Journal of Computer Science, 9 (2): , 2013

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1 Joural of Computer Sciece, 9 (2): , 203 ISSN Kaa ad Ravi, This ope access article is distributed uder a Creative Commos Attributio (CC-BY) 3.0 licese doi:0.3844/jcssp Published Olie 9 (2) 203 ( Secod-Order Statistical Approach for Digital Modulatio Scheme Classificatio i Cogitive Radio Usig Support Vector Machie ad K-Nearest Neighbor Classifier Kaa, R. ad 2 S.Ravi Departmet of Electroics ad Commuicatio Egieerig, Sathyabama Uiversity, Cheai, Idia 2 Departmet of Electroics ad Commuicatio Egieerig, Dr. M.G.R Uiversity, Cheai, Idia Received , Revised ; Accepted ABSTRACT Cogitive radio systems require detectio of differet sigals for commuicatio. I this study, a approach for multiclass sigal classificatio based o secod-order statistical feature is proposed. The proposed system is desiged to recogize three differet digital modulatio schemes such as PAM, 32QAM ad 64QAM. The sigal classificatio is achieved by extractig the 2d order cumulats of the real ad imagiary part of the complex evelope. These secod-order statistical features are give to multiclass Support Vector Machie (SVM) ad K- Nearest Neighbor (KNN) classifier for classificatio. The modulated sigals are passed through a Additive White Gaussia Noise (AWGN) chael before feature extractio. The performace evaluatio of the system is carried usig 400 geerated sigals. Experimetal results show that the proposed method produces a accurate classificatio rate i the rage 65%-89% for SVM classifier ad 65-68% for KNN classifier. Keywords: Cogitive Radio, Secod-Order Statistics, Support Vector Machie, Digital Modulatio. INTRODUCTION A umber of defiitios ca be foud to describe Software Defied Radio, also kow as Software Radio or SDR. Software Defied Radio is defied as: Radio i which some or all of the physical layer fuctios are software defied (Petrova et al., 200). A radio is ay kid of device that wirelessly trasmits or receives sigals i the Radio Frequecy (RF) part of the electromagetic spectrum to facilitate the trasfer of iformatio. I today s world, radios exist i a multitude of items such as cell phoes, computers, car door opeers, vehicles ad televisios. A study of multi-class sigal classificatio based o automatic modulatio recogitio through Support Vector Machies (SVM) is preseted by (Petrova et al., 200). Obviously SDR i Cogitive Radio should be ad services but also to the extesively dyamic ature of badwidth allocatio by (Rajeshree ad Kulat, 20). Cogitive radio is evisioed as the ultimate system that ca sese, adapt ad lear from the eviromet i which it operates. A ew robust Automatic Modulatio Classificatio (AMC) algorithm, which applies Higher- Order Statistics (HOS) i a geeric framework for blid chael estimatio ad patter recogitio, is proposed by (Hsiao-Chu et al., 2008). Feature based method for automatic classificatio ad recogitio of seve digital modulatios for Software Defied Radio is preseted by (Rogaovi et al., 2009). The classificatio is coducted with Artificial Neural Networks (ANN). The performace of eergy detectio based spectrum sesig for several real-world primary sigals of various radio techologies is preseted by (Lopez-Beitez et al., 200). A method for the automatic cofigured ot oly to idepedet stadards, protocols classificatio usig cumulats derived usig fractioal Correspodig Author: Kaa, R., Departmet of Electroics ad Commuicatio Egieerig, Sathyabama Uiversity, Cheai, Idia 235

