Automatic Digital Modulation Identification in Dispersive Channels

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1 roceedngs of e 5 WSEAS Internatona Conference on eecommuncatons and Informatc Istanbu, urey, ay 7-9, 006 (pp409-44) Automatc Dgta oduaton Identfcaton n Dspersve Channes AAOLLAH EBRAHIZADEH, SEYED ALIREZA SEYEDIN Department of Eectrca and Computer Engneerng, Ferdows Unversty of ashad, Noushrvan Insttute of echnoogy IRAN Abstract: - Automatc moduaton type dentfcaton (AI) has seen ncreasng demand for bo mtary and cvan, nowadays. ost of prevous meods have been proposed on cassfcaton of moduatons n addtve whte Gaussan nose (AWGN) channes. However n rea word scenaro communcaton channes suffer from dsperson (fadng). hs paper proposes a nove automatc dgta moduaton types dentfer (ADI) n dspersve envronment. In e ADI s structure, undesred effects of channe are mtgated by an equazer. Hgher order cumuants and moments (up to egh) are used as features and cassfcaton s performed by a mutcass SV-based cassfer. Smuaton resuts show at ADI s abe to dentfy dfferent types of moduatons (e.g. QA64, V.9, and ASK8) w hgh accuracy even at ow SNRs. Key-Words: - Statstca pattern recognton, moduaton, support vector machne, dspersve envronment. Introducton Automatc moduaton type dentfer s a system at recognzes e moduaton type of receved sgna automatcay, and has many appcatons such as eectronc surveance, reat evauaton, sgna confrmaton, spectrum management, software rado, etc. Whst, eary researches were concentrated on anaog moduaton e recent contrbutons n e subect focus more on dgta communcatons due to ncreasng usage of dgta moduatons n many nove appcatons. Generay, AI meods can be categorzed n two man categores: decson eoretc (D) and pattern recognton (R). D approaches use probabstc and hypoess testng arguments to formuate e recognton probem and to obtan e cassfcaton rue [-]. he maor drawbacs of ese approaches are er very hgh computatona compexty, dffcuty wn e mpementaton and ac of robustness to mode msmatch. R approache however, do not need such carefu treatment. R approaches many dvded nto two subsystems: e feature extracton subsystem and e recognton subsystem. he former subsystem s responsbe for extractng promnent characterstcs from receved sgna whch are caed features and e atter, cassfer, s empoyed to ndcate e membershp of moduaton type [-6]. R approaches are smpe to mpement; however, seectons of two subsystems are serous probems. ost of prevous meods have been proposed on cassfcaton of moduatons n AWGNchannes [-8], [-4]. However, n rea word communcaton channe such as wreess communcaton envronment suffer from dsperson (fadng) and most of recognzers at are desgned for AWGN do not preserve er performance under mparment condtons. Research on AI, over fadng channes has been ony performed n a few wors [9-], [5-6]. In [9-0], cassfcaton between SK and SK4 n a fat Rayegh fadng are proposed. In [] a quasoptma souton based on e approxmaton of e og-ehood functon s proposed. In [5], e moduatons were dentfed by appyng e nearest neghbor rue n a two-dmensona feature space. In [6], an dentfer usng neura networ based on combnatons of dfferent order of moments s proposed to dscrmnate dgta moduatons n mutpa fadng. hs paper proposes a nove ADI n tme dsperson channes.fgure shows e scheme of ADI. In s structure, re-processng modue performs: reecton of nose outsde of sgna bandwd, normazaton, carrer frequency estmaton, recovery of compex enveope, etc. Equazaton modue mtgates e channe at s presented n secton. Secton 3 descrbe feature extracton modue. Secton 4, presents e cassfer. In secton 5, some expermenta resuts are shown for consdered dgta moduaton set {SK, SK4, SK8, ASK8, QA3, V9, Star-QA8, and QA64}. Fnay n secton 6 concusons are presented.

