Cumulant-based blind cooperative spectrum sensing method for cognitive radio

Physical Communication (

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Cumulant-based blind cooperative spectrum sensing method for cognitive radio Jun Wang a , Riqing Chen b , Feng Shu c, *, Ruiquan Lin a , Wei Zhu c , Jun Li c , Dushantha Nalin K. Jayakody d a

College of Electrical Engineering and Automation, Fuzhou University, Fuzhou 350108, Fujian Province, China College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fuzhou 350002, Fujian Province, China c School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu Province, China d Department of Control System Optimization, Institute of Cybernetics, National Research Tomsk Polytechnic University, Russia b

article

info

Article history: Received 8 March 2017 Received in revised form 5 November 2017 Accepted 8 November 2017 Available online xxxx Keywords: Cognitive radio Cooperative spectrum sensing Cumulant Non-Gaussian

a b s t r a c t Spectrum sensing is a crucial technology in cognitive radio (CR). Cumulant-based or higher order statistics (HOS) based spectrum sensing methods are often considered in literature for spectrum sensing because cumulants higher than 3-order can be used as a feature to distinguish non-Gaussian signals from Gaussian noise. However, most existing cooperative spectrum sensing methods are based on the assumption that the channel gain is available, which cannot be realistic in practice. In this paper, a novel cumulant-based cooperative spectrum sensing method is proposed. The proposed method does not depend on the noise power, channel gain, or the unknown signal parameters. Additionally, the proposed method is based on Neyman–Pearson (N–P) criteria, thus it is optimal in terms of the performance of detection probability if the false alarm probability is given in advance. Simulation results and analysis are presented to verify the validity and the superiority of the proposed cooperative spectrum sensing method over the existing ones. © 2017 Published by Elsevier B.V.

1. Introduction Spectrum sensing is a crucial technology for secondary users (Sus) in cognitive radio [1]. Its main goal is how to discover the primary users (Pus). Several kinds of spectrum sensing methods have been proposed, such as energy based spectrum sensing methods, autocorrelation based spectrum sensing methods, cyclostationarity based spectrum sensing methods, and multi-cumulant based spectrum sensing methods [2]. Energy based detection methods are usually simple and have admirable performance but they depend on the accurate noise power. If the noise power is unknown, energy based detection methods would suffer the problem of SNR wall and fail to work in the worst case [3,4]. Autocorrelation based spectrum sensing methods, for example, covariance matrix based method [5], eigenvalue based method [6] and oversampling method [7], use autocorrelation values to distinguish autocorrelated signals from white noise and are immune from noise uncertainty. However, if the noise is colored or not white, their detection performances degrade greatly. Cyclostationarity based author. * Corresponding E-mail addresses: [email protected] (W. Jun), [email protected] (R. Chen), [email protected] (F. Shu), [email protected] (R. Lin), [email protected] (W. Zhu), [email protected] (J. Li), [email protected] (D.N.K. Jayakody).

detection methods use cyclostationarity to extract signals from noise [8,9]. Cyclostationarity may come from underlying periodicities of man-made signal, such as coding, modulation and cyclic prefix. As a result, cyclostationarity can be used to distinguish the primary user signal from the noise. But cyclostationarity based methods should know the accurate cyclic frequencies in advance. In practice, because of the uncertainties in CR, such as noise uncertainty [3], signal uncertainty [10], and channel uncertainty, the noise power and cyclic frequencies may not be known exactly in advance and the noise could also be correlated. Thus, the application of energy based methods, autocorrelation based methods and cyclostationarity base methods would be limited. Cumulants of three-order or more can be used as a feature to distinguish non-Gaussian signals from the Gaussian noise, so there are some cumulant-based spectrum sensing methods proposed already. A single-cumulant based method is first proposed in [11]. In [12], the authors further develop a multicumulant based spectrum sensing method. A sequential cumulant-based spectrum sensing method is also given in [13] and a cumulant-based goodness of fit (GoF) test spectrum sensing method is designed in [14]. However, these cumulant-based methods are mainly applied in a scenario with single CR user. Equal gain combination (EGC) scheme is simple and blind. But EGC does not exploit the rich received statistics knowledges sufficiently. Compared with EGC, other weighting combination schemes [15–17] can increase the

