Performance of Cooperative Spectrum Sensing in ... - IEEE Xplore

3 downloads 0 Views 387KB Size Report
[18] N. C. Sagias, D. A. Zogas, G. K. Karagiannidis, and G. S. Tombras,. “Channel capacity and second-order statistics in Weibull fading,” IEEE. Commun. Lett.
Performance of Cooperative Spectrum Sensing in Rician and Weibull Fading Channels Srinivas Nallagonda

Sanjay Dhar Roy and Sumit Kundu, Member IEEE

Dept. of Electronics & Communication Engineering National Institute of Technology, Durgapur Durgapur -713209, India E-mail: [email protected]

Dept. of Electronics & Communication Engineering National Institute of Technology, Durgapur Durgapur -713209, India E-mail: [email protected], [email protected]

Abstract— Detection is compromised when a cognitive radio (CR) user experiences deep shadowing or fading effects. In order to detect the primary user (PU) more accurately, we allow the CR users to cooperate by sharing their information. In this paper we investigate performance of cooperative spectrum sensing scheme using energy detection (ED-CSS) to improve the sensing performance in channels such as Rician and Weibull fading channels. Hard decision combining rule (OR-rule, AND-rule and MAJORITY-rule) is performed at fusion center (FC). The performances of ED-CSS for several values of average SNR are characterized through complementary receiver operating characteristic (ROC) curves (plot of Qm vs. Qf). A comparative performance of ED-CSS has been studied for various data fusion rules in Rician as well as Weibull fading channels. Keywords-Cognitive radio, energy detection, spectrum sensing, fusion rules, detection probability.

I.

cooperative

INTRODUCTION

Cognitive radio (CR) technique has been proposed to solve the conflicts between spectrum scarcity and spectrum under utilization [1]. It allows the CR users to share the spectrum with primary users (PUs) by opportunistic accessing. The CR user can use the spectrum only when it does not create interference to primary users. Therefore, spectrum sensing is an important issue of cognitive radio technology since it needs to detect the presence of primary users accurately and quickly. In many wireless applications, it is of great interest to check the presence and availability of an active communication link when the primary signal is unknown. In such scenarios, one appropriate choice consists of using an energy detector which measures the energy in the received waveform over an observation time window [2]. Spectrum sensing is a hard task because of shadowing, fading and time-varying nature of wireless channels [3]. Due to the severe multipath fading, a cognitive radio may fail to notice the presence of the PU. Cooperative spectrum sensing improves the detection performance. The performance of cooperative spectrum sensing over Rician fading channel is given in [4]. All CR users sense the PU individually and send their sensing information in the form of 1-bit binary decisions (1 or 0) to Fusion center (FC). The hard decision combining rule (OR,

AND, and MAJORITY rule) is performed at FC to make the final decision regarding whether the primary user present or not. Comparison among hard decision fusion rules for the case of cooperative spectrum sensing has been investigated in a Suzuki fading channel [5]. However, the existing works only examined the collaborative spectrum sensing, using energy detection in Log-normal shadowing, Rayleigh fading channel [6]. Weibull fading has been proved to exhibit an excellent fitting for indoor [7] and outdoor [8] environments. The Weibull distribution also provides flexibility in describing the fading severity of the channel and considers special cases such as the well known Rayleigh fading for a certain value of the fading parameter [9].The performance of a single CR user’s spectrum sensing is the best in Weibull fading channel among other channels such as Rayleigh, Nakagami [10]. In this paper, we have studied the performance of cooperative spectrum sensing, using energy detection (EDCSS), over Rician and Weibull fading channels. Specifically our contributions in this paper are as follows: • Evaluating the energy detector performance of a single CR user in terms of missed detection and false detection probabilities over Rician and Weibull fading channels. • Evaluating the overall performance of several cooperative CR users over Rician and Weibull fading channels. Several hard decision fusion rules such as AND, OR and majority Logic are investigated and performance of these fusion rules are compared. • Impact of fading parameters and the number of cooperative CR users on sensing performance has been assessed. • Quantitative comparison of the performances of spectrum sensing scheme with and without cooperation among the CR users. • Impact of channel SNR on overall sensing performance is indicated. • A simulation test bed has been developed in MATLAB to carry out the above performance evaluation. Results obtained via simulation (based on our developed test bed) for the case of Rician fading factor K=0 and Weibull fading parameters V=2, S=1 matches with the result