2 roceedngs of e 5 WSEAS Internatona Conference on eecommuncatons and Informatc Istanbu, urey, ay 7-9, 006 (pp409-44) Receved sgna reprocessng Equazaton Features extracton Cassfer ype of moduaton Fgure: Structure of ADI Channe equazaton In dgta communcaton accordng to e changes n e message frequency, message amptude, message phase, or changes n amptude and phase, we have four man dgta moduaton technque frequency shft eyng (FSK), amptude shft eyng (ASK), phase shft eyng (SK) and quadrature amptude moduaton (QA), respectvey. ost of em are apped n -ary form [7]. In rea word stuatons e transmsson channe s a crtca factor at may cause unrecoverabe dstortons on e sgna, especay n hgher order dgta moduaton where e effect of channe may corrupt e sgna consteaton. In order to mtgate e dsperson effects of e propagaton channe, an equazaton stage s empoyed n e recever. In AI appcaton e tranng sequence at s needed for adustng equazer coeffcents s not avaabe. Hence, e equazaton must be done bndy. When e type of moduaton s unnown, usuay, e Fractonay Spaced Equazer- Constant oduus Agorm (FSE-CA) s one of e commony used bnd equazaton agorm whch are desgned to undo e channe effect wout any nowedge of e channe tsef [8]. he FSE-CA s e ntegraton of two dfferent parts: e constant moduus agorms (CA) and e fractona spaced equazer (FSE). he constant moduus agorm (CA) s a stochastc gradent agorm, desgned to force e equazer weght to eep a constant enveop on e receved sgnas. hu t s desgned for probems where e sgna of nterest has a constant enveope property. However, extensve smuatons have shown at t can st be used n amptude-phase moduaton type but e success of equazaton s decreased w ncreasng of order. As a resut, e CA s expected to have better performance for FSK and SK raer an QA types. he CA cost functon s gven by: J ( ) = E{( y( ) γ ) } () where y () s e equazer output and γ caed e dsperson constant defned by (). 4,0 γ = (),0 where 4, 0 and, 0 are four and second order moment respectvey. he cost functon J () s mnmzed teratvey usng a gradent based agorm w update equaton. In any standard CA equazaton system, e coeffcent taps are baud-spaced. However, t s often desred to use an equazer w taps spaced at a fracton of e data symbo perod. hs confguraton gves e extra degrees of freedom to perform addtona fterng. Such a scheme s caed fractona spaced equazaton (FSE). We assume at e receved sgna s: x ( t ) = = s ( ) h ( t ) + υ ( t ) (3) = where h (t) s e channe mpuse response, s() e sequence of nformaton and υ(t) s AWGN. he response h(t) s assumed to be of fnte eng. Fractonay spaced channe output resutng from tmes oversampng w respect to symbo rate may be wrtten as: t x ) = s( ) h( ) + ( ) = ( ν (4) An equvaent representaton may be formed usng -channe parae fter ban mode. hen e output of e sub-channe h () s gven by: = x ( ) = s( ) h ( ) + ν ( ) : = 0,..., (5) Now, we assume an equazer w () whch s used n cascade w each subchanne h (). he equazer coeffcents (taps) are adusted usng FSE- CA agorm: w ( + ) = w ( ) + ζ x ( ) y ( )( y ( ) γ ) (6) where ζ s e step sze parameter and: x ( ) = [ x ( ),..., x ( ( N )),..., (7) x ( ),..., x ( ( N ))] and superscrpt denotes e subchanne,.e., fractonay samped data are organzed on subchanne bass. It shoud be mentoned because of fractona sampng n channe equazaton stage, e symbo rate needs to be nown or to be estmated pror to choosng e sampng rate 3 Features extracton In AI t s most mportant to fnd a set of features whch coud be used to dscrmnate e members of consdered moduaton set. Among e dfferent types of features at we have evauated and ex-

