Reliable Cooperative Wideband Spectrum Sensing based on Entropy estimation Sesham. Srinu, Samrat L. Sabat School of Physics University of Hyderabad Hyderabad, 500046 Email:
[email protected],
[email protected]
Abstract—In Cognitive Radio (CR), spectrum sensing is an essential concept. It exploits the inefficient utilization of Radio spectrum without deteriorating the Quality of Service (QOS) of licensed/primary user communication. This paper presents the cooperative wideband spectrum sensing technique based on entropy estimation in each subband under probable channel impediments. We have proposed generalized extreme studentized deviate (GESD) test to exclude multiple suspicious cognitive users for reliable cooperative sensing. The simulation results show that the entropy detection method outperforms the energy detection method. It achieved 8dB average signal-to-noise ratio (SNR) improvement while maintaining a false alarm probability of 0.01 and a detection probability of 0.9. The proposed sensing algorithm by excluding suspicious CR is able to detect low average SNR signals of -18.5dB under path loss environment using ten cognitive users in cooperation. Keywords-Cognitive Radio Network, Entropy estimation, Cooperative wideband sensing, Sensing performance, Outliers.
I. I NTRODUCTION The Radio spectrum in an Electro Magnetic Spectrum (EMS) is an indispensable natural resource for evolution of future generation wireless systems. The scarcity of radio spectrum becomes more and more prominent due to the rapid growth of the wireless and data communications. In fact, recent statistical studies on radio spectrum usage have shown that the poor utilization of frequency bands is due to rigid licensing policies. The solution to the spectrum scarcity problem is dynamically looking for the vacant bands and using them opportunistically. Hence, research into novel techniques for efficient utilization of vacant bands is being aggressively engaged by academia and industry. Cognitive Radio (CR) technology allows for usage of unutilized licensed bands by unlicensed users or cognitive users [1]. The fundamental function of CR is spectrum sensing, which enable the CR users to adapt to the environment by detecting white/vacant spaces without degrade the QoS to the primary users (PU) communication. The main requirements for spectrum sensing are fast, robust and reliable signal detection in a negative SNR regime. In the literature, several signal processing techniques have been proposed to enhance the sensing performance, including energy detectors, matched filter detectors, and cyclostationary feature detectors [2]. However, recently the study in [3] shown that the entropy based technique is robust method
Siba K. Udgata Department of Computer & Information Sciences University of Hyderabad Hyderabad, 500046 Email:
[email protected]
of narrowband detection with unknown noise and interference levels. Entropy based detection is based on the concept that the entropy or uncertainty of the received signal reduces if the PU’s signal contains any modulation. The sensing performance of the CR is determined by the factors such as sensing reliability and detection probability. In Cognitive Radio Network (CRN), if only one CR node is used for sensing the signal, then it is termed as single node sensing. In the case of cooperative/multiuser sensing, multiple CR users are sensing the presence of signal. In practice, sensing performance of a single node is often reduced with multipath fading, shadowing, free space path loss, and receiver uncertainty issues in the channel. The study in [2], [4] enhances the sensing performance and mitigated the impact of noise issues through multiuser cooperation by getting diversity gains. The performance of the multinode sensing is evaluated in different collaboration scenarios (soft and hard decision fusion). The study in [5], [6] reports the sensing performance based on soft and hard decision techniques using energy detection method. It has also been shown that the soft decision technique performs better compared to hard decision technique [7]. One more issue in cooperative