Minimum Eigenvalue Detection for Spectrum Sensing in Cognitive Radio

Transcription

1 International Journal of Electrical and Computer Engineering (IJECE) Vol. 4, No. 4, Augut 014, pp. 63~630 ISSN: Minimum Eigenvalue Detection for Spectrum Sening in Cognitive Radio Syed Sajjad Ali, Chang Liu, Minglu Jin School of Information and Communication Engineering, Dalian Univerity of Technology Dalian, China Article Info Article hitory: Received May 6, 014 Revied Jun 16, 014 Accepted Jul 3, 014 Keyword: Cognitive radio Eigenvalue detection Minimum eigenvalue Spectrum ening ABSTRACT Spectrum ening i a key tak for cognitive radio. Our motivation i to increae the probability of detection for pectrum ening in cognitive radio. In thi paper, we propoed a new emi blind method which i baed on minimum Eigenvalue of a covariance matrix. The ratio of the minimum eigenvalue to noie power i ued a the tet tatitic. The method doe not need channel and ignal information a prior knowledge. Eigenvalue baed algorithm perform better than energy detection for correlated ignal. Our propoed method i better than the maximum eigenvalue and energy detection for correlated ignal. We perform Simulation which i baed on digital TV ignal. In all tet, our method perform better than maximum eigenvalue detection and energy detection. Copyright 014 Intitute of Advanced Engineering and Science. All right reerved. Correponding Author: Minglu Jin School of Information and Communication Engineering, Dalian Univerity of Technology, Dalian, China. mljin@dlut.edu.cn 1. INTRODUCTION The Advanced radio technology with emerging application in current tatic and non-overlapped Indutrial, Scientific and Medical (ISM) pectrum band lead in pectrum carcity. Hence, available pectrum hould be efficiently managed to provide higher data rate, which i difficult with current tatic pectrum allocation. According to Federal Communication Commiion (FCC), larger amount of unued pectrum i available in licened pectrum which i not effectively ued due to non-uniform pectral demand in time, frequency and pace. Thi reveal that inadequate pectrum management policie i the main ubject for pectrum carcity. To overcome thi, the FCC approved to allow exiting unlicened radio ervice in the licened TVWS (TV white pace) through Cognitive radio. CR uer hare temporary licened unued pectrum opportunitically without interrupting legitimate uer communication through oftware defined radio. Since, cognitive radio work on econdary bai, it hould vacate current communicating channel whenever primary uer i active in current pectrum band to avoid interference [1-3]. One of the example of Cognitive radio i IEEE 80. wirele regional area network that pectrum reue concept in UHF/VHF band [4]. Many pectrum ening method have been propoed namely Energy detection [5], cyclotationary detection [5], the matched filtering [5], likelihood ratio tet (LRT) [5], covariance baed ening [5] and wavelet-baed ening [5]. Every method ha it own advantage and diadvantage. For example, energy detection i the mot commonly ued becaue it doe not require any information about the ignal and have low complexity. The baic drawback with energy detection i optimal for independent and identically ditributed (i.i.d) ignal, but not for correlated ignal [5]. Matched filter [5] hould know about knowledge of the ignal and different matched filter i required for different ignal. Cyclotationary detection ha much Journal homepage:

2 64 ISSN: higher complexity and require knowledge of the cyclic frequencie [5]. On the other ide eigenvalue baed pectrum ening i much better than exiting ening algorithm becaue it do not need any information of ignal and Channel. Furthermore, it doen t require ynchronization [6-11]. Eigenvalue pectrum ening algorithm can be divided into two type namely noie power baed eigenvalue and eigenvalue without noie power. There have been everal exiting algorithm which do not require noie power. Thee are maximum-minimum-eigenvalue (MME) [6-8], Energy with minimum eigenvalue (EME) [8], maximum-eigenvalue-trace (MET) [9], arithmetic mean-geometric-mean (AM-GM) [9], maximum-eigenvalue-geometric-mean (ME-GM) [10], contra-harmonic-mean-minimum-eigenvalue (CHM) [11], maximum-eigenvalue-harmonic mean (ME-HM) [11] and maximum-eigenvalue-contraharmonic-mean-p (ME-CHM-p) [11]. On the other hand, noie power baed maximum eigenvalue (MAX) detection [1] ha better performance compared with eigenvalue without noie power. In thi paper, author propoed Minimum eigenvalue (MIN) algorithm which i baed on covariance matrix. The ratio of minimum eigenvalue to noie power i ued a the tet tatitic. The propoed method ha a higher probability of detection at low SNR compared with Maximum eigenvalue. The ret of the paper i organized a follow. Section. briefly explain about ytem model and background information. In Section 3, the minimum eigenvalue-baed ening algorithm i propoed and Simulation reult and dicuion are preented in Section 4 and finally concluion in Section 5.. SYSTEM MODEL Conider a ytem in which a receiver/detector with an antenna i connected to ignal proceing unit to proce the ignal. Alo note that the antenna i able to end the received ignal to it i proceing unit. For ignal detection, we ue hypothei teting. Hypothei teting i a method in which we claim the preence of ignal. There are two hypothei namely H 0 or null hypothei and H 1 or alternate hypothei. H 0 i the repreentation for ignal doe not preent or only noie i preent and H 1 i the repreentation for ignal and noie both are preent at ame time. The received ignal at the antenna i given by H : x( n) ( n) 0 (1) H : x( n) ( n) ( n) 1 () n 1,..., N Where ( n ) i the received ource ignal ample paed through a wirele channel coniting of multipath fading, path lo and time diperion effect at antenna/receiver and ( n) i the received noie at antenna/receiver. The received ource ignal can be written a N q p k k k (3) n ( ) h( l ) ( nl) k1 l0 Where N p i the number primary ignal, ( n) tranmitted primary ignal from primary uer or antenna k th, k h k (l) denote the propagation channel coefficient from the k th primary uer or antenna to the receiver/antenna and q k i the channel order for h k. Two probabilitie are of interet for channel ening: probability of detection and probability of fale alarm. Probability of fale alarmp fa define at the hypothei H 0 and probability detection P d, which claim the preence of the primary uer ignal define at the hypothei H 1. IJECE Vol. 4, No. 4, Augut 014 :

3 IJECE ISSN: MINIMUM EIGEN VALUE DETECTION xn ( ) xn ( 1) xn ( 1) 0 X xn ( L1) xn ( L) xn ( L1) x(1) x(1) x(1) x(1) T N X L (4) In the firt tep, we need to build a matrix X with N number of ignal ample received from the antenna /receiver by L (moothing factor) time tacking the ignal ample, then we find ample covariance matrix of matrix X. Our lat tep i to find the minimum eigenvalue. The matrix X can be repreentedahown in (4). Alo note that, to reduce the complexity of the algorithm we need to et the value of L a malla poible Sample Covariance Matrix A ample covariancematrix i a matrix whoe element in the i, j poition i the covariance between the i th and j th element of a random vector. Each element of the vector i a calar random variable with a finite number of oberved ample. The ample covariance matrix of the received ignal can calculate by uing the following formula. Rx 1 ( T XX ) N (5) 3.. Eigenvalue Eigenvalue are calar value called lambda (λ) of a quare matrix A, if there i a nontrivial olution of a vector x called eigenvector uch that: (A -λi) x=0 Or (A- λi) =0. The idea of eigenvalue i ued in ignal detection i to find the noie in ignal ample by finding the correlation between ample. A we know that (ideally) noie ample are uncorrelated with each other. When there i no ignal, the received ignal covariance matrix become identity matrix multiply by noie power ( I) which reult all eigenvalue of thi matrix become ame a noie power Maximum Eigenvalue Vere Minimum Eigenvalue Practically, the maximum eigenvalue fluctuate more rapidly a compared minimum eigenvalue at particular SNR level, or in other word, at particular SNR level, variance of maximum eigenvalue comparatively greater than variance minimum eigenvalue Thi reult more minimum eigenvalue fall above to it threhold value a compared to maximum eigenvalue. Thi i a fundamental reaon which maximize the probability of detection of minimum eigenvalue relative to maximum eigenvalue Algorithm Step 1. Calculate the ample covariance matrix of the received ignal. Step. Obtain the minimum eigenvalue min ( N ) of the ample covariance matrix. Step 3. Deciion: if ( N ) min then ignal i preent otherwie, ignal i abent. Here γ i a threhold and noie power Theoretical Verification Let conider R i the ignal covariance matrix and receiver/antenna the received ignal covariance matrix I R i a follow [6-1]. x i a noie covariance matrix. At R R I x,( LXL),( LXL) L (6) Minimum Eigenvalue Detection for Spectrum Sening in Cognitive Radio (Minglu Jin)

