Spectrum Sensing in Low SNR: Diversity Combining and Cooperative Communications

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1 0 6th International Conference on Industrial and Inforation Systes, ICIIS 0, Aug. 6-9, 0, Sri Lanka Spectru Sensing in Low SR: Diversity Cobining and Cooperative Counications Saan Atapattu, Chintha Tellabura, and Hai Jiang Abstract In this paper, the detection perforance of an energy detector used for cooperative spectru sensing in cognitive radio networks is investigated under very low signal-to-noise ratio SR) levels. The analysis focuses on the derivation of closed-for expressions for the false-alar and the average issed-detection probabilities for two cases over different fading channels: i) with diversity cobining; and ii) with cooperative counications. The detection threshold is optiized by iniizing the total error rate. The analysis is validated by nuerical and sei-analytical Monte-Carlo siulation results, which focus on the sensing requireents defined in IEEE 80.. Index Ters Cognitive radio, cooperative counications, diversity cobining, energy detection, spectru sensing. detection at low SR, and deterines the optial detection threshold so as to eet the stringent IEEE 80. WRA requireents. Using optial detection threshold analysis in [9], it shows that the recoended error rate requireents cannot be achieved even at the optial threshold value in traditional wireless networks. This is a ain drawback in spectru sensing in low SR. In this paper, we address this proble using diversity cobining and/or cooperative counications. The false alar and average issed-detection probabilities are derived, and the optial threshold selection is also discussed with nuerical exaples for low SR region over different fading channels. The rest of this paper is organized as follows. Section II discusses basics of energy detection. Spectru sensing with diversity cobining and cooperative counications are considered in Section III. Section IV presents nuerical and siulation results, followed by concluding rearks in Section V. I. ITRODUCTIO The concept of cognitive radio has been introduced to alleviate the spectru under-utilization proble of wireless counications. One of the ost challenging tasks in cognitive radio networks is spectru sensing, which is required to opportunistically access the idle radio spectru. Aong several spectru sensing techniques such as atched filter, cyclostationary feature detection and eigenvalue detection, II. EERGY DETECTIO the energy detection has gained renewed interests in recent The energy detector decides whether the priary signal is research efforts due to the low coplexity and low ipleentation cost []. The test statistic of an energy detector which is present or not fro the received signal, yt) =θhst)+wt), which follows a binary hypothesis: H proportional to the received signal energy is copared with a 0 signal absent, θ =0) and H threshold to ake the decision on radio spectru availability. signal present, θ =). Here, h, st) and wt) denote the wireless channel gain, the priary signal and the additive When the transitted signal is assued to be deterinistic, white Gaussian noise AWG). The output of the integrator a basic atheatical odel of the test statistic and the of the energy detector is the test statistic which is proportional perforance of the energy detector have been analyzed in [] to the received signal energy, given as [6]. When the transitted signal is assued to be rando, the decision statistic is odeled as a Gaussian process using the central liit theore CLT) [7], [8]. However, a theoretical Λy) = yn) ) perforance analysis is not available. Thus, this paper is n= focused on the theoretical analysis for detection of rando where is the nuber of saples and yn) is the nth saple. signal, using the basic results introduced in [9]. The test statistic is then copared with a threshold λ, and The IEEE 80. wireless regional area networks WRAs) the detection decision is that the priary signal is present if proposal recoends allowable false alar probability and Λy) >λ, or the priary signal is absent otherwise. issed-detection probability be both less than 0. with the The AWG saples wn) are assued to be independent receiver sensitivity being -6dB [0] [3], and axiu and identically distributed i.i.d.) circularly syetric coplex Gaussian CSCG) rando variables with ean zero and sensing tie be less than seconds. These perforance