2 Kaa, R. ad S. Ravi / Joural of Computer Sciece 9 (2): , 203 lower order statistics is proposed by (Naredar et al., 20). The performace of the classifier is preseted i the form of probability of correct classificatio uder oisy ad fadig coditios. A ovel approach based o fuzzy logic to classify sigals with respect to stadards o the basis of kow radio parameters is preseted by (Ahmad et al., 200). Ideally it would like to classify the primary user systems with respect to existig Kow stadards. A ovel desig of the Automatic Modulatio Recogitio (AMR) method with reduced computatioal complexity ad fast processig speed is eeded. A Discrete Likelihood-Ratio Test (DLRT)-based rapid-estimatio approach to idetifyig the modulatio schemes blidly for uiterrupted data demodulatio i real time is described by (Xu et al., 200). Sesig of digitally modulated primary radio sigals is described by (Popoola ad Olst, 20). I achievig this objective, a digital automatic modulatio classifier was developed usig a artificial eural etwork. A ew framework for Cogitive Radio (CR) spectrum sesig based o liear ad polyomial classifiers is proposed by (Hassa et al., 200). A cooperative CR etwork is cosidered i this study with CR odes collaboratig i makig the decisio about spectrum availability. The automatic modulatio classificatio methods based o likelihood fuctios, studies various classificatio solutios derived from likelihood ratio test ad discusses the detailed characteristics associated with all major algorithms is preseted by (Xu et al., 20). Wavelet trasform, a multi resolutio aalysis based classificatio of digitial modulatio scheme is preseted by (Kaa ad Ravi, 202). I this study, a approach for the digital sigals classificatio i cogitive radio based o cumulats ad SVM is preseted. 2. MATERIALS AND METHODS The proposed system for the classificatio of digital sigals i cogitive radio is built based o secod-order statistics, multiclass SVM ad KNN classifier for classificatio. The theoretical backgroud of all the approaches are itroduced here. 2.. Secod-Order Statistics The autocorrelatio fuctio or sequece of a statioary process, x () is defied i Equatio : xx * ( ) = ( ) ( + ) () R m E x x m 236 where, E{ } deotes the esemble expectatio operator. The power spectrum is formally defied as the Fourier Trasform (FT) of the autocorrelatio sequece (the Wieer-Khitchie theorem) is give i Equatio 2: xx ( ) = xx( ) ( π ) (2) P f R m exp j2 fm m= where, f deotes the frequecy. A equivalet defiitio is give i Equatio 3: xx * ( ) = ( ) ( ) (3) P f : E X f X f where, X (f) is the Fourier Trasform of x() is give i Equatio 4: ( ) = ( ) ( π ) (4) X f x exp j2 f = A sufficiet, but ot ecessary, coditio for the existece of the power spectrum is that the autocorrelatio be absolutely summable. The power spectrum is real valued ad oegative, that is, P xx (f) 0; if X () is real valued, the the power spectrum is also symmetric, that is, P xx (f) = -P xx (f). The higher-order momets are atural geeralizatios of the autocorrelatio ad cumulats are specific oliear combiatios of these momets. The firstorder cumulat of a statioary process is the mea C x : E{x(t)} the higher-order cumulats are ivariat to a shift of mea. Hece, it is coveiet to defie them uder the assumptio of zero mea. If the process has ozero mea, the subtract the mea, apply the followig defiitios to the resultig process. The secod-order cumulats of a zero-mea statioary process are defied by (Rogaovi et al., 2009) which is give i Equatio 5: 2x * ( ) ( ) ( ) C k =E X x +k (5) The first-order cumulat is the mea of the process; ad the secod-order cumulat is the auto covariace sequece. Note that for complex processes, there are several ways of defiig cumulats depedig upo which terms are cojugated. The zero-lag cumulats have special ames: C 2x (0) is the variace ad is usually deoted byσ 2 x.

