Energy efficiency optimization of cognitive relay network based on cooperative spectrum sensing

The Journal of China Universities of Posts and Telecommunications June 2015, 22(3): 26–34 www.sciencedirect.com/science/journal/10058885

http://jcupt.xsw.bupt.cn

Energy efficiency optimization of cognitive relay network based on cooperative spectrum sensing Song Yaolian (

), Zhang Fan, Shao Yubin, Long Hua

Faculty of Information Engineering and Automation, Kunming University of Science and Technology, Kunming 650504, China

Abstract This paper focuses on the energy efficiency of cognitive relay (CR) networks with cooperative sensing, joint optimization of the sensing time and the signal-to-noise ratio (SNR) is studied to maximize the energy efficiency of CR network. Theoretical analysis shows that there exists an optimal sensing time and optimal SNR to make the energy efficiency maximized under a constraint of detection probability. Simulation results illustrate that the optimal fusion rule performs better than the OR rule and the AND rule in terms of the energy efficiency. By properly designing the fusion rule threshold as well as the number of cooperative sensing users, the energy efficiency of CR networks can be further improved. Keywords cognitive radio network, cognitive relay network, energy efficiency, sensing time, fusion rule threshold, number of cooperative sensing users

1 Introduction Due to the widespread of wireless services, the fixed spectrum allocation scheme can not meet the constantly increasing service demand, cognitive radio systems have been proposed to efficiently enhance overall spectrum efficiency by allowing secondary users to opportunistically access to the dedicated spectra that have been assigned to primary users. Hence, spectrum sensing is required by the cognitive radio networks (CRNs) to determine the presence of the primary users [1]. However, in practical scenario, it is difficult to achieve satisfactory performance by utilizing non-cooperative methods to detect spectrum holes due to shadowing and multipath effects. Cooperative spectrum sensing approach has thus been proposed to improve sensing performance [2–3]. Cognitive radio based on battery-powered wireless devices can improve spectrum efficiency, meanwhile it will incur lower energy efficiency due to extra sensing time overhead and energy consumption [3]. Therefore, research on energy efficiency of CRNs has been Received date: 16-08-2014 Corresponding author: Song Yiaolian, E-mail: [email protected] DOI: 10.1016/S1005-8885(15)60649-5

considered more and more important in future wireless systems. Maximization the energy efficiency in wireless communications has been proposed for a long time [4–8]. For instance, an energy efficiency optimization problem in cognitive radio multiple-input multiple-output (MIMO) broadcast channels was studied in Ref. [4] under the total power constraint, the interference power constraint and the minimum system throughput constraint. In Ref. [5], the sensing-access strategies and channel sensing order were jointly designed to optimize the energy efficiency of CRNs based on sequential channel sensing. In Ref. [6], the optimal transmission duration and power allocation were designed to improve both energy efficiency and throughput. The impact of different power consumption components on secondary user optimal spectrum sensing duration and transmission duration was addressed in Ref. [7]. The energy efficiency of CRNs based on cooperative spectrum sensing was investigated in Ref. [8], and the impacts of the number of cooperative sensing users as well as the sensing time were shown. Energy efficiency of CRNs can be enhanced by jointly designing the sensing duration and the transmission duration [9]. Since spectrum sensing leads to lower energy efficiency, energy-harvesting technology is

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applied for CRNs to improve both energy efficiency and spectral efficiency. But, secondary transmitter needs to be powered by renewable energy [10–12]. From previous works we can know that the energy efficiency of CRNs can be enhanced by optimizing some parameters or using energy-harvesting technology. However, these previous works didn’t consider the sensing time and the SNR together in CR networks with cooperative spectrum sensing. In this paper, assuming that secondary users in CR networks are battery-powered wireless devices and perform cooperative sensing, we propose an optimal method to enhance the energy efficiency of CR networks. To save energy consumption, we establish an energy- efficient network model with four variables: the sensing time, the SNR, the fusion rule threshold and the number of cooperative sensing users. The CRNs can enhance the energy efficiency as well as spectrum efficiency by considering the SNR and the sensing time together. The energy detector and CR transmission scheme are both addressed. The paper is organized as follows. Sect. 2 depicts the

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system model, followed by the energy detector and cooperative sensing in Sect. 3. The energy efficiency optimization problem is addressed in Sect. 4. The numerical and simulation results are presented in Sect. 5. The paper is concluded in Sect. 6.

