A Joint Timing and Fractionally-Space Blind Equalization Algorithm Zheng Dong a, Kexian Gong b, Lindong Ge

Size: px

Start display at page:

Download "A Joint Timing and Fractionally-Space Blind Equalization Algorithm Zheng Dong a, Kexian Gong b, Lindong Ge"

Rosanna Dawson
5 years ago
Views:

1 Proceedigs of te 2d Iteratioal Coferece O Systems Egieerig ad Modelig (ICSEM-13) A Joit imig ad Fractioally-Space Blid Equalizatio Algoritm Zeg Dog a, Kexia Gog b, Lidog Ge Istitute of Zegzou Iformatio sciece ad tecology, Zegzou , Cia a DZ @163.com, b ggkx@163.com Key ords: blid equalizatio, fractioally-spaced, CMA, timig Abstract. I tis paper, e proposed a joit timig ad fractioally-spaced blid equalizatio algoritm. It adopts Garder algoritm istead of simple do-samplig i covetioal fractioally-spaced equalizatio i order to overcome te problem of tat te filter ca t compesate timig error. e simulatios so tat te performace of te proposed fractioallyspaced equalizatio algoritm is better ta CMA i differet SNR ad i differet umber of cael taps. Itroductio Fractioally-spaced equalizatio (FSE) is compared it te traditioal symbol-spaced equalizatio (SRE), it ca sample te received sigal as te greater rate of symbol rate. Isesitive to samplig pase, fuctioal timig ad compesatio for serious sidebad distortio are te outstadig advatages of te FSE. Furter study suggests tat a limited legt FSE ca completely equalize a FIR cael, ile SRE requires a ifiite legt filter to equalize a FIR cael perfectly. FSE refers to te fractioally-spaced blid equalizatio structure; FSE-CMA is oe of te most popular structures of fractioally-spaced blid equalizatio. FSE-CMA adopts te algoritms of CMA coefficiets updatig, te cosequece of simulatios sos tat it ca play a perfect balaced effect ad it ca better covergece especially for te MPSK sigal. Multi-Cael System Model of Fractioally-Spaced Equalizatio (FSE) May autors ave studied i dept o te structure of FSE; te multicael ad sigle cael system model of FSE as bee studied i [1][2][3]. Cael system model of FSE ca use sigle symbol rate to express te full sigal trasmissio process, every sample poits of eac symbol ca be vieed as a sub-cael, ad terefore FSE ca be trasformed as multi-cael system model [4][5]. Supposig tat te sedig symbol sequece { s } is trasferred troug a liear time-ivariat (LI) cael, te output of te fractioally-spaced cael could be expressed as, r = r = s i i+ v = s i ip + v P i P P i Were refers to fractioally-spaced samplig poits of te cael impulse respose, v refers to fractioally-spaced samplig poits of oise. For te fiite impulse respose cael, te coefficiet of fractioally-spaced cael ca be expressed as vector format = ( 0, 1, 2,, ( L 1) 1) + P.Were L refers to te legt of te cael impulse respose ic samplig space is te rate of symbol period. Fractioal samplig rate model ca be equivalet to a sigle iput multiple output (SIMO) cael model (as so i Fig. 1). e impulse respose oe of te sub-cael p ( p = { 1, 2,, P} ), recorded as ( p ) = ( + 1) P p, could be obtaied troug te over-samplig vector. e output of te correspodig sub-cael could be expressed as, Publised by Atlatis Press, Paris, Frace. 0162

2 Proceedigs of te 2d Iteratioal Coferece O Systems Egieerig ad Modelig (ICSEM-13) L ( p) ( p) ( p) = i i + i= 0 r s v (2) v x r s x r () P y v Fig. 1 multi-cael system model of te /P iterval equalizer As so i te figure of te equalizatio model above, te correspodig coefficiet ( p) of te ( p) sub-cael p is = P + p 1. Accordig to multi-cael output vector r, FSE makes a estimatio about iformatio source sequece s, y L i i i= 0 = r = r () Were ( (2) ( ) P (2) ( p) =,, ), = ( 0, 1, L ), ( ) = r, r,, r r( ) = ( r, r 1,, r L ). e received sigal i te (2) could be expaded to te folloig form: (3) r, r( ) = Hs( ) + v ( ) (4) Were H refers to te cael matrix. e system output could be give e (4) is applied to (3). y = Hs( ) + v( ) (5) Were H refers to te system impulse respose, ic coefficiet as a feature tat samplig poits are at te rate of baud rate. So te multi-cael structure of FSE is equal to a sigle-cael structure. FSE Blid Equalizatio Model e multi-cael system model above is te model of FSE i te abstract, may autors ave give te structure i practice based o FSE model. J.K. ugait proposed FSE-CMA blid equalizatio structure i [6], FSE uses coefficiet updatig algoritm of CMA iverse filter ic combies te advatages of fractioally-spaced ad te CMA. Ad te [7] gives geeral FSE equalizatio realizatio structure (Fig. 2), ic is based o FSE's multi-cael system model. Publised by Atlatis Press, Paris, Frace. 0163

