Reliable Cooperative Spectrum Sensing Algorithm ... - Semantic Scholar
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
Reliable Cooperative Spectrum Sensing Algorithm Based on Dempster-Shafer Theory Jing Li
Jian Liu
Keping Long
School of Communication and Information Engineering, University of Electronic Science and Technology of China (UESTC) Chengdu 611731, China Email: jingli [email protected], {liuj,lkp}@uestc.edu.cn
Abstract—Cooperative spectrum sensing for cognitive radio is recently being studied to minimize uncertainty in primary user detection. In order to improve the detection probability under a sustainable false alarm probability, a reliable scheme for cooperative spectrum sensing based on double threshold energy detection and Dempster-Shafer (D-S) theory is proposed in this paper. In the algorithm, the double threshold method is used to calculate the local spectrum sensing requirements, which is more accurate than using a single threshold. The D-S theory, which is similar to human reasoning, is adopted to combine different sensing decisions from each cognitive user. A final decision is then made in the fusion center, which decides whether the primary user is present or not. To reduce the redundant nodes, we propose the use of node selection. The analytical results match very well with the simulation results. Simulation results show that the reliability of decision is improved due to the accurate calculation of the local sensing information.
I. I NTRODUCTION With the growth of communication applications, the spectrum becomes more and more congested. Traditionally, a large amount of spectrum bands have already been assigned to different users. These licensed users, often referred to as primary users (PU), have the exclusive right to use these bands. However, it has been proved that some frequency bands in the spectrum are often unoccupied, other frequency bands are only partially occupied, and the remaining frequency bands are heavily used. Thus, the inflexible spectrum allocation policy may cause a inefficient use of spectrum resource [1][2]. Different from the traditional spectrum allocation policy, cognitive radio (CR) [3] allows the unauthorized user, called as secondary user (SU), to use the licensed bands when such bands are not occupied by PUs. However, in order not to interfere with the PU’s communication, SUs should continue to monitor the surrounding environment. Generally, for single user, spectrum sensing techniques fall into three categories: energy detection, matched filter detection, and cyclostationary feature detection [4]. If the SU has limited information on the primary signals, then energy detector is optimal. In the method of energy detection, we This work is supported by Chang Jiang Scholars Program of the Ministry of Education of China, National Science Fund for Distinguished Young Scholars (No. 60725104), 973 Program (No. 2007CB310706), National Natural Science Foundation of China (No. 60873263, 60932002, 60932005), 863 Program (No. 2008AA011001, 2008AA011002, 2009AA01Z254, 2009AA01Z215), NCET Program of MoE of China, and the Fundamental Research Funds for the Central Universities (No. ZYGX2009J005).
usually just set one single threshold. In practice, we do not use single user detection, since it is difficult to distinguish between an idle band and a deep fading one for single node, and the final decision is inaccurate. In order to improve the reliability of spectrum sensing, radio cooperation exploiting spatial diversity among secondary users has been proposed. Cooperative spectrum sensing algorithms, such as “and rule”, “or rule”, and “optimal fusion rule”, etc, have been reported. However, an attacker or malicious user can send false local spectrum sensing results to a data fusion center, which will cause data fusion center to make wrong spectrum sensing decisions. The above algorithms are too simple to make a decision and result in poor performance. We employ the DempsterShafer (D-S) theory, which is similar to human reasoning. Based on this algorithm, there is a novel cooperative spectrum sensing algorithm in [5], which calculates the probability function based on the correlation coefficients. However, under the practice condition of distributed cooperative spectrum sensing in CR context, there may be conflicting data, which are not considered. The authors in [6] propose a distributed spectrum sensing scheme, but they do not take into account the distance from the transmission path or different transmission channel conditions. In view of this, Nhan proposes an enhanced scheme for cooperative spectrum sensing based on an enhanced D-S theory in [7], which is adjusted using the relative relationship between nodes for more accuracy. He also utilizes the credible factor to measure the credibility of the sensing results. However, the evaluation stage of each node using a counting rule requires that the fusion center to keep track of the past performance, which increases the burden on the fusion center. Besides, all above articles have a common drawback that is based on single threshold energy detection, which does not deal with uncertain information. Hence, the accuracy is poor. In [8], a double threshold method in energy detector is used to perform spectrum sensing. The accuracy of the local spectrum sensing is higher, but the fusion center makes a decision using hard decision, which is unsuitable for a dynamic CR environment. Compared with the other articles which adopt double threshold energy detection, we first use it to calculate the basic probability assignment, which improves the accuracy of local sensing. As we know, the D-S theory is similar to the natural decision making logic of humans. This capability of assigning uncertainty is effective in dealing with a large range of
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
SU2
SU2
m2(H0),m2(H1),m2(ȍ)
m3(H0),m3(H1),m3(ȍ)
D-S rule of Combination
Our cooperative spectrum sensing system is shown in Fig. 1. SUs continuously sense the surroundings and generate local sensing results using double threshold energy detection scheme. The local sensing information will then be transported to base station (BS), which is a data fusion center. The BS will have a final decision with D-S theory.