presented in [6] for Rayleigh faded channel under same condition, which validates the accuracy of our simulation. The rest of the paper is organized as follows. In Section II, the system model under consideration is described and important notations are listed, the probabilities of detection and of false alarm over additive white Gaussian noise (AWGN) channel, fading channels are described. Results and discussions are presented in section III. Finally we conclude in section IV.

PU

Before describing the system model, we list some useful notations in Table1 [2]-[11]. TABLE 1 Symbol

Noise waveform which is modeled as a zeromean white Gaussian random process One-sided noise power spectral density

n (t )

Fig.2. Block diagram of cooperative spectrum sensing

check that

sin( π x ) i ) . One can easily and ni = n( 2W πx

(3) n i ~ N ( 0 , N 01 W ), for all i. The noise energy can be approximated over the time interval (0, T), as [2]-[11]: 2 ∫ n ( t ) dt =

s (t ) N

01

E

s

0

If we define n ′ = i

=

∫s

2

( t ) dt

0

γ =

A Gaussian variate with mean μ and variance σ2

N ( μ ,σ

2

(.)2

X(t)

(.)

Decide H0 or H1

0

H

0

H1

(1)

According to the sampling theorem, the noise process can be expressed as [12], ∞

∑ n sin c ( 2Wt − i ), i

i = −∞

, then the decision statistic Y can

2

(5)

i

with 2 m degrees of freedom. The same approach is applied when the signal s (t ) is present with the replacement of each

ni by ni + si where si = s( 2Wi ) .The decision statistic Y in this case will have a non-central χ

2

distribution with 2 m

degrees of freedom and a non centrality parameter 2γ [2][11].We can describe the decision statistic in short-hand notations as

⎧⎪ χ 22m , H 0 , Y ~⎨ ⎪⎩ χ 22m ( 2γ ), H 1 .

Pd = P (Y > λ / H 1 ) = Q m ( 2 γ ,

The received signal x ( t ) can be represented as

n (t ) =

(4)

,

(6)

In non-fading environment the probabilities of detection and false alarm are given by the following formulas [2][12]:

Fig.1. Block diagram of an energy detector

n (t ) ⎧ x (t ) = ⎨ ⎩ h * s (t ) + n (t )

∑ n′

2 i

i =1

A. Non-fading environment (AWGN channel)

T



2m

2m

∑n

Y can be viewed as the sum of the squares of 2 m standard Gaussian variates with zero mean and unit variance. Therefore, Y follows a central chi-square ( χ 2 ) distribution

)

We consider a network of N cognitive radio (CR) users using energy detector (ED) with identical threshold (λ) which make hard binary decisions and transmit it to fusion center (FC) for data fusion as shown in Fig.2. All CRs relatively closed to each other form a cluster. The distance between any two CRs is less than the distance between a primary user and a CR or the distance between a CR and the fusion center (FC). The channels between CRs and FC have been considered as ideal channels (noiseless) in this paper. Each CR user is having one energy detector as shown in Fig.1. It receives a signal x(t) as defined below at input and gives a binary decision regarding the presence of the PU. BPF

Y =

1 2W

i =1

Es N 01

Signal-to-noise ratio (SNR)

ni

N 01 W be written as [2]-[11]:

T

Signal energy, E s

FC

CR3

T

Description Signal waveform

Fusion center

CR2

where sin c ( x ) =

II. SYSTEM MODEL

CR1

Primary user

(2)

λ)

(7)

