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IEEE SYSTEMS JOURNAL 1

Optimal Multinode Sensing in a MaliciousCognitive Radio Network

Sesham Srinu and Samrat L. Sabat, Member, IEEE

Abstract—Spectrum sensing is an essential function in cognitiveradio systems for dynamic spectrum access. Multinode sensing isa technique being used in cognitive radio networks to enhancethe sensing performance using space diversity concept. The chal-lenges in multinode spectrum sensing are the prediction of signalstatus in multiple frequency bands in a low signal-to-noise ratio(SNR) regime and sensing reliability. The weighted gain combining(WGC) and the equal gain combining are the two soft decisioncooperative sensing techniques being used frequently in literature.In this paper, we introduce weighted gain cooperative sensingusing differential evolution (DE) and adjusted box-plot methodsto exalt the sensing reliability together with the sensing perfor-mance. The main advantage of the WGC method using DE isthat it can generate optimal weights independent of received signalcharacteristics, which is an indispensable condition to realize thesystem in real time. The proposed optimal cooperative sensingmethod with entropy and cyclic features enhances the sensingperformance, and it is less severe to noise uncertainties comparedwith the traditional sensing methods. It can detect the low SNRsignals up to −24 dB at desired sensing performance (Pf = 0.1and Pd = 0.9) with a frame size of 256 and using five nodesin cooperation. It is a significant improvement for IEEE 802.22WRAN systems, which work under low SNR regime.

Index Terms—Cognitive radio systems, cyclostationary fea-tures, differential evolution (DE), entropy estimation, malicioususer, multinode sensing.

I. INTRODUCTION

OWING to the rapid growth of wireless communication,the scarcity of radio spectrum becomes more prominent.

However, recent statistical studies on radio spectrum usagehave shown that the poor utilization of frequency bands is dueto the rigid licensing policies. The spectrum scarcity and theinefficient utilization of spectrum lead to the development ofcognitive radio technology [1], [2]. The primary function ofcognitive radio is spectrum sensing, which enables the cog-nitive users for dynamic spectrum access (DSA) by detectingspectrum holes or white spaces without causing destructiveinterference to the primary/licensed user communication. Themain requirements for spectrum sensing are fast, robust, andreliable signal detection in a low signal-to-noise ratio (SNR)regime. In the literature, several signal processing techniqueshave been proposed to enhance sensing performance, including

Manuscript received October 19, 2012; revised August 7, 2013; acceptedSeptember 4, 2013.

The authors are with the School of Physics, University of Hy-derabad, Hyderabad-500 046, India (e-mail: [email protected];[email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSYST.2013.2283965

energy detectors, covariance detectors, matched filter detectors,wavelet detectors, and cyclostationary feature detectors [3],[4]. However, most of the traditional sensing algorithms aresensitive to noise variations in the received signal [5], [6].The noise variations or uncertainty in the sensing are due tothe assumption of noise distribution. The traditional sensingalgorithms depend on the Gaussian noise assumption in theirmodels. In fact, the real-time statistical structure of the datadiffers from the Gaussian approximation [5]. Thus, to deal withthis kind of noise variations or noise uncertainty, it is interestingto focus on robust decision algorithms. Cross correlation isused to mitigate the noise uncertainty for energy detectionunder low SNR environment [7]. Coherence-based detection isshown to be the best method to detect weak signals under noiseuncertainty [8]. Recent studies have shown that the entropy de-tection in the frequency domain [entropy (FD)] and spectrum-correlation-density-function-based detection methods are therobust methods for narrow-band detection with unknown noisevariance [8]–[10]. However, the performance of the aforemen-tioned detectors are unable to satisfy the IEEE 802.22 WRANsystem standards [11]. In this paper, we report on entropyestimation using cyclic features of receiving signals.

Multinode/cooperative sensing is being used for spectrumsensing to mitigate the noise effects encountered by each cog-nitive radio [2]. In multinode sensing, two kinds of decisionfusion logics (soft decision fusion and hard decision fusion)are being used in the central node or the fusion center. Amongthese, soft decision fusion techniques such as weighted gaincombining (WGC) and equal gain combining (EGC) methodsare shown to be reliable [4]. The EGC method has been shownto be an effective method for offline evaluation of an algorithmsince it assigns equal weight to all cooperative nodes. However,the performance of EGC is less compared with WGC due toassignment of different weights to different nodes accordingto their signal strengths [12]. Hence, a soft decision fusiontechnique based on WGC is studied and applied for cooperativesensing. In [13], weight vector generation using log-likelihoodratio (LLR) test is proposed to improve the sensing perfor-mance. However, an LLR-based sensing method is optimalwhen the signal and noise variances of the received signal ateach node in the cooperation are known. However, it is notpracticable to know the signal characteristics prior for all thefrequency bands to be scanned. Particle swarm optimization(PSO)-based cooperative sensing has been proposed in [14].However, it requires more number of iterations to convergethe solution. The linear cooperation for spectrum sensing isproposed, and a method that optimizes the modified deflec-tion coefficient (MDC) is proposed to find the weight vector