2 System model and problem formulation We consider a CR cooperative transmission model as shown in Fig. 1(a), where the CR helps the cognitive source (CS) to transmit data. Each transmission link between any two nodes is modeled as a Rayleigh fading channel. One can see that the whole cognitive transmission process can be divided into two phases: Spectrum holes detection on the licensed band and CR transmission. The time duration is allocated between spectrum sensing and CR transmission as depicted in Fig. 1(b), which is divided into one sensing slot and two data transmission slots. Supposing that τ denotes the spectrum sensing duration and T denotes the frame duration, the overall data transmission duration is derived as T − τ .

Fig. 1 System model

In CR network, once secondary users detect the idle licensed spectrum bands, they would utilize these chances to transmit data to their destinations. Each cognitive node, which is equipped with a single antenna, cannot send and receive data at the same time. The CR helps the CS forwarding information to its destination with

amplify-and-forward (AF) mode. The CR cooperative transmission scheme is shown in Table 1. Table 1

The CR cooperative transmission scheme

Slots Slot 1 Slot 2

CR cooperative transmission scheme CS → CR,CD CR → CD

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Firstly, the CS broadcasts its information to both the CR and cognitive destination (CD) during the transmission slot 1. Secondly, CR retransmits data received from CS to CD with AF mode, while CS doesn’t broadcast any information in the slot 2. Throughout the paper, we assume that the channel coefficients are known by the cognitive receivers but not by transmitters, and there exists perfect synchronization between the cooperative nodes. Finally, the receiver combines multiple signals with maximal ratio combination. The normalized capacity of CR network can be expressed as follows [13]. 2 2 2   P h PS PR hSR hRD T −τ  C0 = log 2 1 + S SD + 2 2  2 2  2T σ n2 PS hSR + PR hRD + σ n σ n    (1) where PS is the transmit power of the CS and PR is the

(

transmit power of CR. We assume

)

PS = PR

and

PS + PR = P , P is the allowable total power. σ n2 is the variance of Gaussian noise. hSR , hSD and hRD denote the fading channel coefficients between CS and CR, CS and CD, CR and CD respectively. Each transmission link between any two nodes is modeled as a Rayleigh fading 2 2 2 process with variances δ SD , δ SR and δ RD .

3 Energy detector and cooperative sensing In this section, we discuss the models of cooperative sensing in CRNs. In subsection 3.1, we review the energy detection scheme and analyze the relationship between the detection probability and the false alarm probability. Subsection 3.2 demonstrates the fusion rule. 3.1

Energy detector

Suppose that there are M secondary users to take part in spectrum sensing in CRNs. The binary hypothesis test of ith secondary user for cooperative sensing at tth time instant is formulated as follows. H 0 :yi (t ) = ni (t )  (2)  H 1 :yi (t ) = Pp hpi x(t ) + npi (t )  where x(t ) denotes the signal transmitted by the primary user and yi (t ) is the received signal by the ith secondary user. Pp denotes the transmit power of primary user, hpi denotes the fading channel coefficient of inter-user link between the ith secondary user and primary user. ni (t )

and npi (t ) is

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circularly symmetric complex Gaussian

noise with zero mean and variance σ n2 . Let γ p = Pp σ n2 be the received SNR of the primary user signal measured at the cognitive receiver of interest under the hypothesis H 1 . H 1 denotes the channel occupied by primary user,

H 0 represents a spectrum hole available for secondary users. We assume that the probabilities of H 0 and H 1 are

P (H 0 )

and

P (H 1 )

respectively,

and

meet

P ( H 0 )+ P ( H 1 ) = 1 . Energy detection is the most popular spectrum sensing scheme, thus, we take energy detection into consideration in this paper. Denote the sensing time with τ , and the sampling frequency with f s . The number of samples, calculated as N = τ fs , is supposed to be an integer. The test statistic for energy detector is given by 2 1 N (3) T ( yi ) = ∑ yi ( t ) N t =1 Given the detection threshold η , the false alarm probability and the detection probability are given by  η   Pfi (τ ,η ) = Q   2 − 1 τ fs   σ    n 

(4)