Data Fusion Center
m1(H0),m1(H1),m1(ȍ)
Double Threshold
II. S YSTEM D ESCRIPTION
SU1
Ă
problems that would otherwise become intractable, especially in a fast changing CR environment. At the fusion center, the theory of evidence is adopted to combine different sensing decisions from each SU. In addition, we also use a simple counting method to select nodes. The rest of the paper is organized as follows, in Section II, we describe the system model and D-S theory of evidence; In section III, a novel cooperative spectrum sensing algorithm is given, and we introduce the concept of nodes selection; In Section IV, simulation results about “and” rule, “or” rule, “single user” rule and double threshold energy detection based on D-S theory are shown. Finally, we conclude this paper in section V.
m(H0) m(H1)
mN(H0),mN(H1),mN(ȍ)
SUN
Fig. 2.
m(H1) >m(H0)
Y
N
H0
Spectrum sensing algorithm based on D-S Theory
where i is the index of SU, K is the total number of the SUs. yi (t) represents received data at SU, si (t) is the primary signal, the fading coefficient hi and the additive white Gaussian noise ni (t) are modeled as independent complex Gaussian random variables. The energy received by a single cognitive user is xEi = 2ν |yi (t)|2 which can be approximated as Gaussian distribut=1
tion that H0 : xEi ∼ N (2ν2i , 4ν4i ), H1 : xEi ∼ N (2ν2i + |hi |2 Es , 4ν4i + 2|hi |2 Es 2i ),
(2)
where ν represents time bandwidth, ν = T W . Es is the signal energy of the primary user, and 2i is the zero-mean additive variance of the white Gaussian noise.
SU SU PU BS
surrounding
H1
III. N OVEL COOPERATIVE SPECTRUM SENSING ALGORITHM
SU SU
SU
BS:Base Station PU:Primary User SU:Secondary User
Fig. 1.
The cooperative spectrum sensing algorithm comprises two steps: local sensing and BS fusion. A. Local Sensing
The system of cooperative spectrum sensing
The D-S theory, also known as the theory of belief functions, was first introduced by Dempster in 1960’s, and was later extended by Shafer. The theory is based on two ideas: the idea of obtaining degrees of belief for one question from subjective probabilities for a related question, and Dempster’s rule for combining such degrees of belief when they are based on independent items of evidence. In this way, we develop the spectrum sensing algorithm as shown in Fig. 2. At every node, we use the double threshold to calculate the result of local sensing. At the data fusion center, we may obtain a convergent result with D-S theory and arrive at a final decision by comparing them. The detection problem for local sensing at SUs can be stated in terms of a binary hypothesis test, with the null hypothesis H0 corresponding to PU signal being absent, and the alternative hypothesis H1 corresponding to PU signal being present, as H0 : yi (t) = ni (t), H1 : yi (t) = hi · si (t) + ni (t), i = 1, 2, . . . , K, (1)
Among various methods for spectrum sensing, energy detection offers a simple and quick method to detect primary signal even if the full feature set is unknown. Here, we consider the energy detection for local spectrum sensing. Since it does not need any a priori knowledge of the primary signal, the energy detector is robust to the variation of the primary signal. Moreover, the energy detector does not involve complicated signal processing, and has low complexity. In conventional energy detections, every SU makes their local decisions by comparing their energy with a threshold, as illustrated in Fig. 3. The authors in [8] proposes a scheme that uses two thresholds to detect whether the signal is present, where Ti denotes the collected energy value of the ith SU, as Fig. 4. Decision H0 or H1 will be made when Ti is less or greater than the threshold value. In this model, two thresholds η0 and η1 are used to help the decision of the SU. If energy value exceeds η1 then this user reports H1 , and if it is less than η0 , decision H0 will be made. Otherwise, if it is between the two thresholds, we report its energy value, and send to the fusion center to decide. In this paper, the uncertainty between two thresholds is used to calculate the trust functions, which will certainly improve the accuracy of detection.
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
H0
H1
mi (H1 ) = P {T > η1 |H1 } + P {η0 < T < η1 |H1 } ∞ 1 2 √ = exp[−(x − μ1,i )2 /σ1,i ]dx 2πσ1,i
Ș Fig. 3.
η1
η1
Energy detection with one threshold
√
+ H0
H1
η0
1 2 exp[−(x − μ1,i )2 /σ1,i ]dx, 2πσ1,i (11)
Ș0 Fig. 4.
Ș1
where μ0i , μ1i , σ0i and σ1i represent the mean and variance of xEi .