network is the presence and possible emulation attacks of a multiple outliers in the CRN [8]. Most of the works are concentrated to eliminate single suspicious user in CRN. In this work, the parametric test, generalized Extreme Studentized Deviate (ESD) method is used to counteract or address the problem of multiple outliers in cooperative network [9]. Recent research has spent considerable effort on single band or narrow band cooperative/multinode detection approaches [10]. But, In order to improve the opportunistic throughput, CR must sense the signals in multiple bands or wideband. The objective of this paper is to develop an efficient algorithm to increase the sensing performance in cooperative wideband sensing environment. To achieve this, cooperative wideband spectrum sensing based on entropy estimation in each sub-band/channel (SB) is introduced. In addition, GESD test is used to make the cooperative sensing more efficient with elimination of multiple suspicious CR users in CRN. The entropy estimation method is analyzed and compared with energy detection method [5] under free space path loss. The rest of the paper is organized as follows. Section II de-
978-1-4673-2393-2/12/$31.00 ©2012 IEEE
scribes the proposed cooperative wideband sensing algorithm by excluding suspicious CR. Simulation results are given in section III, followed by conclusions in section IV. II. C OOPERATIVE SENSING ALGORITHM UNDER SUSPICIOUS CRN Consider that the frequency bandwidth is divided into ‘𝐾 ’ non-overlapping SBs. It is assumed that some of the SBs (𝑃𝑜 out of 𝐾) are vacant for particular time duration and in specific geographic location with a constraint that 1 ≤ 𝑃𝑜 ≤ 𝐾. Hence, these vacant SBs are available for opportunistic spectrum access. Fig. 1 represents an overview of cooperative wideband spectrum sensing model. In this model, each CR encounters or in different noise environment. All CR users are participated in cooperation where each CR senses the entire wideband (contains 0,1,....,(K-1) SBs) and sends the measurement or decision to the FC. Finally, FC makes the global decision by aggregating the received local sensing information in each SB and informs the global decision to all cooperating CR users.
that 𝑘 ∈ {0, ...., (𝐾 − 1)}, and 𝑁 is the total number of samples considered for sensing purpose. The algorithms are analyzed with the following assumptions, 1) the noise in each SB (w𝑘 ) follows Gaussian, independent and identically distributed (𝑖.𝑖.𝑑) with mean zero and 2 2) the received signal in each subband (s𝑘 ) is variance 𝜎𝑤 a stochastic signal, and it follows Gaussian 𝑖.𝑖.𝑑 with mean 𝜇𝑠 and variance 𝜁 2 and 3) the channel gain (ℎ), transmitted signal (s𝑘 ), and the additive white Gaussian noise (w𝑘 ) are independent of each other, the channel is time invariant during the sensing period such that, each node the channel coefficients (ℎ𝑚 ) are having nonzero mean and unit variance complex Gaussian random variables. In the case of cooperative detection technique, two kinds of decision fusion logic (soft decision fusion and hard decision fusion) are being used in FC. In this work, soft decision fusion methods (weighted gain combining (WGC) and equal gain combining (EGC)) are applied to improve the reliability of cooperative sensing. Due to noise uncertainty in the medium some nodes have a better signal strength than other nodes. Therefore, the FC will give different weights to different nodes based on the strength of the received signal [11]. The FC generates a global decision based on the following threshold test. The cooperative detection probability based on energy detection using WGC fusion is, 𝑀 H1k ( ) ∑ (𝑘) 𝑘 𝜓𝑎−𝑚 (𝑟).Θ𝑚 ≷ 𝜆𝑘𝑒 𝐶𝑑−𝑤𝑔𝑐 𝜆𝑘𝑒 , 𝑡𝑠 =
(1)
H0k
𝑚=1
∑𝑀 1 𝑘 𝑘 𝑘 where 𝜓𝑎−𝑚 (𝑟)=𝐸𝑥𝑝(𝜓𝑚 (𝑟)) = 𝑀 𝑚=1 𝜓𝑚 (𝑟). 𝑘 Where 𝜆𝑒 is the threshold depends on desired false alarm probability, 𝑡𝑠 is the sensing duration, Θ𝑚 is the weight factor 𝜁2 2 for 𝑚𝑡ℎ node, formulated as Θ𝑚 = 𝜎2 (𝜎2m +𝜁 2 ) , where 𝜁𝑚 w −m
w −m
m
2 and 𝜎𝑤−𝑚 are the variances of signal and noise at 𝑚𝑡ℎ node, 𝑘 and 𝜓𝑚 (𝑟) is the energy measurement of the 𝑚𝑡ℎ CR (or 𝑚𝑡ℎ node) in 𝑘 𝑡ℎ SB, which is given as
Fig. 1.