 η  τ fs   (5) Pdi (τ ,η ) = Q   2 − γ p − 1  σn  2γ p +1   where Q ( x ) is the complementary distribution function of standard Gaussian Process, i.e.,

∫

+∞ x

Q ( x) = 1

2π ⋅

2

e − t / 2 dt . For a target detection probability Pdi , the

false alarm probability related to the target detection probability is as follows [2]. (6) Pfi (τ ,η ) = Q Q −1 ( Pdi ) 2γ p + 1 + γ p τ f s  3.2

Fusion rule

In order to improve the performance of spectrum sensing, cooperative spectrum sensing is taken into account. When binary local decisions are reported to the fusion center, it will make a final decision according to some fusion rules, such as the OR rule, AND rule and k out of M rule. We use the k out of M rule in this paper, which is introduced as following. k out of M rule: Assume there are M secondary users taking part in cooperative sensing. If k secondary users detect a primary user present together, the fusion center will declare that the primary user is active. Suppose that

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2 2 2 the decision processes performed byc all secondary users = 0.5 P H 0 (1 − PF (η ,τ , k ) ) , d = hSD , e = hSR and f = hRD . are independent, the detection probability and the false For a fixed fusion rule threshold k, the parameters a, b, c, d, alarm probability under this rule are rewritten as follows. e and f are constants and greater than zero. The energy M M −i M  i efficiency can thus be rewritten as PD (τ , k ,η ) = ∑  Pdi (τ ,η ) (1 − Pdi (τ ,η ) ) (7) i =k  i    c γ 2 ef M , = log 1 + + (11) d ζ γ τ γ ( )   2 M M − i   i i i a + bγ eγ + f γ + 1  PF (τ , k ,η ) = ∑  Pf (τ ,η ) (1 − Pf (τ ,η ) ) (8)  i =k  i  Fixing the fusion rule threshold k = kɶ and the When k = 1 , the k out of M rule is equivalent to OR spectrum sensing time τ , we can find that ζ ( γ ) tends rule. When k = M , the k out of M rule becomes the AND to zero when γ approaches zero, namely rule. (12) lim ζ ( γ ) = 0

γ →0

4 Energy efficiency optimization

Furthermore, as γ approaches infinite, we also can

The energy efficiency of CR network is modeled as N (γ ,τ ) (9) ζ ( γ ,τ ) = th E ( γ ,τ ) where

N th ( γ ,τ ) = ( T − τ ) C0 (1 − Pf (η ,τ ) ) P ( H 0 ) T

find that ζ ( γ ) tends to zero, namely

  γ 2 ef c log 2 1 + d γ +  e + f + 1 γ γ  = lim ζ ( γ ) = lim γ →∞ γ →∞ a + bγ

is

 feγ 2 ( e + f ) 2 feγ cd + −  + Pf γ H+ 1 1(−eγP + τf γ + 1)2 P H 0 1 −P τeγ + 1 lim γ →∞   γ 2 ef ( ln 2 ) b 1 + d γ +  e + f + 1 γ γ  

the average throughput, and the average energy consumed by CR network is given by

E ( γ ,τ ) = τ Pτ + PcT + T − τ γσ

= τ P + PT + (T − τ ) γσ n2  P ( H 0 ) (1 − Pf (τ ) ) + P ( H1 ) (1 − Pd (τ ) )  . Pτ is the spectrum sensing power, Pc denotes the circuit power.

(13) According to Eq. (12) and (13), we can infer that ζ ( γ )

P = γσ n2 is the transmit power of secondary user. The energy efficiency function ζ ( ⋅) can be expresses as the bits successfully transmitted by secondary user with per Joule at one unit bandwidth. According to the definition, the energy efficiency of CR network with cooperative spectrum sensing is written as T −τ  max ζ (τ , γ , k ) = P ( H 0 ) (1 − PF (η ,τ , k ) ) {M τ Pτ +  τ ,γ , k T  2  PT  c + ( T − τ ) γσ n  P ( H 0 ) (1 − PF (η ,τ , k ) ) +  −1  P ( H1 ) (1 − PD (η ,τ , k ) )  ⋅   2 2 2   γ hSR hRD 1 2   log 2 1 + hSD γ + 2 2    2 h + h + 1 γ γ SR RD     s.t. 0≤τ ≤T  0<γ <∞   1≤k≤M  PD ( k ,τ ,η )≥PD  (10) 2 Let a = M τ Pτ + PcT , b = (T − τ ) σ n  P ( H 0 ) (1 − PF (η ,τ , k

