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  • 1. Chandrasekhar Korumilli, Chakrapani Gadde, I.Hemalatha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1004-1009 Performance Analysis of Energy Detection Algorithm in Cognitive Radio Chandrasekhar Korumilli1, Chakrapani Gadde2, I.Hemalatha3 1 ( P.G.Student Department of Electronics and Communications, Sir CRR College of engineering, Eluru) (2P.G.StudentDepartment of Electronics and Communications, Sir CRR College of engineering, Eluru) 3 ( Associate prof Department of Electronics and Communications, Sir CRR College of engineering, Eluru)ABSTRACT spectrum from primary licensed users or to share In cognitive radio systems, secondary the spectrum with the primary users. A cognitiveusers should determine correctly whether theprimary user is absent or not in a certain radio is able to able to fill in the spectrum holes andspectrum within a short detection period. serve its users without causing harmful interferenceSpectrum detection schemes based on fixed to the licensed user. To do so, the cognitive radiothreshold are sensitive to noise uncertainty; the must continuously sense the spectrum it is using inenergy detection based on dynamic threshold order to detect the re-appearance of the primarycan improve the antagonism of noise user [3]. Once the primary user is detected, theuncertainty; get a good performance of cognitive radio should withdraw from the spectrumdetection while without increasing the computer instantly so as to minimize the interference. This iscomplexity uncertainty and improves detection very difficult task as the various primary users willperformance for schemes are sensitive to noise be employing different modulation schemes, datauncertainty in lower signal-to-noise and large rates and transmission powers in the presence ofnoise uncertainty environments. In this paper variable propagation environments and interferencewe analyze the performance of energy detector generated by other secondary users [1].spectrum sensing algorithm in cognitive radio. The paper is organized as follows. Section 2By increasing the some parameters, the discuss the spectrum sensing problem, overview ofperformance can be improved as shown in the spectrum sensing methods and the performance ofsimulation results. energy detector spectrum sensing algorithm inKeywords - cognitive radio, detection threshold, cognitive radio. Section 3 discusses thedynamic threshold detection, noise uncertainty performance of dynamic threshold based spectrum detection in cognitive radio systems. Section 41. INTRODUCTION discusses the conclusion and future in this field of With the development of a host of new study.and ever expanding wireless applications andservices, spectrum resources are facing huge 2. SPECTRUM SENSING PROBLEMdemands. Currently, spectrum allotment is done byproviding each new service with its own fixed 2.1 ENERGY DETECTIONfrequency block. As more and more technologies Spectrum sensing is a key element inare moving towards fully wireless, demand for cognitive radio communications as it must bespectrum is enhancing. In particular, if we were to performed before allowing unlicensed users toscan the radio spectrum, including the revenue-rich access a vacant licensed band. The essence ofurban areas, we find that some frequency bands in spectrum sensing is a binary hypothesis-testingthe spectrum are unoccupied for some of the time, problemand many frequency bands are only partiallyoccupied, whereas the remaining frequency bands H0: X (N) =W (N)are heavily used [1]. It indicates that the actual H1: X (N) =S (N) +W (N) (1)licensed spectrum is largely under-utilized in vasttemporal and geographic dimensions [2].A remedy Where N is the number of samples,to spectrum scarcity is to improve spectrum N=2TW, T is duration interval ,W is bandwidth, Sutilization by allowing secondary users to access (N) is the primary user’s signal, W (N) is the noiseunder-utilized licensed bands dynamically and X (N) is the received signal. H0 and H1 denotewhen/where licensed users are absent. that the licensed user is present or not, respectively. Cognitive radio is a novel technology The noise is assumed to be additive white Gaussianwhich improves the spectrum utilization by noise (AWGN) with zero mean and is a randomallowing secondary users to borrow unused radio process. The signal to noise ratio is defined as the ratio of signal power to noise power 1004 | P a g e