3 Kaa, R. ad S. Ravi / Joural of Computer Sciece 9 (2): , Support Vector Machie Support Vector Machies (SVMs) are a set of related supervised learig methods that aalyze data ad recogize patters, used for classificatio ad regressio aalysis. The stadard SVM is a o-probabilistic biary liear classifier, i.e. it predicts, for each give iput, which of two possible classes the iput is a member of. A classificatio task usually ivolves with traiig ad testig data which cosists of some data istaces. Each istace i the traiig set cotais oe target value (class labels) ad several attributes (features). SVM has a extra advatage of automatic model selectio i the sese that both the optimal umber ad locatios of the basis fuctios are automatically obtaied durig traiig. The performace of SVM largely depeds o the kerel (Smola et al., 998). The mathematical derivatio of SVM classifier preseted by (Xiao-Jua ad Da, 200) is as follows. SVM is essetially a liear learig machie. For the iput traiig sample set defied i Equatio 6: (x i,y i),i...,x R,y, = + (6) The classificatio hyperplae equatio is let to be i Equatio 7: ( ω.x) + b= 0 (7) Thus the classificatio margi is 2/ ω. To maximize the margi, which is to miimize ω, the optimal hyperplae problem is trasformed to quadratic programmig problem as follows i Equati 8: mi Φ( ω ) = ( ωω, ) 2 s.t.y (( ω.x) + b,i =,2...l i (8) After itroductio of Lagrage multiplier, the dual problem is give i Equatio 9: maxq( α ) = α y yαα K(x x ) i= i i i i i j i j i. j i= 2 i= i= s.t yα = 0, α 0,i=,2,..., (9) Accordig to Kuh-Tucker rules, the optimal solutio must satisfy i Equatio 0: α i(y i((w.x i) + b) = 0,i=,2,... (0) That is to say if the optio solutio is i Equatio ad 2: 237 α = ( α, α,..., α ),i=,2,... () w * * * * T 2 i The: * * = αi yixi i= * * * i i i i j i i= b = y y α (x.x ), j j α 0 (2) For every traiig sample poit x i, there is a correspodig Lagrage multiplier. Ad the sample poits that are correspodig to a i = 0 do t cotribute to solve the classificatio hyperplae while the other poits that are correspodig to a i > 0 do, so it is called support vectors. Hece the optimal hyperplae equatio is give i Equatio 3: α iy i(x i.x j) + b= 0 (3) x, SV The hard classifier i Equatio 4 is: y= sg α y (x.x ) + b i i i j (4) x, SV For oliear situatio, SVM costructs a optimal separatig hyperplae i the high dimesioal space by itroducig kerel fuctio K (x.y) = φ(x)φ(y) hece the oliear SVM is give i Equatio 5: mi Φ( ω ) = ( ωω, ) 2 s.t.y (( ωϕ. (x )) + b),i =,2,...l i i Ad its dual problem is give i Equatio 6: l l l max L( α ) = α y yαα K(x.x ) i= i i j i j i j i= 2 i= i= s.t. yα = 0,0 α C.i =,2,...,l i i i (5) (6) Thus the optimal hyperplae equatio is determied by the solutio to the optimal problem. A SVM classifier ca predict the iput data ito two distict classes. However, it ca be used as multiclass classifiers by treatig a K-class classificatio problem as K two-class problems. This is kow as oe vs. rest or oe vs. all classificatio. The SVM classifier implemetatio is stadard implemetatio. I the MATLAB eviromet the

4 Kaa, R. ad S. Ravi / Joural of Computer Sciece 9 (2): , 203 LIBSVM software is used. LIBSVM is a itegrated software for support vector classificatio, regressio ad distributio estimatio. It also supports multi-class classificatio KNN Classifier I patter recogitio, the K-Nearest Neighbor algorithm (K-NN) is a method for classifyig objects based o closest traiig examples i the feature space. K-NN is a type of istace-based learig where the fuctio is oly approximated locally ad all computatio is deferred util idetificatio. I K-NN, a object is classified by a majority vote of its eighbors, with the object beig assiged to the class most commo amogst its k earest eighbors (k is a positive iteger, typically small). If k =, the the object is simply assiged to the class of its earest eighbor. The eighbors are take from a set of objects for which the correct idetificatio is kow. This ca be thought of as the traiig set for the algorithm, though o explicit traiig step is required Proposed System The proposed system for the classificatio of digital sigals i cogitive radio maily cosists of two differet phases which iclude the traiig phase ad classificatio phase. All the phases are explaied i detail i the followig sub sectios. Three differet types of digital modulatio schemes are cosidered for the classificatio (PAM, 32QAM ad 64QAM) Traiig Phase I the proposed method, 2d order cumulats of real ad imagiary part of the complex evelope are used as features for the classificatio of digital sigals. The traiig phase is show i Fig.. The geerated sigal is first modulated by usig PAM, 32QAM ad 64QAM modulatio schemes. These modulated sigals are passed through a AWGN chael with a predefied SNR level. The secod-order statistical features extracted from the received sigals ad stored i the database for the classificatio purpose. The SVM ad KNN classifiers are traied by usig the database geerated i the traiig phase. The algorithm is as follows. Algorithm I: Traiig Phase [Iput] Geerated sigals [Output] the feature vector of all modulated sigal with oise as Database (DB) ) Modulate the sigal by usig PAM modulatio scheme ) Pass the modulated sigal through a AWGN chael with predefied SNR level 3) Calculate the 2d order cumulats by Equatio (5) 4) Step 3 is repeated for real ad imagiary part of the complex evelope. 5) Isert this feature vector ad the kow class ito the database. 6) Repeat the above steps for 32QAM ad 64QAM modulatio schemes. Figure 2-4 shows the geerated sigal, modulated sigal ad db oisy sigal for PAM, 64QAM ad 32 QAM respectively Classificatio Phase I the classificatio phase, the ukow sigal is classified as ay oe of the three modulatio types. The secod order statistical features are extracted from the ukow sigal ad this feature vector is processed with the features i the database by usig the SVM ad KNN classifier. The algorithm is as follows. Fig.. Block diagram of feature extractio phase