}

    =0

is a continuous positive function. Therefore, for any given τ , there exists a certain γ ( 0 < γ < ∞ ) value to make that ∂ζ ( γ )

∂γ

=0

(14)

γ

For a given detection probability PD (η ,τ , k ) = PD , there are A = P ( H 0 ) γσ n2 , B = P ( H1 ) (1 − PD ) γσ n2 and C = PcT . Fixing k and γ , Eq. (10) can be thus written as

T ζ (τ ) =

(T − τ ) P ( H 0 ) (1 − PF (τ , kɶ ) ) C0

(15)

) )

( (

τ MPτ + C + (T − τ ) A 1 − PF (τ , kɶ ) + B

Letting

D = P ( H 0 ) C0 T and

making

the

first

derivative of ζ (τ ) with respect to τ , we can obtain

( ))) = ( ) ( ) )) ( ( H  1 − P η ,τ , k ɶ  − D ( (1 − P (τ , k ) ) + (T − τ ) ∇P (τ , kɶ ) )  τ MP +   

ζ (τ ) =

H 0 1 − P η ,τ , k ) ) + P ( H1 ) (1 − PD (η ,τ , k ) )  , c = 0.5 (T − τ ) T  P ( H 0 ) ⋅ 1 − P

+P

(

(

∂ D (T − τ ) 1 − PF τ , kɶ ∂ζ = ∂τ ∂ τ MP + C + (T − τ ) A 1 − P τ , kɶ + B τ F

1

F

, ,k

F

τ

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( ( ( )) ) C + ( T − τ ) ( A (1 − P (τ , kɶ ) ) + B )  

C + (T − τ ) A 1 − PF τ , kɶ + B  τ MPτ +  

(

( )) ( )

Therefore, we can achieve that ∂ζ − D (TMPτ + C ) lim ∇ζ (τ ) = lim = = 2 τ →T τ →T ∂τ (TMPτ + C )

−2

−

F

(

( ))

D (T − τ ) 1 − PF τ , kɶ  MPτ − A 1 − PF τ , kɶ −  B − (T − τ ) A∇PF τ , kɶ  [τ MPτ + 

( (

)

−

−2

C + (T − τ ) A 1 − PF τ , kɶ + B  (16)  ∇PF (τ ) can be obtained by making the first derivative

( ))

of PF (τ , kɶ ) with respect to τ . ∇PF (τ ) is written as

M  M − kɶ kɶ −1 ∇PF (τ ) = kɶ   Pf (τ ) (1 − Pf (τ ) ) ∇Pf (τ ) + ɶ k  M M −i M! i −1 ∑ɶ i i !( M − i )! Pf (τ ) (1 − Pf (τ ) ) ∇Pf (τ ) − i = k +1 M −1

M! i ∑ɶ ( M − i ) i !( M − i )! Pf (τ ) 1 − i =k

Pf (τ ) )

(

M − i −1

∇Pf (τ )

(17)

Taking into account m = i −1 M −i M! i −1 ∑ɶ i i !( M − i )! Pf (τ ) (1 − Pf (τ ) ) ∇Pf (τ ) = i = k +1 M

M −1

M! ∑ m !( M − m − 1)! P (τ ) (1 − P (τ ) ) m

f

M − m −1

f

∇Pf (τ )

m = kɶ

(18) We can therefore obtain that M  M − kɶ kɶ −1 ∇PF (τ ) = kɶ   Pf (τ ) (1 − Pf (τ ) ) ∇Pf (τ ) ɶ k 

(

where ∇Pf (τ ) = − 1

− Q

P ⋅ 2γ p + 1 + γ p τ f s

)

2

(19)

 2π γ p f s 2 τ exp  − Q −1 ( Pdi ) ⋅ 

)(

(

)

)

2,

When τ → 0 , it can be deduced that lim Pf (τ ) = 1 , τ →0

lim PF (τ ) = 1 , lim ∇Pf (τ ) = −∞ and lim ∇PF (τ ) = −∞ . τ →0

τ →0

τ →0

Obviously, A, B, C and D are positive constants. From Eq. (16), we can obtain that ∂ζ − DT ( C + BT )( −∞ ) lim ∇ζ (τ ) = lim = = 2 τ →0 τ → 0 ∂τ ( C + BT )

DT ∞ (20) >0 C + BT When τ → T , it can be deduced that lim Pf (τ ) = 0 , τ →T

lim PF (τ ) = 0 ,

τ →T

lim ∇Pf (τ ) = 0

τ →T

and

lim ∇PF (τ ) = 0 .

