Cooperative Cognitive Radio Network with Soft Data ...

Cooperative Cognitive Radio Network with Soft Data Fusion in Rayleigh Fading Channel Srinivas Nallagonda, Member IEEE

N. Ashok Kumar

Dept. of ECE M.V.S.R Engineering College Affiliated to Osmania University, Hyderabad, India 501510 Email: [email protected]

Dept. of ECE Avanthi’s Scientific Technological & Research Academy Hyderabad, India 501512 Email: [email protected]

Abstract—The performance of a cooperative cognitive radio network (CCRN) is proposed in this paper. Soft data fusion operation is performed at fusion center (FC) on the energy values obtained from different cognitive radios (CRs). More precisely, we analyze the performance of CCRN with several soft fusion schemes: square law selection (SLS), maximal ratio combining (MRC), square law combining (SLC), and selection combining (SC) in noisy and Rayleigh faded environment. Towards that, we derive closed-form expressions for probability of detection for all soft data fusion schemes in Rayleigh fading channel. A comparative performance of soft data fusion schemes for CCRN has been illustrated for different network parameters. Index Terms—Cognitive radio, soft data fusion, Probability of detection .

I. I NTRODUCTION The spectrum of primary users (PUs) can be opportunistically accessed and shared by secondary users (SUs) provided it does not cause detrimental interference to the PUs [1]. Therefore, sensing the spectrum of a PU is important, since it is essential to detect the presence of PUs reliably. The operation is quite challenging when the PU signal format is unknown. In such scenarios, utilization of an energy detector (ED) is the suitable choice to detect the status of a PU [2], [3]. When compared to a single CR sensing, cooperative spectrum sensing (CSS) helps increasing the reliability of detection in the presence of uncertainties in sensing (S) channel. More precisely, in CSS, it is possible to improve the detection performance where all CRs sense the PU individually and report their sensing information to a fusion center (FC) via reporting (R) channels. Next, the FC fuses the received local sensing information to decide about the presence or the absence of the PU and reports back to the CRs. There are several soft and hard decision combining fusion schemes which can be implemented at FC to perform the fusing operation [4]. In [5], the detection performance of soft data schemes in Rician fading is presented. In the case of soft data fusion, CRs forward the entire sensing data (i.e., received energies at each CR) to the FC without performing any local binary decision at each CR (where ‘1’ or ‘0’ is forwarded to the FC in the case of hard decision fusion [6]). In this paper, we follow the same approach of [5] to develop analytical framework in noisy and Rayleigh faded environment and to evaluate the performance of CCRN with soft data fusion schemes: SLC, MRC, SLS, and

SC, through complementary receiver operating characteristics (CROC). Appropriate analytical formulations and a simulation test bed has been proposed using which our formulations have been validated. The work is partitioned in to next three sections. The system model related to several soft schemes for CSS has been discussed in Section II. Further, the probability of detection expressions for various fusion schemes in Rayleigh fading are derived. In Section III, simulation and analytical results are discussed. In Section IV, conclusions are presented. II. S YSTEM M ODEL Fig. 1 shows a proposed CCRN with N CRs, a fusion center (FC), and a primary user (PU). Each CR senses the PU individually using energy detector (ED) which is shown in Fig. 2 and send its sensing data in the form of energy values to the FC through R-channels. Next, the FC gathers these sensing data (energy values) which are coming from individual CRs. Then, FC employs any one of the soft data combining techniques such as square law selection (SLS), square-law combining (SLC), selection combining (SC), and maximal ratio combining (MRC) to make the decision of PU (presence or absence) globally. Signals from multiple CRs are combined to achieve an improved average SNR. In this paper, we assume that fading and noise affecting the S-channels while the R-channels are considered as ideal (noiseless) channels. The received signal at k-th CR, xk (t) can be written as: ( nk (t) : H0 xk (t) = (1) hk (t)s(t) + nk (t) : H1 where s(t) is the PU signal with energy Es and nk (t) is the additive white Gaussian noise (AWGN) at k-th CR. The Schannel fading coefficient for the k-th CR is denoted as hk . Two hypotheses, denoted as H0 and H1 which indicates PU’s absence and presence, respectively. When the PU is absent i.e. under hypothesis H0 , CR receives only the noise signal at the input of the energy detector and the noise energy at k-th CR can be approximated over the time interval (0, T ), following [2], [3] as: Z T 2u 1 X 2 n (2) n2k (t)dt = 2W i=1 ki 0