Cooperative wideband spectrum sensing model
Assuming that there are 𝑀 nodes in the cooperation and the received signals of all nodes are statistically independent, then the composite hypothesis test can be written as 𝑘 (𝑛), 𝑚 = 0, 1, 2, ........, 𝑀 − 1 𝐻0𝑘 : R𝑘𝑚 (𝑛) = W𝑚
𝑘 𝐻1𝑘 : R𝑘𝑚 (𝑛) = ℎ𝑘𝑚 ∗ S𝑘𝑚 (𝑛) + W𝑚 (𝑛), 𝑛 = 0, 1, ..., 𝑁 − 1
𝑘 In which R𝑘𝑚 (𝑛), W𝑚 (𝑛), and S𝑘𝑚 (𝑛) can be compactly represented in the matrix form as
R𝑘𝑚 (𝑛) = [r0𝑚 , r1𝑚 , r2𝑀 , ................., r(𝐾−1) ] 𝑚 𝑘 0 1 2 (𝐾−1) ] W𝑚 (𝑛) = [w𝑚 , w𝑚 , w𝑚 , .............., w𝑚 𝑘 0 1 2 (𝐾−1) ] S𝑚 (𝑛) = [s𝑚 , s𝑚 , s𝑚 , .............., s𝑚 Where r𝑘 , w𝑘 and s𝑘 are the received signal, noise and primary user signal sequences of length 𝑁 in 𝑗𝑘 𝑡ℎ SB such
𝑘 𝜓𝑚 (𝑟) =
𝑁 −1 ∑
[𝑟𝑘 (𝑛).𝑟𝑘∗ (𝑛)], ∀𝑚
(2)
𝑛=0
In the case of entropy estimation method, the cooperative wideband detection probability using WGC is 𝑀 H0k ( ) ∑ (𝑘) 𝑄𝑑−𝑤𝑔𝑐 𝜆𝑘𝜖 , 𝑡𝑠 = 𝜙𝑘𝑎𝑣𝑔−𝑚 (𝑟).Θ𝑚 ≷ 𝜆𝑘𝜖 , 𝑘 = 0, 1, ..., (𝐾−1) H1k
𝑚=1
(3) where 𝜙𝑘𝑎𝑣𝑔−𝑚 (𝑟) is the expected value, 𝜆𝑘𝜖 is the threshold for entropy detection [3], and 𝜙𝑘𝑚 (𝑟) is the entropy measurement of the 𝑚𝑡ℎ CR in 𝑘 𝑡ℎ SB, given as 𝜙km (𝑟) = −
𝐿 ∑ 𝑓𝑘 𝑖
𝑖=1
𝑁
log𝑏
𝑓𝑖𝑘 , ∀𝑚 𝑁
(4)
where 𝑓𝑖𝑘 denote the frequencies of the 𝑖𝑡ℎ bin of the 𝑘 𝑡ℎ 𝐿 ∑ subband according to the histogram method with 𝑓𝑖𝑘 = 𝑁 . Therefore the probability of each bin 𝑝𝑘𝑖 =
𝑓𝑖𝑘 𝑁 .
