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International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 International Journal of Electronics and Communication IJECET – 6464(Print), ISSN 0976 – 6472(Online) Volume 2, Number 1, Jan - April (2011), © IAEME Engineering & 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.html COGNITIVE 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, India ABSTRACT Cognitive radio is proposed as a solution to rationalize the concept of recycling the spectrum in today’s spectrum hungry scenario. Here unlicensed users utilize the licensed frequency band when that particular band is not in use. Spectrum sensing is important to sense the arrival of primary user. In this paper, sensing is done by energy detector and two figures of merit namely probability of false alarm and probability of detection are calculated by treating the received signal as Rayleigh distributed. Keywords: Cognitive radio, probability of false alarm, probability of detection 1. INTRODUCTION Available unlicensed spectrum has become a scarce resource for communication due to recent advances in wireless technology [1]. Fixed spectrum allocation to different services also causes limited usage of frequency bandwidth. However, recent studies of Federal Communications Commission (FCC) have shown that 70% of allocated spectrum in US has no proper utilization and in time domain also spectrum is utilized insignificantly [6]. This brings the concept of opportunistic spectrum usage approach, where unlicensed spectrum users utilize the unused licensed frequency bands by finding spectrum holes. Cognitive radio is proposed as a reconfigurable device of the unlicensed spectrum user that finds the spectrum holes under dynamic spectrum changing situation [2, 6]. In this paper, licensed users are declared as primary users whereas unlicensed users as secondary users. It is already said that secondary users make use of unused primary spectrum with tolerable interference to primary network [4] but they are to vacate the frequency band as primary users appear. Secondary users search for appropriate spectrum hole to run the communication process. Spectrum sensing is one of the important features in cognitive radio concept for finding an appropriate spectrum hole as well as realizing a primary user’s appearance while utilizing a licensed frequency band [3]. Primary user sends a pilot signal of low 17 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 bandwidth and low power during its arrival and the secondary user senses this within a specific sensing time [7] and vacates the band. Here, suboptimal as well as non-coherent energy detection scheme by radiometer is considered where any prior knowledge of pilot signal is not required [4]. In this paper, section 2 deals with the entire system model where the decision regarding the arrival of primary user is specified by binary hypotheses. An appropriate test statistic is formed and two figures of merit namely probability of false alarm and probability of detection are calculated. These calculations are justified by simulation results. Section 3 concludes the paper. 2. THE SYSTEM MODEL 2.1 Framing of hypotheses and calculations of the figures of merit The total process of primary signal sensing can be described by the following binary hypotheses [null hypothesis H0 and alternative hypothesis H1] as follows: H0: y(n) = w(n) decide pilot signal is absent H1: y(n) = x(n) + w(n) decide pilot signal is present 2 where x(n) ~ CN ( 0, σ x ) is the transmitted primary signal within the sensing time and 2 w(n) ~ CN( 0, σ w ) is the white Gaussian noise. Here CN denotes circularly symmetric complex Gaussian (CSCG) distribution. The fading effect of the channel is neglected. This immediately follows that 2 y(n) ~ CN( 0, σ w ) under H0 2 2 y(n) ~ CN( 0, (σ x + σ w ) ) under H1 Since y(n) is a complex variable, the modulus of y(n) is taken into account neglecting the phase 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 H1 The 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 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 Now, since Rayleigh distribution is a chi-square distribution with 2 degrees of freedom, it is found that T follows chi-square distribution with 2N degrees of freedom under both H0 and H1, that is 2 T ~ χ 2N under both H0 and H1 but with different parameters. T is compared with a pre-settled threshold 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 th In this decision procedure two types of errors generally occur. Type I error: Decision is taken in favour of H1 when H0 is true Type II error: Decision is taken in favour of H0 when H1 is true Since both of these errors cannot be simultaneously reduced, one error is specified to a fixed value, whereas the other error is reduced. A common approach is to specify the probability 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 – probability of false alarm (Pfa) and probability of detection (Pd) . Pfa is the probability of Type I error i.