4 66 ISSN: Above equation repreent when the ignal i preent the received ignal covariance matrix R i the x um of ignalcovariance matrix R and noie covariance matrix I. Note that practically, to reduce the complexity of the algorithm we choe a mall value of L. At thi cae, if there i ignal the minimum eigenvalue of received ignal covariance matrix i greater than noie power λ ( R ). We can min x repreent eigenvalue of a received ignal covariance matrix a follow [6-1]. λ ( R ) λ ( R ) (7) n x n Where λ and λ are the eigenvalue of received covariance matrix R repectively. Surely, if the ignal i preent other ide, when ignal i not preent, the ignal covariance matrix 0 R and ignal covariance matrix x λ ( R ) λ ( R ) which reult min min x min. On the R i equal to zero, thi reult the, if the ratio minimum eigenvalue λ ( R ). Hence, ignal can alo be detected by checking the ratio min min x i greaterthen threhold, ignal i preent otherwie, ignal i abent. Where γ i threhold (theoretically γ=1) Complexity The algorithm run in two part. Part1: calculation of the covariance matrix. Part : the eigenvalue decompoition of the covariance matrix. For the firt part, the complexity of a calculating covariance matrix 3 i OLN ( ) and for econd part, complexity of calculating eigenvalue i OL ( ). The total complexity (multiplication and addition, repectively) i therefore a follow: 3 ( ) OL ( ) OLN (8) 4. SIMULATION AND DISCUSSION In thi ection, we will dicu the effect of ample length, moothing factor, ROC and preent the probability of detection with different SNR level. Alo noted that the eigenvalue ditribution of R i very x complicated [13-16]. Thi make theoretical determination of threhold very difficult. However, we et a threhold by uing imulation, the method to find threhold iat firt generate white Gauian noie a the input (no ignal). In Second tep obtained minimum eigenvalue of noie ample and ort thee eigenvalue in decendingorder. Latly take i th eigenvalue a a threhold to meet p 0.1requirement. Value of i can fa be calculate by n p fa.where n i number of iteration and p i.e. probability of fale alarm. fa Our all tet for the algorithm are baed on the captured ATSC DTV ignal, thee ignal are collected at Wahington D.C USA. The location of the receiver i mile away from the DTV tation [17]. The ampling rate of the vetigial ideband (VSB) DTV ignal i MHz [18] on the other ide the ampling rate at the receiver i two time higher than the tranmit rate. IJECE Vol. 4, No. 4, Augut 014 :

5 IJECE ISSN: Figure 1. Probability of detection for DTV Signal SNR=-7, L=16. In Figure 1, we tet the impact of the number of ample. The SNR i fixed at -7dB and vary the number of ample from to It i een that the P d of the Minimum eigenvalue algorithm increae more rapidly a compared with blindeigenvaluealgorithm with the number of ample, while the energy detection almot have no changed. In Figure, we tet the impact of the moothing factor. We fix the SNR at -7 db, N= and vary the moothing factor L from 4 to 16. It i een that the probability of detection of all algorithm lightly decreae with increae of L, but the probability of detection of minimum eigenvalue icomparativelygreater than the exiting eigenvalue detectionalgorithm. Figure. Impact of moothing factor for DTV Signal SNR=-7, N= Minimum Eigenvalue Detection for Spectrum Sening in Cognitive Radio (Minglu Jin)

6 68 ISSN: Figure 3. Receiver operating curve for DTV Signal L=16, N= Figure 4. Probability of detection for DTV Signal L=16, N= In Figure 3, the Receiver Operating Characteritic (ROC) curve i hown where the ample ize i N= , L=16 and SNR=-4, -6, -8. We lightly adjut the threhold to keep all the method having the ame value. For the energy detection, the threhold i baed on the predicted noie power and theoretical formula i very inaccurate to obtain the target P fa. The graph how that minimum eigenvalue i the bet among all the method. Figure 4, give the probability for DTV ignal. We etmoothing factor L=16, wwhite noie are added to obtain the variou SNR level where the ample ize i N= Thi reult how that the detection probability of minimum eigenvalue detection algorithm perform better thantraditionaleigenvalue and energy detectionalgorithm. 5. CONCLUSION In thi paper, we propoe a new eigenvalue pectrum ening algorithm baed on covariance matrix. The ratio of the minimum eigenvalue to noie power i ued a tet tatitic the method need only noie power. The propoed method i better than maximum eigenvalue detection and the energy detection for correlated ignal. Our method can be ued for variou ignal detection application without knowledge of ignal and the channel. IJECE Vol. 4, No. 4, Augut 014 :