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detection probability but they are not blind and need to know the exact SNR of every Su, which may not be realistic in cognitive radio. In this paper, a novel cumulant-based cooperative spectrum sensing method is proposed. The method first receives the test statistic of every Su in the network, and then calculates the estimated optimum coefficients according to Neyman–Pearson (N– P) criteria and some nonparametric approximations, and then constructs the total test statistic by linearly combining the test statistics and the estimated optimum coefficients and also establishes the threshold by using the estimated optimum coefficients, finally makes the decision by comparing the test statistic with the threshold. The main benefit of the proposed method is that it is blind. In other words, it is independent of noise power, channel gain or unknown signal parameters and only needs the known variables such as false alarm probability, the number of Sus and the received signal. 2. Conventional cumulant-based spectrum sensing method for a single Su A typical spectrum sensing problem is usually casted as the following binary hypothesis testing problem:

Fig. 1. System block diagram of the proposed method.

{

x(t) = n(t) H0 x(t) = s(t) + n(t) H1

(1)

where x(t) is the received signal, s(t) is the unknown non-Gaussian primary signal, n(t) is the additive Gaussian noise (AGN) (maybe white or colored) with zero mean, and H0 or H1 respectively denotes the absence or presence of s(t). Given T data samples, a kth order cumulant can be estimated by [18]: cˆkx (τ ) ≜

P ∑

ˆ v1,p x · · · m ˆ vNp ,p x (−1)(Np −1) (Np − 1)!m

(2)

p=1

where P is the number of partitions of the set x(t), . . . ,x(t + tk−1 ), Np is the number of parts in partition p, vi,p is the number of elements ˆ v1,p x represents the sample kth order in part i of partition p, and m moment [18]: T −1 1∑

ˆ kx (τ ) ≜ m

T

x(t)x(t + τ1 ) · · · x(t + τk−1 )

(3)

t =0

ˆ [ Define a 1 × N ]vector of cumulant estimators Ckx (τ ) ≜ cˆk1 x (τ1 ), . . . , cˆkN x (τN ) , the test statistic ∆c of cumulant-based

simple and blind. But EGC does not exploit the rich information of the received statistics sufficiently. In order to solve this problem, a new blind cooperative method is proposed here. The method first receives the test statistic of every Su in the network, and then calculates the estimated optimum coefficients according to N-P criteria and some nonparametric approximations, and then constructs the total test statistic by linearly combining the test statistics and the estimated optimum coefficients and also establishes the threshold by using the estimated optimum coefficients, finally makes the decision by comparing the test statistic with the threshold. The system block diagram is depicted in Fig. 1. Hereinafter, the superscript i denotes the ith user in the CRN. So the distributions of the ith CR users test statistic become

∆(i) c ∼

χN2

{ χ

(i) 2 N (T Ckx (

{ χ

2 N (T Ckx (

χN2 H0 1 ′ τ )Σ− C ( τ )) H1 c kx

(χ 2 /α )1/3 − [1 − 2(1 + β )/9α] ′

′2

P(χ |v, λ) ≈ Pn (x), x =

√ 2(1 + β )/9α [ ] α ≜ v + λ, β ≜ λ/(v + λ)

(7)

(4)

where P(χ |v, λ) denotes the probability density function (PDF) of non-central chi square distribution with non-central parameter λ and v degrees of freedom and Pn (x) denotes the PDF of normal distribution. Hence, let

(5)

∆(i) ≜

ˆ c is the estimated covariance matrix of Cˆ kx (τ ). where Σ According to [12], the distributions of test statistic ∆c are: ∆c ∼

(6)

The non-central Chi-square distribution can be approximated by the normal distribution according to the following formula [19, (26.4.28)]:

detection method is: 1 ˆ′ ˆ− ∆c = T Cˆ kx (τ )Σ c Ckx (τ )

H0

′

−1

(i) τ )Σ(i) Ckx (τ )) H1 c

Hence, given FAP Pfa , the threshold γ of cumulant-based detection method is γ = χN2 ,P , where χN2 ,P is the chi-square value fa fa with N degrees of freedom at Pfa level. Hence by comparing the test statistic ∆c with the threshold γ , one can decide whether a primary signal is present or not.