Energy detection with double threshold
B. Base Station Fusion Generally, in the non-fading environment, we assume hi is deterministic, the probabilities of detection, false alarm and missing detection are as computed as follows √ (3) Pd,i = P {Ti > η1 |H1 } = Qν ( 2γ, η1 ), Pf,i = P {Ti > η1 |H0 } = Pm,i
Γ(ν, η1 /2) , Γ(ν)
(4)
= P {Ti ≤ η0 |H1 } = 1 − P {η0 < Ti < η1 |H1 } − Pd,i ,
(5)
where Pd,i , Pf,i and Pm,i are the detection probability, false alarm probability, and missing detection probability of the ith SU respectively, γ is the SNR, η0 and η1 are two thresholds. Γ(a) and Γ(a, b) are complete and incomplete gamma functions respectively and Qν (a, b) is the generalized Marcum function. From the above formula, we have Pf,i · Γ(ν) = Γ(ν, η1 /2),
0
gamma function. Then we can obtain
η1 = 2P −1 (ν, 1 − Pf,i ),
(8)
η0 = 2/3 · η1 ,
(9)
According to the D-S theory, we know that mi (H0 ), mi (H1 ), mi (Ω) are used to indicate the basic probability assignment for the signal. The following probability functions are derived. mi (H0 ) = P {T < η0 |H0 } + P {η0 < T < η1 |H0 } η0 1 2 √ = exp[−(x − μ0,i )2 /σ0,i ]dx 2πσ0,i + η0
A⊂Ω
In D-S theory, two functions named belief (bel) and plausibility (pl) are defined to characterize the uncertainty and the support of certain hypotheses. m(B), (14) bel(A) = B⊆A
(6)
Γ(ν, η1 /2) = Γ(ν) − Γ(ν) · P (ν, η1 /2), (7) z ν−1 −t 1 t · e dt is lower order incomplete where P (ν, z) = Γ(ν)
−∞ η1
As we know, D-S theory has been applied to many areas, such as troubleshooting, diagnostic test and multi-data fusion [9]. As a theory to manage uncertainty, D-S evidence theory is a good choice for decision making in CR system. Let Ω denote a finite set of mutually exclusive and exhaustive hypotheses, called the frame of discernment. The basic probability assignment (BPA) is a function m from 2Ω to [0, 1], defined as: m(φ) = 0, (12) m(A) = 1. (13)
pl(A) =
(15)
where bel measures the minimum or necessary support for that hypothesis, and pl reflects the maximum or potential support. Two BPA’s m1 and m2 on Ω, induced by two independent items of evidence, can be combined by the so called D-S rule of combination to yield a new BPA m = m1 ⊕ m2 , the orthogonal sum of m1 and m2 , defined as m(A)
= m1 (A1 ) ⊕ m2 (A2 ) m1 (A1 )m2 (A2 ) A1 ∩A2 =A . = m1 (A1 )m2 (A2 )
(16)
A1 ∩A2 =A
At the data fusion center, decisions associated with credibility from distributed SUi are combined using Equation (16) according to D-S theory of combination, resulting in final credibility of CR system for each hypothesis in the form of BPA, namely m(H0 ) and m(H1 ), as
1 2 √ exp[−(x − μ0,i )2 /σ0,i ]dx, 2πσ0,i
m(B),
A∩B=φ
m(H0 ) = (10)
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
K
A1 ∩A2 ∩...AK =H0 i=1
1−
mi (Ai )
K
A1 ∩A2 ∩...AK =Θ i=1
, mi (Ai )
(17)
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
K
A1 ∩A2 ∩...AK =H1 i=1
m(H1 ) =
1−
SU1
mi (Ai )
K
A1 ∩A2 ∩...AK =Θ i=1
.
(18) SU2
mi (Ai )
H0 H1
: m(H0 ) > m(H1 ) : m(H1 ) ≥ m(H0 ).
(19)
C. Node Selection Although cooperative spectrum sensing can greatly improve sensing performance, many nodes in the network are redundant. With the increasing nodes, more and more system resources are consumed, and the transmission efficiency of the system will decrease continuously. Hence, we choose to remove the redundancy of the SUs. Different from the other cluster-based sensing algorithm, the information of the SU to the fusion center has an arrangement of both large and small, as Mi = αmi (H1 ) + βmi (H0 ),
(20)
that is the accuracy function of every SU to determine whether the signal is present, where α represents the probability that the node has correctly sensed that the primary use is present, and β is the probability that the node has correctly sensed the primary use is absent. The authors in [10] proposes a simple counting rule that is used to calculate α and β. For the ith sensing node, at the tth moment, we use ωi (t) to expresses the state of current decision, where ωi (t) ∈ {ω1 , ω2 , ω3 , ω4 }, ω1 , ω2 , ω3 and ω4 are as follow ω1 ω2 ω3 ω4
: εi = 1 and : εi = 1 and : εi = −1 and : εi = −1 and
ε0 = 1 ε0 = −1 ε0 = −1 ε0 = 1,
where ε0 is the center decision, and εi is the node decision. We use n1 , n2 , n3 and n4 to represent the time that ω1 , ω2 , ω3 and ω4 have occurred respectively. Hence, α and β can be obtained as n1 α= , (21) n1 + n2 β=
n3 . n3 + n4
(22)
Fig. 5 gives the diagram of node selection. The steps are as follow. Step1: SUs calculate mi (H0 ) and mi (H1 ), get Mi using Equation (20), and then send the local results to the fusion center. Step2: The fusion center has a queue about Mi , which is listed in descending order. It chooses the larger ones to fuse with D-S theory and decides whether the signal is present.
SU3
ing Stopp ge a s s e m
all SUs
The fusion center
Node selection message
selected SUs
Selecting nodes
F dec inal isio n
M2 M3 ĂĂ
By comparing m(H0 ) and m(H1 ), the final decision is made upon a following simple strategy
Ordering
M1
SUN
MN
H0/H1
Deciding
Fig. 5.
