International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976International Journal o...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976– 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976– 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976– 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976– 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976– 6464(Print), ISSN 097...
International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976– 6464(Print), ISSN 097...
Upcoming SlideShare
Loading in …5
×

Cognitive radio spectrum sensing and performance evaluation of energy detector under consideration of rayleigh distribution of the received signal

262 views

Published on

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
262
On SlideShare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
4
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Cognitive radio spectrum sensing and performance evaluation of energy detector under consideration of rayleigh distribution of the received signal

  1. 1. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976International Journal of Electronics and Communication IJECET– 6464(Print), ISSN 0976 – 6472(Online) Volume 2, Number 1, Jan - April (2011), © IAEMEEngineering & Technology (IJECET)ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online)Volume 2, Number 1, Jan – April (2011), pp. 17-23 ©IAEME© IAEME, http://www.iaeme.com/ijecet.htmlCOGNITIVE RADIO: SPECTRUM SENSING AND PERFORMANCE EVALUATION OF ENERGY DETECTOR UNDER CONSIDERATION OF RAYLEIGH DISTRIBUTION OF THE RECEIVED SIGNAL SRIJIBENDU BAGCHI Dept. of Electronics and Communication, RCC Institute of Information Technology, Kolkata, IndiaABSTRACTCognitive radio is proposed as a solution to rationalize the concept of recycling thespectrum in today’s spectrum hungry scenario. Here unlicensed users utilize the licensedfrequency band when that particular band is not in use. Spectrum sensing is important tosense the arrival of primary user. In this paper, sensing is done by energy detector andtwo figures of merit namely probability of false alarm and probability of detection arecalculated by treating the received signal as Rayleigh distributed.Keywords: Cognitive radio, probability of false alarm, probability of detection1. INTRODUCTION Available unlicensed spectrum has become a scarce resource for communicationdue to recent advances in wireless technology [1]. Fixed spectrum allocation to differentservices also causes limited usage of frequency bandwidth. However, recent studies ofFederal Communications Commission (FCC) have shown that 70% of allocated spectrumin US has no proper utilization and in time domain also spectrum is utilizedinsignificantly [6]. This brings the concept of opportunistic spectrum usage approach,where unlicensed spectrum users utilize the unused licensed frequency bands by findingspectrum holes. Cognitive radio is proposed as a reconfigurable device of the unlicensedspectrum user that finds the spectrum holes under dynamic spectrum changing situation[2, 6]. In this paper, licensed users are declared as primary users whereas unlicensedusers as secondary users. It is already said that secondary users make use of unusedprimary spectrum with tolerable interference to primary network [4] but they are tovacate the frequency band as primary users appear. Secondary users search forappropriate spectrum hole to run the communication process.Spectrum sensing is one of the important features in cognitive radio concept for findingan appropriate spectrum hole as well as realizing a primary user’s appearance whileutilizing a licensed frequency band [3]. Primary user sends a pilot signal of low 17
  2. 2. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976– 6464(Print), ISSN 0976 – 6472(Online) Volume 2, Number 1, Jan - April (2011), © IAEMEbandwidth and low power during its arrival and the secondary user senses this within aspecific sensing time [7] and vacates the band. Here, suboptimal as well as non-coherentenergy detection scheme by radiometer is considered where any prior knowledge of pilotsignal is not required [4].In this paper, section 2 deals with the entire system model where the decision regardingthe arrival of primary user is specified by binary hypotheses. An appropriate test statisticis formed and two figures of merit namely probability of false alarm and probability