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for all possible cognitive radio systems [15]. However, theMDC-based method is a suboptimal solution, which incursperformance degradation. In this paper, we propose to usedifferential evolution (DE) algorithm to exalt the cooperativespectrum sensing performance. A DE algorithm is an evolu-tionary computation method and has been applied in diversedomains of science and engineering applications [16]. DE eval-uates the optimal values for a set of parameters by repeatedlymaking pseudorandom changes to their values. The numberof parameters is referred as the dimension of the problem.After making changes, the algorithm evaluates the fitness of thesolution. It became a popular evolutionary algorithm because itis simple to implement, has better performance in comparisonwith other evolutionary algorithms, and has less number ofcontrol parameters and less space complexity [16].

One more issue in the cooperative sensing is the presence andpossible emulation attacks of malicious/suspicious cognitive ra-dio (SCR) users, where malicious cognitive users intentionallyreport/send the false measurement to other cognitive/secondaryusers and thereby wrongly influence the multinode or global de-cision [17], [18]. The performance of the single malicious userelimination becomes unreliable because of multiple malicioususers in the network. Most of the works in the literature areconcentrated to eliminate single malicious user in the cognitiveradio network (CRN). In [17], authors proposed malicious userdetection based on sequential detection, where sensing hasbeen carried out at different time frames. However, in real-time applications, the sensing must be done for a single timeframe. Moreover, it has been reported that, if the model followsa log-normal distribution, the generalized extreme studentizeddeviate (GESD) test is the best method for multiple malicioususer elimination [13], [19]. In fact, the wireless communi-cation model may have any kind of distribution. Hence, amultiple malicious user elimination method using an adjustedbox-plot (ABP) test is proposed for skewed and normal datadistributions.

The objective of this paper is to develop an efficient multin-ode wideband sensing algorithm to enhance the sensing reliabil-ity along with the sensing performance in the low SNR regime.The cooperative sensing is performed in a noisy CRN, wherefew malicious users are involved in the sensing process alongwith the genuine cognitive users. The contribution of this paperis twofold.

1) We perform multinode wideband spectrum sensing basedon entropy and cyclic features [entropy (CF)] in eachsubband/channel under noise uncertainty. This is basedon the concept that the Fourier transform of the cyclicautocorrelation function gives the power spectrum at dif-ferent cyclic frequencies and its strength will vary widelyfor signal compared with noise [4].

2) A WGC method based on an ABP method and a DE algo-rithm is proposed to increase the reliability together withthe sensing performance. The ABP test is considered due toits ability to eliminate multiple malicious users in the coop-erative network for all possible data distributions [20].

In addition, three previous traditional sensing algorithms [21]are compared with the proposed method (with and without

suspicious users in the network). The receiver operating char-acteristic (ROC) curves are determined from the MATLABsimulations for the sensing algorithms using Digital VideoBroadcasting-Terrestrial (DVB-T) signals of different strengthsfor the application to IEEE 802.22 WRAN standards.

This paper is organized as follows. Section II describes theweighted gain cooperative wideband sensing algorithm basedon LLR and DE algorithms. Section III describes the proposedmultiple malicious user elimination techniques in the network.Simulation results are given in Section IV, followed by conclu-sions in Section V.

II. COOPERATIVE WIDEBAND SPECTRUM

SENSING ALGORITHM

Consider that the frequency bandwidth is divided into “K”nonoverlapping subbands. It is assumed that some of the sub-bands (β) are vacant for a particular time duration and in aspecific geographic location with a constraint that 1 ≤ β ≤ K.Hence, these vacant subbands are available for DSA. Fig. 1illustrates the concept of weighted gain cooperative spectrumsensing using DE algorithm. We consider a noisy CRN, whichcontains few malicious cognitive users along with the genuinecognitive users. Here, several cognitive users in one particulargeographic area are observing the same hypotheses indepen-dently and transmitting their soft measurements to an ABPand sigma limit test block for SCR user elimination. Eachsecondary user in the multinode sensing is confronting differ-ent channel impediments. The DE unit generates the optimalweights, which depend on the individual soft measurementsfrom genuine cognitive users and the objective/fitness function.The global decision is evaluated using the optimal weights andindividual soft measurements from each node.