′2

√ 3

(i)

∆c

(8)

under H0 , according to (7) we have α = N, and β = 0, and ∆ the following approximate distribution:

∆(i) 1

N3

{ } 2 2 ∼N 1− ,

The cumulant-based cooperative spectrum sensing method is proposed in this section. Due to the uncertainties in CR, the cooperative methods should be preferred to be blind. The EGC scheme is

has

(9)

9N 9N

(i)

3. Proposed cumulant-based spectrum sensing method for multiple Sus

(i)

(i)−1

(i)′

under H1 , let λ(i) ≜ T Ckx (τ )Σc Ckx (τ ), according to (7), we have α = N + λ(i) , β = λ(i) /(N + λ(i) ) and ∆(i) has the following approximate distribution:

∆(i) 1

(N + λ(i) ) 3

∼N

⎧ ⎨ ⎩

2(1 + 1−

λ(i) ) N +λ(i)

9(N + λ(i) )

,

2(1 +

⎫

λ(i) )⎬ N +λ(i)

9(N + λ(i) ) ⎭

(10)

Please cite this article in press as: W. Jun, et al., Cumulant-based blind cooperative spectrum sensing method for cognitive radio, Physical Communication (2017), https://doi.org/10.1016/j.phycom.2017.11.001.

W. Jun et al. / Physical Communication (

∆FC ∼

{(

⎧ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎩N

( w(i)

i=1

1 3

P ∑

2

–

3

}

H0 w , 1 3 } ) P9N ( )2 ∑ 2 w(i) (N + 2λ(i) ) 2(N + 2λ ) 1 H1 , (N + λ(i) ) 3 − 5 4 9(N + λ(i) ) 3 9(N + λ(i) ) 3 i=1

1−

N

{ P ∑

)

2

)

N

9N

(i)

i=1 (i)

(13)

Box I.

Consequently, ∆(i) has the approximate distributions as shown in (i)−1

(i)

(11), where λ(i) ≜ T Ckx (τ )Σc

∆ ∼ (i)

⎧ ⎪ ⎪ ⎪ ⎨

{( N

1−

{ ⎪ (i) 1 ⎪ ⎪ ⎩N (N + λ ) 3 −

(i)′

Ckx (τ )

)

2 9N

}

2

1

N3,

H0

1

9N 3 } 2(N + 2λ(i) ) 2(N + 2λ(i) ) 5

9(N + λ(i) ) 3

,

4

9(N + λ(i) ) 3

(11) H1

At the fusion center, the total test statistic ∆FC can be defined as

∆FC ≜

P ∑

w ∆ (i)

(i)

(12)

where P is the number of CR users in the network and w (i) are the coefficients ∑P ( (i) )2 to be optimized and satisfy the normalized condition = 1. Assume every CR user in the network has the i=1 w same N and T for simplicity so that ∆FC has the approximate distributions in (13) (see (13) given in Box I). As a result, given false alarm probability Pfa , the threshold γFC can be established as:

γFC = Q −1 (Pfa )

2 1

9N 3

( ) P ∑ 2 1 w(i) + 1− N3 9N

(14)

i=1

where Q (·) is the Q -function. The detection probability Pd can be given in (15). According to the N-P criteria, given false alarm probability Pfa , we should find the optimum coefficients w (i) (i = 1, . . . , P) to maximize the detection probability Pd . Note that Q -function is a monotonic decreasing function, so the maximum value of Q -function is the minimum value of the argument in Q -function. By taking the partial derivative of the argument in the Q -function with respect to w (i) and setting it to zero, we get (16). Then we have (17). As a result, w (i) can be obtained in (18). Hence, define Θ( in (19), we get w (i) in ) ∑P (i) 2 = 1 , we further (20). Note the normalized condition i=1 w have the equation in (21). So that Θ can be rewritten in (22). (i) Applying (22) into (20), we get wopm in (23). According to (23), the (i) optimum coefficients w (i = 1, . . . , P) rely on λ(i) (i = 1, . . . , P) which cannot be known exactly. However we note that λ(i) can be (i) (i) estimated by ∆c , hence we have w ˆ opm in (24) (see Eqs. (15)–(24) in Box II). From (24), it can be seen that the optimal coefficients can be estimated by N (the number of cumulants used in spectrum (i) sensing) and ∆c (the received test statistic from every CR user), which are known in advance. Hence the optimal coefficients can be blindly calculated. Applying (24) into (14), we get the threshold of the proposed method:

√ γFC = Q

−1

(Pfa )

Algorithm 1 Proposed cumulant-based blind cooperative spectrum sensing method. Input: T samples of the received signal x(i) (t). Output: The decision result whether the Pu signal presents or not. Steps: (i) 1) Based on T samples of the [received signal ] x (t), given k1 ,. . . ,kN and fi1 ,. . . ,fiN (fii = τ1 , . . . , τki −1 ), construct the (i)

i=1

√

unknown signal parameters and channel gain, hence the proposed method is blind. Based on the above results, we summarize our proposed method as indicated in Algorithm 1.