etrics reflect the overall efficiency and reliability of the cognitive network at very low SR. However, an energy detector The signal saples sn) are fro an i.i.d. rando process with variance E[ wn) ]=σw where E[ ] stands for expectation. perfors poorly at low SR due to noise uncertainty. For low ean zero and variance E[ sn) ]=σs. For a sufficiently SR spectru sensing, a basic analytical odel is given in [9] large nuber of saples, the statistics of Λy) can be which provides theoretical analysis for perforance of energy obtained using CLT. Thus, the probability density function PDF) of Λy) under H 0, f Λ H0 x), is a noral distribution The authors are with the Departent of Electrical and Coputer Engineering, University of Alberta, Edonton, AB T6G V4, Canada eail: {atapattu, with ean σw and variance σw. 4 For given h, the PDF chintha, hai.jiang}@ece.ualberta.ca). of Λy) under H, f Λ H, h x), is a noral distribution with //$ IEEE

2 0 6th International Conference on Industrial and Inforation Systes, ICIIS 0, Aug. 6-9, 0, Sri Lanka ean σw + γ) and variance σw 4 + γ) for a coplexvalued phase-shift keying PSK) signal where γ = h σ s σw is the instantaneous receive SR. Therefore, the false alar probability, and the issed-detection probability P γ), can be evaluated as [7, eqs. 7) and 0) ]. A. Low SR Model Under the low SR assuption i.e., σs σw), the signal has a little ipact on the variance of the test statistic under H. Thus, the PDF f Λ H, h x) can be approxiated as a noral distribution with ean σw + γ) and variance σw.this 4 approxiation is used in the rest of this paper. Therefore, and P γ) can be derived as [9] = ) λ σ Erfc σ w ) w P γ) = ) λ σ Erfc w + γ), 3) σ w respectively, where Erfcz) = e t dt is the copleentary error function [4]. In [9], the accuracy of the z approxiation is confired by coparing approxiated and exact cuulative distribution function CDF) and receiver operating characteristic ROC) curves. π B. Average Missed-Detection Probability The average issed-detection probability over AWG channel is in the for of 3) when γ is replaced by the average SR,, where = E[γ]. However, the received signal is affected by the fluctuations of the propagation channel due to path loss, large-scale fading and sall-scale fading. When the SR distribution is f γ γ), the average issed-detection probability, P, can be calculated as P = 0 P x)f γ x)dx. The Rayleigh and akagai- fading channels, which can odel a variety of fading effects, are considered in [9], in which the average issed-detection probability over Rayleigh fading channel, P Ray P Ray = [ Erfc, is derived as σ w λ σ w ) e ψ + 4 σ w! λ σ w σ Erfc w λ + )] σ w, and the average issed-detection probability over akagai fading channel for integer ), P ak, is derived as ) P ak = Γ) I,p,, σ w λ 5) where In, p, a, b) ) n n p n σ w ) p= [ p +4pab Erfcb) e 4a Erfcb+ a) p p In the following section, we use these results to derive the false alar and the average issed-detection probabilities for diversity receptions and cooperative counications scenarios. 4 4) ]. III. PERFORMACE AALYSIS WITH DIVERSITY COMBIIG AD COOPERATIVE COMMUICATIOS As shown in [9], it is very difficult to eet the sensing requireents of IEEE 80. WRAs proposal in low-sr environent. Therefore, diversity cobining and/or cooperative counications can be used to iprove the detection perforance, since the two techniques can iprove end-to-end SR and the effective nuber of test statistics at the detector at the cost of processing delay and ipleentation coplexity. In this section, detection capability of these techniques is analyzed assuing low SR environents. A. Using Diversity Reception Techniques In traditional diversity techniques such as axial ratio cobining MRC), selection cobining SC), etc., the energy detector follows the cobiner. For MRC or SC, the energy detector processes the saples of cobined signal of L diversity branches as its test statistics. Thus, the effective nuber of saples for a test statistic,, is independent of L. Further, these diversity techniques do not guarantee a significant SR iproveent with a oderate nuber of diversity branches in low SR such -0dB. And also, a coherent cobining technique such as MRC needs channel state inforation in non-coherent energy detection, which increases the design coplexity. Due to these drawbacks of aforeentioned diversity techniques, energy-law cobining techniques such as square-law cobining SLC) and square-law