τ →T

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D <0 TMPτ + C

(21)

According to Eq. (20) and (21), we can obtain that there exists a sensing time to make ∇ζ (τ ) = 0 among the range 0≤τ ≤T . The optimal sensing time, which can maximize the energy efficiency of CRN, can be obtained when the equality constraint in formula (10) is satisfied. Given the sensing time τ , the SNR γ and the number of secondary users M, the energy efficiency optimization problem of CR network can be turned into  max ζ ( k ) = P ( H 0 ) (1 − PF ( k ) ) C0 {M τ Pτ + PT c + (T − τ ) ⋅ k  −1  2 γσ n  P ( H 0 ) (1 − PF ( k ) ) + P ( H1 ) (1 − PD ( k ) )    s.t. 1≤k≤M  PD ( k ,η )≥PD  (22) The energy efficiency of Eq. (22) for different fusion rules threshold k ( 1≤k≤M ) can be acquired through simulations. Then the optimal fusion rule kopt out of M

}

can be obtained, which can make energy efficiency maximized. Given the sensing time τ , the SNR γ and the fusion rule threshold k =  M 2  , where · is the ceiling function, the energy efficiency optimization problem can be rewritten as     M       c + 2γ p max +M1 +ζγ(pM τ) =f s P ( H20) 1 − PF  2   C0  M τ Pτ + PT           M     2 (T − τ ) γσ n  P ( H 0 ) 1 − PF    +  2       −1     M       P ( H1 ) 1 − PD  ,η         2       s.t. 1 < M ≤50     M    PD  ,η ≥PD  2    (23) The energy efficiency with the  M 2  out of M ( 1 < M ≤50 ) fusion rule can be obtained through simulations. We can find that the energy efficiency of CR network can be further improved by optimizing M.

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5 Numerical and simulation results In this section, simulations are resorted to investigate the optimal performance of energy efficiency in CR network. In the following simulations, it is assumed that the channels between any two nodes experience Rayleigh fading. The modulated signal bandwidth of primary users is 6 MHz. Setting f s = 6 MHz , T = 20 ms , P ( H 0 ) = 0.8 , 2 n

Pc = 200 mW , Pτ = 100 mW and σ = 1 (normalized

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From Fig. 3, it is easy to see that the optimal fusion rule threshold kopt can be obtained through simulations for different number of cooperative users M ( M = 5 and M = 11 ) under different γ p , which can make the energy efficiency of CR network maximized. It is obvious that there exists different optimal fusion rule threshold kopt for different γ p . Therefore, we should adopt optimal fusion rule kopt out of M based on γ p in CR network.

noise variance). The target detection probability for secondary users is set to PD = 0.95 in order to provide primary user with sufficiently protection. In cognitive relay 2 2 2 network, δ SD , δ SR and δ RD are set to 1, 5 and 5. From Fig. 2(a), we can know that the optimal sensing time for energy efficiency and throughput maximization will decrease by using cooperative spectrum sensing technology. Obviously, the optimal sensing time for energy efficiency optimization is smaller than that of throughput optimization. In Fig. 2(b), there exists different optimal sensing time for different fusion rules. When γ p of primary user is greater than a certain value, the optimal sensing time of AND rule is the biggest, and the optimal sensing time of optimal fusion rule is smallest.