Assuming that there are M nodes in the cooperation and thatthe received signals of all nodes are statistically independent,then the composite hypothesis test can be written as

Hk0 : Rm(n) =Wm(n), m = 1, 2, . . . ,M

Hk1 : Rm(n) =hm · Sm(n) +Wm(n)

where Rm(n), Wm(n), and Sm(n) can be expressed as

Rm(n) =[r0m, r1m, r2m, . . . , r(K−1)

m

]Wm(n) =

[w0

m,w1m,w2

m, . . . ,w(K−1)m

]Sm(n) =

[s0m, s1m, s2m, . . . , s(K−1)

m

]where rk, wk, and sk are the received signal, the noise, and theprimary user signal in the kth subband (k ∈ {0, . . . , (K − 1)}),respectively; m = 1, 2, . . . ,M ; n = 0, 1, . . . , (N − 1); and Nis the total number of samples considered for sensing.

The algorithms are analyzed with the following assumptions.1) The noise in each subband (wk) lies in the neighborhood

of a nominal Gaussian with mean zero. Thus, we modelthe fact that there is at most x dB of uncertainty in thenoise processes. All the moments of the noise processmust be close to the nominal noise moments [5], i.e., we


SRINU AND SABAT: OPTIMAL MULTINODE SENSING IN A MALICIOUS COGNITIVE RADIO NETWORK 3

Fig. 1. Proposed cooperative sensing model with ABP and DE algorithms.

assume that E(wkN) = [(1/δ)E(wk

N−a), δE(wkN−a)],

where wkN−a ∼ N(0, σ2

w), σ2w is the noise variance of the

nominal Gaussian, and δ = 10x/10 > 1.2) The received signal in each subband (sk) is a stochastic

signal, which follows Gaussian independent and identi-cally distributed with mean μs and variance ζ2.

3) The channel gain (h), transmitted signal (sk), and theadditive white Gaussian noise (AWGN) (wk) are in-dependent of each other. The channel is time invariantduring the sensing period such that channel coefficients(hm) are having nonzero mean and unit variance complexGaussian random variables.

A. Cooperative Sensing Using LLR Test

To enhance the cooperative sensing performance, differentweights are assigned to the cognitive users according to theirreceived signal strength. In this method, the weights to eachcognitive radio in the network are evaluated using an LLR test,which is given as [19]

log

[P(Zk|Hk

1

)P(Zk|Hk

0

)]

Hk1

≷Hk

0

λke (1)

where Zk is a vector of soft decisions. The preceding teststatistic for cooperative sensing can be written as

M∑m=1

(N−1∑n=0

|rm[n]|2 ·Θm

)Hk

1

≷Hk

0

λke (2)

where the statistic∑N−1

n=0 |rm[n]|2 = ψm is the energy mea-surement of the mth node, Θm is the weight assigned to the mthnode, and Θm = (ζ2m/(σ2

w−m(σ2w−m + ζ2m))) [13], where ζ2m

and σ2w−m are the variances of signal and noise at the mth node.

Intuitively, for K number of subbands, (2) can be formulated as

Qd-wgc=

M∑m=1

ψkavg-m ·Θm

Hk1

≷Hk

0

λke , k=0, 1, . . . , (K−1) (3)

where ψkavg-m(r) = E(ψk

m) = (1/M)∑M

m=1 ψkm, λk

e is thethreshold that depends on the desired false alarm probability,and ψk

m is the energy measurement of the mth cognitive radioin the kth subband.

In the case of the spectral coherence function (SCF) detectionmethod, the cooperative wideband detection probability usingWGC is [20]

Qd-wgc=M∑

m=1

Γkavg-m ·Θm

Hk1

≷Hk

0

λkc , k=0, 1, . . . , (K−1) (4)

where Γkavg-m = E(Γk

m(r)). The test statistic, i.e., Γkm, is based

on the spectral average over number of cyclic frequencies,which can be expressed as

Γkm =

∣∣∣∣∣ 1

nα

∑α

Cαr (f)

∣∣∣∣∣ ∀m (5)

where Cαr (f) is the estimated SCF in the kth subband, which is

evaluated as [22]

Cαr (f)

∼= Sαr (f)

[Sr(f + α/2)Sr(f − α/2)]1/2(6)

and where α is a cyclic frequency, index “r” is the receivedsignal sequence in each subband, and λk

c is the threshold forsignal detection in the kth subband [4], [23].