The diagram of selecting node
Step3: If the same decision is repeated three times, the fusion center stops fusing data, and sends a end message to each node. At the same time, it sends node selection message to SUs whose Mi ’s are used. These selected nodes are part of a node cluster that is the smallest group to sense PU. IV. P ERFORMANCE EVALUATION AND SIMULATION RESULTS
In this section, we evaluate the performance of the algorithm developed in the previous sections. We first solve the Equations (8) and (9), and then calculate the values of m(H0 ), m(H1 ) using Equations (17) and (18), compare these values to make a final decision using Equation (19). Based on the results computed from this algorithm, we then output the node selection. Within the node selection, the fusion center performs the ordering function defined in Equation (20), and then decides which nodes are selected. This accuracy of final decision is compared with other schemes through simulation. In our simulation, we focus on the channels that do not have shadowing and have equal gain. In addition, we assume that the cognitive region of interest only consists of one licensed user and the fusion center has no spectrum sensing capabilities. The probabilities of whether the licensed user is present are not equal. The number of cognitive users that participates in cooperative spectrum sensing is 10. We also consider the following parameters: the SNR increases from 5dB to 15dB, the false alarm probability pf equals 0.001, and the time bandwidth ν is 5. According to different methods, (i.e., using D-S theory under double threshold, “or”, “and” and “single user”), we can obtain the following two curves, as shown in Fig. 6 and Fig. 7. Fig. 6 shows that the detection probability Qd of double threshold is higher than “or” when the SNR is 5. The probability of detection increases by 0.20, and the pecentage of missing probability reduces more. The performance of other methods is worse. For example, the method of “and” is not as good as single user detection method. As the SNR increasing, the probability of detection tends to 1, especially after 10. On the contrary, the missing detection probability Qm is clearly lower than other methods. Similarly, the missing probability tends to 0 as the increasing of the SNR, which is shown in Fig. 7. In addition, in the calculation of the confidence intervals using Equations (11) and (12), we take the uncertainty into account. They provide evidence that cooperative sensing is
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
1 0.9
double threshold or and single user
The detection probability Qd
0.8 0.7
1 K=10 K=15 K=20
0.98 0.96 The detection probability Qd
more “accurate” than single node and double threshold, and that the D-S theory of evidence is appropriate for our proposed parameter “credible”. In addition, with the same SNR, the performance of the method of double threshold improves greatly.
0.94 0.92 0.9 0.88 0.86
0.6
0.84
0.5
0.82
5
0.4 0.3
Fig. 8.
10 SNR/dB
15
Qd in the method of double threshold with different SUs’ numbers
0.2
V. C ONCLUSIONS
0.1 0
5
10 SNR/dB
Fig. 6.
15
Qd in different spectrum sensing methods
1 0.9
The missing probability Qm
0.8 double threshold or and single user
0.7 0.6 0.5 0.4
In this paper, we propose a new cooperative sensing algorithm to improve the utilization efficiency of the radio spectrum. Through simulation results, we observe that the algorithm based on double threshold energy detection and D-S theory increases the reliability of detection quite dramatically. We may remove redundant users, thereby reducing network overhead, improving system transmission efficiency, and optimizing the network resources, using node selection. We did not consider the case that different SUs contribute differently to the fusion center. In our future work, we will enhance the algorithm by defining a different probability function mi (H0 ) and mi (H1 ), which is used to measure the credibility of each node.
0.3
R EFERENCES
0.2 0.1 0
5
10 SNR/dB
Fig. 7.
15
Qm in different spectrum sensing methods
Using different numbers of SU, the detection probabilities are different in the method of double threshold, as shown in Fig. 8. However, when the number of users reaches a certain level, the improvement in detection performance saturates. For example, when K=15, Qd is more than 0.97. Such a high probability meets our requirement. Suppose the overhead of one node is 1, then 20 is the overhead of 20 nodes. In fact, 10 nodes can achieve the same performance with 20 nodes, while reducing by half of the cost. Therefore, we must choose the appropriate number of SU to avoid the waste caused by detection time. Hence, node selection plays a very important role in cognitive radio. Clearly, the proposed algorithm has a relatively high reliability in the case that the SNR is low. It is better than the other methods without D-S theory. We can reduce the number of nodes to bring down the network overload by node selection.
[1] M. McHenry, “Frequency agile spectrum access technologies,” in FCC Workshop on Cognitive Radio, May. 2003. [2] G. Staple and K. Werbach, “The end of spectrum scarcity,” IEEE Spectrum archive., vol. 41, no. 3, pp. 48-52, Mar. 2004. [3] J. Mitola III and G. Q. Maguire, “Cognitive radio: Making software radios more personal,” IEEE Pers. Commun., vol. 6, no. 4, pp. 13-18, Aug. 1999. [4] D. Cabric, S. M. Mishra, and R. W. Brodersen, “Implementation issues in spectrum sensing for cognitive radios,” in Proc. Asilomar Conf. on Signals, Sys., and Comput., vol. 1, pp. 772-776, Nov. 2004. [5] X. Zheng, J. Wang, Q. Wu and J. Chen, “Cooperative spectrum sensing algorithm based on Dempster-Shafer theory,” in Proc. of IEEE Journal of PLA Univ. of Science and Technol., pp. 218-221, 2008. [6] Q. Peng, K. Zeng, J. Wang and S. Li, “Distributed spectrum sensing scheme based on credibility and evidence theory in cognitive radio context,” in Proc. of IEEE 17 th Int. Symp. on Personal, Indoor and Mobile Radio Commun., pp. 1-5, Sept. 2006. [7] N. Nhan, X. T. Kieu and I. Koo, “Cooperative spectrum sensing using enhanced Dempster-Shafer theory of evidence in cognitive radio,” IEEE Commun. Lett., vol. 13, pp. 492-494, 2009. [8] J. Zhu, Z. Xu, F. Wang, B. Huang and B. Zhang, “Double threshold energy detection of cooperative spectrum sensing in cognitive radio,” in Proc. of Int. Conf. on Cognitive Radio Oriented Wireless Networks Commun. (CrownCom), pp. 1-5, 2008. [9] G. Shafer, A mathematical theory of evidence, Princeton, NJ: Princeton Univ. Press, 1976. [10] N. Mansouri and M. Fathi, “Simple Counting Rule for Optimal Data Fusion,” in Proc. of IEEE Conf. on Control Appl. (ICCA2003), vol. 2, pp. 1186-1191, 2003.