(8) P f = P (Y > λ / H 0 ) = Γ ( m , λ / 2 ) / Γ ( m ) where Γ (.,.) is the incomplete gamma function [14] and is the generalized Marcum Q-function [13]. If the Q m (.,.) signal power is unknown, we can first set the false alarm probability P f to a specific constant. By equation (8), the detection threshold

λ can be determined. Then, for the fixed

the detection probability Pd can be

number of samples 2 TW

evaluated by substituting the independent of

γ

λ in (7). As expected, Pf is

since under H 0 there is no primary signal present. When h is varying due to fading, equation (7) gives the probability of detection as a function of the instantaneous SNR, γ . In this case, the average probability of detection ( Pd

increases, the effect of fading decreases, while for the special case of V = 2 , the Weibull PDF of Z reduces to the Rayleigh PDF. For V = 1 the Weibull PDF of Z reduces to the well known negative exponential PDF. The corresponding CDF of Z can be expressed as [16],

⎛ rV F Z ( r ) = 1 − exp ⎜⎜ − ⎝ S

) may be derived by averaging (7) over fading statistics [6],

Pd =

∫Q

m

(9)

( 2 γ , λ ) f γ ( x ) dx

x

where f γ ( x ) is the probability distribution function (PDF) of SNR under fading. B. Rician fading channel of

If the signal strength follows a Rician distribution, the PDF will be [11]:

γ

f (γ ) =

K +1

γ

exp(−K −

(K +1)γ

γ

⎛ K(K +1)γ )I0 ⎜⎜ 2 γ ⎝

⎞ ⎟,γ ≥ 0, (10) ⎟ ⎠

PdRic , is then obtained by substituting (10) in

(9) and substituting x for

2 γ . The resulting expression can

It may be noted that the n-th power of a Weibull distributed random variable with parameters (V , S ) is another Weibull distributed random variable with parameters (V / n , S ) [15]. Thus γ is also a Weibull distributed random variable with parameters V / 2 , (a γ )V / 2 where a = 1 / Γ (1 + 2 / V ). The PDF of γ can then be derived from (14) by replacing V with

(

V / 2 and

f γ (γ ) =

V /2

V 2 (a γ

⎛ λ ( K + 1 ) ⎞⎟ 2Kγ P dRic | u = 1 = Q ⎜ , . ⎜ K +1+ γ K +1+ γ ⎟ ⎠ ⎝ (11) For K=0, this expression reduces to the Rayleigh expression with u=1[11].

γ = E (Z 2 )

Z be the magnitude of h , i.e. Z = h . If

R = X + j * Y is a Rayleigh distributed random variable, the Weibull distributed random variable can be obtained by transforming R and using (12) as, 2 /V

(13)

From equation (13), The PDF of Z can be given as V f Z (r ) =

V V −1 r r exp( − ) S S

Es = S N 01

(14)

with S = E ( Z V ) and E (.) denoting the expectation. V is the Weibull fading parameter expressing how severe the fading can be ( V > 0 ) and S is the average fading power. As V

/ 2 −1 )

⎛ γ exp[ − ⎜⎜ ⎝ aγ

⎞ ⎟⎟ ⎠

V /2

]

(17)

2 /V

2 ⎞ Es ⎛ Γ ⎜1 + ⎟ V ⎠ N 01 ⎝

(18)

Here E ( Z 2 ) is the second moment of Z which can be obtained from the generalized expression for moments as given below [17]: E (Z

In the Weibull fading model, the channel fading coefficient h can be expressed as a function of the Gaussian in-phase X and quadrature Y elements of the multipath components [15][16] (12) h = ( X + j * Y ) 2 /V where j = − 1

Z = R

)V / 2

(γ ) (V

as [18],

γ is the average SNR given as:

where

Let

)

S with (aγ )

be solved for u=1 using [13, Eq. (45)] to yield

C. Weibull fading channel

(15)

In Weibull fading the instantaneous signal-to-noise ratio at a cognitive radio is given by [17]: E γ = Z2 s (16) N 01

where K is the Rician factor. The average Pd in the case of a Rician channel,

⎞ ⎟⎟ ⎠

n

) = S

n /V

n ⎞ ⎛ Γ ⎜1 + ⎟ V ⎠ ⎝

(19)

where n is a positive integer and Γ (.) is the Gamma function. The average Pd in the case of a Weibull channel, Pd ,Weibu can be obtained analytically by substituting (17) in (9) and substituting x for

2γ .