where nki = n(i/(2W )), u = T W indicates time-bandwidth product, T indicates observation time, and W indicates PU signal’s bandwidth. It can check easily that nki is Gaussian with mean zero and variance N01 W (nki ∼ N (0, N01 W ); ∀i where N01 W is spectral density of one-sided noise power).

E1

CR1

MRC

Ideal R-channels

SLC E2

SC

CR2

Primary user (PU)

1−

Qf

N Y

[1− √ Qu ( 2γk ,√ λ)] √ Qu ( 2γrc , λ) √ √ QN u ( 2γlc , λ) √ √ Qu ( 2γsc , λ) k=1 p

1 − [1 − Γ(u, λ/2)/Γ(u)]N Γ(u, λ/2)Γ(u) Γ(N u, λ/2)/Γ(N u) Γ(u, λ/2)/Γ(u)

FC

E3 CR3

Qd

Combining Schemes SLS

Cognitive Radio users Noisy and Faded S-channels

TABLE I Qd AND Qf EXPRESSIONS FOR DIFFERENT SOFT DATA SCHEMES FOR AWGN ENVIRONMENT.

Fusion center

EN

¯ d ) may scheme, the average overall detection probability (Q be derived i.e., Z ∞ ¯ Qd = Qd fγ (γ)dγ (4)

CRN

0

Fig. 1. Cooperative spectrum sensing scenario.

(⋅ )

xk (t)

T

2

∫ (⋅ )dt

Signal squarer

Integrator

H0

Ek

or

H1

0

BPF

Threshold device

Fig. 2. Energy detector with local decision.

√ If we define n0ki = nki / N01 W , the received signal energy under H0 at k-th CR, denoted as Ek , can be written as: Ek =

2u X

n02 ki

(3)

i=1

The same approach is followed to evaluate the received signal energy under hypothesis H1 at the k-th CR when the primary signal is present with the replacement of each nki terms with nki + si , where si = s(i/(2W )). A. Soft Data Fusion Schemes Over Non-fading Channel Table I shows the expressions for overall detection and false alarm probabilities at FC under the SLS fusion, MRC fusion, SLC fusion, and SC fusion schemes following [7], [8] under PN non-faded (AWGN) environment. The symbols γrc = i=1 γi denotes the instantaneous SNR at the output PN k k of the MRC combiner; γlc = k=1 γ , where γ denotes the instantaneous S-channel SNR at k-th CR; and γsc = max(γ 1 , γ 2 , ..., γ N ) denotes the instantaneous SNR at the output of the SC combiner [9]. Also one can easily observe that the expressions for Qd and Qf for SLC scheme can be obtained from the expressions of MRC scheme by substituting simply u with N u as we know that γrc = γlc . B. Soft Data Fusion Schemes Over Rayleigh Fading Channel It is seen from Table I that the expression for Qd of any soft data fusion scheme gives as a function of the S-channel SNR (γ). Under fading scenario, by averaging Qd of any fusion