In the case of the entropy (FD) detection method, the coop-erative wideband detection probability using WGC is [13]

Qd-wgc=

M∑m=1

φkavg-m ·Θm

Hk0

≷Hk

1

λkε , k=0, 1, . . . , (K−1) (7)

where φkavg-m is the expected value, λk

ε is the threshold for en-tropy (FD) detection, and φk

m is the entropy measurement of themth cognitive radio in the kth subband, which can be written as

φkm = −

L∑i=1

fki

Nlogb

fki

N∀m (8)



where fki denote the frequencies of the ith bin of the kth sub-

band according to the histogram method with∑L

i=1 fki = N .

In the case of the entropy (CF) method, entropy and cyclicproperties of the received signal are examined to sense the fre-quency band. The cooperative wideband detection probabilityusing WGC is

Qd-wgc=

M∑m=1

Φkavg-m ·Θm

Hk0

≷Hk

1

λkε , k=0, 1, . . . , (K−1) (9)

where Φkavg-m = E(Φk

m). The entropy, i.e., Φkm, of the correla-

tion values at different cyclic frequencies of the received signalcan be expressed as

Φkm(s) = −

L∑i=1

(pki)log pki ∀m (10)

where pki denotes the frequency of the ith bin for the kthsubband. The threshold value for the signal detection can begiven as

λkε = Hk

L + σkwQ

−1(1− Pf ) (11)

where HkL = ln(L/

√2) + (γ/2) + 1 is the estimated entropy

of Sαr (Ω) under AWGN, γ is the Euler–Mascheroni constant,

and Q(·) is the complementary distribution function of thestandardized Gaussian [Q(x) = (1/

√2π)

∫∞x exp(−t2/2)dt]

evaluated at (1− Pf ). In general, the central fusion nodedoes not have prior information about the SNR. Therefore,in the case of EGC, equal weights are given to all nodes,and their measurements are aggregated to make the globaldecision.

B. Cooperative Sensing Using DE Algorithm

The DE algorithm is applied to evaluate the optimal weightsfor weighted gain cooperative spectrum sensing.

Problem Formulation: In this case, the problem isformulated to find a set of weight values that maximizesthe cooperative detection probability. Mathematically, it can beexpressed as

max Qd-wgc, s.t.M∑

m=1

wm = 1, 0 < wm < 1. (12)

In DE algorithm, cooperative detection probability Qd-wgc isconsidered as the objective function. In this algorithm, forweight optimization, the population of size “P ” is initialized as

ΘI = [Θ1,G,Θ2,G, . . . ,ΘP,G] , i = 1, 2, . . . , P

where Θi,G is a vector containing “M” number of randomweights at the “Gth” generation. The best weight set in eachgeneration is the one that gives optimal values for detectionprobability. The next generations of vectors are generated asfollows. For every vector Θi,G (target vector), the followingthree steps are performed.

Mutation: Three mutually distinct random vectors Θr1,G,Θr2,G, and Θr3,G are taken such that i �= r1 �= r2 �= r3. Amutant vector/donor vector is generated according to the ex-pression [16]

Vi,G+1 = Θr1,G + F · (Θr2,G −Θr3,G) (13)

where F ∈ [0, 2] is a constant that controls the magnitude of thedifferential variation.

Crossover: The diversity of the vector set is increased bydeveloping a trial vector as

uj,i,G+1=Vj,i,G+1 if (rand(j)≤CR) or j= rnbr(i)=Θj,i,G if (rand(j)>CR) or j �= rnbr(i)

(14)

where j = 1, 2, . . . ,M , and rand(j) is the random numbergenerator with outcome ∈ [0, 1]. CR is the crossover constant∈ [0, 1], which has to be chosen by the user, and rnbr(i) is arandomly chosen index from {1, 2, . . . ,M}, which ensures thatthe trial vector ui,G+1 gets at least one parameter from donorvector vi,G+1.

Selection: In this process, the trial vector ui,G+1 is com-pared with the target vector Θi,G+1, and the one that givesthe best values for cumulative probability of detection ispassed on to the next generation as Θi,G+1. The algo-rithm is continued until the optimum weight vector (Θopt =[Θopt(1),Θopt(2), . . . ,Θopt(M)]) is found. The cooperative de-tection probability with the optimal weights can be determinedby replacing the random weights.

III. MULTIPLE MALICIOUS COGNITIVE

USER ELIMINATION IN CRN

In multinode sensing, few malicious users degrade the reli-ability of sensing by sending false soft decision to the fusioncenter. We study the methods of detecting malicious users andintroduce the elimination process to increase the cooperativesensing reliability. The ABP method is considered to addressthe problem of multiple malicious user detection and suppres-sion in the network [20]. We assume that the distribution ofthe soft measurement data (Zk) lies in some neighborhood ofnormal Gaussian. It is also considered that the data set containsthe soft decisions from all possible attacking strategies suchas always YES, always NO, and from deep faded nodes. Inpractice, all preceding attacking strategies severely degrade thesystem performance.