selection SLS) are ore attractive for energy detection in cognitive radio. The energy-law cobining techniques cobine the energy of each branch to get the final test statistic. Therefore, the effective nuber of saples depends on L [4]. In what follows, the average issed-detection probabilities of SLC and SLS techniques are derived in low SR. ) Square-Law Cobining SLC): Each diversity branch has a square-law device which perfors the square-andintegrate operation. The cobiner is ipleented following the square-law operation. The decision statistic has L effective saples fro L diversity branches each branch has saples) which is given with a for of ) as L Λ SLC y) = Λy i ) where Λy i ) is the test statistic of the ith branch. With CLT, the PDF of Λ SLC y) under H 0 is a noral distribution with ean Lσw and variance Lσw, 4 and the PDF of Λ SLC y) under H is a noral distribution with ean Lσw + γ) and variance Lσw 4 + γ). For low SR, the false alar probability, and the issed-detection probability under AWG channels can be evaluated as ) and 3), respectively, with being replaced by L. With the aid of 5), the average issed-detection probability, P SLC, over akagai- fading channels can be derived as P SLC = ) Γ) I,p, ) L, Lσ w λ. Lσ w p= 6)

3 0 6th International Conference on Industrial and Inforation Systes, ICIIS 0, Aug. 6-9, 0, Sri Lanka 3 ) Square-Law Selection SLS): Siilar to SLC, each diversity branch has a square-law operation before selection cobing. In SLS, the branch with the axiu decision statistic is to be selected such as y SLS = ax{y,..., y L } [4]. The CDF of y SLS can be written for independent decision statistics as F ysls x) =P y SLS x) =P y x,..., y L x) 7) = F yi x) where F yi x) is the CDF of y i. The false alar probability is P SLS f = P y SLS λ H 0 )= Py SLS λ H 0 ) = L F y i λ H 0 ) = L P y 8) i λ H 0 )) = ) L where is given in ). Siilarly, under H, the isseddetection probability can be written as P SLS = F yi λ H )= P y i λ H )= P γ i ) where P γ i ) is given in 3) with γ i being the instantaneous SR at the ith branch. If the SR distribution of the ith branch is f γi γ i ), the average issed-detection probability can be evaluated as P SLS = L P 0 x)f γi x)dx. For i.i.d. akagai- fading branches, i.e., each branch has the sae average SR, the average issed-detection probability, P SLS can be given as P SLS = where P ak is given in 5). P ak ) L 9) B. Using Cooperative Counications Cooperative counications can iprove the signal detection capability as sharing and cobing the inforation of interediate cognitive nodes called cooperative nodes). As any previous work efforts are focused on the ediu or high SR region [5] [7], the ipact of cooperative counications in low SR is not obvious. To investigate this case, we consider the decision fusion strategy in which each cooperative node akes a decision on the priary user activity, and the individual -bit decisions are reported to the fusion center. If there are K cooperative nodes and the fusion center has k-out-of-k fusion rule i.e., the fusion center decides the presence of priary activity if there are k or ore cooperative nodes that individually decide the presence of priary activity), the false alar and the average isseddetection probabilities of cooperative counications over akagai- fading channels are K ) P Coop K f = ) i ) K i, 0) i P Coop = K i=k i=k K i ) ) i K i P,i ak P,i) ak, ) respectively, where P,i ak is the average issed-detection probability at the ith cooperative node, which is equal to 5) with being replaced by the ith channel average SR i. As shown in previous studies [7] [9], since cooperative counications provide a higher diversity advantage, the detection capability and counication reliability are iproved. Such a setup includes the reporting channels that are utually orthogonal to avoid the inter-channel interference and data collision at the fusion center. Orthogonal channels are realized either by using frequency devision FDMA) or tie devision TDMA) ultiple access techniques. As FDMA requires larger frequency bandwidth, it is not a good solution for the frequency scarcity proble. In TDMA, each reporting channel requires different tie slot which has duration τ r.if we neglect other processing delays at the cooperative nodes and the fusion center, the nuber of cooperative) nodes that can participate in the cooperation is K τ fs τ r where τ is the axiu allowable sensing tie and f s is the sapling frequency