Detection Performance of Soft Data Fusion in Rician Fading Channel for Cognitive Radio Network Srinivas Nallagonda and V. Chandra Sekhar Department of ECE M.V.S.R Engineering College Osmania University, Hyderabad, India 501510 Email:
[email protected] [email protected]
Aniruddha Chandra
S. Dhar Roy and S. Kundu
Department of ECE Department of Radio Electronics National Institute of Technology Brno University of Technology Durgapur, India 713209 Brno, Czech Republic 61600 Email:
[email protected] Email: s
[email protected] [email protected]
Abstract—A cooperative spectrum sensing (CSS) scheme for cognitive radio network (CRN) is proposed in this paper. The energy values from different cognitive radios (CRs) are used to perform the soft combining operation. More precisely, we analyze the performance of CSS with several soft data fusion schemes: square law selection (SLS), maximal ratio combining (MRC), square law combining (SLC), and selection combining (SC) in Nakagami-n (Rician) fading environment. Towards that, an expression of detection probability in closed-form for each soft data fusion scheme in Rician fading channel is derived. A comparative performance of soft data fusion schemes has been illustrated for different network and channel parameters. Further, the performance comparison between soft data and hard decision combining schemes (such as majority-rule, AND-rule, and OR-rule) is also investigated. Index Terms—Cooperative spectrum sensing, soft data fusion, fading channel, detection probability.
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 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).
The existing literature on ED based CSS [5], assumes several fading models in S-channels such as Rayleigh, Nakagamim, Rician, Hoyt, Weibull, and Log-normal shadowing for sensing. In these cases, the performance of CSS is evaluated only under several hard decision fusions such as majority-rule, AND-rule, and OR-rule. In contrast to hard decision fusion, it is possible to implement soft data fusion schemes (SLS, MRC, SLC, and SC) at FC to improve the performance of CSS further [6]. However, in [6], the results on the basis of simulation framework is only presented. This has motivated us to develop analytical framework and to evaluate the performance of CSS with soft data fusion schemes in fading channel. For analytical tractability, we assume that the R-channels are considered as ideal [7] where as S-channels are assumed to be noisy and Nakagami-n (Rician) fading. Rayleigh fading channels in which the reflected and scattered waves are dominated by one strong component are modeled by Nakagamin distribution, known as the Rician distribution [8]. In this paper, we investigate the performance analysis of CSS with different soft data fusions: SLC, MRC, SLS, and SC, through complementary receiver operating characteristics (CROC) in Rician fading channel. Appropriate analytical formulations and a simulation test bed has been proposed using which our formulations have been validated. Specifically, in this paper, our contributions are as follows: •
•
•
•
¯d) The expressions of overall probability of detection (Q for different soft data fusion schemes such as SLS, MRC, SLC, and SC in Rician channel are derived analytically. ¯ d for To the best of our knowledge the derivation of Q Rician case is not available in the literature. The variable substitution method (or theta approach) is proposed in this paper to solve the unsolvable expression ¯ d for SC fusion scheme in Rician channel. of Q Impacts of channel and network parameters: fading parameter (K); time-bandwidth product (u); average Schannel SNR; and the number of CRs (N ) on overall sensing performance is investigated. Qualitative performance comparison of soft data fusion schemes (SLC, MRC, SLS, and SC) with the hard decision fusion schemes has been studied.
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 Rician fading are derived. In Section III, simulation and analytical results are discussed. In Section IV, conclusions are presented.
Cognitive Radio users Noisy and Faded S-channels
E2
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). If we define n0ki = nki / N01 W , the received signal energy under H0 at k-th CR, denoted as Ek , can be written as: 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 )).
FC
E3 CR3
Fig. 1 shows a proposed CSS system 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 Nakagami-n (Rician) 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
Ideal R-channels
CR2
II. S YSTEM M ODEL
Ek =
E1
CR1
Primary user (PU)
Fusion center
EN
CRN
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.