𝑖=1
One more issue in the cooperative sensing is the presence of a few suspicious/outliers CR in the CRN. We used generalized ESD test to counteract the problem of one or more suspicious CR users in cooperative network. The test is more prominent when the data set is of length more than 25 [9]. But, the number of CR in cooperation should be as low as possible to avoid control channel overhead. For this reason, we have accumulated the measured entropy of all cooperative nodes 𝜏 times (iterations) such that (𝑀 ∗ 𝜏 ) > 25. In this process, it is assumed that the number of suspicious users in CRN is at most ‘𝑢’ such that 𝑢 < 𝑀 and the observed data set of ‘𝑀 ’ cooperative users on 𝑘 𝑡ℎ SB is univariate that follows an approximately normal distribution. Thus, the observed data set (𝑋) contains the elements in the first iteration as, {𝜑𝑘1 , 𝜑𝑘2 , ........, 𝜑𝑘𝑀 }. where 𝜑𝑚 may be the soft measurement of either energy or 𝑘 (𝑟) or 𝜙𝑘𝑚 (𝑟)) of 𝑚𝑡ℎ node at 𝑘 𝑡ℎ SB. Because entropy (i.e.,𝜓𝑚 the SCR detection is independent of SB, we will omit the ‘k’ on measurement. Based on the total of (M*𝜏 ) observations for 𝜏 iterations, the number of SCRs in CRN are calculated as follows: The single ESD in a random normal sample is defined as { } ¯ 𝜑𝑖 − 𝑋 𝑗 = 1, 2, ........., 𝑢 , (5) ℜ𝑗 = max 𝑖 = 1, 2, ...., (𝜏 ∗ 𝑀 ) 𝑖 𝑆𝑋−𝑑𝑒𝑣 ¯ and 𝑆𝑋−𝑑𝑒𝑣 denoting the sample mean and sample where 𝑋 standard deviation of data set (𝑋). If 𝑗=1, ℜ1 is the 1𝑠𝑡 ESD which is associated with the largest or the smallest order observation in the data set, say 𝜑1 . In the second recursive calculation, 𝜑1 is discarded from ¯ the set (but 𝜑1 may not be an ultimate outlier). The new 𝑋 and 𝑆𝑋−𝑑𝑒𝑣 (excluding 𝜑1 ) are recalculated from the reduced sample of length (𝜏 ∗ 𝑀 ) − 1. Eqn. (5) is used again to recalculate ℜ2 . The process is continued until ℜ1 , ℜ2 , ......, ℜ𝑢 are computed, and each of this is individually compared with a critical value 𝜒𝑗 as follows 𝜒𝑗 = √
(𝑀 − 𝑗)𝑡𝑀 −𝑗−1,𝑝 (𝑀 − 𝑗 − 1 + 𝑡2𝑀 −𝑗−1,𝑝 )(𝑀 − 𝑗 + 1)
(6)
where 𝑡𝑀 −𝑗−1,𝑝 is the 100𝛼 percentage point from the 𝑡distribution with}(𝑀 − 𝑗 − 1) degrees of freedom, and 𝑝 = { 𝛼 1 − 2(𝑀 −𝑗+1) , where 𝛼=0.05 is the significance level for the overall test. The number of SCR are determined by finding the largest ‘𝑗’ such that ℜ𝑗 ≥ 𝜒𝑗 The SCR set using GESD test is given by ℜ = {ℜ1 , ℜ2 , ........., ℜ𝑗 }, ℜ𝑗 ∈ 𝑋, 𝑗 ≤ 𝑢 The indices of the SCR corresponding to data set (𝑋) can be expressed in a matrix form as, ⎛
1 𝑀 +1 .. .
⎜ ⎜ 𝐼(ℜ) = ⎜ ⎝ 𝑀 (𝜏 − 1) + 1
2 𝑀 +2 .. .
... ... .. .
𝑀 (𝜏 − 1) + 2 . . .