of the energy detector. Therefore, K is liited by the sensing tie. C. Threshold Selection The threshold, λ, which varies for 0 to is a coon paraeter for the false alar, the detection and the isseddetection probabilities which are denoted as λ), P d λ) and P λ), respectively. The traditional way of setting the threshold is based on the false alar probability. Such a threshold selection does not always guarantee the requireents of IEEE 80. WRAs proposal in practice. In this paper, the optial threshold λ is selected such that the total error rate defined as λ) λ)+p λ) is iniized. This is a possible way of selecting the threshold to satisfy both false alar and issed-detection probability requireents [0]. As discussed in [9], the required error rates 0. and P 0.) ay not be achieved at the optial threshold value for given and σ w in low SR, but they can be achieved by increasing. However, sensing tie, τ, isalso increased when is increased because τf s. Therefore, a possible solution is to use a diversity cobining or cooperative counications technique. For exaple, the optial threshold in SLC can be derived as [9, eq. 8)] with being replaced by L, and it can be further approxiated for low SR as λ Lσ w + ) +γ Lσw which iplies that the sensing tie can be reduced when the nuber of diversity branches increases. More nuerical exaples will be given in the next section. IV. UMERICAL/SIMULATIO RESULTS AD DISCUSSIO This section provides nuerical and sei-analytical Monte- Carlo siulation results. We define the noralized threshold as ˆλ λ, i.e., the threshold is noralized by the nuber of saples. We denote Pe = λ ), Pf = λ ), and P = P λ ) where λ is the optial threshold. Fig. shows the ROC curves of i) SLC, SLS cobining techniques, and ii) a cooperative spectru sensing network. 5

4 0 6th International Conference on Industrial and Inforation Systes, ICIIS 0, Aug. 6-9, 0, Sri Lanka P d SLC L= SLS L= 0. SLC L=5 SLS L=5 K= K=0 K= SLC L= SLC L=3 SLS L= SLS L=3.5 oralized Threshold Fig. : ROC curves for SLC and SLS diversity techniques and cooperative counications. Fig. 3: Total error rate versus noralized threshold for diversity techniques SLS and SLC) K= =-5dB K= =-0dB K=0 =-5dB K=0 =-0dB oralized threshold Fig. : Total error rate versus noralized threshold for cooperative counications. For SLC and SLS cobining techniques with =-0dB, σw =, and = 0 3 per branch over akagai- fading, the detection capability is significantly increased with L due to the effect of diversity advantage. The detection perforance difference between SLC and SLS is not clear-cut because two ROC curves of SLC and SLS cross each other for a given L. The ipacts of the nuber of cooperative nodes K) on the detection capability are shown when = -0dB σw =, and = 0 4 over AWG channels. It clearly shows that larger K iproves detection perforance. The total error rate versus noralized threshold for a cooperative sensing network over AWG channel is shown in Fig. when =-5dB, -0dB, σw =5 and = 0 3. The optial threshold is ˆλ 6, 7 when K =for =- 0dB, -5dB, respectively. Thus, the approxiation ˆλ σw is valid for the cooperative case with sall K. However, when K is increased, this approxiation is no longer valid tightly because the effective SR is increased considerably with K, and therefore, it has a significant contribution for ˆλ, e.g., ˆλ 8 for K =0. The total error rate versus noralized threshold for SLC and SLS diversity reception techniques over AWG channel is shown in Fig. 3 when = -0dB, L =, 3, σw =5 and = 0 3. The optial threshold values for SLS are ˆλ 6 for L = and ˆλ 67 for L =3. In this case, the approxiation ˆλ σw is also valid. On the other hand, for SLC, the optial threshold values are ˆλ.507 for L =and ˆλ.6 for L =3which confirs that ˆλ Lσw. Fig. 4 shows error rates at the optial threshold Pe, Pf, and P ) versus. Fig. 4a is for SLC with L=, 3 over Rayleigh fading channels at = -0dB. We chose Rayleigh channel because akagai- > ) and AWG channel odels require a saller nuber of saples than in the Rayleigh channel. As in Fig. 4a, requireent 0.) can be achieved when. 0 4 and , and P requireent P 0.) can be achieved when and for L = and L = 3, respectively. Therefore, to eet both and P requireents, we should have and for L =and L =3, 6 respectively. Thus the required sapling rates f s = τ with τ sec) are at least 970kHz and 647.5kHz for L =and L =3, respectively. Fig. 4b is for cooperative counications with K=, 3 and 4 over Rayleigh fading channels at = -0dB. The requireent can be achieved when ,