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
Reliable Cooperative Spectrum Sensing Algorithm Based on Dempster-Shafer Theory Jing Li
Jian Liu
Keping Long
School of Communication and Information Engineering, University of Electronic Science and Technology of China (UESTC) Chengdu 611731, China Email: jingli [email protected], {liuj,lkp}@uestc.edu.cn
Abstract—Cooperative spectrum sensing for cognitive radio is recently being studied to minimize uncertainty in primary user detection. In order to improve the detection probability under a sustainable false alarm probability, a reliable scheme for cooperative spectrum sensing based on double threshold energy detection and Dempster-Shafer (D-S) theory is proposed in this paper. In the algorithm, the double threshold method is used to calculate the local spectrum sensing requirements, which is more accurate than using a single threshold. The D-S theory, which is similar to human reasoning, is adopted to combine different sensing decisions from each cognitive user. A final decision is then made in the fusion center, which decides whether the primary user is present or not. To reduce the redundant nodes, we propose the use of node selection. The analytical results match very well with the simulation results. Simulation results show that the reliability of decision is improved due to the accurate calculation of the local sensing information.
I. I NTRODUCTION With the growth of communication applications, the spectrum becomes more and more congested. Traditionally, a large amount of spectrum bands have already been assigned to different users. These licensed users, often referred to as primary users (PU), have the exclusive right to use these bands. However, it has been proved that some frequency bands in the spectrum are often unoccupied, other frequency bands are only partially occupied, and the remaining frequency bands are heavily used. Thus, the inflexible spectrum allocation policy may cause a inefficient use of spectrum resource [1][2]. Different from the traditional spectrum allocation policy, cognitive radio (CR) [3] allows the unauthorized user, called as secondary user (SU), to use the licensed bands when such bands are not occupied by PUs. However, in order not to interfere with the PU’s communication, SUs should continue to monitor the surrounding environment. Generally, for single user, spectrum sensing techniques fall into three categories: energy detection, matched filter detection, and cyclostationary feature detection [4]. If the SU has limited information on the primary signals, then energy detector is optimal. In the method of energy detection, we This work is supported by Chang Jiang Scholars Program of the Ministry of Education of China, National Science Fund for Distinguished Young Scholars (No. 60725104), 973 Program (No. 2007CB310706), National Natural Science Foundation of China (No. 60873263, 60932002, 60932005), 863 Program (No. 2008AA011001, 2008AA011002, 2009AA01Z254, 2009AA01Z215), NCET Program of MoE of China, and the Fundamental Research Funds for the Central Universities (No. ZYGX2009J005).
usually just set one single threshold. In practice, we do not use single user detection, since it is difficult to distinguish between an idle band and a deep fading one for single node, and the final decision is inaccurate. In order to improve the reliability of spectrum sensing, radio cooperation exploiting spatial diversity among secondary users has been proposed. Cooperative spectrum sensing algorithms, such as “and rule”, “or rule”, and “optimal fusion rule”, etc, have been reported. However, an attacker or malicious user can send false local spectrum sensing results to a data fusion center, which will cause data fusion center to make wrong spectrum sensing decisions. The above algorithms are too simple to make a decision and result in poor performance. We employ the DempsterShafer (D-S) theory, which is similar to human reasoning. Based on this algorithm, there is a novel cooperative spectrum sensing algorithm in [5], which calculates the probability function based on the correlation coefficients. However, under the practice condition of distributed cooperative spectrum sensing in CR context, there may be conflicting data, which are not considered. The authors in [6] propose a distributed spectrum sensing scheme, but they do not take into account the distance from the transmission path or different transmission channel conditions. In view of this, Nhan proposes an enhanced scheme for cooperative spectrum sensing based on an enhanced D-S theory in [7], which is adjusted using the relative relationship between nodes for more accuracy. He also utilizes the credible factor to measure the credibility of the sensing results. However, the evaluation stage of each node using a counting rule requires that the fusion center to keep track of the past performance, which increases the burden on the fusion center. Besides, all above articles have a common drawback that is based on single threshold energy detection, which does not deal with uncertain information. Hence, the accuracy is poor. In [8], a double threshold method in energy detector is used to perform spectrum sensing. The accuracy of the local spectrum sensing is higher, but the fusion center makes a decision using hard decision, which is unsuitable for a dynamic CR environment. Compared with the other articles which adopt double threshold energy detection, we first use it to calculate the basic probability assignment, which improves the accuracy of local sensing. As we know, the D-S theory is similar to the natural decision making logic of humans. This capability of assigning uncertainty is effective in dealing with a large range of
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
SU2
SU2
m2(H0),m2(H1),m2(ȍ)
m3(H0),m3(H1),m3(ȍ)
D-S rule of Combination
Our cooperative spectrum sensing system is shown in Fig. 1. SUs continuously sense the surroundings and generate local sensing results using double threshold energy detection scheme. The local sensing information will then be transported to base station (BS), which is a data fusion center. The BS will have a final decision with D-S theory.