A. Generalized Extreme Studentized Deviate (GESD) Method

In this method, the number of malicious users in the networkcan be calculated as [13], [19] follows.

The single extreme studentized deviate (ESD) in a randomnormal sample is defined as

j = maxi

{∣∣ϕi − X̄∣∣

SX-dev

},

j = 1, 2, . . . , ui = 1, 2, . . . , (τ ∗M)

(15)



where ϕi, X̄ , and SX-dev denote the ith element, the samplemean, and the sample standard deviation of data set “X ,”respectively.

If j = 1, 1 is the first ESD, which is associated withthe largest or the smallest order observation in the data set,for example, ϕ1. In the second recursive calculation, ϕ1 isdiscarded from the set (but ϕ1 may not be an ultimate outlier).The new X̄ and SX-dev (excluding ϕ1) are recalculated fromthe reduced sample of length (τ ∗M)− 1. Equation (15) isused again to recalculate 2. The process is continued until1, 2, . . . ,u are computed, and each of this is individuallycompared with a critical value χj as follows:

χj =(M − j)tM−j−1,p√(

M − j − 1 + t2M−j−1,p

)(M − j + 1)

(16)

where tM−j−1,p is the 100α percentage point from thet-distribution with (M − j − 1) degrees of freedom, and p ={1− (α/(2(M − j + 1)))}, where α = 0.05, is the signifi-cance level for the overall test. The malicious users are deter-mined by finding the largest “j” such that j ≥ χj .

The SCR set using the GESD test is given by

= {1,2, . . . ,j}, j ∈ X, j ≤ u.

The final SCR can be determine based on the followingequality for a fixed value of m [13], i.e.,

τ∑itr=1

[I()]itr,m = τ

[(τ − 1)

2M +m

](17)

where I() are the indices of the malicious cognitive users.

B. Adjusted Box-Plot (ABP) Method

The traditional box-plot and GESD methods have the lim-itation that the more skewed the observed data, the moreobservations may be detected as malicious users. Hence, asophisticated method based on the ABP test is used to excludemultiple malicious nodes for the skewed and normal soft datadistribution. The skewness of the observed data is derived fromthe med-couple, i.e., ξ. It can be defined as

ξ = median H(ϕi, ϕj),ϕi ≤ ϕ̃ ≤ ϕj

ϕi �= ϕj.

The value of the med-couple ξ is in between −1 and 1. If ξ =0, the data are symmetric, and the ABP becomes the traditionalbox plot. If ξ > 0, the data have a right skewed distribution,whereas if ξ < 0, the data have a left skewed distribution.

The function “H” is expressed as

H(ϕi, ϕj) =(ϕj − ϕ̃)− (ϕ̃− ϕi)

(ϕj − ϕi).

For the special case ϕi = ϕj = ϕ̃, the function H is defineddifferently [24]. Let ω1 < . . . < ωq denote the indices of the

Fig. 2. Model of the sigma limit test.

observations, which are tied to the median ϕ̃, i.e., xωl= ϕ̃, for

all l = 0, . . . , q, then

H(ϕωi, ϕωj

) =

⎧⎨⎩

−1 if i+ j − 1 < q0 if i+ j − 1 = q+1 if i+ j − 1 > q.

The lower and upper intervals of the ABP are

[Q1 − 1.5e−3.5∗ξ(Q3 −Q1),

Q3 + 1.5e4∗ξ(Q3 −Q1)]

if ξ ≥ 0 (18)[Q1 − 1.5e−4∗ξ(Q3 −Q1),

Q3 + 1.5e3.5∗ξ(Q3 −Q1)]

if ξ ≤ 0 (19)

where Q1 and Q3 are the first and third quartiles of the soft dataset. The observations that fall outside the interval are consideredas malicious users (scr) in the network.

In addition, the deep faded nodes are identified and sup-pressed using sigma limits applied to each node in the coop-eration. Fig. 2 represents the overview of the sigma limit test.The red dots are the measured soft data of each node in thecooperation. The control lines represent the decision cut pointsto decide whether an observed node is a deeply faded node ornot. This can be formulated as

Ωc = E(Πm)± � ·

√√√√1

τ

τ−1∑u=0

(ϕkMu+m − Π̄m

)2(20)

where Πm = {ϕkm, ϕk

M+m, ϕk2M+m, . . . , ϕk

(τ−1)M+m} is thepast accumulated soft data set of the mth node of the kthsubband, and ϕk

2M+m is the entropy measurement in thirditeration of the mth node of the kth subband. The order of sigmalimit “�” depends on the channel properties.