D. Cooperative spectrum sensing in fading channels Detection performance can be improved by allowing different cognitive radio users to cooperate by sharing their information. We have assumed that the noise, fading statistics and average SNR are the same for each CR user. Assuming independent decisions, the fusion problem where k out of N CR users are needed for decision can be described by binomial distribution based on Bernoulli trials where each trial represents the decision process of each CR user. The generalized formula for overall probability of detection, Qd for the k out of N rule is given by [5]:

⎛N ⎞ l (20) ⎟ P (1 − P )N − l d ⎟ d l=k l ⎝ ⎠ where Pd is the probability of detection for each individual CR user as defined by (7) & (9). The OR-fusion rule (i.e. 1 out of N rule) can be evaluated by setting k=1 in equation (20): N

∑ ⎜⎜

⎛ N⎞ ⎛ N⎞ N−l N−l Qd,OR = ∑⎜⎜ ⎟⎟Pdl (1− Pd ) =1−⎜⎜ ⎟⎟Pdl (1− Pd ) =1− (1− Pd )N l l l =1 ⎝ ⎠ ⎝ ⎠ l =0 N

(21)

The AND-rule (i.e. N out of N rule) can be evaluated by setting k=N in equation (20): N ⎛N⎞ N −l (22) Qd , AND = ∑ ⎜ ⎟Pdl (1 − Pd ) = ( Pd ) N ⎜ ⎟ l=N ⎝l⎠ Finally, for the case of MAJORITY-rule (i.e. N/2 out of N) the Qd ,MAJ is evaluated by setting k = ⎣N / 2⎦ in (20). Similarly, the overall probability of false alarm, Q f for the

0

10

(i) (ii) (iii) (iv)

-1

10 P ro b a b ilt y o f M is s in g (P m )

Qd =

(v)

-2

10

-3

10

AWGN Rician fading: K=3 Rician fading: K=6 Rayleigh Fading: v=2, S=1

-4

10 -4 10

Weibull Fading: v=5, S=1.0616 -3

10

-2

10 Probability of False Alarm (Pf )

-1

0

10

(i) -1

10

III. RESULTS AND DISCUSSIONS

Fig.3 shows complementary ROC (Pm vs. Pf) curves for the single CR user’s spectrum sensing in Rician and Weibull fading channels. Different values of Rician factor, K=3, 6 and Weibull parameters [10], V=2, S=1; V=5, S=1.0616 are considered. Rayleigh fading channel characteristics would be achieved in a Weibull fading channel if V, S are set to 2, 1 respectively. Increase in Rician factor K=3, 6 and Weibull parameters V=2, S=1; V=5, S=1.0616, significantly decrease the probability of missed detection [curves (ii), (iii); curves (i), (iv) respectively]. We can say that the performance of energy detector in Weibull fading channel (particularly for V=5, S=1.0616) is better than the performance in Rayleigh fading channel (V=2, S=1) and Rician fading channel (K=3, 6). A plot for non-fading (pure AWGN) case is also provided for comparison. Fig.4 shows complementary ROC (Qm vs. Qf) curves for 3 cooperative CR users under Rician (K=5) and Weibull (V=5, S=1.0616) fading. Non- fading AWGN curve is shown for comparison (AWGN curve matched with curve in [6]-[11]). We can observe in this figure, fusing the decisions of 3 CR users cancels the effect of fading on the detection performance effectively. Moreover, with increase in N=1 to 3 [curves (i), (iv); curves (ii), (v)], cooperative spectrum sensing outperforms AWGN local sensing [curve (iii)]. This is due to the fact that for larger N, with high probability there will be a user with a channel better than that of the non-fading AWGN case. Again we observe that the performance of ED-CSS in

10

Fig.3. Performance of a single cognitive radio user for different Rician and Weibull fading channel parameters , γ =10dB, m=5.

case of OR, AND, and MAJORITY rule can be evaluated by replacing Pd with Pf in equations (20), (21), and (22) respectively.