A. Soft Data Fusion Schemes Over Non-fading Channel In the case of CSS with MRC fusion scheme, all CRs send their respective energy values with appropriate weighting to the FC. Then FC gathers all the data (energy values with appropriate weighting) from all CRs, and combines. The combined energy value is passed through an ED and makes a global decision about the PU. It may be noted that as we assume R-channels to be ideal (noiseless), the MRC rule at FC becomes simple summation of the received signals from all the CRs [9]. The SC scheme which selects the signal from the branch with the largest instantaneous S-channel SNR, and performs energy detection based on the signal from the selected path. The less complexities and less power consumption are offered by SC scheme as compared to MRC fusion scheme. In low SNR, a significant improvement in SNR with a limited number of branches is not guaranteed by the MRC and SC schemes. It is also noted that, MRC (a coherent combining technique) needs information on each channel status in the case of non-coherent detection, which results in high design complexity. SLC and SLS (energy-law combining techniques) are more attractive diversity techniques for energy detection [10] to overcome the drawbacks of MRC. The final test statistic can be obtained by the energy-law combining techniques which fuse the energy of each branch. Under the SLC fusion scheme, the squared and integrated energy vectors E 1 , E 2 , · · ·, E N , from N distributed PN CRs are gathered at a FC, where the test statistic, Elc = k=1 E k is formed at FC. Under the SLS fusion scheme, the FC only selects the branch with the largest energy i.e. Els = max(E1 , E2 , · · ·, EN ). This largest energy is compared with the threshold and final decision is taken place at FC. Table I shows the expressions for overall detection and false alarm probabilities at FC under the SLS fusion, MRC
TABLE I Qd AND Qf EXPRESSIONS FOR DIFFERENT SOFT DATA SCHEMES FOR AWGN ENVIRONMENT. Qd
Combining Schemes SLS MRC SLC SC
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)
fusion, SLC fusion, and SC fusion schemes following [9], [11] 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 [12]. 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 Rician 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 ¯ d ) may scheme, the average overall detection probability (Q be derived i.e., Z ∞ ¯d = Q Qd fγ (γ)dγ (4) 0
where fγ (γ) indicates the PDF of γ under fading and it depends on type of fusion scheme. From [9] and [11], 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. Assuming independent and identically distributed (i.i.d) N number of Rician faded S-channels, the average Qd in Rician ¯ d,ls,Ric , can be obtained by fading under SLS scheme, Q substituting PDF of the SNR of SLS and Marcum-Q function of Qd in the form of infinite series [5, (21)] given in Table I in (4) as: N Y 1+K ¯ d,ls,Ric = 1 − Q 1− exp(−K) γ¯k k=1 n+1 ∞ X γ¯k Γ(u + n, λ/2) (5) × Γ(u + n) 1 + K + γ ¯ k n=0 K(1 + K) × 1 F1 n + 1; 1; . 1 + K + γ¯k
¯ d,ls,Ray can be achieved by An alternative expression of Q putting K = 0. The above result is an entirely new result and is not available in the literature. Under MRC fusion scheme, the average Qd in Rician ¯ d,rc,Ric , can be evaluated by substituting PDF of fading, Q the SNR at the output of MRC combiner [6] and Qd given in Table I in (4) i.e., N2−1 1+K 1+K ¯ Qd,rc,Ric = exp(−N K) γ¯ N K γ¯ Z ∞ p √ (1 + K)γrc × Qu 2γrc , λ exp − (6) γ¯ 0 s ! N K(1 + K)γrc (N −1)/2 ×γrc IN −1 2 γ¯ By expressing Marcum-Q function in the form of infinite series as below, the integral in (6) can be evaluated as N2+1 1+K ¯ Qd,rc,Ric = N K exp(−N K) N K γ¯ Z ∞ X Γ(u + n, λ/2) ∞ 1 + K + γ¯ × exp −γrc (7) Γ(u + n)n! 0 γ¯ n=0 s ! N K(1 + K)γrc n+ N 2−1 ×γrc IN −1 2 dγrc γ¯ and with the help of result given [8, (B.16)], the above integral can be solved as to obtain N 1+K ¯ d,rc,Ric = exp(−N K) Q 1 + K + γ¯ n ∞ X Γ(u + n, λ/2) Γ(n + N ) γ¯ (8) × Γ(u + n)n! Γ(N ) 1 + K + γ¯ n=0 N K(1 + K) × 1 F1 n + N ; N ; . 1 + K + γ¯ ¯ d,rc,Ray can be achieved by An alternative expression of Q putting K = 0 in (8). This is also a new result and is not available in the literature. Under SLC scheme, the average Qd in Rician fading, ¯ d,lc,Ric , can be evaluated by substituting N u in place of each Q ¯ d,lc,Ric reduces to u in (8). Using [13], we have verified that Q ¯ d,lc,Ray for K = 0. The expression for SLC fusion in case of Q Rician fading channel is also a new result. In a communication whose faded channel is diversity assisted, considering N -order SC for receivers, the CDF of N -order SC combiner output SNR is N Fγsc (γ) = [Fγ (γ)] . (9) By differentiating the CDF, it’s PDF can be obtained as f (γsc ) =