Data Fusion Center
m1(H0),m1(H1),m1(ȍ)
Double Threshold
II. S YSTEM D ESCRIPTION
SU1
Ă
problems that would otherwise become intractable, especially in a fast changing CR environment. At the fusion center, the theory of evidence is adopted to combine different sensing decisions from each SU. In addition, we also use a simple counting method to select nodes. The rest of the paper is organized as follows, in Section II, we describe the system model and D-S theory of evidence; In section III, a novel cooperative spectrum sensing algorithm is given, and we introduce the concept of nodes selection; In Section IV, simulation results about “and” rule, “or” rule, “single user” rule and double threshold energy detection based on D-S theory are shown. Finally, we conclude this paper in section V.
m(H0) m(H1)
mN(H0),mN(H1),mN(ȍ)
SUN
Fig. 2.
m(H1) >m(H0)
Y
N
H0
Spectrum sensing algorithm based on D-S Theory
where i is the index of SU, K is the total number of the SUs. yi (t) represents received data at SU, si (t) is the primary signal, the fading coefficient hi and the additive white Gaussian noise ni (t) are modeled as independent complex Gaussian random variables. The energy received by a single cognitive user is xEi = 2ν |yi (t)|2 which can be approximated as Gaussian distribut=1
tion that H0 : xEi ∼ N (2ν2i , 4ν4i ), H1 : xEi ∼ N (2ν2i + |hi |2 Es , 4ν4i + 2|hi |2 Es 2i ),
(2)
where ν represents time bandwidth, ν = T W . Es is the signal energy of the primary user, and 2i is the zero-mean additive variance of the white Gaussian noise.
SU SU PU BS
surrounding
H1
III. N OVEL COOPERATIVE SPECTRUM SENSING ALGORITHM
SU SU
SU
BS:Base Station PU:Primary User SU:Secondary User
Fig. 1.
The cooperative spectrum sensing algorithm comprises two steps: local sensing and BS fusion. A. Local Sensing
The system of cooperative spectrum sensing
The D-S theory, also known as the theory of belief functions, was first introduced by Dempster in 1960’s, and was later extended by Shafer. The theory is based on two ideas: the idea of obtaining degrees of belief for one question from subjective probabilities for a related question, and Dempster’s rule for combining such degrees of belief when they are based on independent items of evidence. In this way, we develop the spectrum sensing algorithm as shown in Fig. 2. At every node, we use the double threshold to calculate the result of local sensing. At the data fusion center, we may obtain a convergent result with D-S theory and arrive at a final decision by comparing them. The detection problem for local sensing at SUs can be stated in terms of a binary hypothesis test, with the null hypothesis H0 corresponding to PU signal being absent, and the alternative hypothesis H1 corresponding to PU signal being present, as H0 : yi (t) = ni (t), H1 : yi (t) = hi · si (t) + ni (t), i = 1, 2, . . . , K, (1)
Among various methods for spectrum sensing, energy detection offers a simple and quick method to detect primary signal even if the full feature set is unknown. Here, we consider the energy detection for local spectrum sensing. Since it does not need any a priori knowledge of the primary signal, the energy detector is robust to the variation of the primary signal. Moreover, the energy detector does not involve complicated signal processing, and has low complexity. In conventional energy detections, every SU makes their local decisions by comparing their energy with a threshold, as illustrated in Fig. 3. The authors in [8] proposes a scheme that uses two thresholds to detect whether the signal is present, where Ti denotes the collected energy value of the ith SU, as Fig. 4. Decision H0 or H1 will be made when Ti is less or greater than the threshold value. In this model, two thresholds η0 and η1 are used to help the decision of the SU. If energy value exceeds η1 then this user reports H1 , and if it is less than η0 , decision H0 will be made. Otherwise, if it is between the two thresholds, we report its energy value, and send to the fusion center to decide. In this paper, the uncertainty between two thresholds is used to calculate the trust functions, which will certainly improve the accuracy of detection.
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
H0
H1
mi (H1 ) = P {T > η1 |H1 } + P {η0 < T < η1 |H1 } ∞ 1 2 √ = exp[−(x − μ1,i )2 /σ1,i ]dx 2πσ1,i
Ș Fig. 3.
η1
η1
Energy detection with one threshold
√
+ H0
H1
η0
1 2 exp[−(x − μ1,i )2 /σ1,i ]dx, 2πσ1,i (11)
Ș0 Fig. 4.
Ș1
where μ0i , μ1i , σ0i and σ1i represent the mean and variance of xEi .