where fγ (γ) indicates the PDF of γ under fading and it depends on type of fusion scheme. From [7] and [8], it is observed that the PDF of SLS combining scheme for Rician fading channel is same as its basic PDF of SNR under that fading and the PDF of SLC scheme for Rician channel is same as PDF of MRC of that faded channel, only is replaced γrc ¯ f ), with γlc . The average overall false alarm probability (Q is same as the expressions for Qf for all soft data fusion schemes, as given in Table I, when the S-channel is corrupted by fading due to independence of Qf from SNR. SLS fusion in Rayleigh fading: The average Qd in Rayleigh ¯ d,ls,Ray , can be evaluated as fading under SLS scheme, Q N u−1 Y X  λ n 1 ¯ d,ls,Ray = 1 − Q 1−α 2 n! n=1 k=1   (5)  γ¯k λ × 1 F1 1; n + 1; −β . 2(1 + γ¯k ) where α = exp(−λ/2)/(1 + γ¯k ), and β = exp (−λ/2(1 + γ¯k )). MRC fusion in Rayleigh fading: Under MRC fusion scheme, the PDF of the SNR at the output of MRC combiner for Rayleigh fading in S-channel is given by [9]:   1 γrc N −1 f (γrc )Ray = (γ ) exp − ; γrc > 0, rc (N − 1)!¯ γN γ¯ (6) Now the average Qd in Rayleigh fading under MRC scheme, ¯ d,rc,Ray , can be evaluated by substituting (6) in (4) as Q Z ∞ p √  1 ¯ d,rc,Ray = Q Q 2γ , λ u rc γ¯ N (N − 1)! 0 (7)   γrc N −1 dγrc , ×γrc exp − γ¯ With a simple substitution of variables, γrc /¯ γ = z 2 , (7) can be rewritten as Z ∞  p √  2 ¯ d,rc,Ray = Q Qu z 2¯ γ, λ (N − 1)! 0 (8) 2N −1 2 ×z exp(−z )dz.

Now using [6], the integral in (8) can be solved by substituting q = N , p2 = 2, a2 = 2¯ γ , b2 = λ, and the final expression ¯ for Qd,rc,Ray becomes  N u−1 X  λ n exp(−λ/2) 1 ¯ Qd,rc,Ray = 1 + γ¯ 2 n! n=1     λ γ¯ λ + exp − × 1 F1 N ; n + 1; 2(1 + γ¯ ) 2(1 + γ¯ ) "N −2  (9)    k X γ¯ λ¯ γ 1 × Lk − 1 + γ¯ 1 + γ¯ 2(1 + γ¯ ) k=0  N −1  #  1 λ¯ γ 1 + γ¯ LN −1 − . + γ¯ 1 + γ¯ 2(1 + γ¯ ) SLC fusion in Rayleigh fading: The average Qd in ¯ d,lc,Ray , can be evaluated by substituting Rayleigh fading, Q N u in place of each u in (9). The expression for SLC fusion in case of Rayleigh fading channel is also a new result. SC fusion in Rayleigh fading: For Rayleigh faded Schannels with average SNR of γ¯ per channel, inserting the PDF and CDF from [5], the expression for the PDF of combiner output SNR becomes [9]   N −1 N γsc f (γsc )Ray = 1 − exp − γ¯ γ¯ (10)   γsc ; γsc ≥ 0, × exp − γ¯ Utilizing the relation [?, (4.13)] N   X N N k [1 − exp(−x)] = (−1) exp(−kx), k

The end results given in (5), (9), and (14) are in closed-form and are entirely new results. III. R ESULTS AND D ISCUSSIONS In the current section, Simulation and numerical results are presented and discussed for relevant values of the network parameters such as average S-channel SNR (¯ γ ), Rician parameter (K), number of CRs (N ), and time-bandwidth product (u) as well as for different soft data fusion schemes (SLS, MRC, SLC, and SC). The simulation is developed in MATLAB/Mathematica. The simulation flow for evaluating the performance CSS with SLC fusion is shown in Figure 3. Start

Set count1=0, count2=0, S-

channel SNR, N, λ, simul

Generate s, nk with 2TW samples, S-channel coefficient hk, and true hypothesis H {H0 and H1}

For i=1:simul

For k=1: N

Xk=nk

Yes

Xk=hk*s + nk

(11) ELC=E1+ E2…+Ek for SLC ELS=max(E1, E2.Ek) for SLS

The f (γsc )Ray in (10) can be written in a more suitable form as  N −1 k X (−1) N − 1 1 f (γsc )Ray = N k+1 γ¯ /(k + 1) k k=0 (12)   γsc × exp ; γsc ≥ 0. γ¯ /(k + 1) Now inserting the expression for PDF of combiner output SNR given in (12) into (4) i.e.  N −1 k X (−1) N − 1 k + 1 ¯ d,sc,Ray = N Q k+1 k γ¯ k=0 (13)   Z ∞ √ √ (k + 1)γsc × Qu ( 2γsc , dγsc λ ) exp γ¯ 0 Finally we obtain i