⎞ 𝑀 2𝑀 ⎟ ⎟ ⎟ ⎠ 𝑀 ∗𝜏
The final SCR can be determine based on the following equality for a fixed value of 𝑚, 𝜏 ∑ 𝑖𝑡𝑟=1
[ [𝐼(ℜ)]𝑖𝑡𝑟,𝑚 = 𝜏
(𝜏 − 1) 𝑀 +𝑚 2
] (7)
The effective cooperative detection probability for soft decision fusion (WGC and EGC) can be calculated using Eqns. (1) and (3) with the set 𝐸 = {𝑥 : 𝑥 ∈ 𝑋 and 𝑥 ∈ / ℜ𝑠𝑐𝑟 }. Where “ℜ𝑠𝑐𝑟 ” is the set of SCR. III. S IMULATION R ESULTS In order to illustrate the performance of proposed wideband spectrum sensing algorithm, DVB-T signal is considered under AWGN and Rayleigh fading channel environment. The path loss effects are also considered in the cooperative sensing simulation. The detector estimates the entropy of the received signal within the desired frequency SB and compares it with the corresponding threshold. The threshold is computed to achieve tolerable false alarm probability and assumed same for all subband detection (𝑖.𝑒., 𝜆1𝜀 = 𝜆2𝜀 = 𝜆3𝜀 = ..... = 𝜆𝐾 𝜀 ). The frequency spectrum bandwidth under assessment is divided into 𝐾 SBs. In each of the channel PU may be either present or absent. We have adopted the grouping concept in [12] to speed up the simulation. Hence, assumed five bands (𝑃𝑜 =5) are unoccupied randomly within the 𝐾 (𝐾=9) SBs. We compare the performance of the two detectors under different noisy environment. Simulations are carried out without considering the noise uncertainty, according to the authors reported in [3]. Since the non existence of closed form solution for 𝑃𝑑 and 𝑃𝑓 , the performance of the detection is analyzed using Monte Carlo methods for 20000 iterations. In our simulation, cooperative CRs are assumed to have configurations as shown in Fig. 1. The performance of the proposed cooperative wideband sensing is evaluated with different soft decision fusion techniques. Moreover, we have considered two cases of CR network geometry, ideal distance case (IDC) and different/random distance case (DDC). In case of IDC, it is assumed that all cooperative CRs are located in equal distance from the PU transmitter where the free space loss is negligible. In case of DDC, it is assumed all cooperative CRs are distributed randomly over the considered geographic area and located within 3-10km from PU transmitter. Figs. 2 and 3 illustrate the Average SNR vs. detection probability of wideband sensing based on energy detection and entropy detection using WGC fusion logic. In this simulation, variable number of nodes 𝑀 =3, 5, and 10, 𝑃𝑓 =0.01, and 𝑁 =256 are used. From the figures, the performance of entropy shows superiority even in different distance case as compared to energy detection method. It is obvious that the performance is reduced due to free space path loss. This is due to the dependency of signal strength on distance. Moreover, the performances of both the detection methods are reduced with increase in cooperation level under random distance case. Hence, there must be a trade-off between number of nodes and the performance due to path loss. In general, the FC does
0.9
0.9
0.8
0.8 Probability of detection
1
0.7 0.6 0.5 0.4 0.3