Energy detection with double threshold
B. Base Station Fusion Generally, in the non-fading environment, we assume hi is deterministic, the probabilities of detection, false alarm and missing detection are as computed as follows √ (3) Pd,i = P {Ti > η1 |H1 } = Qν ( 2γ, η1 ), Pf,i = P {Ti > η1 |H0 } = Pm,i
Γ(ν, η1 /2) , Γ(ν)
(4)
= P {Ti ≤ η0 |H1 } = 1 − P {η0 < Ti < η1 |H1 } − Pd,i ,
(5)
where Pd,i , Pf,i and Pm,i are the detection probability, false alarm probability, and missing detection probability of the ith SU respectively, γ is the SNR, η0 and η1 are two thresholds. Γ(a) and Γ(a, b) are complete and incomplete gamma functions respectively and Qν (a, b) is the generalized Marcum function. From the above formula, we have Pf,i · Γ(ν) = Γ(ν, η1 /2),
0
gamma function. Then we can obtain
η1 = 2P −1 (ν, 1 − Pf,i ),
(8)
η0 = 2/3 · η1 ,
(9)
According to the D-S theory, we know that mi (H0 ), mi (H1 ), mi (Ω) are used to indicate the basic probability assignment for the signal. The following probability functions are derived. mi (H0 ) = P {T < η0 |H0 } + P {η0 < T < η1 |H0 } η0 1 2 √ = exp[−(x − μ0,i )2 /σ0,i ]dx 2πσ0,i + η0
A⊂Ω
In D-S theory, two functions named belief (bel) and plausibility (pl) are defined to characterize the uncertainty and the support of certain hypotheses. m(B), (14) bel(A) = B⊆A
(6)
Γ(ν, η1 /2) = Γ(ν) − Γ(ν) · P (ν, η1 /2), (7) z ν−1 −t 1 t · e dt is lower order incomplete where P (ν, z) = Γ(ν)
−∞ η1
As we know, D-S theory has been applied to many areas, such as troubleshooting, diagnostic test and multi-data fusion [9]. As a theory to manage uncertainty, D-S evidence theory is a good choice for decision making in CR system. Let Ω denote a finite set of mutually exclusive and exhaustive hypotheses, called the frame of discernment. The basic probability assignment (BPA) is a function m from 2Ω to [0, 1], defined as: m(φ) = 0, (12) m(A) = 1. (13)
pl(A) =
(15)
where bel measures the minimum or necessary support for that hypothesis, and pl reflects the maximum or potential support. Two BPA’s m1 and m2 on Ω, induced by two independent items of evidence, can be combined by the so called D-S rule of combination to yield a new BPA m = m1 ⊕ m2 , the orthogonal sum of m1 and m2 , defined as m(A)
= m1 (A1 ) ⊕ m2 (A2 ) m1 (A1 )m2 (A2 ) A1 ∩A2 =A . = m1 (A1 )m2 (A2 )
(16)
A1 ∩A2 =A
At the data fusion center, decisions associated with credibility from distributed SUi are combined using Equation (16) according to D-S theory of combination, resulting in final credibility of CR system for each hypothesis in the form of BPA, namely m(H0 ) and m(H1 ), as
1 2 √ exp[−(x − μ0,i )2 /σ0,i ]dx, 2πσ0,i
m(B),
A∩B=φ
m(H0 ) = (10)
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
K
A1 ∩A2 ∩...AK =H0 i=1
1−
mi (Ai )
K
A1 ∩A2 ∩...AK =Θ i=1
, mi (Ai )
(17)
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
K
A1 ∩A2 ∩...AK =H1 i=1
m(H1 ) =
1−
SU1
mi (Ai )
K
A1 ∩A2 ∩...AK =Θ i=1
.
(18) SU2
mi (Ai )
H0 H1
: m(H0 ) > m(H1 ) : m(H1 ) ≥ m(H0 ).
(19)
C. Node Selection Although cooperative spectrum sensing can greatly improve sensing performance, many nodes in the network are redundant. With the increasing nodes, more and more system resources are consumed, and the transmission efficiency of the system will decrease continuously. Hence, we choose to remove the redundancy of the SUs. Different from the other cluster-based sensing algorithm, the information of the SU to the fusion center has an arrangement of both large and small, as Mi = αmi (H1 ) + βmi (H0 ),
(20)
that is the accuracy function of every SU to determine whether the signal is present, where α represents the probability that the node has correctly sensed that the primary use is present, and β is the probability that the node has correctly sensed the primary use is absent. The authors in [10] proposes a simple counting rule that is used to calculate α and β. For the ith sensing node, at the tth moment, we use ωi (t) to expresses the state of current decision, where ωi (t) ∈ {ω1 , ω2 , ω3 , ω4 }, ω1 , ω2 , ω3 and ω4 are as follow ω1 ω2 ω3 ω4
: εi = 1 and : εi = 1 and : εi = −1 and : εi = −1 and
ε0 = 1 ε0 = −1 ε0 = −1 ε0 = 1,
where ε0 is the center decision, and εi is the node decision. We use n1 , n2 , n3 and n4 to represent the time that ω1 , ω2 , ω3 and ω4 have occurred respectively. Hence, α and β can be obtained as n1 α= , (21) n1 + n2 β=
n3 . n3 + n4
(22)
Fig. 5 gives the diagram of node selection. The steps are as follow. Step1: SUs calculate mi (H0 ) and mi (H1 ), get Mi using Equation (20), and then send the local results to the fusion center. Step2: The fusion center has a queue about Mi , which is listed in descending order. It chooses the larger ones to fuse with D-S theory and decides whether the signal is present.
SU3
ing Stopp ge a s s e m
all SUs
The fusion center
Node selection message
selected SUs
Selecting nodes
F dec inal isio n
M2 M3 ĂĂ
By comparing m(H0 ) and m(H1 ), the final decision is made upon a following simple strategy
Ordering
M1
SUN
MN
H0/H1
Deciding
Fig. 5.
The diagram of selecting node
Step3: If the same decision is repeated three times, the fusion center stops fusing data, and sends a end message to each node. At the same time, it sends node selection message to SUs whose Mi ’s are used. These selected nodes are part of a node cluster that is the smallest group to sense PU. IV. P ERFORMANCE EVALUATION AND SIMULATION RESULTS
In this section, we evaluate the performance of the algorithm developed in the previous sections. We first solve the Equations (8) and (9), and then calculate the values of m(H0 ), m(H1 ) using Equations (17) and (18), compare these values to make a final decision using Equation (19). Based on the results computed from this algorithm, we then output the node selection. Within the node selection, the fusion center performs the ordering function defined in Equation (20), and then decides which nodes are selected. This accuracy of final decision is compared with other schemes through simulation. In our simulation, we focus on the channels that do not have shadowing and have equal gain. In addition, we assume that the cognitive region of interest only consists of one licensed user and the fusion center has no spectrum sensing capabilities. The probabilities of whether the licensed user is present are not equal. The number of cognitive users that participates in cooperative spectrum sensing is 10. We also consider the following parameters: the SNR increases from 5dB to 15dB, the false alarm probability pf equals 0.001, and the time bandwidth ν is 5. According to different methods, (i.e., using D-S theory under double threshold, “or”, “and” and “single user”), we can obtain the following two curves, as shown in Fig. 6 and Fig. 7. Fig. 6 shows that the detection probability Qd of double threshold is higher than “or” when the SNR is 5. The probability of detection increases by 0.20, and the pecentage of missing probability reduces more. The performance of other methods is worse. For example, the method of “and” is not as good as single user detection method. As the SNR increasing, the probability of detection tends to 1, especially after 10. On the contrary, the missing detection probability Qm is clearly lower than other methods. Similarly, the missing probability tends to 0 as the increasing of the SNR, which is shown in Fig. 7. In addition, in the calculation of the confidence intervals using Equations (11) and (12), we take the uncertainty into account. They provide evidence that cooperative sensing is
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the IEEE Globecom 2010 proceedings.