Fig. 3

Optimal fusion rule threshold versus γ p

In Fig. 4(a), we compare the SNR opt of different fusion schemes under different γ p . It is easy to see that there are different SNR opt to maximize the energy efficiency of CR network with different fusion schemes. In CR network, the SNR opt with optimal fusion rule kopt out of M is the smallest, while the SNR opt with non-cooperative sensing scheme is the biggest. From Fig. 4(b), we can know that cooperative sensing can improve the energy efficiency of CR network under low γ p region. (a) τ opt based on cooperative sensing

(b) τ opt based on different fusion rules Fig. 2 τ opt for energy efficiency and throughput optimization based on cooperative sensing

(a) SNR opt of different fusion schemes

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(b) Energy efficiency maximization of different fusion schemes

Fig. 4

SNR opt and energy efficiency maximization of

different fusion schemes

The energy efficiency of optimal fusion rule

kopt out

of M is superior to that of other fusion schemes. Generally speaking, cooperative sensing can enhance the energy efficiency of CR network, and make optimal SNR opt reduced. In Fig. 5, energy efficiency based on 3 out of 5 rule are compared with that of non-cooperative sensing scheme under γ p = −20 dB . Obviously, the energy efficiency with cooperative sensing outperforms that of non-cooperative sensing. From Fig. 5(a), we can know there exists optimal sensing time to maximize the energy efficiency of CR network, and the optimal sensing time of cooperative sensing scheme is smaller than that of non-cooperative sensing scheme. From Fig. 5(b), we can know that there exists optimal SNR to make the energy efficiency maximized.

(b) Energy efficiency with different sensing time Fig. 5 Energy efficiency comparison for different sensing schemes

Fig. 6 illustrates three-dimensional graph of the energy efficiency with cooperative sensing. It is obvious that there exists optimal sensing time and optimal SNR to make the energy efficiency of CR network maximized. When τ opt = 3 ms , SNR opt = 1.4 dB , we can achieve the maximization of energy efficiency ζ max = 43 bits/(s ⋅ Hz ⋅ J) .

Fig. 6 Energy efficiency of CR transmission versus sensing time and SNR

We Assume that γ p = −20 dB and SNR = 5 dB , the

(a) Energy efficiency with different SNR

sensing time τ is set to 4ms unless otherwise stated. In CR network, the throughput and the energy efficiency with k out of M fusion rule versus the fusion rule threshold k is shown in Fig. 7.

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smaller, to achieve the maximum of throughput need more cooperative sensing users. From Fig. 8(b), there exists optimal number of cooperative sensing users to maximize the energy efficiency of CR network. In addition, the optimal number of cooperative sensing users M is closely related to γ p , and the optimal number of cooperative sensing users M is increasing with the decrease of γ p .

(a) Throughput versus k

(a) Throughput versus M

(b) Energy efficiency versus k Fig. 7 Throughput and energy efficiency versus k with different M

From Fig. 7(a), we see that the throughput is increasing with the number of cooperative sensing users M. However, the growth rate is declining, and finally tends to be a constant. In other words, when M reaches a certain value, the throughput cannot be effectively improved by increasing M. From Fig. 7(b), we know that there exists optimal fusion rule threshold k to maximize the energy efficiency of CR network for different number of cooperative sensing users M. The energy efficiency with kopt out of M rule is increasing with M (M<4). When M is greater than 4, the energy efficiency is decreasing with M. This is because that the increase of the number of cooperative sensing user M will lead to increase of energy consumption M τ Pτ . Therefore, from the energy efficiency point of view, it is not suitable for much more secondary users to take part in cooperative sensing. Fig. 8 illustrates the throughput and the energy efficiency versus the number of cooperative sensing users M based on  M 2  out of M rule. From Fig. 8(a), the throughput increases with the number of cooperative sensing users, and tends to a fixed value. When γ p is

(b) Energy efficiency versus M Fig. 8 Throughput and energy efficiency versus M with different γ p

6 Conclusions In this paper, we have presented energy efficiency maximization based on cooperative sensing in CR network, our idea proves that cooperative spectrum sensing can sufficiently enhance the energy efficiency of CR network. The impacts of the sensing time and the SNR on the energy efficiency are shown through analysis and simulations. In addition, we have also shown that the energy efficiency of CR network can be further improved by optimizing fusion rule threshold and the number of cooperative sensing users.

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Acknowledgements 6.

The authors would like to thank the reviewers for their detailed reviews and constructive comments, which have helped to improve the quality of this paper. This work was supported by the National

7.

Science Fund under Grant No. 6087215, the Yunnan Research Program of Application Foundation under Grant No.2011FB035 and

8.

the School training fund under granted No.KKZ3201403010.

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(Editor: Lu Junqiang)