3 Proceedigs of te 2d Iteratioal Coferece O Systems Egieerig ad Modelig (ICSEM-13) v x r s x r () P y v Fig. 2 multi-cael system model of FSE If te equalizatio algoritm i Fig. 2 uses CMA, te suc equalizer is called FSE-CMA. is is a multi-cael structure ad relatively complicated. e sigle-cael FSE realizatio structure illustrated i Fig. 3 ca be give. v s y r y Fig. 3 sigle cael system model of FSE Compared it multi-cael model, it is more similar to te structure of SRE, ile it also as a extractio module ad could be realized easier.fse-cma is tat FSE adopts te equalizatio algoritm (coefficiet updatig algoritm) of CMA, accordig to te FSE sigle-cael realizatio structure [4][8]. Improved Fractioally-spaced Blid Equalizatio Algoritm I order to solve te problem tat FSE-CMA caot track te symbol rate, te improved structure of practical FSE-CMA-imig, as so i Fig. 4, is proposed. r y Fig. 4 structure diagram FSE-CMA-imig e do-samplig module is replaced it timig module. imig algoritms ave effect o iterpolatio filter to sycroize sigal symbol rate, terefore te iverse filter of FSE oly plays a fuctio of equalizatio. e structure also ca be regarded as te combiatio of equalizatio ad timig algoritms. e iverse filter is located i te forefrot of sycroous structure ic compesates te cael excelletly to make subsequet algoritm could ork uder o cael distortio circumstace. Garder proposed te timig error detectio algoritm i te receiver, ic is simple ad oly eeds to samplig poits for eac symbol ad oe of te to samplig is te best samplig poits of symbol (i.e. judge symbols setece accordig to tis samplig poits). Its advatages are ofacig judgmet, ad timig recovery is fully idepedet it carrier pase. erefore Garder's imig sycroizatio algoritm is adopted i FSE-CMA-imig. Performace Simulatio ad Aalysis of FSE-CMA-IMING e covergece speed ad performace of FSE-CMA-IMING is simulated i Matlab. Modulatio mode adopts QPSK, 2 samplig poits eac symbol, te great amplitude is 8192, Publised by Atlatis Press, Paris, Frace. 0164

e structure of te equalizer adopts trasverse iverse filter of 15 tap, te iitial value of ceter tap is l+0i, oters are 0. parameter is 65 selected as R CMA =134217728, step legt is μ = 2.

4 Proceedigs of te 2d Iteratioal Coferece O Systems Egieerig ad Modelig (ICSEM-13) samplig rate is 5M/s, frequecy sift is 25 KHz ad pase sift is 0.15π. e complex cael used i algoritm simulatio is expressed as =[ i, i, i, i, i, i, i]. e structure of te equalizer adopts trasverse iverse filter of 15 tap, te iitial value of ceter tap is l+0i, oters are 0. parameter is 65 selected as R CMA = , step legt is μ = 2. imig algoritms uses Garder's timig algoritms. e covergece performace of te equalizer is expressed it by remaiig itersymbol iterferece (ISI), te expressio of ISI (ere use logaritm form) is: ISI = 10log k 2 2 k ( )* W( k) k ( )* W( k) k ( )* W( k) 2 max max (6) Symbol * meas covolutio. Fig. 5 ad 6 illustrate respectively te ISI ad costellatio of FSE-CMA-imig e sigalto-oise ratio (SNR) is 30dB. Judgig from te costellatio covergece is very good at ig SNR (30dB). Sice tere are frequecy sifts, te 7,500 output symbols of FSE-CMA-imig symbol beave as a circle. Fig. 5 simulatio result of ISI Fig. 6 costellatio cart after algoritm covergece FSE-CMA-imig covergece is faster, about 500 symbols for QPSK at 30dB ca be coverget, ad te costellatio cart is very clear. Fig. 7 ad 8 are give for receivig costellatio ad FSE-CMA-imig s output costellatio respectively at 10dB SNR. Fig. 7 costellatio cart of received sigal i SNR 10dB Fig. 8 output of FSE-CMA-imig i SNR 10dB Because of te lo SNR, ite oise makes costellatio poits tick, ile it is still a circle. Ad compared it receivig sigal costellatio cart te timig effect still is more obvious. e iverse filter of FSE-CMA-imig is fractioally-spaced. I simulatio if add cael distortio to te sigals, te te ISI of FSE-CMA-imig ould t be calculated. Similarly, if addig cael distortio to fractioally-spaced sigal, te ISI of CMA ca t be calculated. If addig cael distortio i symbol iterval ad fractioal iterval, te actual cael distortio effect is differet. e ISI caot be compared. But te calculatio of es ( k ) ad coefficiet of cael ad iverse filter is irrelevat, it ca be used for te performace compariso betee CMA ad FSE-CMA -imig. Steady-state error es ( k) is expressed as Publised by Atlatis Press, Paris, Frace. 0165

Proceedigs of te 2d Iteratioal Coferece O Systems Egieerig ad Modelig (ICSEM-13) 2 e ( k) = y( k) R s CMA (7) We a 7 tap complex cael is supposed ad CMA algoritm ad FSE-CMA-imig bot use 15 tap iverse

e iverse filter s tap umber is 7 at te ig sigal-to-oise ratio 30dB ad lo SNR 10dB respectively, te steady-state error is so i Fig. 11 ad 12.