∂Fγsc (γ) N −1 = N [Fγ (γ)] fγ (γ). ∂γ
(10)
where fγ (γ) and Fγ (γ) are the PDF and CDF for single fading channel, respectively [8]. For SC fusion scheme, the expression for the PDF of SNR at the SC combiner output is
0
10
−1
10
¯m Q
obtained by substituting the basic PDF and CDF of SNR under Rician faded channel in (10). However, it becomes difficult to evaluate (4) after making substitutions of Qd given in Table I and (10). There is an another alternative approach that states: ¯ d,sc obtained from (4) can be An alternative expression for Q expressed by substituting γsc with tan θ and dγsc with sec2 θdθ following the variable substitution approach studied by [8], [14] Z π/2 ¯ d,sc = Q Qd,sc (tan θ)f (tan θ) sec2 θdθ. (11)
−2
10
u = 1, K = 0, SLC fusion u = 1, K = 3, SLC fusion
0
u = 1, K = 0, MRC fusion
The average detection probability, under SC scheme, in case ¯ d,sc,Ric is evaluated as of Rician channel, Q Z π/2 √ √ ¯ Qd,sc,Ric = C Qu ( 2tan θ, λ ) 0
In the current section, 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) . 0
10
−1
10
SNR=10 dB, SLS, Simul SNR = 10 dB, SLS, Theory
Qm
SNR = 10 dB, SLC, Simul SNR = 10 dB, SLC, Theory SNR = 0 dB, MRC, Simul SNR = 0 dB, MRC, Theory SNR = 5 dB, MRC, Simul SNR = 5 dB, MRC, Theory −3
SNR = 10 dB, MRC, Simul
10
SNR = 10 dB, MRC, Theory SNR = 10 dB, SC, Simul SNR = 10 dB, SC, Theory −4
10
−4
10
u = 5, K = 3, SLS fusion u = 5, K = 0, SC fusion
10
III. R ESULTS AND D ISCUSSIONS
10
u = 5, K = 0, SLS fusion
u = 5, K = 3, SC fusion
−4
s ! K(1 + K) tan θ (1 + K) tan θ × exp − I0 2 γ¯ γ¯ s " !#N −1 √ 2(1 + K) tan θ × 1 − Q1 2K, sec2 θdθ. γ¯ (12) where C = N (1 + K) exp (−K) /¯ γ . The above result is a new result.
−2
u = 1, K = 3, MRC fusion −3
10
−3
10
−2
10
−1
10
0
10
Qf
Fig. 3. 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).
−4
10
−3
10
−2
10
¯f Q
−1
10
0
10
Fig. 4. Impact of Rician parameter (K) and u on performance of soft data fusions (N = 3 and γ ¯ = 10 dB).
¯ m versus Q ¯ f ) in AWGN environment In Figure 3, 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 Pd of individual CR which ¯ d after cooperation i.e. overall Q ¯ m (=1further improves Q ¯ Qd ) reduces. Results based on derived expressions match with the results based on simulation testbed) under the same SNR 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. In Figure 4, the impacts of two different Rician fading parameters such as K = 0 and K = 3 on the CSS performance are shown. Different fusion cases such as SLS, MRC, SLC, and SC are performed at FC. For K = 0, characteristics of Rayleigh faded channel would be obtained. Decrease in fading severity (characterized by a higher value of K) decreases the overall missed detection probability at FC. We also observe ¯ m for a from this figure that a smaller u results in a smaller Q ¯ fixed value of Qf , K, N , and γ¯ for all fusion schemes. Again MRC guarantees best performance among all fusion schemes under same network and channel parameters. Figure 5 depicts the performance comparison between hard decision (majority-rule, AND-rule, and OR-rule) and soft data (SLS, MRC, SLC, and SC) combining fusion rules based ¯ d vs Q ¯ f plots (ROC). In this case, the same detection on Q threshold (λ) is assumed at each CR. The CSS performance
number of CRs in worse S-channel fading condition, MRC can be used. The performance of CSS with any type of fusion scheme outperforms single CR based spectrum sensing (nofusion case). Results based on derived expressions in the paper match with the results based on Monte Carlo simulations.