The genuine cognitive users set E can be identified with thefollowing function:

E={x : x∈X and x /∈ scr}∩{x : x∈X and x /∈ f} (21)

where “ f” is a deep faded node [13].



Hence, the optimal multinode detection probability using DEand ABP for energy and SCF methods can be evaluated as

Qd-wgc(opt) =

M∑m=1

Υkavg-m ·Θopt(m)

Hk1

≷Hk

0

λka ∀k (22)

where Υkm and λk

a are the soft measurement and the thresholdof either energy detection or SCF detection, respectively.

Similarly, the optimal multinode detection probability usingDE and ABP for entropy (FD) and entropy (CF) methods canbe evaluated as

Qd-wgc(opt) =

M∑m=1

Υkavg-m ·Θopt(m)

Hk0

≷Hk

1

λkφ ∀k (23)

where Υkm and λk

φ are the soft measurements and thresholds ofexamined entropy detection methods.

IV. SIMULATION RESULTS

The ROC curves in terms of Pd against Pf (or Pm =(1− Pd) versus Pf ) and SNR against Pd are evaluated forthe sensing algorithm. DVB-T signals of different strengthsare considered for the application to IEEE 802.22 WRANstandards. MATLAB is used as a tool for analyzing the de-tection performance through extensive simulations. The sim-ulations are performed according to the grouping concept tospeed up the simulation [25]. The traditional sensing tech-niques based on energy, SCF, and entropy estimation of thereceived signal are also simulated for performance compari-son. The frequency spectrum bandwidth under assessment isdivided into K subbands. In each band, licensed user maybe present or absent. Hence, in the simulation, it is assumedthat five subbands (β = 5) are randomly unoccupied withinthe K(K = 9) available frequency bands. The performancesof considered detection algorithms are analyzed by two cri-teria: 1) weighted gain cooperative sensing performance withsuspicious/malicious cognitive radio (WSCR) users in the net-work and 2) weighted gain cooperative sensing performancewithout suspicious cognitive radio (WOSCR) users in the net-work. The detector estimates the test statistic of the receivedsignal within the band and compares it with the correspondingthreshold. The threshold is computed to achieve a tolerable falsealarm probability and is assumed the same for all the subbands(i.e., λ1

ε = λ2ε = λ3

ε = . . . = λKε ). The performance of the al-

gorithm is evaluated through extensive simulations with givensignal strength in presence of noise uncertainty. The lower andupper bounds of noise uncertainty are considered as −1.5 and1.5 dB, respectively. Owing to the nonexistence of a closed-form solution for Pd and Pf , the performance of the detectionis analyzed using Monte Carlo methods for 10 000 iterations. Inthe simulation, cooperative cognitive users are assumed to haveconfigurations shown in Fig. 1. The performance of the pro-posed cooperative wideband sensing is evaluated with differentcollaboration scenarios of soft decision fusion techniques. Thedifferent distance case (DDC) is considered to include the pathloss effects in the simulation, where the cooperative nodes are

Fig. 3. Estimated entropy with noise power variations [entropy (CF)].

randomly distributed over the considered geographic area andlocated within 3–10 km from the licensed user transmitter.Moreover, it is also assumed that the sensing is performed ina noisy CRN, where few malicious cognitive users are involvedalong with the genuine cognitive users.

There are generally two approaches to estimate the entropyof the received signal. The first approach fixes bin width “Δk

cf”so the number of bins “L” changes with noise power. Theother approach fixes L and the Δk

cf changes with the spectrummagnitude. Here, we choose the later method for its robustnessagainst noise uncertainty. Simulation results of the proposedmethod under noise uncertainty are shown in Fig. 3, whichplots the estimated entropy versus the variations of the noisepower. The result shows that minor changes in the noise powerlead to a significant change in the estimated entropy in caseof fixed Δk

cf . However, this power change does not affectthe estimated entropy of the proposed detector with fixed L.In this simulation, the measured noise power is consideredas −100 dBm; the noise power is varied up to 20% of themeasured value. The performance is examined at two differentfalse alarm probabilities, i.e., Pf = 0.1 and 0.01. In practice, areasonable noise uncertainty is 1 dB [6], [7]. It is observed thatthe estimated entropy remains constant for a fixed bin number,whereas the entropy is linearly proportional to the noise powerunder a fixed Δk

cf . In the figure, the proposed detector based onentropy and cyclic properties with fixed L is a robust sensingtechnique against noise uncertainty.