5 Proceedigs of te 2d Iteratioal Coferece O Systems Egieerig ad Modelig (ICSEM-13) 2 e ( k) = y( k) R s CMA (7) We a 7 tap complex cael is supposed ad CMA algoritm ad FSE-CMA-imig bot use 15 tap iverse filters at te 30dB ig SNR ad 10dB lo SNR respectively, te steady-state error is so i Fig. 9 ad 10. e iverse filter s tap umber is 7 at te ig sigal-to-oise ratio 30dB ad lo SNR 10dB respectively, te steady-state error is so i Fig. 11 ad 12.We iverse filter s tap umber is 5 at te ig sigal-to-oise ratio 30dB ad lo SNR 10dB respectively, te steady-state error is so i Fig. 13 ad 14. Fig. 9 steady-state error of 15 tap iverse filter i SNR 30dB Fig. 10 steady-state error of 15 tap iverse filter i SNR 10dB Fig. 11 steady-state error of 7 tap iverse filter i SNR 30dB Fig. 12 steady-state error of 7 tap iverse filter i SNR 10dB Fig. 13 steady-state error of 5 tap iverse filter i SNR 30dB Fig. 14 steady-state error of 5 tap iverse filter i SNR 10dB e compariso sos tat FSE-CMA-imig is caracterized by loer steady-state error. e steady-state error of FSE-CMA-imig is sigificatly belo to te CMA at ig SNR; at lo SNR te steady-state error of FSE-CMA-imig is sligtly belo te CMA. We equalizer legt is less ta cael order, FSE-CMA-imig is sigificatly better. Summary A joit timig ad fractioally-spaced equalizatio algoritm is proposed i tis paper. It adopts Garder algoritm istead of do-samplig i covetioal fractioally-spaced equalizatio to Publised by Atlatis Press, Paris, Frace. 0166

6 Proceedigs of te 2d Iteratioal Coferece O Systems Egieerig ad Modelig (ICSEM-13) solve te problem of tat te filter ca t compesate timig error. I te ed, te simulatio ad aalysis sos tat te proposed algoritm as te iger performace ta CMA it differet umber of iverse filter taps. Refereces [1] Dirk..M.Slock, Costatios. B.Papadias. Blid Fractioally-Spaced Equalizatio Based o Cyclostatioarity[J],IEEE raso I,1994.3: [2] Su Souyu, Zeg Juli, Xu Zogyog, Zag Qi. Bid Fractioally Spaced Equalizatio via Modified Costat Modulus Algoritm[J]. ACA ELECRONICA SINICA, 2003,31(11): [3] Li Sog, Ge Lidog. Performace Aalysis of Fractioally-Spaced Equalizer Adapted Via te Costat M odulus Algoritm[J]. Joural of Iformatio Egieerig Uiversity, 2004, 5(2): [4] A.Nasir, S.Durrai ad R.A.Keedy, Blid Fractioally Spaced Equalizatio ad imig Sycroizatio i ireless Fadig Caels[J], i Proc. 2d Iteratioal Coferece o Future Computer ad Commuicatio, vol3, Wua, Cia, pp15-19, May,2010 [5] Dirk..M.Slock. Blid Fractioally-spaced Equalizatio, Perfect-recostructio Filter Baks ad Multicael Liear Predictio[J], IEEE raso I,1994.4: [6] J.K ugait,a Parallel Multimodel CMA/Godard Adaptive Filter Bak Approac o Fractioally-Spaced Blid Adaptive Equalizatio[J], IEEE Cof o Commuicatios, : [7] J.K.ugait. O Fractioally-Spaced Blid Adaptive Equalizatio uder Symbol imig Offsets Usig Godard Ad Related Equalizers[J]. IEEE Cof o Commuicatios : [8] J.R.ricier, C.R.Joso. Blid Fractioally-spaced equalizatio of digital cable V[C].I Proc.8t IEEE Worksop Statistical Sigal Proc. Corfu Greece, Publised by Atlatis Press, Paris, Frace. 0167

Complex Algorithms for Lattice Adaptive IIR Notch Filter

4th Iteratioal Coferece o Sigal Processig Systems (ICSPS ) IPCSIT vol. 58 () () IACSIT Press, Sigapore DOI:.7763/IPCSIT..V58. Complex Algorithms for Lattice Adaptive IIR Notch Filter Hog Liag +, Nig Jia