ofdetection are calculated. These calculations are justified by simulation results. Section 3concludes the paper.2. THE SYSTEM MODEL2.1 Framing of hypotheses and calculations of the figures of merit The total process of primary signal sensing can be described by the following binaryhypotheses [null hypothesis H0 and alternative hypothesis H1] as follows:H0: y(n) = w(n) decide pilot signal is absentH1: y(n) = x(n) + w(n) decide pilot signal is present 2where x(n) ~ CN ( 0, σ x ) is the transmitted primary signal within the sensing time and 2w(n) ~ CN( 0, σ w ) is the white Gaussian noise. Here CN denotes circularly symmetriccomplex Gaussian (CSCG) distribution. The fading effect of the channel is neglected.This immediately follows that 2y(n) ~ CN( 0, σ w ) under H0 2 2y(n) ~ CN( 0, (σ x + σ w ) ) under H1Since y(n) is a complex variable, the modulus of y(n) is taken into account neglecting thephase part. Thus it is obtained that 2 y (n) ~ Rayleigh ( 1 σ w ) 2 under H0 2 2 y (n) ~ Rayleigh ( 1 (σ x + σ w )) 2 under H1The test statistic (T) can be found from energy-detection scheme as N T = ∑ [ y ( n) ] 2 (1) n =1 (Proof of (1) is shown in Appendix A) 18
  3. 3. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976– 6464(Print), ISSN 0976 – 6472(Online) Volume 2, Number 1, Jan - April (2011), © IAEMENow, since Rayleigh distribution is a chi-square distribution with 2 degrees of freedom, itis found that T follows chi-square distribution with 2N degrees of freedom under both H0and H1, that is 2 T ~ χ 2N under both H0 and H1 but with different parameters. T is compared with a pre-settledthreshold value γ th and decision is taken as follows: Decide in favour of H0 if T < γ th Decide in favour of H1 if T > γ thIn this decision procedure two types of errors generally occur.Type I error: Decision is taken in favour of H1 when H0 is trueType II error: Decision is taken in favour of H0 when H1 is trueSince both of these errors cannot be simultaneously reduced, one error is specified to afixed value, whereas the other error is reduced. A common approach is to specify theprobability of Type I error and the probability of Type II error is decreased.Two figures of merit are generally proposed for any signal detection scheme – probabilityof false alarm (Pfa) and probability of detection (Pd) . Pfa is the probability of Type I errori.e. the probability of misjudging the arrival of primary signal under H0, i.e. Pfa = P (T > γ th | H0 ) 1 ∞ ∫σth2 exp(−t )t dt N −1 i.e. Pfa = γ (2) Γ( N ) wProbability of Type II error is known as probability of misdetection ( P ). Pd is the mdprobability of correctly identifying the arrival of primary signal under H1 i.e. it is thecomplementary of P mdThis means, Pd = P (T > γ th | H1 ) 1 ∞ ∫σ 2γ+thσ 2 exp(−t )t dt N −1 i.e. Pd = (3) Γ( N ) w x (Proofs of (2) and (3) are shown in Appendix B) 19
  4. 4. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976– 6464(Print), ISSN 0976 – 6472(Online) Volume 2, Number 1, Jan - April (2011), © IAEME2.2 The simulation results 2 2In the simulation results, it is assumed that σ w = 1 as well as σ x = 1 . Here Pfa and Pd areplotted with γ th .Figure 1 shows the Pfa vs. γ th (dB) plot. It can be easily found that Pfa falls rapidly withincreasing value of γ th . As a small value of Pfa is desirable, so from this point of view,γ th should be a large value. Figure 1: Pfa vs. γ th (dB) plotFigure 2 shows the Pd vs. γ th (dB) plot. Here it is also found that Pd value falls with theincreasing value of γ th . As high value of Pd is desired, so from this point of view,γ th should be a small value. So, from both the figures, it is found that obtaining lower value of Pfa and higher value ofPd simultaneously is not possible because both of these objectives are self-contradictory.For this reason, we are to compromise between the two and choose an appropriatethreshold value so that the system performance can be optimized. For example, if wechoose the range 0 < Pfa < 0.5 and 0 < Pd < 0.5 as the system constraints, a proper 20