Fig. 4 illustrates the performance of the DE algorithm interms of the number of iterations against detection probability.In the simulation, we have considered that the population sizefor the DE algorithm is 30, the number of generations is 100,the number of nodes M is 5, and the SNRs of the all nodesare in between −20 and 0 dB. In the figure, it is shown thatthe proposed DE solution converges after around 25 iterations,which is so fast that it can ensure that the computation com-plexity of the proposed method meets real-time requirementsof spectrum sensing for cognitive radio, whereas the PSO-basedweighted cooperative sensing needs 50 iteration to converge thesolution.



Fig. 4. Performance of the DE algorithm.

Fig. 5. ROC curves of weighted gain cooperative sensing methods.

Fig. 5 shows the performance comparison of the proposedDE-based WGC algorithm with the LLR-based WGC and EGCalgorithms under probable noise impediments in the channel.We considered that the number of secondary users (M) is 5 andthat the SNRs of the all nodes are in between −20 and 0 dB. Inthe case of the EGC method, the weights are equally generatedwith the constraint that the sum of the weights should be equalto 1. The detection probability of the equal weight coopera-tion method cannot be an optimal method because of equalimportance to each cognitive node in cooperation, and there issignificant performance stagnation due to improper assignmentof weights to each node. In the case of the LLR-based WGCmethod, the weight (Θm) for each node is evaluated based onsignal and noise variances of the received signal. This techniqueis the optimal method for cooperation when the received signalcharacteristics are known. However, it is not always the caseavailable for all the frequency bands. In the case of the proposedweight generation method, the weights are generated using DEalgorithm with cumulative detection probability as the objectivefunction as per (14). In the simulation results in Fig. 5, it isshown that the performance of the introduced method matches

Fig. 6. Average SNR versus Pd of LLR- and DE-based WGC methods[entropy (CF)].

with the LLR-based method with the added advantage of weightgeneration, which is independent of received signal character-istics. Hence, the technique can be used for real-time CRNs forspectrum sensing.

Fig. 6 illustrates the average SNR against detection proba-bility of cooperative wideband sensing based on LLR and theproposed DE-based WGC methods. In this simulation, variablenumbers of nodes, i.e., M = 3, 5, and 8, are considered withPf = 0.1 and 0.01, L = 15, and N = 256. In the figure, it isshown that the detection probability depends on the false alarmprobability. It reduces as the false alarm probability increases.Moreover, the performance is increased with increase in coop-eration level due to diversity gains. In Fig. 6, it is shown thatthe performance of the DE-based WGC method degrades from−23 to −21.5 dB for five nodes, as the false alarm probabilityreduces from 0.1 to 0.01. From close observation, it can befound that the proposed WGC method outperforms the LLR-based WGC method as the number of nodes in the cooperationincreases.

Fig. 7 illustrates the average SNR versus detection proba-bility of cooperative wideband sensing based on entropy andcyclic features with the EGC method. From the figure, it is ob-served that there is a significant performance improvement withthe increase in the tolerance level (from Pf = 0.01 and 0.1). InFig. 7, it is shown that the performance of the EGC methoddegrades from −22 to −21 dB for five nodes, as we reduce thefalse alarm probability from 0.1 to 0.01. From Figs. 5 and 6, itcan be noted that the performance of WGC is better comparedwith EGC. This is owing to the assignment of different weightsto different nodes according to their signal strengths. Theperformance of EGC fusion also increases with the number ofnodes increase in the cooperation.

Fig. 8 shows the ability of eliminating the malicious userswith GESD, ABP, box-plot, median absolute deviation (MAD),Grubs, and Dixon’s tests in terms of SNR against detectionprobability. The number of cognitive users (M = 5 and 8),N = 256, and Pf = 0.1 are examined in the simulation. Fromthe figure, it is observed that the GESD method is the bestmethod for eliminating multiple suspicious users with large



Fig. 7. Average SNR versus Pd of EGC [entropy (CF)].

Fig. 8. Performance comparison of the ABP test with various outlier tests.

number of observations (τ = 8 iterations), which follow thelog-normal distribution. However, its sensitivity reduces asthe number of observed data samples reduces. For the GESDmethod, the upper bound of outliers is considered to be “u”= 4τ during the simulation. On the other hand, the ABP methodgives the same performance for any size of data and for allpossible data distributions. It is obvious that the algorithmiccomplexity is less using the ABP compared with using theGESD method. The performances of various outlier detectionmethods given in [17], [26], and [27] are also simulated andcompared with the proposed method. Moreover, the deeplyfaded nodes are suppressed by sigma limit test in the coopera-tive network. The process of elimination of deeply faded nodesis given in (20). If the observation set of a node with τ iterationcrosses the control lines 2τ/3 times, then the node is detectedas a deeply faded node (“ f”). The sigma limits of control linedepend on the channel environment.