1 0.9
double threshold or and single user
The detection probability Qd
0.8 0.7
1 K=10 K=15 K=20
0.98 0.96 The detection probability Qd
more “accurate” than single node and double threshold, and that the D-S theory of evidence is appropriate for our proposed parameter “credible”. In addition, with the same SNR, the performance of the method of double threshold improves greatly.
0.94 0.92 0.9 0.88 0.86
0.6
0.84
0.5
0.82
5
0.4 0.3
Fig. 8.
10 SNR/dB
15
Qd in the method of double threshold with different SUs’ numbers
0.2
V. C ONCLUSIONS
0.1 0
5
10 SNR/dB
Fig. 6.
15
Qd in different spectrum sensing methods
1 0.9
The missing probability Qm
0.8 double threshold or and single user
0.7 0.6 0.5 0.4
In this paper, we propose a new cooperative sensing algorithm to improve the utilization efficiency of the radio spectrum. Through simulation results, we observe that the algorithm based on double threshold energy detection and D-S theory increases the reliability of detection quite dramatically. We may remove redundant users, thereby reducing network overhead, improving system transmission efficiency, and optimizing the network resources, using node selection. We did not consider the case that different SUs contribute differently to the fusion center. In our future work, we will enhance the algorithm by defining a different probability function mi (H0 ) and mi (H1 ), which is used to measure the credibility of each node.
0.3
R EFERENCES
0.2 0.1 0
5
10 SNR/dB
Fig. 7.
15
Qm in different spectrum sensing methods
Using different numbers of SU, the detection probabilities are different in the method of double threshold, as shown in Fig. 8. However, when the number of users reaches a certain level, the improvement in detection performance saturates. For example, when K=15, Qd is more than 0.97. Such a high probability meets our requirement. Suppose the overhead of one node is 1, then 20 is the overhead of 20 nodes. In fact, 10 nodes can achieve the same performance with 20 nodes, while reducing by half of the cost. Therefore, we must choose the appropriate number of SU to avoid the waste caused by detection time. Hence, node selection plays a very important role in cognitive radio. Clearly, the proposed algorithm has a relatively high reliability in the case that the SNR is low. It is better than the other methods without D-S theory. We can reduce the number of nodes to bring down the network overload by node selection.
[1] M. McHenry, “Frequency agile spectrum access technologies,” in FCC Workshop on Cognitive Radio, May. 2003. [2] G. Staple and K. Werbach, “The end of spectrum scarcity,” IEEE Spectrum archive., vol. 41, no. 3, pp. 48-52, Mar. 2004. [3] J. Mitola III and G. Q. Maguire, “Cognitive radio: Making software radios more personal,” IEEE Pers. Commun., vol. 6, no. 4, pp. 13-18, Aug. 1999. [4] D. Cabric, S. M. Mishra, and R. W. Brodersen, “Implementation issues in spectrum sensing for cognitive radios,” in Proc. Asilomar Conf. on Signals, Sys., and Comput., vol. 1, pp. 772-776, Nov. 2004. [5] X. Zheng, J. Wang, Q. Wu and J. Chen, “Cooperative spectrum sensing algorithm based on Dempster-Shafer theory,” in Proc. of IEEE Journal of PLA Univ. of Science and Technol., pp. 218-221, 2008. [6] Q. Peng, K. Zeng, J. Wang and S. Li, “Distributed spectrum sensing scheme based on credibility and evidence theory in cognitive radio context,” in Proc. of IEEE 17 th Int. Symp. on Personal, Indoor and Mobile Radio Commun., pp. 1-5, Sept. 2006. [7] N. Nhan, X. T. Kieu and I. Koo, “Cooperative spectrum sensing using enhanced Dempster-Shafer theory of evidence in cognitive radio,” IEEE Commun. Lett., vol. 13, pp. 492-494, 2009. [8] J. Zhu, Z. Xu, F. Wang, B. Huang and B. Zhang, “Double threshold energy detection of cooperative spectrum sensing in cognitive radio,” in Proc. of Int. Conf. on Cognitive Radio Oriented Wireless Networks Commun. (CrownCom), pp. 1-5, 2008. [9] G. Shafer, A mathematical theory of evidence, Princeton, NJ: Princeton Univ. Press, 1976. [10] N. Mansouri and M. Fathi, “Simple Counting Rule for Optimal Data Fusion,” in Proc. of IEEE Conf. on Control Appl. (ICCA2003), vol. 2, pp. 1186-1191, 2003.
978-1-4244-5637-6/10/$26.00 ©2010 IEEE