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 ) w Probability of Type II error is known as probability of misdetection ( P ). Pd is the md probability of correctly identifying the arrival of primary signal under H1 i.e. it is the complementary of P md This 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 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 2.2 The simulation results 2 2 In the simulation results, it is assumed that σ w = 1 as well as σ x = 1 . Here Pfa and Pd are plotted with γ th . Figure 1 shows the Pfa vs. γ th (dB) plot. It can be easily found that Pfa falls rapidly with increasing 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) plot Figure 2 shows the Pd vs. γ th (dB) plot. Here it is also found that Pd value falls with the increasing 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 of Pd 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 appropriate threshold value so that the system performance can be optimized. For example, if we choose the range 0 < Pfa < 0.5 and 0 < Pd < 0.5 as the system constraints, a proper 20 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 threshold value may be chosen satisfying both of these constraints and maximizing the throughput. Figure 2: Pd vs. γ th (dB) plot 3. 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 the received signal as Rayleigh distributed also provides improved system performance. An appropriate threshold value may be chosen to meet the desired specifications of the system. 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 Access in Fading Environments”, In proc. of DySPAN’05, November 2005. [3] D. Cabric, A.Tkachenko and R.W.Brodersen, “Spectrum sensing measurements of pilot, energy and collaborative detection”, IEEE Military Communications Conference (MILCOM), 2006 21 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 Topics in Signal Processing, vol 2, no. 1, pp. 4-17, February 2008 [5] D. Cabric, A. Tkachenko, R.W. Brodersen, “Experimental Study of Spectrum Sensing based on Energy Detection and Network Cooperation”, in Proc. of 1st Intl. Workshop on Technology and Policy for Accessing Spectrum (TAPAS 2006), Boston, August 2006. [6] W.Y.Lee and I.F.Akyildiz, “Optimal Spectrum Sensing Framework for Cognitive Radio 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 for Cognitive 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 and practical challenges”, Proc. IEEE Symp. New Frontiers in Dynamic Spectrum Access Networks (DySPAN), Baltimore, MD, Nov. 2005 [9] J. Hillenbrand, T.A.Weiss and F.K.Jondral, “Calculation of Detection and False Alarm 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 for Cognitive Radios”, IEEE Signal Processing Magazine, pp. 60-72, November 2008 [11] U.Madhow,” Fundamentals of Digital Communication”, Cambridge University Press, 2008 [12] H. Arslan, “Cognitive Radio, Software Defined Radio, and Adaptive Wireless Systems”, Springer, 2007 [13] D. Cabric. S.M. Mishra. R.W. Brodersen, “Implementation Issues in Spectrum Sensing”, 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, 2007 APPENDIX A Derivation of the test statistic (T) and its distribution under H0 and H1 According to Neyman-Pearson lemma, a test statistic will be most powerful if it is formulated in such a way so that inside the critical region (i.e. the region where H0 is to be 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 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 2 2 2 2 where σ 12 = 1 σ w and σ 2 = 1 (σ w + σ x ) 2 2 2 N K/ σ2N i.e. ∑ [ y ( n) ] 2 ≥ ln N / where K = K 2 N σ1 n =1 1 1 2 2 − 2 N σ 1 σ2 N This follows that T = ∑ [ y (n) ] n =1 2 Since Rayleigh distribution is a chi-square distribution with 2 degrees of freedom, T follows chi-square distribution with 2N degrees of freedom under both H0 and H1, that is 2 T ~ χ 2N 2 with parameters σ 12 under H0 and σ 2 under H1 APPENDIX B Derivation of Pfa and Pd 1 ∞ ∫γ th exp(−u / 2σ 1 )u du 2 N −1 By definition, Pfa = P (T > γ th | H0) = 2 N (2σ ) Γ ( N ) 1 1 ∞ ∫σ 2 N −1 Substituting t = u / 2σ 12 , we get Pfa = γ th exp(−t )t dt Γ( N ) w Following the same approach, we get , 1 ∞ Pd = Γ(N ) ∫σ γ σ 2 th + 2 exp( − t ) t N −1 dt w x 23

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