The average SNR versus detection probabilities of the pro-posed weighted gain cooperative wideband sensing based onABP and DE for the considered detection methods are shown

Fig. 9. Average SNR versusPd of the proposed method [energy, entropy (FD)].

Fig. 10. Average SNR versus Pd of the proposed method [SCF, entropy (CF)].

in Figs. 9 and 10. These simulations correspond to the numberof nodes M = 3, 5, and 8, with Pf = 0.1 and N = 256. Inthe case of the energy detection, the data set (X) contains theenergy measurement of all users in cooperation. The optimalcooperative detection probability is computed by aggregatingthe soft measurements from genuine cognitive users and theircorresponding optimal weights as per (22) and (23). From thefigures, it is observed that Pd increases for all detection tech-niques after elimination of malicious users in the cooperativenetwork. Moreover, the proposed method has shown superiorperformance, even in DDC, as compared with the other threeother examined detection methods. The SNRwall under DDCenvironment for the four considered sensing techniques withsuspicious cognitive radio (WSCR) users and without suspi-cious cognitive radio (WOSCR) users are tabulated in Table I.The SNRwall is defined as the minimum SNR that a cognitiveuser can detect with Pd = 0.9 and Pf = 0.1 [5]. In the caseof WSCR, the four detection algorithms such as energy, SCF,entropy (FD), and entropy (CF) are able to detect the signals ofaverage SNR as −14.5, −20, −18, and −23 dB, respectively,



TABLE ISNRwall OF DETECTION METHODS USING WGC (DE)

AFTER ELIMINATION OF SCR USER

with five secondary users in cooperative network. In the caseof WOSCR, the preceding algorithms are able to detect signalsof average SNR as −16, −22, −20, and −24 dB, respectively,with same number of users in cooperative network. From thetable, it is observed that the performance gain of entropy (CF)without malicious users in the network is approximately 8 dBcompared with energy, 4 dB compared with entropy (FD), and2 dB compared with SCF, which is a significant performanceimprovement in negative SNR regime for IEEE 802.22 WRANsystems. Finally, it can be concluded that the proposed approachof wideband sensing enhances the sensing performance andreliability compared with other sensing methods.

V. CONCLUSION

In this paper, we have proposed a WGC technique based onABP and DE algorithms. The main advantage of the introducedmethod with the DE algorithm is that it does not requireany prior information of signal strength or characteristics forweight generation. We considered the ABP test for multiplemalicious user elimination due to its applicability and effec-tiveness for skewed and normal data distributions. From thesimulation results, it is concluded that the proposed coopera-tive sensing method based on entropy and cyclic features isrobust against noise uncertainty. According to the simulationresults, the proposed WGC technique algorithm can sense thespectrum efficiently and outperforms the other sensing (energy,SCF, and entropy detection) methods. From close observation,it is found that the proposed WGC method outperforms theLLR-based WGC method as the number of nodes in the coop-eration increases. The proposed sensing technique can detect−24 dB signals even under noisy CRN with five cognitiveusers in cooperation. In addition, it shows −8, −4, and −2 dBperformance improvement compared with energy, entropy, andSCF detection methods of same set of simulation parameters,respectively. In an extremely noisy environment, it is a sig-nificant performance improvement for cognitive radio systems.Hence, we conclude that the proposed method can be appliedfor real-time cooperative sensing for cognitive radio systems.The field-programmable gate array implementation of the pro-posed cooperative sensing is under development for real-timeapplications.

ACKNOWLEDGMENT

The authors are grateful to the University Grants Com-mission (UGC), Government of India for providing necessarysupport to carry out this research work.

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Sesham Srinu was born in Vijayawada, India, in1983. He received the M.Sc. (with honors) de-gree in electronic sciences from Andhra Univer-sity, Visakhapatnam, India, in 2008. He is currentlyworking toward the Ph.D. degree in electronic sci-ences in Hyderabad Central University (University ofHyderabad), Hyderabad, India.

His current research interests include the develop-ment of spectrum sensing algorithms for cognitiveradio and wireless communications and the hardwareimplementation of signal processing algorithms.

Samrat L. Sabat (M’13) received the Ph.D. degreein electronics from Berhampur University, India,in 2004.

He is currently a Reader in electronics with theUniversity of Hyderabad, Hyderabad, India. His re-search interests include signal processing algorithmfor cognitive radio, sensor signal processing, swarmintelligence techniques and its applications, andthe hardware implementation of signal processingalgorithms.