3 roceedngs of e 5 WSEAS Internatona Conference on eecommuncatons and Informatc Istanbu, urey, ay 7-9, 006 (pp409-44) permented, hgher order moments and hgher order cumuants up to eght, produced e most effectve features. hese features provde a good way to descrbe e shape of e consteaton. Foowng subsecton brefy descrbe ese features. 3. oments (om.s) robabty dstrbuton moments are a generazaton of concept of e expected vaue, and can be used to defne e characterstcs of a probabty densty functon. Reca at e genera expresson moment of random varabe s gven by [9]: µ = ( s µ ) f ( s) ds (8) where µ s e mean of e random varabe. he defnton for e moment for a fnte eng dscrete sgna s gven by: = N = µ ( s µ) f ( s ) (9) where N s e data eng. In s study sgnas are assumed to be zero mean. hus Eq. (9) becomes: = N s = µ f ( s ) (0) Next, e auto-moment of e random varabe may be defned as foows: p q q = E[ s ( s ) ] () pq where p caed moment order and s stands for compex conugaton. Assume a zero-mean dscrete sgna sequence of e form s = a + b. Usng (), dfferent orders of moment derved, e.g.: = E[ s ( s ) ] = E[( a + b) ( a b)] () 4 4 = E[ a b ] 3. Cumuants (Cum.s) Consder a scaar zero mean random varabe s w characterstc functon: ts f ˆ ( t) = E{ e } (3) Expandng e ogarm of e characterstc functon as a ayor sere one obtans: r ( t) r ( t) og fˆ( t) = ( t) + + L + +L (4) r! e constants, n (4), caed e cumuants. he symbosm for p order of cumuant s smar to e p order moment. ore specay: C pq = Cum[ 3..., s, s 443,..., s ] (5) ( p q) terms ( q) terms For exampe: C = Cum( s ) (6) 8 It can be computed reaton between moments and cumuants. 3.3 Reaton between Cum.s and om.s he n order cumuant s a functon of e moments of orders up to ncudng n. oments may be expressed n terms of cumuants as: s,.., s = Cum s... um s (7) [ n ] { } [ ] [{ } ] v v v where e summaton ndex s over a parttons v = ( v,..., v q ) for e set of ndexes (,,..., n ), and q s e number of eements n a gven partton. Cumuants may be aso be derved n terms of moments. he n order cumuant of a dscrete sgna s (n) s gven by: q Cum [.., sn ] = ( ) ( q )! E[ s ].. E[ s ] (8) v v v q where e summaton s beng performed on a parttons v = ( v,..., v q ) for e set of ndces (,,..., n ).For exampe: 3 C63 = (9) 4 C 80 = (0) abe shows chosen features for consdered set (eoretca vaues under e constrant of unt varance). In s tabe, for smpfyng, we substtute e moduatons SK, SK4, SK8, ASK8, QA3, V9, Star-QA8 and QA64 w,, 3, 4, 5, 6, 7 and 8 respectvey. abe: Chosen features C C C C Support Vectors achne (SV) Support Vector achne (SV) s a supervsed machne earnng technque at can be apped for bo bnary and mut-cass cassfcaton [30]. he SV s based on structura rs mnmzaton (SR) prncpe at gves t to have hghy generazaton abty comparson oer approaches (e.g. neura networ etc.[3]. 4. Bnary SV he bnary SV performs cassfcaton tass by constructng optma separatng hyperpanes (OSH).

4 roceedngs of e 5 WSEAS Internatona Conference on eecommuncatons and Informatc Istanbu, urey, ay 7-9, 006 (pp409-44) OSH maxmzes e margn between e two nearest data ponts beongng to two separate casses. he dea of SV can be expressed as foows. Suppose e tranng set, d ( x, y ), =,,...,, x R, y {, + } can be separated by e hyperpane w x + b = 0, where w r s weght vector and b s bas. If s hyperpane maxmze e margn, en e foowng nequaty s vad for a nput data: y ( w x + b),for a x =,,..., () he margn of e hyper-pane s / w r, u e probem s: maxmzng e margn by mnmzng of w subect to (), at s a convex quadratc programmng (Q) probem at Lagrange mutpers are used to sove t: L = w λ [ y ( w x + b) ] () = where λ, =,..., are e Lagrange mutpers ( λ 0).he souton to s Q probem s gven by mnmzng L w respect to w and b. After dfferentatng L w respect to w and b and settng e dervatves equa to 0, yeds: w λ x (3) = = y It can obtan e dua varabes Lagrangan by mposng e Karush-Kuhn-ucer (KK) condtons: L = λ λ λ y y x x (4) d = = = o fnd e OSH, t must maxmze L d under e constrants of λ = 0, and λ 0.hose tranng = y ponts for whch e equaty n () hods are caed support vectors (SV) at can satsfy λ f 0. he optma bas s gven by: b = y w x (5) for any support vector x. For nput data w a hgh nose eve, SV uses soft margns can be expressed as foows w e ntroducton of e non-negatve sac varabesξ, =,..., : y ( w x + b) ξ for =,,..., (6) o obtan e OSH, t shoud be mnmzng e Φ = w + C ξ subect to constrants (6), = where C s reguarzaton constant at contros how heavy tranng errors are penazed. In e nonneary case e SV map e tranng pont nonneary, to a hgh-dmensona feature r r space usng erne functon K( x, x ), where