 (−1) N − 1 i+1 ¯ Qd,sc,Ray = N i + 1 i (i + 1 + γ¯ ) i=0   u−1 X  λ n γ¯ λ × F 1; n + 1; 1 1 2 2(i + 1 + γ¯ ) n=1   exp(−λ/2) λ(i + 1) × + exp − . n! 2(i + 1 + γ¯ )

H==H1 ?

Ek=(1/N01W)*sum (abs(Xk 2))

k=0

N −1 X

No

(14)

No Stop

ELC>lambda

Yes count1= count1+1 for H1 count2= count2+1 for H0

QdLC= count1 /Simul Qf LC= count2 /Simul

End

Fig. 3. Flow chart for simulation process of CCRN with SLC fusion.

¯ m versus Q ¯ f ) in AWGN environment In Figure 4, CROC (Q is shown for various soft data fusion schemes such as SLS, MRC, SLC, and SC. The impact of γ¯ on performance of CSS with MRC fusion case is also shown. It is observed that ¯ m reduces when any one of γ¯ and Q ¯ f increases. Higher Q γ¯ (noise power is low) improves P¯d of individual CR which ¯ d after cooperation i.e. overall Q ¯ m (=1further improves Q ¯ d ) reduces. Results based on derived expressions match with Q the results based on simulation testbed) under the same SNR

no fusion case (single CR user) is also shown for comparison ¯m purpose. As in Fig.4, it is observed from Fig. 5 that Q reduces when any one of γ¯ , Qf , and N increases. In addition, ¯ m for a fixed value of Q ¯f . a smaller u results in a smaller Q Increase in cooperation among the CR users leads to cancel the effects of fading in the S-channel so that the detection performance can be improved as compared to single CR user case. Moreover, higher γ¯ improves the probability of detection ¯ d ) of individual CR users which further improves the Q ¯d (Q ¯ after cooperation. For example, at Qf =0.1, and N = 3, as the ¯ m decreases by 69.99% γ¯ increases from 7 dB to 10 dB, Q with SLS fusion, by 71.90% with SLC fusion, by 76.93% with MRC fusion, and by 64.04% with SC fusion.

0

Probability of Missed Detection (Qm)

10

−1

10

−2

10

SNR=10dB, SLS, Simul SNR=10dB, SLS, Theory SNR=10dB, SLC, Simul SNR=10dB, SLC, Theory SNR=0dB, MRC, Simul SNR=0dB, MRC, Theory SNR=5dB, MRC, Simul SNR=5dB, MRC, Theory SNR=10dB, MRC, Simul SNR=10dB, MRC, Theory SNR=10dB, SC, Simul SNR=10dB, SC, Theory

−3

10

−4

10

−4

10

−3

10

IV. C ONCLUSION −2

−1

10 10 Probability of False Alarm (Qf)

0

10

Fig. 4. Performance of soft data fusions (SLS, MRC, SLC, and SC) for various values of γ ¯ in AWGN channel (u=5, N =3, both simulation and analytical results are shown).

conditions, which shows our simulation test bed and analytical approach are validated with each other. We also observe that MRC fusion based CSS performance is better as compared to the other schemes such as SLS, SLC, and SC but MRC scheme requires channel state information. The SLC fusion does not require any information about channel status and still present better performance than SLS, and SC. Thus when no channel information is available, the best scheme is SLC.