7 IJECE ISSN: ACKNOWLEDGEMENTS The author would like to ay thank to anonymou reviewer for their valuable comment and uggetion for improving the paper. REFERENCES [1] J. Mitola and G.Q. Maguire. Cognitive radio: making oftware radio more peronal, IEEE Peronal Commun, vol. 6, no. 4, pp , [] S. Haykin. Cognitive radio: brain-empowered wirele communication, IEEE Tran. Commun, vol. 3, no., pp. 01-0, 005. [3] D. Cabric, S.M. Mihra, D. Willkomm, R. Broderen, and A. Woliz. A cognitive radio approach for uage of virtual unlicened pectrum, in Proc. 14th IST Mobile Wirele Commun. Summit, June 005. [4] 80. Working Group, IEEE P80./D0.1. Draft Standard for Wirele Regional Area Network, [Online]. Available: May 006. [5] Zeng, Y., Liang, Y.C., Hoang, A.T., Zhang, R. A review on pectrum ening for cognitive radio: challenge and olution, EURASIP J. Adv.Signal Proce., 010, Article id [6] Y.H. Zeng and Y.C. Liang. Eigenvalue baed ening algorithm, IEEE /0118r0, July 006. [7] Y.H. Zeng and Y.C. Liang. Maximum-minimum eigenvalue detection for cognitive radio, in Proceeding of the 18 th International Sympoium on Peronal, Indoor and Mobile Radio Communication (PIMRC 07), Athen, Greece, September007. [8] Y.H. Zeng and Y.C. Liang. Eigenvalue-baed pectrum ening algorithm for cognitive radio, IEEE Tranaction on Communication, vol. 57, no. 6, pp , 009. [9] Zeng, Y., Liang, Y.-C. Robut pectrum ening in cognitive radio. Proc. IEEE Int. Symp. on Peronal, Indoor and Mobile RadioCommunication (PIMRC), 010. [10] Pillay, N., Xu, H. Blind eigenvalue-baed pectrum ening for cognitive radio network, IET J. Commun., 01 [11] Pillay, N., Xu, H. Eigenvalue-baed pectrum hole detection for Nakagami-m fading channel with Gauian and impule noie, IET J. Commun. vol.6, no 13, pp , 01. [1] Zeng, Y., Koh, C.L., Liang, Y.C, Maximum eigenvalue detection: theory and application. Proc. IEEE Int. Conf. on Communication (ICC), pp , May 008. [13] A.M. Tulino and S. Verd u, Random Matrix Theory and WireleCommunication. Hanover, USA: now Publiher Inc., 004. [14] I.M. Johntone, On the ditribution of the larget eigenvalue inprinciple component analyi, The Annal of Statitic, vol. 9, no., pp , 001. [15] K. Johanon. Shape fluctuation and random matrice, Comm. Math.Phy., vol. 09, pp , 000. [16] Z.D. Bai. Methodologie in pectral analyi of large dimenional random matrice, a review, StatiticaSinica, vol. 9, pp , [17] V. Tawil, 51 captured DTV ignal. [Online]. Available: May 006. [18] W. Bretl, W.R. Meintel, G. Sgrignoli, X. Wang, S.M. Wei, and K. Salehian. ATSC RF, modulation, and tranmiion, Proc. IEEE, vol. 94, no. 1, pp , 006. BIOGRAPHIES OF AUTHORS Syed Sajjad Ali received the B.Sc. degree from the Univerity of Karachi, Karachi, Pakitan, and the M.S degree from the Mohammed Ali Jinnah Univerity, Karachi, Pakitan. He worked a a lecturer in the Intitute of Buine and Technology, Karachi, Pakitan Before, he alo worked in Lucky Cement a a Network and Communication Engineer. He i currently puruing the Ph.D. degree from School of Information and Communication Engineering, Dalian Univerity of Technology, Dalian, China under the uperviion of Prof. Minglu JIN. Hi reearch interet are in wirele communication and ignal proceing. He i particularly intereted in Signal detection in Cognitive radio. Minimum Eigenvalue Detection for Spectrum Sening in Cognitive Radio (Minglu Jin)

8 630 ISSN: Chang Liu i currently a Mater candidate in School of Information and Communication Engineering, Dalian Univerity of Technology, Dalian, China. Hi reearch interet include Spectrum Sening in Cognitive radio, MIMO and Beam forming Technique. Minglu Jin i a Profeor in the School of Electronic & Information Engineering at Dalian Univerity of Technology, china. He received the Ph.D. and M.Sc. degree from Beihang Univerity, china, the B.Eng. degree from Univerity of Science & Technology of China. He wa a Viiting cholar in the Arimoto Lab. at Oaka Univerity, Japan from 1987 to He wa a Reearch Fellow in Radio & Broadcating Reearch Lab. at ETRI, Korea from 001 to 004. Profeor JIN' reearch interet are in the general area of ignal proceing and communication ytem. Specific current interet are non-inuoidal function theory and it application, power amplifier linearization, radio over fiber, nulling antenna technique. IJECE Vol. 4, No. 4, Augut 014 :