2 1

9N 3

( ) P ∑ 2 1 (i) + 1− N3 w ˆ opm 9N

(25)

i=1

According to (24) and (25), the threshold is only related to N and (i) the estimated optimal coefficient w ˆ opm , which can be known or can be calculated in advance, and does not rely on the noise power,

test statistic ∆c at the i-th CR user as (4) and send it to the fusion center. (i)

2) The fusion center converts ∆c to ∆(i) (i = 1, . . . , P) as (8) and then calculates the estimated optimum coefficients (i) w ˆ opm (i = 1, . . . , P) as (24). 3) The fusion center calculates the threshold γFC as (25) and then calculates the total test statistic ∆FC as ∆FC ≜ ∑P (i) ˆ opm ∆(i) . i=1 w 4) At the fusion center, the total test statistic ∆FC is compared with the threshold γFC to determine the presence of the primary user signal. If ∆FC is larger than γFC , the decision that the Pu signal is present is made; otherwise, the contrary decision is made.

As for the complexity of the proposed method, we first need P cube root operations to get ∆(i) (i = 1, . . . , P), 3P 2 + 3P cube root operations, P square root operations, 17P 2 + 16P multiplications (i) and P 3 + 9P 2 + 10P additions to get w ˆ opm (i = 1, . . . , P), and need P multiplications and P − 1 additions to get the test statistic ∆FC . Moreover, we need 3 multiplications and P additions to get the threshold γFC . In total, the proposed method needs about 3P 2 + 4P cube root operations, P square root operations, 17P 2 + 17P + 3 multiplications and P 3 + 9P 2 + 12P − 1 additions. 4. Simulation results and analyses In this section, simulation results and analysis are presented to evaluate the proposed cooperative method. The primary signal is assumed to be an BPSK signal with its symbol interval T0 = 10/fc , where fc denotes the carrier frequency. The primary user signal is oversampled 10 times. The noise is additive colored Gaussian and is expressed as n(t) = 0.90n(t − 1) + u(t), where u(t) represents the additive white Gaussian noise with zero mean and unit variance. The cumulants used here are two 4-th order cumulants with the lag vector τ 1 = [0, 0, 0] and τ 2 = [0, 0, 1], respectively. So that N is 2. From Fig. 2 to Fig. 4, ‘‘Pfa ’’ means the FAP, ‘‘Pd ’’ means the detection probability, ‘‘CBC’’ means the proposed cumulant-based blind cooperative method, ‘‘EG-x dB’’ means the energy based equal gain

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⎧[ √ )] ⎫ ( ) ( P P ∑ ∑ ⎪ ⎪ 2 2(N + 2λ(i) ) 2 1 1 ⎪ ⎪ (i) −1 (i) (i) ⎪ ⎪ ⎪ ⎪ N3 + 1− w − Q (Pfa ) w (N + λ ) 3 − ⎪ ⎪ 1 5 ⎨ ⎬ 9N (i) ) 3 9N 3 9(N + λ i=1 i=1 Pd = Q √ ⎪ ⎪ ∑P 2(w(i) )2 (N +2λ(i) ) ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ 4 i=1 ⎩ ⎭ 9(N +λ(i) ) 3 √ )⎤ ( ⎡ ) ( P P ∑ ∑ 2 2 2(N + 2λ(i) ) ⎥ 1 1 ⎢ −1 (i) (i) (i) ⎦ ⎣Q N3 + 1− w − w (N + λ ) 3 − (Pfa ) 1 5 9N 9N 3 9(N + λ(i) ) 3 i=1 i=1 d

  ∑P √

(

)2 (N +2λ(i) )

2 w (i)

i =1

4 9(N +λ(i) ) 3

dw (i)

[

2 9N

(

1−

(

1

)

N3 −

√

(

2 w (i)

∑P

i=1

Q

=

1

−1

2

( + 1−

1

)

2

N

9N

1 3

P ∑

w −

2

∑P

(i) i=1 w

(

(N + λ

1

(i) 3 )

√

(

2 w (i)

∑P

−

2(N +2λ(i) )

√

1

√3 2

(N + λ(i) ) 3 −

− )

2(N +2λ(i) ) 5

3(N +λ(i) ) 3

i=1

P ∑

w

(i)