  • 2. Chandrasekhar Korumilli, Chakrapani Gadde, I.Hemalatha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1004-1009 Under the assumption of absolutely nodeterministic knowledge about the signal X (n),i.e., we assume that we know only the averagepower in the signal. In this case the optimaldetector is energy detector or radiometer can berepresented as [23]  N 1 DY   Y n X n    1 H1 N n 0   H0 (2) Where D(Y) is the decision variable and isthe decision threshold, N is the number of samples.If the noise variance is completely known, thenfrom the central limit theorem the followingapproximations can be made [24] DY H 0  ~ N  n ,2  n N 2 4  Figure 1 ROC curves of energy detectionDY H 1  ~ N  P   n ,2( P   n ) 2 2 2 N  (3) scheme with different SNRWhere P is the average signal power and  2 n is the Figure 2 is the numerical results of (7) for given PFA (0.0.9), SNR=-15dB. It shows that thenoise variance. Using these approximations performance is improved by increasing N, andThe probability expressions are probability of detection can be improved by  2  increasing N value even if the SNR is much lower,    n  PFA  Pr D(Y )   H 0  Q   as long as N is large enough without noise  2 4 N  uncertainty.  n  (4)      (P   n ) 2PD  Pr D(Y )   H 1   Q    2( P   2 ) 2 N   n  (5)      (P   n ) 2 PMd  1  PD  1  Q   2( P   2 ) 2 N   n  (6)Where Q (·) is the standard Gaussiancomplementary cumulative distribution function(CDF). PD, PFA and PMd represent detectionprobability, false alarm probability and missingprobability respectively.From (4) and (5) eliminating threshold    N  2 Q 1 PFA  Q 1 PD   SNR 2 2 (7) Figure 2 ROC curves of energy detection scheme with different N PWhere SNR  ,  n is the normalized noise 2 n 2power. Figure 1 shows the numerical results of(7) for given PFA (0.0.9), sample number N=500,with different SNR values with that theperformance is improved by increasing SNR value 1005 | P a g e
  • 3. Chandrasekhar Korumilli, Chakrapani Gadde, I.Hemalatha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1004-10092.2 NOISE UNCERTAINTY environments. This indicates that the choice of a fixed threshold is no longer valid under noiseNow, considering the case with uncertainty in the uncertainty and threshold should be chosen flexiblenoise model [20], the distributional uncertainty of based on the necessities.noise can be represented as  2  [ n /  ,  n ] 2 2 is the noise uncertainty coefficient and  >1Now    n 2 PFA  Q  (8)   2 2 / N   n     (P   n / N ) 2  PD  Q   (P   2 /  ) 2 / N   n  (9) eliminating threshold  and equating bothequations we have    N  2 Q1 PFA  (1/   SNR)Q1PD  SNR  (  1/  )2 2 (10) Figure 3 ROC curves of energy detection scheme with different  Comparing (10) with (7), there is almostno contribution to the whole expression results if 3. DYNAMIC THRESHOLDthere is a tiny change of ρ; however, SNR−2 and Performance of cognitive radio declined(SNR − (ρ − 1/ρ)) −2 should be mainly discussed sharply due to noise uncertainty and cognitiveand compared. When ρ ≈ 1, then SNR−2 ≈ (SNR − users’ accessing will be serious interference to(ρ − 1/ρ)) −2, the numerical value of (10) and (7) are licensed users. This should be avoided in dynamicalmost the same; When ρ is larger and suppose ρ = spectrum access technology. For this reason, a new1.05, then (ρ − 1/ρ) = 0.0976 ≈ 0.1, if SNR = 0.1, algorithm combating the noise uncertainty iswell then (SNR − (ρ − 1/ρ)) −2 ≈ 0, substituting into presented [21][20].equation (10) to be N →∞. In other words, only Assume that the dynamic threshold factor 𝜌infinite detection duration can complete detection, and 𝜌′ > 1 the distributional of dynamic thresholdwhich is impracticable. A tiny fluctuation of in the interval   [ /  ,   ]average noise power causes performance dropseriously, especially with a lower SNR. Then the probability relationships are represented Figure 3 shows the numerical result of as(10) probability of false alarm on X-axis andprobability of detection on Y-axis for an SNR=-    n 2 15dB, PFA = (0, 0.9), N=500 and varying the noise PFA     2 2 / N uncertainty value.  n  (11) From the Figure it is seen that the  performance gradually drops as the noise factorincreasing. This indicates that Energy detector is      P n PD   2    very sensitive to noise uncertainty. It means thatcognitive users predict the spectrum to be idle no    P n 2 2     N matter whether there are primary users present or (12)absent. Consequently, cognitive users are harmfulto licensed users when primary users are present. After simplifying (11) and (12) we get theThis situation often occurs in cognitive radio relationship for SNR, N, PFA , PD and  systems, particularly in lower signal-to-noise ratio  environments. In order to guarantee a good N  2 Q 1PFA    2 1  SNRQ 1PD  2performance, choosing a suitable threshold is veryimportant. Traditional energy detection algorithmsare based on fixed threshold and we have verified     2 SNR   2  1  2 (13)that performance decreased under noise uncertainty 1006 | P a g e