1 0.9
¯d Q
0.8 0.7
R EFERENCES
0.6
[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, A. Chandra, S. D. Roy, S. Kundu, P. Kukolev and A. Prokes, “Detection performance of cooperative spectrum sensing with hard decision fusion in fading channels,” International Journal of Electronics (Tylor & Francis), DOI:10.1080/00207217.2015.1036369, pp. 1-25, May 2015. [6] S. Nallagonda, S. Bandari, S. D. Roy and S. Kundu, “Performance of cooperative spectrum sensing with soft data fusion schemes in fading channels,” in Proceedings of Annual IEEE India Conference (INDICON’13), pp. 1-6, IIT Mumbai, India, December 2013. [7] V. Jamali, R. A. Sadegh Zadeh, S. Hamid Safavi and S. Salari, “Optimal cooperative wideband spectrum sensing in cognitive radio networks,” in Proc. IEEE ICUFN, pp. 317-374, June 2011. [8] A. Chandra, “Performance analysis of diversity combining techniques for digital signals in wireless fading channels,” PhD Thesis, Jadavpur University, India, August 2011. [9] 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. [10] S. Atapattu, C. Tellambura and H. Jiang, “Spectrum sensing in low SNR: diversity combining and cooperative communications,” in Proc. IEEE ICIIS, pp. 16-19, August 2011. [11] 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. [12] M. K. Simon, M. S. Alouini, “Digital Communication over Fading Channels,” John Wiley and Sons, 2nd edition, NJ, USA, December 2004. [13] I. S. Gradshteyn and I. M. Ryzhik, “Table of Integrals, Series and Products,” Academic Press/ Elsevier, 7th edition, San Diego, CA, USA, March 2007. [14] S. Haghani and N. C. Beaulieu, “M -ary NCFSK with S + N selection combining in Rician fading,” IEEE Transactions on Communication, vol. 54, no. 3, pp. 491-498, March 2006.
0.5
No fusion OR rule
0.4
AND rule 0.3
Majority rule
0.2
SLS fusion SLC fusion
0.1 0 −4 10
MRC fusion SC fusion −3
10
−2
10
¯f Q
−1
10
0
10
Fig. 5. Performance comparison between hard decision [5] and soft data fusions under Rician fading (K = 3, γ ¯ = 10 dB, u = 5, and N = 3).
with no-fusion (N = 1) case is also shown for the comparison purpose. As the figure indicates, all fusion schemes outperform the single CR (N = 1) based sensing except AND rule. From the figure, we observe that the OR-rule performs better than the other hard decision fusion rule majority-rule or ANDrule and . The MRC soft data fusion outperforms all other soft data fusion schemes (SLS SLC, and SC) as well as all hard decision fusion rules (majority-rule, AND-rule, and ORrule). More precisely, it is shown that all soft data fusion schemes outperform hard decision fusion rules (AND-rule and majority-rule) except OR-rule. However, these benefits are obtained at the cost of a larger bandwidth for the R-channel. The hard decision fusion rules occur with less complexity, but also with a lower detection performance than soft combination ¯ f = 0.0001, Q ¯ d is above 0.91, schemes. In particular, for Q 0.77, 0.59, 0.51, 0.66, 0.02, and 0.22 for MRC, SLC, SLS, SC, OR-rule, AND-rule, and majority-rule, respectively. Thus MRC fusion yields the best performance among all the fusion rules. IV. C ONCLUSION The performance of CSS have been evaluated with a proposed analytical framework under several soft data fusion schemes (SLS, MRC, SLC, and SC) using energy detection in Rician 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 CSS with soft data fusion schemes have shown excellent performance improvement as compared to CSS with hard decision fusion rules. The MRC fusion scheme has been shown to outperform other schemes such as SLS, SLC, and SC in AWGN as well as Rician fading in Schannel. To achieve better detection performance with lower