√ 3

√ (N + λ ) −

w(i) = P ∑

[

i=1

5

(

3(N + λ(i) ) 3

√

2(N + 2λ(i) ) 5

3(N + λ(i) ) 3

√

2(N + 2λ(i) )

−

3

−

N

3N

√ )

√ − 2

2

3N

1 3

2

2 9N

N

)

N

1 3

]

(

∑P

1

w(i)

)2

w(i)

i=1

− Q −1 (Pfa )N − 6 −

4w (i) (N + 2λ(i) ) 4

9(N + λ(i) ) 3

(

)2

(N +2λ(i) ) 4

4

(N +λ(i) ) 3

√ √3 2

2 3N

−

)

1

N3

∑P

(i) i=1 w

]·

(N + λ(i) ) 3

(N + 2λ(i) )

(18)

(N +2λ(i) ) 4

)

( −Q

−1

(Pfa )N

(N + λ(i) ) 3

− 61

(N + 2λ(i) )

(N + λ(i) ) 3 (N + 2λ(i) )

−

−

2

3N

N

1 3

P ∑

] w

(19)

(i)

i=1

Θ

(20)

Θ2 = 1

(21)

1

3(N + λ(i) ) 3

]2

2 3(N + λ

2

]

2

√ −

√ )

3

√ −

√

4

1 3

·

)3

4

2

5

9(N + λ(i) ) 3

(N +λ(i) ) 3

2(N + 2λ(i) )

√ )

√ − 3

1−

5

2

(

(

3(N + λ(i) ) 3

2

i=1

[

(i) 13

(N + λ ) −

4

∑K (

(17)

2(N + 2λ(i) )

(i) 13

9(N +λ(i) ) 3

(

Θ≜ [

w

)2 (N +2λ(i) )

√3

5 3(N +λ(i) ) 3

( (i)

i=1

i=1

√3

P ∑

(i)

i=1

√(

w(i) = [

)]

5

9(N +λ(i) ) 3

)2 (N +2λ(i) )

9N 3

[

(16)

4

2

(Pfa )

·

=0

)]

9(N +λ(i) ) 3

√

[

2(N +2λ(i) )

1

(N + λ(i) ) 3 −

(15)

1

(i) ) 3

1

Θ=  ( )2 (  √ ) √ 5 4 (i) ∑ 3(N + λ(i) ) 3 3 2 2 1 (N + λ ) 3 √ P 3 − √ − N − √ i=1 1 3N (N + 2λ(i) ) 2(N + 2λ(i) ) 2 3(N + λ(i) ) 3 ( 5 4 √ ) 1 √ (i) ) 3 3(N +λ(i) ) 3 2 √ √3 − 2 N 3 (N +λ (i) − − 1 (i) 3N (N + 2 λ ) 2(N +2λ ) 2 3(N +λ(i) ) 3 (i) wopm =  ( )2 (  √ ) √ 5 4 (i) ∑ 3 2 2 3(N + λ(i) ) 3 1 (N + λ ) 3 √ P − √ − N3 − √ i=1 1 3N (N + 2λ(i) ) 2(N + 2λ(i) ) 2 3(N + λ(i) ) 3 (i) 5

3(N +∆c ) 3

√

w ˆ

(i) opm

(i) 2(N +2∆c )

−

(

√ √3 2

−

2 3N

)

4 1 (N +∆(i) ) 3 c (i) (N +2∆c )

N3

(22)

(23)

√

−

2 (i) 1

3(N +∆c ) 3

=  ( )2 (  √ ) √ (i) 4 (i) 5 ∑ 3(N + ∆c ) 3 3 2 2 1 (N + ∆c ) 3 √ P − √ − N3 − √ i=1 (i) (i) (i) 1 3N 2 2(N + 2∆c ) (N + 2∆c ) 3(N + ∆c ) 3

(24)

Box II.

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Fig. 2. Curves of detection probability versus the number of samples of the proposed cooperative method with Pfa = 0.01, and SNR = −3 dB.

)

–

5

Fig. 3. ROC curves of the proposed cooperative method and EGC cooperative method, SNR = −6 dB, T = 8000.