5 Kaa, R. ad S. Ravi / Joural of Computer Sciece 9 (2): , 203 Fig. 2. Geerated sigal, PAM modulated sigal ad db oisy sigal Fig. 3. Geerated sigal, 64 QAM modulated sigal ad db oisy Sigal 239

Kaa, R. ad S. Ravi / Joural of Computer Sciece 9 (2): 235-243, 203 Fig. 4.

6 Kaa, R. ad S. Ravi / Joural of Computer Sciece 9 (2): , 203 Fig. 4. Geerated sigal, 32 QAM modulated sigal ad db oisy sigal Algorithm II: Idetificatio Algorithm [Iput] ukow sigal ad the database [Output] the class of the sigal to which this ukow sigal is assiged () Calculate the 2d order cumulats by Equatio 5 (2) Step is repeated for real ad imagiary part Of the ukow sigal (3) Test with the traied SVM ad KNN classifier ad fid the class of the ukow sigal Performace Metrics The performace of the proposed method for the classificatio of digital modulatio scheme is measured by cofusio matrix, classificatio accuracy ad Positive Predictive Value (PPV). The performace evaluatio methods are defied below Cofusio Matrix A cofusio matrix represets iformatio about actual ad classified cases produced by a classificatio system. Performace of such system is commoly evaluated by classifyig the correct ad icorrect patters. The typical costructio of the cofusio matrix for the two class problem is preseted i Table. 240 Table. Cofusio Matrix for the two class problem Actual Test Positive Negative Positive True Positive (TP) False Positive (FP) Negative FN (False egative) TN (True egative) 2.9. Classificatio Accuracy Classificatio accuracy is the maily familiar method to evaluate the performace of the classifiers. Classificatio accuracy has bee computed based o the umber of correctly classified digital sigals i order to evaluate the efficiecy ad robustess of the algorithm. The classificatio accuracy is defied i Equatio 7: Totalumber of correctly classifiedsigals Classificatio Accuracy= (7) Totalumber of sigals 2.0. Positive Predictive Value (PPV) The PPV or precisio rate is the proportio of digital sigals with positive test results which are correctly classified. It is a critical measure of the performace of the proposed method, as it reflects the probability that a positive test reflects the uderlyig coditio beig tested for. The PPV is defied i Equatio 8:

Kaa, R. ad S. Ravi / Joural of Computer Sciece 9 (2): 235-243, 203 True Positives PPV= TruePositives + FalsePositives 3.