(ii) (iii)

Qm

The simulation results are obtained using the following system parameters: Time-bandwidth product, m = 5, average SNR, γ =10dB and Qf =0.1.

0

10

-2

10

(iv) (v)

-3

10

AWGN N=1,Rician Fding,No collab N=3,Rician Fding N=1,Weibull Fding,No collab

-4

10 -4 10

N=3,Weibull Fding -3

10

-2

10 Qf

-1

10

0

10

Fig.4. Qm vs. Qf under Rician (K=5) and weibull fading (V=5, S=1.0616) for 3 CR users ( γ =10dB, m=5), OR rule.

Weibull fading channel is better than the performance in Rician fading channel under the same condition. Fig.5 shows the probability of detection Qd vs. γ under Rician (K=5) and Weibull (V=5, S=1.0616) fading scenarios for 3 cooperative CR users. Non- fading AWGN curve is also shown for comparison. We have chosen Qf as 0.1 and m=5 for each curve in this figure. We observe that there is an excellent improvement in performance of ED-CSS with increase in N and average SNR [curves (v), (ii); curves (iv), (i)]. In particular, for a probability of detection equal to 0.9, spectrum sensing without cooperation (N=1) requires γ ≈ 12dB while cooperative sensing with N=3 only needs approximately 8dB for individual CR users. We observe that the performance of ED-CSS in Weibull fading channel is better than the performance in Rician fading channel under the same condition.

performance has been improved with cooperation among the CR users. The performance of ED-CSS has been assessed via probability of detection under several values of average channel SNR in both fading channels. Several data fusion rules such as AND, OR and MAJORITY are in both fading channels compared with each other through complementary ROC. Finally we have shown that cooperative spectrum sensing, using energy detection performs better for Weibull fading channel than Rician fading channel under same conditions.

1 (i) (ii)

0.9

(iii) (iv) (v)

0.8 0.7

Qd

0.6 0.5 0.4

REFERENCES

0.3 AWGN

0.2

N=1,Rician Fding,No collab N=3,Rician Fding

0.1 0

[1]

N=1,Weibull Fding,No collab N=3,Weibull Fding

0

2

4

6

8

10 12 SNR (dB)

14

16

18

[2] 20

[3]

Fig.5. Qd vs. γ under Rician (K=5) and weibull fading (V=5, S=1.0616) for 3 CR users ( γ =10dB, m=5), OR rule.

[4]

0

10

(i) (ii)

[5]

-1

10

Qm

(iii) -2

[6]

(iv)

10

[7] -3

10

(v)

Rician: OR-rule Rician: AND-rule

(vi)

[8]

Rician: Majority-rule Weibull: OR-rule -4

10 -4 10

[9]

Weibull: AND-rule Weibull: Majority-rule -3

10

-2

10

-1

10

0

10

Qf

[10]

Fig.6. Performance of hard decision fusion rules via Qm vs. Qf under Rician and Weibull fading channels for N=5 CR users , ( γ =10dB, m=5). [11]

Fig.6 shows complementary ROC (Qm vs. Qf) curves for 5 cooperative CR users under Rician (K=5) and Weibull (V=5, S=1.0616) fading, m=5 and average SNR γ =10dB. We observe that for a particular value of Qf = 0.1 probability of missed detection Qm is 0, 0.1 and above 0.8 for OR-rule, MAJORITY and AND-rules respectively. We can say that OR-rule performs better than MAJORITY and AND-rules (curves (v), (iii) and (i); curves (vi), (iv) and (ii) respectively). We observe that the performance of hard decision fusion rules in Weibull fading channel is better than the performance in Rician fading channel under the same condition. IV. CONCLUSION We have studied the performance of the single CR user and cooperative CR users based spectrum sensing using energy detection under Rician and Weibull fading channels in terms of miss detection and false alarm probabilities. The