near separaton may be possbe. he famous erne functons are near, poynoma, rada bass functon (RBF), and sgmod. Havng seected a erne functon, e Q probem s: Ld = λ λλ y y K( x, x ) (7) = = = After tranng, e foowng, e decson functon, becomes: f ( x) = sgn( y λ K( x, x ) + b ) (8) = 4. utcass SV-based cassfer In s research, we have derved at a nove, smpe and effectve souton for combnng bnary SVs to construct a mut-cass cassfer. In our agorm, we use an approach smar to e one reported n reported n [3]. Our approach can be descrbed as foows: Let { : =,,.., N} be N cassesof sgnas.we construct N cassfers { f : =,,.., N} and each cassfer s traned by e meod of one-cassversus-e-rest; at e cassfer f s traned for versus e rest of e casses. hen n e sgna cassfcaton phase, e cassfers perform accordng to e foowng decson rue: x f f = max{ f ( x) f 0; =,..., N } (9) where e functon f (x) provdes e dstance of x to e decson surfaces. 5 Expermenta resuts In smuatons we have used e channe mode at has been ntroduced n [33]. ADI was tested under condtons: typca urban propagaton envronment, mobe speed =85 m/h. SNR eves are consdered 0-0 db. he symbo rate s assumed to be nown (or estmated). Whe cassfyng usng our mut-cass SV-based, we used bo Gaussan RBF (GRBF) and poynoma (OLY) erne functons and obtaned a tte bt better performance n e case of OLY; however, e computatona speed of cassfcaton was faster n e case of GRBF. Hence, we used GRBF n our experments r r w K( x, x ) = exp( / x ).abes -4 x show confuson matrx for ree seected SNR eve db, 8dB and 7dB. As we see, e resuts mpy how ADI can dentfy moduaton type w e hgh accuracy n dspersve channes even at ow SNR. hs s due e two facts: chosen nove fea-

5 roceedngs of e 5 WSEAS Internatona Conference on eecommuncatons and Informatc Istanbu, urey, ay 7-9, 006 (pp409-44) tures and cassfer. he chosen feature have hghy effectve propertes n sgna representaton at enabe e cassfer to separate moduaton set w hgh accuracy, on e oer hand, e SVs act exceent on non-separabe data (ow SNR). abe: Confuson matrx at SNR=dB (%) abe3: Confuson matrx at SNR=8dB (%) abe4: Confuson matrx at SNR=7dB (%) As mentoned n secton, CA shows good resuts for SK type but for QA type when e number of states ncreases (hgher order) and/or e SNR eve decrease ts performance degrades. However, smuatons mpy good resuts for ese types of moduatons. he reason for s property shoud be ooed for n chosen features and cassfer at cover e weaness of equazer. For comparson e performance of SV w oer cassfer, we consder a rada bass functon neura networ (RBF-NN) [34]. abe5, show e performance of RBF-NN for smar stuaton n SNR=dB (ow SNR). It s found n ow SNR e RBF-NN shows poor performance. he reason maybe at, n ow SNR e constructon of neura networ s not proper. It shoud be mentoned, ough, e success rate of RBF-based system s ower an SV- based system, but t s hgher an a system at uses oer features and RBF-NN as a cassfer. abe6 shows e performance of a system at utzes RBF-NN and features n [9]. abe5: Confuson matrx at SNR=dB for RBF-NN abe6: SNR=dB for RBF-NN and features n [9] (%) Concuson AI s an mportant ssue n communcaton ntegence and eectronc support measure systems. In s paper, we present ADI to dentfy dgta moduatons types n dspersve channes. ADI uses hgher order moments and cumuants up to eght as features and a mutcass SV-based cassfer. Smuaton resuts show ADI s abe to dscrmnate dfferent types of moduatons w hgh accuracy even at ow SNR. References: [] C.- S. Long, K.. Chugg, and A. oydoro Furer resuts for dgta quadrature moduaton cassfcaton n AWGN, roc. ILCO,994, pp [] A. oydoro and K. Km, On e detecton and cassfcaton of quadrature dgta moduaton n broadband nose, IEEE rans. Commun.,Vo.38, No.8,990, pp.99-. [3] C. Le artret, and D. Botea, A genera maxmum ehood cassfer for moduaton cassfcaton, roc. ICASS, Vo. 4, 998, pp [4]. anagotou, and A. oydoro Lehood rato tests for moduaton cassfcaton roc. ILCO, 000, pp [5] E. E. Azzouz, and A. K. Nand, Automatc dentfcaton of dgta moduaton Sgna rocessng, Vo. 47, No., 995, pp

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