  • 4. Chandrasekhar Korumilli, Chakrapani Gadde, I.Hemalatha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1004-1009 Figure 4 shows the performance of energy Eliminating threshold detection scheme, probability of false alarm on X- we get the inter relationship for SNR, N, PFA , PDaxis and probability of detection on Y-axis. and  2    1   N  2   Q 1 PFA      SNR Q 1 PD        (16) 2        SNR          In (16), when  ≈ ρ and  ρ ≈ ρ/  ≈ 1,  SNR        ≈ 2 (SNR) and −2  (1/ρ+SNR) ≈ (1+SNR). We substitute (16) with the above approximate unequal expressions, and we can get that the numerical value of (16) is almost the same to (7). Therefore, dynamic threshold detection algorithm can overcome the noise uncertainty as long as a suitable dynamic threshold factor is chosen. Comparing (16) with (13), supposing SNR = 0.1 and  and ρ both closer to 1, it is clear that Figure 4 ROC curves of energy detection scheme with no noise uncertainty, with noise  SNR       2  SNR    1  2 . uncertainty, and with dynamic threshold Consequently, detection duration N has been shortened largely to N= 500 with the sameHere we have taken a SNR=-15dB, PFA  0,0.09 , probability parameters PD and PFA as shown in Figure 5 It can be concluded that as long as theN=1500, noise uncertainty1.02 and dynamic dynamic threshold factor is suitable, even if there isthreshold1.001.It is observed that the performance noise uncertainty, we can get a better spectrumis improved by using a dynamic threshold performance. To attaining the same performance, the detection time of dynamic threshold energy3.1 NOISE UNCERTAINTY AND DYNAMIC detection Algorithm is less than the traditionalTHRESHOLD version. Figure 5 is the numerical results of (7), We have discussed two cases that existing (13) and (16). With the same parameters as before.noise uncertainty and dynamic thresholdrespectively, this section will give the expressionsthat considering noise uncertainty and dynamicthreshold together, we got expressions of falsealarm probability and detection probabilityThe noise variance in the interval  2 2   ,  n   n  Now the probability relations are represented as        n  2 PFA  Q  (14)   n 2  2  N     2   P  n          PD  Q (15)   2  2   P  n      N  Figure 5 ROC curves of energy detection    scheme with N=500, different ρ and  1007 | P a g e
  • 5. Chandrasekhar Korumilli, Chakrapani Gadde, I.Hemalatha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1004-1009 Dissertation, Virginia Polytechnic Institute Where ρ = 1.00 denotes that the average and State University, September 2006.noise power keeps constant (without noise [9] FCC, “Spectrum policy task force,”uncertainty);  = 1.00 denotes that the algorithm Technology Advisory Councildid not use dynamic threshold (the threshold is (TAC),Briefing, Tech. Rep., 2002.fixed); otherwise, it represents cases with noise [10] Z. L. W. H. S. J. Carl R.Stevenson, Geralduncertainty and dynamic threshold. From Figure 5 Chouinard and W. Caldwell, “Ieee 802.11it indicates that a tiny fluctuation of average noise the first cognitive radio wireless regionalpower causes a sharp decline in detection area network standard,” IEEE Standards inperformance. The dynamic threshold makes the Communications, pp. 130–138, Januaryperformance improve significantly as the dynamic 2009threshold factor increasing. If a suitable dynamic [11] T. Yucek and H. Arsla, “A survey ofthreshold factor is selected, the falling proportion spectrum sensing algorithms for cognitiveof performance caused by noise uncertainty can be radio applications,” IEEE Communicationsomitted and the performance may be more Surveys & Tutorials, vol. 11, no. 1, pp. 116–accurate. 130, March 2009. [12] X. C.X.Wang, H.H.Chen and M.GuiZani, “Cognitive radio network management,”4. CONCLUSION IEEE Vehicular Technology Magazine, vol. Energy detection based on fixed threshold 3, no. 1, pp. 28–35, 2008.are sensitive to noise uncertainty, a fractional [13] W. Gardner and C. Spooner, “Signalchange of average noise power causes decreasing interception: performance advantages ofthe performance quickly. According to the cyclic-feature detectors,” IEEE Transactionsdrawback in Matched filter which not sensitive to on Communications, vol. 40, no. 1, pp. 149–noise uncertainty, by using dynamic threshold the 159, January 1992.performance can be improved as compared with the [14] H. P. Zhi Quan, Shuguang Cui and A.fixed threshold. The computer simulations of the Sayed, “Collaborative wideband sensing fordynamic threshold based energy detection cognitive radios,” IEEE Signal Processingalgorithm in cognitive radio improve the detection Magazine, vol. 25, no. 6, pp. 60–73,performance but in practical how acquire the November 2008.detection threshold and how to improve the [15] Y. Zeng and Y.