Ideal distance case−M=3 M=5 M=10 Different distance case−M=3 M=5 M=10
0.2 0.1 0 −16
−14
−12
−10 −8 −6 Average SNR (d B)
−4
−2
0.6 0.5 0.4
0
0
1
0.9
0.9
0.8
0.8
0.7 0.6 0.5 0.4 Ideal distance case, M=10 M=5 M=3 Different distance case, M=10 M=5 M=3
0.2 0.1 −28
−26
−24
−22
−20
−18
−16
−14
−12
−10
Average snr (d B)
−15
−10 −5 Average SNR (d B)
0
Fig. 4. Average SNR Vs Pd of wideband sensing using EGC fusion. (𝑁 =128, Energy detection, IDC)
1
0.3
Pf=0.1, M=3 M=5 M=10 Pf=0.01, M=3 M=5 M=10 Pf=0.001, M=3 M=5 M=10
0.3
0.1
Fig. 2. Average SNR Vs Pd of wideband sensing using WGC fusion. (𝑁 =256, 𝑃𝑓 =0.01, Energy detection)
Probability of detection
0.7
0.2
Probability of detection
Probability of detection
1
0.7 0.6 0.5 Pf=0.1, M=10 M=5 M=3 Pf=0.01, M=10 M=5 M=3 Pf=0.001, M=10 M=5 M=3
0.4 0.3 0.2 0.1 −28
−26
−24
−22
−20
−18
−16
−14
−12
−10
Average SNR (d B)
Fig. 3. Average SNR Vs Pd of wideband sensing using WGC fusion. (𝑁 =256, 𝑃𝑓 =0.01, Entropy detection)
Fig. 5. Average SNR Vs Pd of wideband sensing using EGC fusion. (𝑁 =128, Entropy detection, IDC)
not have the prior information about SNR. In practical, EGC is reliable fusion logic. Hence, further simulation results are carried out using EGC fusion logic. Figs. 4, 5 represent the Average SNR vs. Pd curves of wideband sensing using energy and entropy detection method using EGC fusion logic. The simulation parameters are 𝑀 =3, 5 and 10, 𝑁 =128, 𝑃𝑓 =0.1, 0.01, and 0.001. From the figures, it is clear that the performances of both detection methods are increases when either the number of CR in cooperation or false alarm probability increases. In conclusion, performance of entropy detection outperforms the energy detection for the same simulation parameters. In Fig. 6, it can be seen that the significant performance
improvement of the detection algorithms (energy, entropy) when we exclude the suspicious CR users. For the generalized ESD, we have taken ‘𝑢’=4𝜏 (the upper bound of outliers). The data set 𝑋 depends on the detection technique being used for spectrum sensing. In case of energy detection, the data set 𝑋 contains the energy measurement of all CR in cooperation. The simulation results corresponding to the withsuspicious-CR (WSCR) and without-suspicious-CR (WOSCR) in the cooperation are tabulated in Table I. It compares the performance (𝑆𝑁 𝑅𝑤𝑎𝑙𝑙 [13]) achieved for required (𝑃𝑑 ) and (𝑃𝑓 ) for both detection methods using EGC fusion logic under DDC. Here, the number of nodes (𝑀 =5, 8 and 10) and sample length (𝑁 =256) are considered. For instance, the performance
are reduced due to path loss and is further reduced with increase of number of nodes in the cooperation. The average performance loss is around 2.1dB for energy and 1.4dB for entropy detection method respectively. In addition, proposed sensing algorithm without suspicious CR is able to detect low average SNR signals of -18.5dB under path loss environment at 𝑃𝑑 ≥ 0.9, and 𝑃𝑓 ≤ 0.01 using ten CRs in cooperation. The FPGA implementation of proposed wideband sensing algorithm is under development.