7 Kaa, R. ad S. Ravi / Joural of Computer Sciece 9 (2): , 203 True Positives PPV= TruePositives + FalsePositives 3. RESULTS AND DISCUSSION (8) A set of 400 sigals with segmet size of 024samples are geerated. These 400 sigals are modulated by usig PAM, 32QAM ad 64QAM modulatio schemes ad passed through a AWGN chael of predefied SNR level. Amog these 400 sigals per modulatio scheme are separated ito two set ad 300 sigals per modulatio scheme are radomly selected as traiig set ad the remaiig 00 sigals per modulatio scheme as testig set. The SNR level used i the proposed system are 0,, 5 ad 0 db. For each modulated scheme, there the 600 modulated sigal corrupted by AWGN per each segmets. Table 2-5 shows the cofusio matrix obtaied from the SVM classifier for 024 samples at SNR level 0,, 5 ad 0 db respectively ad Positive Predictive Value (PPV) also show. Table 6-9 shows the cofusio matrix obtaied from the KNN classifier for 024 samples at SNR level 0,, 5 ad 0 db respectively ad Positive Predictive Value (PPV) also show. From the results it is cocluded that the classificatio accuracy icreases as SNR icreases ad the SVM outperforms the KNN classifier. Figure 5 shows the overall classificatio accuracy of the proposed system. I Table, Amog the 400 sigals geerated per each modulatio scheme for 0 db, the true positive value for PAM, 64QAM ad 32QAM are 6, 400 ad 267 respectively. The overall classificatio rate for 024 samples at 0,, 5 ad 0 db is 65.25, 73.33, ad Figure 5-8 shows the classificatio rate of the proposed system usig differet classifier with differet oise levels for PAM, 64 QAM ad 32QAM respectively. Table 2. SVM Classificatio accuracy for 024 samples at 0 Modulatio type PAM 64QAM 32QAM PPV PAM QAM QAM Accuracy (%) Table 3. SVM Classificatio accuracy for 024 samples at Modulatio type PAM 64QAM 32QAM PPV 32 QAM QAM Accuracy (%) PAM Table 4. SVM Classificatio accuracy for 024 samples at 5 Modulatio type PAM 64QAM 32QAM PPV PAM QAM QAM Accuracy (%) Table 5. SVM Classificatio accuracy for 024 samples at 0 Modulatio type PAM 64QAM 32QAM PPV PAM QAM QAM Accuracy (%) Table 6. KNN Classificatio accuracy for 024 samples at 0 Modulatio type PAM 64QAM 32QAM PPV PAM QAM QAM Accuracy (%) Table 7. KNN Classificatio accuracy for 024 samples at Modulatio type PAM 64QAM 32QAM PPV PAM QAM QAM Accuracy (%) Table 8. KNN Classificatio accuracy for 024 samples at 5 Modulatio type PAM 64QAM 32QAM PPV PAM QAM QAM Accuracy (%) Table 9. KNN Classificatio accuracy for 024 samples at 0 Modulatio Type PAM 64QAM 32QAM PPV PAM QAM QAM Accuracy (%) Fig. 5. Overall classificatio rates (%) for 024 samples

Kaa, R. ad S. Ravi / Joural of Computer Sciece 9 (2): 235-243, 203 Fig. 6.

classificatio accuracy of the PAM scheme for 0 db is much lesser tha all other schemes used.

5. REFERENCES Fig. 7. Classificatio rate of the proposed method for 64QAM Modulatio scheme with differet oise levels Fig. 8.

8 Kaa, R. ad S. Ravi / Joural of Computer Sciece 9 (2): , 203 Fig. 6. Classificatio rate of the proposed method for PAM Modulatio scheme with differet oise levels outperforms the KNN classifier for digital sigal classificatio ad also it is observed that the classificatio accuracy of the PAM scheme for 0 db is much lesser tha all other schemes used. Cofusio matrix is used to evaluate the performace of the proposed system ad the experimetal results prove that the proposed system provides satisfactory performace for the multi sigal classificatio. 5. REFERENCES Fig. 7. Classificatio rate of the proposed method for 64QAM Modulatio scheme with differet oise levels Fig. 8. Classificatio rate of the proposed method for 32QAM Modulatio scheme with differet oise levels 4. CONCLUSION I this study, a approach for multiclass sigal classificatio based o secod-order statistical features is preseted. The 2d order cumulats of the real ad imagiary part of the complex evelope are used as features for multi sigal classificatio. The proposed system tested o three differet modulatio schemes PAM, 32QAM ad 64QAM. Two differet classifier, SVM ad KNN classifier are used to classify the digital sigals. From the results, SVM classifier 242 Ahmad, K. U. Meier ad H. Kwasicka, 200. Fuzzy logic based sigal classificatio with cogitive radios for stadard wireless techologies. Proceedigs of the IEEE 5th Iteratioal Coferece o Cogitive Radio Orieted Wireless Networks ad Commuicatios, Ju. 9-, IEEE Xplore Press, Caes, pp: -5. Hassa, Y., M. El-Tarhui ad K. Assaleh, 200. Compariso of liear ad polyomial classifiers for co-operative cogitive radio etworks. Proceedigs of the IEEE 2st Iteratioal Symposium o Persoal Idoor ad Mobile Radio Commuicatios, Sept , IEEE Xplore Press, Istabul, pp: DOI: 0.09/PIMRC Hsiao-Chu, W., M. Saquib ad Z. Yu, Novel automatic modulatio classificatio usig cumulat features for commuicatios via multipath chaels. IEEE Tras. Wireless Commu., 7: DOI: 0.09/TWC Kaa, R. ad S. Ravi, 202. Digital sigals classificatio i cogitive radio based o discrete wavelet trasform. Proceedigs of the Iteratioal Coferece o Cotrol Egieerig ad Commuicatio Techology, Dec. 7-9, IEEE Xplore Press, Liaoig, pp: DOI: 0.09/ICCECT

