.t. ⎨ ⎪⎩ξi ≥ 0 , i = 1,..., n where g ( x ) is the mapping function that maps x into a high 2
j =1
n
+ ∑∑α jα k K ( x j , xk ) j =1 k =1
From (6) if α i < C , γ i > 0 . So, from (8) we have ξi = 0 . So, if 0 < α i < C ,
dimension space (HDS), ξ = (ζ 1 ,..., ζ n ) and ζ i is the slack variable of i-th training sample and C is a constant which determines the trade-off between the hyper-sphere volume and outliers. The Lagrangian dual form of (1) is as follows max L ( R, e, ξ , α , γ ) s.t. α i , γ i ≥ 0 , i = 1,..., n (2) T
n
j =1
T
(
)
⎞ −∑α i − g ( xi ) g ( xi ) + 2e g ( xi ) − e e ⎟ i =1 ⎠ n
(
T
T
T
)
i∈SV
(3)
(5)
∂L = 0 → α i = C − γ i , i = 1,…, n ∂ξ
(6)
γ iξi = 0, i = 1,…, n
Using the transformed to
above
conditions,
n
n
i =1 j =1
(8) is (9)
where K ( xi , x j ) = g ( xi )T g ( x j ) . From (2) and (6) we have 0 ≤ α i ≤ C . So, the Lagrangian dual form of the program (1) can be restated as follows n
n
α
i =1
j
i =1 j =1
(10)
⎧n ⎪∑α i = 1; s.t. ⎨ i =1 ⎪0 ≤ α ≤ Cm , i = 1, …, n; i i ⎩ which is a conventional quadratic program and can be solved easily. From (5), we have n
g ( xi ) − e 2 = K ( xi , xi ) − 2∑α j K ( xi , x j )
(11)
j =1
n
i
j
2
(14)
THE PROPOSED METHOD
n
max max ∑α i K ( xi , xi ) − ∑∑α iα j K ( xi , x j ) α
i
A CR network with one primary user (PU) and K secondary users (SU) is shown in Fig. 1 where SUs sense the spectrum using energy detection method and sensing results are sended to fusion center (FC) without quantization. During these K SUs, M malicious nodes are presented. Malicious nodes can be “always yes” which always sends high energy to FC or “always no” which always report low energy to FC. “Always yes” nodes increase false alarm probability, because they always report presence of PU, even when PU is absent. Furthermore, because “always no” nodes report absence of PU, they decrease detection probability of PU. The channels between PU and SUs and also between SUs and FC are assumed flat fading channels. FC collects sensing data from all SUs and identifies malicious nodes based on SVDD method. After malicious nodes detection, FC delet them from decision phase. In the decision phase, FC votes between trusted sensing results. If voting result is above a predefined threshold λ , PU is present, else PU is absent. Base station (BS) is equipped by antenna arrays with N elements. PU and i-th SU have single antennas.
n
L ( R, e, ξ , α , γ ) = ∑α i K ( xi , xi ) − ∑∑α iα j K ( xi , x j ) i =1
III.
(7) L ( R, e, ξ , α , γ )
∑ ∑α α K ( x , x ) ≤ R
i∈SV j∈SV
where SV is the set of indices of training samples whose αi ≠ 0 .
For the optimal solution, the following conditions are satisfied n ∂L = 0 → ∑α i = 1 (4) ∂R i =1
α i ( g ( x i ) − e 2 − R 2 − ξi ) = 0 , i = 1, …, n
j =1 k =1
K ( x, x ) − 2 ∑α i K ( x, xi ) +
n ∂L = 0 → e = ∑α i g ( xi ) ∂e i =1
n
Finally, the unknown datum x is inside the hyper-sphere if g ( x ) − e 2 ≤ R 2 or equivalently if
where α = (α1 ,..., α n ) , γ = ( γ 1 ,..., γ n ) and n n n ⎛ L ( R, e, ξ ,α , γ ) = inf ⎜ R 2 + C ∑ξi − ∑γ iξi − ∑α i R 2 + ξi i =1 i =1 i =1 ⎝
n
R 2 = K ( xi , xi ) − 2∑α j K ( xi , x j ) + ∑∑α jα k K ( x j , xk ) (13)
δ ,γ
T
(12)
n
n
+ ∑∑α jα k K ( x j , xk )
Figure 1. system model.
j =1 k =1
202
Let en [ k ] be measured energy by n-th SU in the k-th sensing interval, H1 and H 0 be the presence and absent hypothesis, respectively. Then we have
20 18 16
⎧ 2 ⎪ ∫ hn ( t ) s ( t ) + zn ( t ) dt ; H1 ⎪ Tk (15) en [ k ] = ⎨T +T −1 k 2 ⎪ ; H0 ⎪ ∫ zn ( t ) dt ⎩ Tk where T is sensing duration, s ( t ) is PU’s transmitted signal, hn ( t ) is the channel between PU and n-th SU and zn ( t ) is the additive white guassian noise of this channel. Each SU sends its sensing result to FC without quantization. Then FC delete malicious users using SVDD approach which is discussed in section II i.e. the goal of the FC is to find the smallest sphere that encloses all the sensing results. So, after applying the SVDD method in FC, outliers will be omitted.