Table 1 Samples versus different detection probabilities of the proposed cooperative method, Pfa = 0.01, SNR = −3 dB. Detection Probability

EGC 2-Sus

CBC 2-Sus

EGC 3-Sus

CBC 3-Sus

0.40 0.50 0.60 0.70 0.80 0.90 0.95

2966 4076 5430 6863 8815 11705 14214

2413 3472 4664 5986 7797 10752 13220

1863 2730 3657 4751 5943 7973 9910

1296 1881 2771 3738 5050 7003 8837

cooperative method with x dB noise uncertainty, ‘‘x-Sus’’ means there are x secondary users in the cooperative sensing network and ‘‘theo’’ means the theoretical values. The tapering window wm (t) is wm (t) ≡ 1 and ws (t) is a Kaiser window of length-201 with β parameter of 10. All simulation results are obtained from 10000 Monte Carlo runs except for the theoretical values. Fig. 2 illustrates the curves of detection probability versus the number of samples of the proposed cumulant-based blind cooperative method for different numbers of Sus. Observing this figure, we find that the detection probability grows gradually with the total number of samples. We set Pfa = 0.01, SNR = −3 dB. According to Fig. 2, the proposed cooperative method can save about 10%– 30% on samples when the same detection probability is achieved compared with the EGC method. Furthermore, as shown in Fig. 2, increasing the number of secondary users will make the sample saving more obvious. On summary, the proposed blind method is more efficient in terms of the number of needed samples. As a comparison, the detection probability at local node without cooperation is also depicted. It can be seen clearly the local cumulantbased method without cooperation is far inferior to the proposed cooperative method. Moreover, we also give the theoretical detection probability curves of the proposed cooperative method for 2 Sus and 3 Sus. Due to the estimation errors, the theoretical curves are somewhat higher than the simulated curves. But when the number of samples is increased, the differences between the theoretical curves and the simulated curves are decreased, which can prove the validity of (15). Table 1 lists the approximate number of samples of the proposed method and EGC method by first setting a target detection probability and then running several Monte Carlo Runs to see how many averaged samples are needed to achieve the given detection probability. From Table 1, if the detection probability should be

Fig. 4. Curves of detection probability versus SNR for different cooperative methods with Pfa = 0.01, and T = 8000.

0.5, the proposed method of 2-Sus or 3-Sus needs about 1881 or 3472 samples, respectively while the EGC method of 2-Sus or 3-Sus needs about 2730 or 4076 samples, respectively. So the proposed method saves about 31.1% or 14.8% samples, respectively. Fig. 3 shows the ROC (Receiver Operating Characteristic) curves of the proposed scheme and the EGC scheme for different numbers of Sus. We set SNR = −6 dB,T = 8000. From Fig. 3, it can be seen that the simulated false alarm probability (FAP) curves of the proposed method are well consistent with the theoretical values, hence the expression in (25) concerning the establishment of the threshold is correct. Moreover, it can also be seen that the proposed cooperative method is superior to the EGC method for different numbers of secondary users. Fig. 4 demonstrates the curves of detection probability versus SNR of different detectors for different numbers of secondary users. Here, we set Pfa = 0.01, T = 8000. According to Fig. 4, it is obvious that the detection probability of energy based equal gain cooperative method with 0 dB noise uncertainty (ideal energy based detector) is always one so that it is the best one among all methods. When SNR is low, the proposed cumulant-based blind cooperative method is about 1.0 dB higher than the cumulantbased EGC method. When SNR is high, the CBC method is about