9 Kaa, R. ad S. Ravi / Joural of Computer Sciece 9 (2): , 203 Lopez-Beitez, M., F. Casadevall ad C. Martella, 200. Performace of spectrum sesig for cogitive radio based o field measuremets of various radio techologies. Proceedigs of the Europea Wireless Coferece, Apr. 2-5, IEEE Xplore Press, Lucca, pp: DOI: 0.09/EW Naredar, M., A.P. Viod, A.S. Madhukumar ad A.K. Krisha, 20. Automatic modulatio classificatio for cogitive radios usig cumulats based o fractioal lower order statistics. Proceedigs of the 30th URSI Geeral Assembly ad Scietific Symposium, Aug. 3-20, IEEE Xplore Press, Istabul, pp: -4. DOI: 0.09/URSIGASS Petrova, M., P. Mahoe ad A. Osua, 200. Multiclass classificatio of aalog ad digital sigals i cogitive radios usig support vector machies. Proceedigs of the 7th Iteratioal Symposium o Wireless Commuicatio Systems, Sept. 9-22, IEEE Xplore Press, New York, pp: DOI: 0.09/ISWCS Popoola, J.J. ad R.V. Olst, 20. Applicatio of eural etwork for sesig primary radio sigals i a cogitive radio eviromet. Proceedigs of the AFRICON, Sept. 3-5, IEEE Xplore Press, Livigstoe, pp: -6. DOI: 0.09/AFRCON Rajeshree, R.D. ad K.D. Kulat, 20. SDR desig for cogitive radio. Proceedigs of the 4th Iteratioal Coferece o Modelig, Simulatio ad Applied Optimizatio, Apr. 9-2, IEEE Xplore Press, Kuala Lumpur, pp: -8. DOI: 0.09/ICMSAO Rogaovi, M.M., A.M. Neskovi ad N.J. Neskovic, Applicatio of artificial eural etworks i classificatio of digital modulatios for software defied radio. Proceedigs of the IEEE EUROCON, May 8-23, IEEE Xplore Press, St.- Petersburg, pp: DOI: 0.09/EURCON Smola, A.J., B. Scholkopf ad K.R. Muller, 998. The coectio betwee regularizatio operators ad support vector kerels. Neural Netw., : DOI: 0.06/S (98)00032-X Xiao-Jua, C. ad L. Da, 200. Medical Image Segmetatio Based o Threshold SVM. Proceedigs of the Iteratioal Coferece o Biomedical Egieerig ad Computer Sciece, Apr , IEEE Xplore Press, Wuha, pp: -3. DOI: 0.09/ICBECS Xu, J.L., W. Su ad M. Zhou, 200. Software-defied radio equipped with rapid modulatio recogitio. IEEE Tras. Vehic. Techol., 59: DOI: 0.09/TVT Xu, J.L., W. Su ad M. Zhou, 20. Likelihood-ratio approaches to automatic modulatio classificatio. IEEE Tras. Syst. Ma Cyberet., 4: DOI: 0.09/TSMCC

Radar emitter recognition method based on AdaBoost and decision tree Tang Xiaojing1, a, Chen Weigao1 and Zhu Weigang1 1

Radar emitter recognition method based on AdaBoost and decision tree Tang Xiaojing1, a, Chen Weigao1 and Zhu Weigang1 1 Advaces i Egieerig Research, volume 8 d Iteratioal Coferece o Automatio, Mechaical Cotrol ad Computatioal Egieerig (AMCCE 7) Radar emitter recogitio method based o AdaBoost ad decisio tree Tag Xiaojig,