1 0.9
Probability of detection
0.8 0.7 0.6 Ene,WSCR,M=5 M=8 M=10 Ene,WOSCR,M=5 M=8 M=10 Ent,WSCR,M=5 M=8 M=10 Ent,WOSCR,M=5 M=8 M=10
0.5 0.4 0.3 0.2 0.1 −22
−20
−18
−16
R EFERENCES
−14
−12
−10
−8
−6
−4
Average SNR (d B)
Fig. 6. Average SNR Vs 𝑃𝑑 without suspicious CR using energy and entropy detection (𝑁 =256, 𝑃𝑓 =0.01, EGC, DDC) TABLE I T HE LEAST AVERAGE SNR REQUIRED TO ACHIEVE REQUIRED (𝑃𝑑 ) V S (𝑃𝑓 ) OF ENERGY AND ENTROPY DETECTION UNDER DDC Detection technique, methodology Energy, DDC with Suspicious CR Energy, DDC without Suspicious CR Entropy, DDC with Suspicious CR Entropy, DDC without Suspicious CR
𝑀 =5 -6dB -6.75dB -15.5dB -16dB
𝑀 =8 -7dB -8.75dB -16dB -17.5dB
𝑀 =10 -7.5dB -9.5dB -16.5dB -18.5dB
improvement of entropy detection method with elimination of suspicious CR under DDC is 2dB (-16.5dB to -18.5dB) approximately. IV. C ONCLUSIONS In this paper, we have performed wideband spectrum sensing based on entropy and energy measurement in each subband within the considered band. It has been shown that proposed wideband detection algorithm based on entropy estimation with multiple suspicious CR user elimination (using GESD) can sense the spectrum efficiently and it outperforms the energy detection method. We have considered two cases of CR network geometry, IDC and DDC to investigate the path loss effect on cooperative wideband sensing. Simulation results have shown that the performance of both detection methods
[1] T. Yucek and H. Arslan, “A survey of spectrum sensing algorithms for cognitive radio applications,” IEEE Communications Surveys and Tutorials, vol. 11, no. 1, pp. 116 –130, April 2009. [2] I. F. Akyildiz, B. F. Lo, and R. Balakrishnan., “Cooperative spectrum sensing in cognitive radio networks: A survey,” Physical Communication, vol. 4, no. 1, pp. 40–62, July 2011. [3] Y. L. Zhang, Q. Y. Zhang, and T. Melodia, “A frequency-domain entropy-based detector for robust spectrum sensing in cognitive radio networks,” IEEE Communications Letters, vol. 14, no. 6, pp. 533 –535, June 2010. [4] D. Duan, L. Yang, and C. Jose, “Cooperative diversity of spectrum sensing for cognitive radio systems,” IEEE transactions on signal processin,, vol. 58, no. 6, pp. 3218–3227, June 2010. [5] M. Derakhtian, F. Izedi, A. Sheikhi, and M. Neinavaie, “Cooperative wideband spectrum sensing for cognitive radio networks in fading channels,” IET Signal Processing, vol. 6, no. 3, pp. 227 –238, may 2012. [6] S. Srinu, S. L. Sabat, and S. K. Udgata, “Wideband spectrum sensing based on energy detection for Cognitive Radio Network,” in World Congress on Information and Communication Technologies (WICT)), Dec. 2011, pp. 651 –656. [7] S. Srinu, S. L. Sabat, and S. Udgata, “FPGA implementation of cooperative spectrum sensing for Cognitive Radio Networks,” in IEEE proceedings, UKIWCWS, Dec 2010, pp. 1–5. [8] P. Kaligineedi, M. Khabbazian, and V. Bhargava, “Malicious user detection in a cognitive radio cooperative sensing system,” IEEE Transactions on Wireless Communications, vol. 9, no. 8, pp. 2488 –2497, august. 2010. [9] R. C. Yu, H. W. Teh, and P. A. Jaques., “Quality control of semicontinuous mobility size-fractionated particle number concentration data,” Atmospheric Environment, vol. 38, no. 20, pp. 3341 – 3348, Oct. 2004. [10] Z. Quan, S. Cui, A. Sayed, and H. Poor, “Optimal multiband joint detection for spectrum sensing in cognitive radio networks,” IEEE Transactions on Signal Processing, vol. 57, no. 3, pp. 1128 –1140, March 2009. [11] S. Srinu and S. L. Sabat, “FPGA implementation and performance study of spectrum sensing based on entropy estimation using cyclic features,” Computers & Electrical Engineering, 2012. [Online]. Available: http://dx.doi.org/10.1016/j.compeleceng.2012.07.001 [12] A. Taherpour, S. Gazor, and M. Nasiri-Kenari., “Wideband spectrum sensing in unknown white Gaussian noise,” IET Communications, vol. 2, no. 6, pp. 763–771, feb. 2008. [13] R. Tandra and A. Sahai, “SNR walls for signal detection,” IEEE Journal of Selected Topics in Signal Processing, vol. 2, no. 1, pp. 4–17, Feb 2008.