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0.5 dB higher than EGC method. The detection probability of the energy based equal gain cooperative method with 1.0 dB noise uncertainty is the worst one among all methods. As a result, we make a conclusion the proposed cumulant-based cooperative method performs better than the cumulant-based EGC method, energy based cooperative method with noise uncertainty, but worse than the ideal energy based cooperative method in terms of detection probability performance. 5. Conclusion In this paper, we make an investigation on spectrum sensing methods. A novel cumulant-based cooperative spectrum sensing method is presented, which is nonparametric and blind. The method adopts the Neyman–Pearson (N–P) criteria. In terms of detection probability performance, it is optimal when the false alarm probability is fixed. Compared to blind EGC method, the proposed blind method can save about 10%-30% on number of samples. Additionally, the proposed method achieves an SNR gain of about 0.5–1.0 dB over the cumulant-based EGC method, energy based cooperative method with noise uncertainty for a given detection probability. Thus, the detection probability of the proposed cooperative method is higher than that of existing blind method EGC. Acknowledgments This work was supported in part by the National Natural Science Foundation of China (Nos. 61301096, 61304260, 61271230, and 61472190), the Open Research Fund of National Key Laboratory of Electromagnetic Environment, China Research Institute of Radiowave Propagation (No. 201500013),and the open research fund of National Mobile Communications Research Laboratory, Southeast University, China (No. 2013D02). References [1] J. Mitola, G. Maguire, Cognitive radios: Making software radios more personal, IEEE Pers. Commun. 6 (4) (1999) 13–18. [2] E. Axell, G. Leus, E. Larsson, H. Poor, Spectrum sensing for cognitive radio: State-of-the-art and recent advances, IEEE Signal Process. Mag. 29 (3) (2012) 101–116. [3] R. Tandra, A. Sahai, SNR walls for signal detection, IEEE J. Sel. Areas Commun. 2 (1) (2008) 4–17. [4] B. Chen, T. Liu, F. Shu, J. Wang, On performance comparison of wideband multiple primary user detection methods in cognitive radios, in: International Conference on Wireless Communications, Networking and Mobile Computing, WiCom, Beijing, China, 2009. [5] Y. Zeng, Y.-C. Liang, Spectrum sensing algorithms for cognitive radio based on statistical covariances, IEEE Trans. Veh. Technol. 58 (4) (2009) 1804–1815. [6] Y. Zeng, Y.-C. Liang, Eigenvalue-based spectrum sensing for cognitive radios, IEEE Trans. Commun. 57 (6) (2009) 1784–1792. [7] W. Han, C. Huang, J. Li, Z. Li, S. Cui, Correlation-based spectrum sensing with oversampling in cognitive radio, IEEE J. Sel. Areas Commun. 33 (5) (2015) 788– 802. [8] J. Lunden, S. Kassam, V. Koivumen, Robust nonparametric cyclic correlationbased spectrum sensing for cognitive radio, IEEE Trans. Signal Process. 58 (1) (2010) 38–52. [9] W. Jun, H. Jiwei, F. Minghui, W. Hongjun, Nonparametric multicycle spectrum sensing method by segmented data processing for cognitive radio, Circ. Syst. Signal Process. 33 (1) (2014) 299–307. [10] M. Lopez-Benitez, F. Casadevall, Signal uncertainty in spectrum sensing for cognitive radio, IEEE Trans. Commun. 61 (4) (2013) 1231–1241. [11] G. Giannakis, M. Tsatsanis, Signal detection and classification using matched filtering and higher order statitics, IEEE Trans. Acoust. Speech Signal Process. 38 (7) (1990) 1284–1296. [12] W. Jun, J. Xiufeng, B. Guangguo, C. Zhiping, H. Jiwei, Multiple cumulants based spectrum sensing methods for cognitive radios, IEEE Trans. Commun. 60 (12) (2012) 3620–3631. [13] H.-Y. Hsieh, H.-K. Chang, M.-L. Ku, Higher-order statistics based sequential spectrum sensing for cognitive radio, in International Conference on ITS Telecommunications (ITST), St. Petersburg, Russia, 2011, pp. 696–701.

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[14] S. Kashef, P. Azmi, Cumulant based Kolmogorov-Smirnov spectrum sensing, in: Malaysia International Conference on Communications (MICC), Kuala Lumpur, Malaysia, 2013, pp. 104–109. [15] E. Peh, Y.-C. Liang, Y.L. Guan, Y. Zeng, Cooperative spectrum sensing in cognitive radio networks with weighted decision fusion schemes, IEEE Trans. Wirel. Commun. 9 (12) (2010) 3838–3847. [16] Z. Bao, D. Ni, S. Zhang, Weighted reliability cooperative spectrum sensing algorithm, in: 24th Wireless and Optical Communication Conference, Tapei, China, 2015, pp. 5–8. [17] A. Jaitawat, P. Karmakar, Comparison of different weight assignment strategy in weighted cooperative spectrum sensing, in: 7th International Conference on Computational Intelligence, Communication Systems and Networks, Riga, 2015, pp. 53–58. [18] A. Dandawate, G. Giannakis, Asymptotic theory of mixed time averages and kth order cyclic-moment and cumulant statistics, IEEE Trans. Inform. Theory 41 (1) (1995) 216–232. [19] M. Abramowitz, I. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Washington, DC, 1972.