The performance of CCRN have been evaluated with a proposed analytical framework under several soft data fusion schemes (SLS, MRC, SLC, and SC) using energy detection in Rayleigh faded sensing channel. Missed detection performance based on our developed framework is presented under several numbers of CRs, time-bandwidth products and fading severity parameters. The MRC fusion scheme has been shown to outperform other schemes such as SLS, SLC, and SC in AWGN as well as Rayleigh fading in S-channel. To achieve better detection performance with lower number of CRs in worse Schannel fading condition, MRC can be used. The performance of CCRN with any type of fusion scheme outperforms single CR based spectrum sensing (no-fusion case). Results based on derived expressions in the paper match with the results based on Monte Carlo simulations. R EFERENCES

0

Probability of Missed Detection (Qm)

10

−1

10

u=5, SNR=7 dB, N=1 (No fusion) u=5, SNR=10 dB, N=1 (No fusion) u=5, SNR=7 dB, N=3 (SLS fusion) u=5, SNR=10 dB, N=3 (SLS fusion) u=1, SNR=10 dB, N=3 (SLS fusion) u=5, SNR=7 dB, N=3 (SLC fusion) u=5, SNR=10 dB, N=3 (SLC fusion) u=1, SNR=10 dB, N=3 (SLC fusion) u=5, SNR=7 dB, N=3 (MRC fusion) u=5, SNR=10 dB, N=3 (SLC fusion) u=1, SNR=10 dB, N=3 (SLC fusion) u=5, SNR=7 dB, N=3 (SC fusion) u=5, SNR=10 dB, N=3 (SC fusion)

−2

10

−3

10

−4

10

−3

10

−2

−1

10 10 Probability of False Alarm (Qf)

0

10

Fig. 5. Performance of CSS with different soft data fusions (SLS, SLC, MRC, and SC) for various values of u, γ ¯ , and N in Rayleigh fading channel.

¯ m versus Q ¯ f ) under Rayleigh faded In Fig. 5, CROC (Q environment is shown for various fusions such as SLS, SLC, MRC, and SC. The performance of CSS under such schemes is evaluated and compared to each other for various values of γ¯ , u, and number of cooperative CR users (N ). The curve for

[1] A. Ghasemi and E. S. Sousa, “Opportunistic spectrum access in fading channels through collaborative sensing?,” IEEE Transactions on Wireless Communication, vol. 2, no. 2, pp. 71-82, March 2007. [2] H. Urkowitz, “Energy detection of unknown deterministic signals,” Proceedings of IEEE, vol. 55, no.4, pp. 523-531, April 1967. [3] F. F. Digham, M. -S. Alouini and M. K. Simon, “On the energy detection of unknown signals over fading channels,” in Proceedings of IEEE International Conference on Communications (ICC’03), Alaska, USA, pp. 3575-3579, May 2003. [4] I. F. Akyildiz, B. F Lo and R. Balakrishnan, “Cooperative spectrum sensing in cognitive radio networks: A survey,” Physical Communication, vol. 4, no. 1, pp. 40-62, March 2011. [5] S. Nallagonda, V. Chandra Sekhar, A. Chandra, S. D. Roy and S. Kundu,“Detection Performance of Soft Data Fusion in Rician Fading Channel for Cognitive Radio Network,” in Proceedings of International Symposium on Wireless Personal Multimedia Communications (WPMC’15), pp. 1-5, Hyderabad, India, December 2015. [6] S. Nallagonda, A. Chandra, S. D. Roy and S. Kundu,“Detection performance of cooperative spectrum sensing with hard decision fusion in fading channels,” International Journal of Electronics, vol. 103, no. 2, pp. 297-321, March 2016. [7] D. Teguig, B. Scheers and V. Le Nir, “Data fusion schemes for cooperative spectrum sensing in cognitive radio networks,” in Military Communications and Information Systems Conference (MCC’12), pp. 1-7, Gdansk, October 2012. [8] H. Sun, A. Nallanathan, J. Jiang and C. -X. wang, “Cooperative spectrum sensing with diversity reception in cognitive radios,” in Proc. IEEE CHINACOM, pp. 216-220, August 2011. [9] M. K. Simon, M. S. Alouini, “Digital Communication over Fading Channels,” John Wiley and Sons, 2nd edition, NJ, USA, December 2004.