5 0 6th International Conference on Industrial and Inforation Systes, ICIIS 0, Aug. 6-9, 0, Sri Lanka 5 Error rate L= L= P L= L=3 L=3 P L=3 are considered. The false-alar and the average isseddetection probabilities are derived over fading channels. As iniizing the total error rate, the optial detection threshold is also deterined using nuerical analysis. It is shown that increasing the nuber of saples by increasing the diversity order through diversity cobining or cooperative counications) is a possible way to eet the fundaental sensing requireents specified in IEEE 80. WRAs proposal, which are on channel detection tie seconds), false alar probability 0.) and issed-detection probability 0.) at low SR -0dB). Error rate P a) b) K= K=3 K=4 Fig. 4: Error rates at the optial threshold value total error: P e ; false alar: P f ; and issed-detection: P )versus nuber of saples for a) SLC diversity technique; b) cooperative spectru sensing and.7 0 4, and P requireent can be achieved when ,. 0 5 and for K=, 3 and 4, respectively. To eet both and P requireents, we should have ,. 0 5 and for K=, 3 and 4. V. COCLUSIO The low SR detection perforance of the energy detector is studied for spectru sensing in cognitive radio networks where diversity cobining and cooperative counications 7 REFERECES [] R. Tandra and A. Sahai, SR walls for signal detection, IEEE J. Select. Topics in Signal Processing, vol., no., pp. 4 7, Feb [] H. Urkowitz, Energy detection of unknown deterinistic signals, Proc. of the IEEE, vol. 55, no. 4, pp , Apr [3] V. Kostylev, Energy detection of a signal with rando aplitude, in Proc. IEEE Int. Conf. Coun. ICC), May 00, pp [4] F. F. Digha, M. S. Alouini, and M. K. Sion, On the energy detection of unknown signals over fading channels, IEEE Trans. Coun., vol. 55, no., pp. 4, Jan [5] S. Atapattu, C. Tellabura, and H. Jiang, Energy detection of priary signals over η μ fading channels, in Proc. Int. Conf. Industrial and Inforation Systes ICIIS), Dec. 009, pp. 8. [6], Perforance of an energy detector over channels with both ultipath fading and shadowing, IEEE Trans. Wireless Coun., vol.9, no., pp , Dec. 00. [7] Y.-C. Liang, Y. Zeng, E. Peh, and A. T. Hoang, Sensing-throughput tradeoff for cognitive radio networks, IEEE Trans. Wireless Coun., vol. 7, no. 4, pp , Apr [8] Z. Quan, S. Cui, A. Sayed, and H. Poor, Optial ultiband joint detection for spectru sensing in cognitive radio networks, IEEE Trans. Signal Processing, vol. 57, no. 3, pp. 8 40, Mar [9] S. Atapattu, C. Tellabura, and H. Jiang, Spectru sensing via energy detector in low SR, in Proc. IEEE Int. Conf. Coun. ICC), June 0. [0] C. Cordeiro, K. Challapali, D. Birru, and S. S.., IEEE 80.: An introduction to the first wireless standard based on cognitive radios, Journal of Counications JCM), vol., no., pp , Apr [] S. J. Shellhaer, Spectru sensing in IEEE 80., in st IAPR Workshop on Cognitive Inforation Processing, 008. [] C. Stevenson, G. Chouinard, Z. Lei, W. Hu, S. Shellhaer, and W. Caldwell, IEEE 80.: The first cognitive radio wireless regional area network standard, IEEE Coun. Mag., vol. 47, no., pp , Jan [3] S. Shellhaer, A. Sadek, and W. Zhang, Technical challenges for cognitive radio in the TV white space spectru, in Proc. Infor. Theory and Applications Workshop, Feb. 009, pp [4] I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 6th ed. Acadeic Press, Inc., 000. [5] A. Ghasei and E. S. Sousa, Collaborative spectru sensing for opportunistic access in fading environents, in Proc. IEEE DySPA, ov. 005, pp [6] W. Zhang and K. Ben Letaief, Cooperative counications for cognitive radio networks, Proc. of the IEEE, vol. 97, no. 5, pp , May 009. [7] W. Zhang and K. Letaief, Cooperative spectru sensing with transit and relay diversity in cognitive radio networks, IEEE Trans. Wireless Coun., vol. 7, pp , Dec [8] G. Ganesan and Y. Li, Cooperative spectru sensing in cognitive radio, part I: Two user networks, IEEE Trans. Wireless Coun., vol. 6, no. 6, pp. 04 3, June 007. [9] S. Atapattu, C. Tellabura, and H. Jiang, Energy detection based cooperative spectru sensing in cognitive radio networks, IEEE Trans. Wireless Coun., vol. 0, no. 4, pp. 3 4, Apr. 0. [0] W. Zhang, R. Mallik, and K. Letaief, Optiization of cooperative spectru sensing with energy detection in cognitive radio networks, IEEE Trans. Wireless Coun., vol. 8, no., pp , Dec. 009.