[12] [13] [14] [15] [16] [17] [18]

S. Haykin, “Cognitive radio: brain-empowered wireless communications,” IEEE J. Select. Areas Commun, vol. 23, pp. 201-220, Feb. 2005. H. Urkowitz, “Energy detection of unknown deterministic signals,” Proceedings of IEEE, vol. 55, pp. 523–231, April 1967. S D. Cabric, S. M. Mishra, and R. W. Brodersen, “Implementation issues in spectrum sensing for cognitive radios,” in Proc. of Asilomar Conf. on Signals, Systems, and Computers, Nov. 7-10, 2004, vol. 1, pp. 772–776. Jiaqi Duan and Yong Li, “Performance analysis of cooperative spectrum sensing in different fading channels,” in Proc. IEEE Interantional conference on Computer Engineering and Technology (ICCET’10), pp. v3-64-v3-68, June 2010. Spyros Kyperountas, Neiyer Correal, Qicai Shi and Zhuan Ye, “Performance analysis of cooperative spectrum sensing in Suzuki fading channels,” in Proc. of IEEE International Conference on Cognitive Radio Oriented Wireless Networks and Communications (CrownCom’07), pp. 428-432, June 2008. A. Ghasemi and E. S. Sousa, “Collaborative spectrum sensing for opportunistic access in fading environments,” in Proc. of 1st IEEE Symp. New Frontiers in Dynamic Spectrum Access Networks, Baltimore, USA, Nov. 8-11, 2005, pp. 131-136. H. Hashemi, “The indoor radio propagation channel,” Proc. IEEE, vol. 81, no. 7, pp. 943–968, Jul. 1993. N. S. Adawi et al., “Coverage prediction for mobile radio systems operating in the 800/900 MHz frequency range,” IEEE Trans. Veh. Technol., vol. 37, no. 1, pp. 3–72, Feb. 1988. M. H. Ismail and M. M. Matalgah, “BER analysis of BPSK modulation over the Weibull fading channel with CCI,” IEEE Vehicular Technology Conference, pp.1-5, 25-28 Sept 2006. Srinivas Nallagonda, Sudheer Suraparaju, Sanjay Dhar Roy and Sumit Kundu, “Performance of energy detection based spectrum sensing in fading channels,” accepted in IEEE International Conference on Computer and Communication Technology (ICCCT’11), Sept. 2011. F. F. Digham, M.-S. Alouini and M. K. Simon, “On the energy detection of unknown signals over fading channels,” in Proc. of IEEE International Conference on Communications (ICC’03), pp. 3575–3579, May 2003. C.E. Shannon, “Communication in the presence of noise,” proc. IRE, vol. 37, pp. 10-21, January 1949. A. H. Nuttall, “Some integrals involving the QM function,” IEEE Transactions on Information Theory, vol. 21, no. 1, pp. 95–96, January1975. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 5th ed. Academic Press, 1994. Mzabalazo Lupupa, and Mqhele E. Dlodlo, “Performance analysis of transmit antenna selection in Weibull fading channel,” 9-th IEEE conference (AFRICON-09), pp. 1-6, Sept. 2009. N.C. Sagias, and G.K. Karagiannidis, “Gaussian class multivariate Weibull distributions: theory and applications in fading channels, ”IEEE Trans. Inf. Theory, vol. 51, no. 10, pp. 3608-3619, Oct. 2005. N. C. Sagias, and G. S. Tombras, “On the cascaded Weibull fading channel model,” Journal of the Franklin Institute, 344, pp. 1-11, 2007. N. C. Sagias, D. A. Zogas, G. K. Karagiannidis, and G. S. Tombras, “Channel capacity and second-order statistics in Weibull fading,” IEEE Commun. Lett., vol. 8, no. 6, pp. 377-379, Jun. 2004.