-C. Liang, “Covariance baseddetection performance by other sensing methods. signal detections for cognitive radio,” 2nd IEEE International Symposium on NewREFERENCES Frontiers in Dynamic Spectrum Access [1] S.Haykin,“Cognitive radio:brain-empowered Networks, pp. 202–207, April 2007. wireless communications,” IEEE [16] K.B.Letaief and W. Zhang, “Cooperative J,Select.Areas in Commun, vol. 23, no. 2, communications for cognitive radio pp. 201–220, february 2005. networks,” Proceedings of the IEEE, vol. 97, [2] V. K.Bhargava and E. Hossain, Cognitive no. 5, pp. 878–893, May 2009. Wireless Communication Networks, 1st ed. [17] H.Urkowitz, “Energy detection of unknown Springer, 2007. deterministic signals,” Proceedings of the [3] J.Mitola, “Cognitive radio an integrated IEEE, vol. 55, no. 4, pp. 523–531, April agent architecture for software defined,” 1967. Ph.D. dissertation, KTH Royal Institute of [18] M. F.F.Digham and M.K.Simon, “On energy Technology, Stockholm,Sweden, 2000. detection of unknown signal over fading [4] R. RUBENSTEIN, “Radios get smart,” channel,” Proceedings of IEEE International IEEE Spectrum,consumer electronics, pp. Conference on Communications (ICC03), 46–50, February 2007. pp. 3575–3579, May 2003. [5] J.Mitola, “Cognitive radio:making software [19] A.H.Nuttal, “Some integrals involving qm radio more personal,” IEEE Personal function,” IEEE Transaction on Information Communications, vol. 6, no. 4, pp. 13–18, Theory, vol. 21, no. 1, pp. 95–96, January 1999. 1975. [6] B. A.Fette, Cognitive Radio, 1st ed. Newnes, [20] T. L. Jinbo Wu, Guicai and G. Yue, “The 2006. performance merit of dynamic threshold [7] FCC, “Notice of proposed rulemaking and energy detection algorithm in cognitive order,” ET, Docket 03-222, December 2003. radio systems,” The 1st International [8] J. O. Neel, “Analysis and design of cognitive Conference on Information Science and radio networks and distributed radio Engineering (ICISE2009), IEEE Computer resource management algorithms,” Doctoral Society, 2009. 1008 | P a g e
  • 6. Chandrasekhar Korumilli, Chakrapani Gadde, I.Hemalatha / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.1004-1009 [21] H. L. Gui-cai Yu, Yu-bin Shao and G. xin communications. Published papers in many Yue, “Dynamic threshold based spectrum international journals and Conferences. detection in cognitive radio systems,” Wicom’09 5th International Conference on Wireless Commun’s,Networking and Mobile Computing, 2009. [22] R. Tandra and A. Sahai, “SNR walls for signal detection,” EEE Journal of Selected Topics in Signal Processing, vol. 2, no. 1, pp. 4–17, February 2008. [23] R. Tandra, “Fundamental limits on detection in low SNR,” Master’s thesis, University of California, Berkeley, 2003. [24] S.M.Kay, Fundamentals of Statistical Signal Processing: Detection Theory. Englewood Cliffs: Prentice-Hall, 1998, vol. 2. Authors 1 Chandrasekhar Korumilli received his B.Tech from Pragati Engineering College in 2008. Currently he ispursuing his M.Tech from SIR C.R.ReddyCollege of engineering college, Eluru westGodavari district, Adhrapradesh. His areas ofinterest are wireless communications, computernetworking and Cognitive Radio. He has publisheda paper in international journals relating to“Throughput Improvement in Wireless MeshNetworks by Integrating with Optical Network”and presented papers in many internationalconferences. 2 Chakrapani Gadde received his B.Tech from Lakireddy Balireddy College of engineering in 2008. Currently he is pursuing his M.Tech from SIR C R Reddy College ofengineering college, Eluru west Godavaridistrict,Andhrapradesh. His areas of interest are wirelesscommunications and computer networking. He haspublished papers in international journals relatingto “Mitigation of near far effect in GPS receivers”.3 I.Hemalatha received B.Tech from Sir CRRCollege of Engineering, M.Tech from JNTUKakinada. Currently she is working as an AssociateProf at Sir C R Reddy College of Engineering,Eluru west Godavari district, Andhrapradesh. Sheis having Twelve years of teaching experience andguided many students during this period. Her areasof interest are Speech Processing and wireless 1009 | P a g e