14
IV.
reputation rate
Tk + T −1
12 10 8 6 4 reputation rate threshold
2 0
0
2
4
6
8 10 12 number of SUs
14
16
18
20
Figure 3. SUs’ reputation rates in the presence of PU and “always no” malicious nodes, N = 20 , M = 4 .
Figure 4 and Fig. 5 show the SUs’ reputation rates in the H 0 scenario for both “always yes” and “always no” malicious users, respectively. Similar to Fig. 3 and Fig. 4, users 17 to 20 are malicious and reputation rates that assigned to these malicious nodes are low. To evaluate the performance of the proposed method based on SVDD algorithm, detection probability of PU is plotted in Fig. 6 versus number of malicious nodes. In this simulation, “always no” malicious nodes are considered. Furthermore the H1 hypothesis is assumed. As it can be seen, as the number of malicious increases, detection probability decreases, but the performance of FC is robust due to increasing the number of malicious users. For example, if the minimum detection probability is set to 0.9, by increasing malicious nodes up to 40 percent, the proposed algorithm has a good performance. Figure 7 shows false alarm probability based on different number of malicious nodes. In this simulation, “always yes” malicious nodes are considered and the H 0 scenario is assumed. As it’s seen, the false alarm probability increases as the number of malicious nodes increases.
COMPUTER SIMULATION RESULTS
In this section, simulation results are presented to evaluate the performance of the proposed algorithm. In the simulations, we use flat Raleigh fading channels for PU and SUs such that the elements of the channel matrices are independent and have normal zero mean Gaussian distributions. The modulation is QPSK and results are obtained for 1000 realizations of channels. Meanwhile, the number of SUs is K = 20 . The SUs’ reputation rates are shown in Fig. 2 and Fig. 3 in the presence of “always yes” and “always no” malicious users, respectively. Reputation rates are computed based on SVDD algorithm. Also, these simulations are done under H1 hypothesis. In the simulations, users 17 to 20 are malicious. As it’s seen, reputation rates that assigned to these malicious nodes are low. So, FC can distinguish malicious nodes by comparing the reputation rate of each SU with a predefined threshold. If the reputation rate is below a threshold, that SU is a malicious one, otherwise it is a trusted node.
20 20
18
18
16
16 reputation rate
14
reputation rate
14 12 10 8
10 8 6
6
4
4
2 reputation rate threshold
2 0
12
0
2
4
6
0 8 10 12 number of SUs
14
16
18
20
0
2
4
6
8 10 12 number of SUs
14
16
18
Figure 4. SUs’ reputation rates in the absence of PU with “always yes” malicious nodes, N = 20 , M = 4 .
Figure 2. SUs’ reputation rates in the presence of PU and “always yes” malicious nodes, N = 20 , M = 4 .
203
20
V.
20
In this paper, a new robust algorithm is proposed for spectrum sensing in cognitive radio networks to mitigate spectrum sensing data falsification (SSDF) attack. We employ support vector data description (SVDD) in sensing procedure. The SVDD algorithm distinguishes malicious nodes from trusted ones and omits them form decision phase. Then the algorithm votes between trusted nodes to decide whether the spectrum is empty. Simulation results show that the performance of the proposed algorithm is good.
18 16 14 reputation rate
CONCLUSION
12 10 8 6 4 2 0
0
2
4
6
8 10 12 number of SUs
14
16
18
REFERENCES
20
Figure 5. SUs’ reputation rates in the absence of PU with “always no” malicious nodes, N = 20 , M = 4 .
[1]
[2]
1 0.9 probability of detection ( Pd )
0.8
[3]
0.7 0.6
[4]
0.5
[5]
0.4 0.3 0.2
[6]
0.1 0
1
2
3
4 5 6 7 number of malicious nodes
8
9
10
[7]
Figure 6. Detection probability of PU in the presence of PU with “always no” malicious nodes versus different number of malicious nodes, N = 20 .
[8]
1
probability of false alarm ( Pf )
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
1
2
3
4 5 6 7 number of malicious nodes
8
9
10
Figure 7. False alarm probability in the presence of PU with “always yes” malicious nodes versus different number of malicious nodes, N = 20 .
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