  5. 5. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976– 6464(Print), ISSN 0976 – 6472(Online) Volume 2, Number 1, Jan - April (2011), © IAEMEthreshold value may be chosen satisfying both of these constraints and maximizing thethroughput. Figure 2: Pd vs. γ th (dB) plot3. CONCLUSION Primary signal sensing is an important feature in cognitive radio domain.Suboptimal detection scheme by energy detector is the most popular scheme in this area.Detection should be robust even for weak pilot signal i.e. in the low SNR regime.Generally pilot signal contains 1-10% of the total primary signal power. Treating thereceived signal as Rayleigh distributed also provides improved system performance. Anappropriate threshold value may be chosen to meet the desired specifications of thesystem.REFERENCES[1] S. Haykin, “Cognitive Radio: Brain-empowered wireless communications”, IEEE J.Selected Areas in Communications, vol. 23, no. 2, pp. 201-220, Feb 2005[2] A. Ghasemi, E.S. Sousa, “Collaborative Spectrum Sensing for Opportunistic Accessin Fading Environments”, In proc. of DySPAN’05, November 2005.[3] D. Cabric, A.Tkachenko and R.W.Brodersen, “Spectrum sensing measurements ofpilot, energy and collaborative detection”, IEEE Military Communications Conference(MILCOM), 2006 21
  6. 6. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976– 6464(Print), ISSN 0976 – 6472(Online) Volume 2, Number 1, Jan - April (2011), © IAEME[4] R. Tandra and A.Sahai, “SNR Walls for Signal Detection”, IEEE J. Selected Topicsin Signal Processing, vol 2, no. 1, pp. 4-17, February 2008[5] D. Cabric, A. Tkachenko, R.W. Brodersen, “Experimental Study of Spectrum Sensingbased on Energy Detection and Network Cooperation”, in Proc. of 1st Intl. Workshop onTechnology and Policy for Accessing Spectrum (TAPAS 2006), Boston, August 2006.[6] W.Y.Lee and I.F.Akyildiz, “Optimal Spectrum Sensing Framework for CognitiveRadio Networks”, IEEE Transactions on Wireless Communications, vol 7, no. 10, pp.3845-3858, October 2008[7] Y.C.Liang, Y.Zeng, E.C.Y. Peh and A.T.Hoang, “ Sensing-Throughput Tradeoff forCognitive Radio Networks”, IEEE Transactions on Wireless Communications, vol 7,no.4, pp. 1326-1336, April 2008[8] A.Sahai and D.Cabric, ” A tutorial on spectrum sensing: Fundamental limits andpractical challenges”, Proc. IEEE Symp. New Frontiers in Dynamic Spectrum AccessNetworks (DySPAN), Baltimore, MD, Nov. 2005[9] J. Hillenbrand, T.A.Weiss and F.K.Jondral, “Calculation of Detection and FalseAlarm Probabilities in Spectrum Pooling Systems”, IEEE Communication Letters, vol 9,no. 4, pp.349-351, April 2005[10] Z. Quan, S.Cui, H.V.Poor and A.H.Sayed, ”Collaborative Wideband Sensing forCognitive Radios”, IEEE Signal Processing Magazine, pp. 60-72, November 2008[11] U.Madhow,” Fundamentals of Digital Communication”, Cambridge UniversityPress, 2008[12] H. Arslan, “Cognitive Radio, Software Defined Radio, and Adaptive WirelessSystems”, Springer, 2007[13] D. Cabric. S.M. Mishra. R.W. Brodersen, “Implementation Issues in SpectrumSensing”, In Asilomar Conference on Signal, Systems and Computers, November 2004.[14] K.C.Chen and R.Prasad, “Cognitive Radio Networks”, John Wiley & Sons. Ltd,2009[15] S.L.Miller and D.G.Childers, “Probability and Random Processes”, Academic Press,2007APPENDIX ADerivation of the test statistic (T) and its distribution under H0 and H1According to Neyman-Pearson lemma, a test statistic will be most powerful if it isformulated in such a way so that inside the critical region (i.e. the region where H0 is tobe rejected) it satisfies f(Y|H1) ≥ K f(Y|H0) (A1)where Y = [|y(1)|, |y(2)|,……., |y(N) |] and f(Y) denotes the joint density function of all| y (n) |, K being an arbitrary constant.Considering the |y(n)|s are i.i.d. random variables, we can write from (A1) 22
  7. 7. International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976– 6464(Print), ISSN 0976 – 6472(Online) Volume 2, Number 1, Jan - April (2011), © IAEME N y ( n)  [ y ( n) ] 2  N y ( n)  [ y ( n) ] 2 ∏ 2 σ2 exp−  2 2σ 2   ≥ K ∏ 2 exp− n =1 σ 1  2σ 12   n =1    where σ 12 = 1 σ w and σ 2 = 1 (σ w + σ x ) 2 2 2 2 2 2 2 N K/ σ2Ni.e. ∑ [ y ( n) ] 2 ≥ ln N σ1 / where K = K 2 N n =1  1 1  2  2 − 2 N σ   1 σ2  NThis follows that T = ∑ [ y (n) ] n =1 2Since Rayleigh distribution is a chi-square distribution with 2 degrees of freedom, Tfollows chi-square distribution with 2N degrees of freedom under both H0 and H1, that is 2T ~ χ 2Nwith parameters σ 12 under H0 and σ 2 under H1 2APPENDIX BDerivation of Pfa and Pd 1 ∞ ∫γ th exp(−u / 2σ 1 )u du 2 N −1By definition, Pfa = P (T > γ th | H0) = 2 N (2σ ) Γ ( N ) 1 1 ∞ ∫σ 2 N −1Substituting t = u / 2σ 12 , we get Pfa = γ th exp(−t )t dt Γ( N ) wFollowing the same approach, we get , 1 ∞ Pd = Γ(N ) ∫σ γ σ 2 th + 2 exp( − t ) t N −1 dt w x 23

×