Wang Jun received the B.S. and M.S. degrees in Communication and Information System from HoHai University, Nanjing, China, in 2003 and 2006, respectively; and the Ph.D. degree in Communication and Information System from Southeast University, Nanjing, China, in 2012. He now is a faculty member of College of Electrical Engineering and Automation, Fuzhou University, Fuzhou, China. He is also a member of Fujian integrated circuits design center (FJICC). His current research interests include statistical signal processing, cyclostationary signal analysis, Ultrawide band wireless communication and cognitive radios.

Riqing Chen received his B.Eng. degree of Communication Engineering from Tongji University, China, in 2001; M.Sc. degree of Communications and Signal Processing from Imperial College London, UK, in 2004; and Ph.D. degree of Engineering Science from University of Oxford, UK, in 2010. He is currently lecturing at the Faculty of Computer Science and Information Technology, Fujian Agriculture and Forestry University (FAFU), Fujian, China. His research interests include network security, spread coding, signal processing, and wireless sensor technologies.

Feng Shu was born in 1973. He received the Ph.D., M.S., and B.S. degrees from the Southeast University, Nanjing, in 2002, XiDian University, Xian, China, in 1997, and Fuyang teaching College, Fuyang, China, in 1994, respectively. From Oct. 2003 to Oct. 2005, he is a post-doctor researcher with the National Key Mobile Communication Lab at the Southeast University. From Sept. 2009 to Sept. 2010, he is a visiting post-doctor at the University of Texas at Dallas. In October 2005, he joined the School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, China, where he is currently a Professor and supervisor of Ph.D and graduate students. He is also with Fujian Agriculture and Forestry University and awarded with Mingjian Scholar Chair Professor in Fujian Province. His research interests include wireless networks, wireless location, and array signal processing. He has published about 200 scientific and conference papers, of which more than 100 are in archival journals including more than 20 papers on IEEE Journals and 43 SCI-indexed papers. He holds four Chinese patents. He serves as an Editor for IEEE Access. Dr. Feng is a Member of IEEE and he has served as session chair or technical program committee member for various international conferences, such as IEEE WCSP 2016, IEEE VTC 2016, etc. Email: [email protected].

Ruiquan Lin received the M.S. and Ph.D. degrees from Fuzhou university, Fuzhou, China. He is now a faculty member of College of Electrical Engineering and Automation, Fuzhou University, Fuzhou, China. His current research interests include signal processing and adaptive control.

Please cite this article in press as: W. Jun, et al., Cumulant-based blind cooperative spectrum sensing method for cognitive radio, Physical Communication (2017), https://doi.org/10.1016/j.phycom.2017.11.001.

W. Jun et al. / Physical Communication ( Wei Zhu received the B.S. degree in electronic information engineering at Suzhou University of Science and Technology, Suzhou, China, in 2015. Now, he is with the School of Electronic and Optical Engineering Nanjing University of Science and Technology, Nanjing, China and seeks his M.S. degree from the university. His research interests include wireless communication, physical-layer security, and mobile networks.

Jun Li (M’09-SM’16) received the Ph.D. degree in electronic engineering from Shanghai Jiao Tong University, Shanghai, China, in 2009. From January 2009 to June 2009, he was with the Department of Research and Innovation, Alcatel Lucent Shanghai Bell, as a Research Scientist. Since 2015, he is with the School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, China. His research interests include network information theory, channel coding theory, wireless network coding, and cooperative communications.

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Dushantha Nalin K. Jayakody (M14) received the B. Eng. degree (with first-class honors) from Pakistan in 2009 and was ranked as the merit position holder of the University (under SAARC Scholarship). He received his MSc degree in Electronics and Communications Engineering from the Department of Electrical and Electronics Engineering, Eastern Mediterranean University, Cyprus in 2010 (under the University full graduate scholarship) and ranked as the first merit position holder of the department. He received the Ph. D. degree in Electronics and Communications Engineering in 2014, from the University College Dublin, Ireland. From Sept 2014–Sept 2016, he has held a Postdoc position at the Coding Information Transmission group, University of Tartu, Estonia and University of Bergen, Norway. From 2016, he is a Professor at the Department of Control System Optimization, Institute of Cybernetics, National Research Tomsk Polytechnic University, Russia. Dr. Jayakody is a Member of IEEE and he has served as session chair or technical program committee member for various international conferences, such as IEEE PIMRC 2013/2014, IEEE WCNC 2014/2016, IEEE VTC 2015 etc.

Please cite this article in press as: W. Jun, et al., Cumulant-based blind cooperative spectrum sensing method for cognitive radio, Physical Communication (2017), https://doi.org/10.1016/j.phycom.2017.11.001.