M-Algorithm Combied Equliztio d Decodig for Mobile / Persol Commuictios Stef A. Fechtel d Heirich Meyr Ache Uiversity of Techology, ISS, Templergrbe 55, D-52056 Ache, Germy Abstrct Third-geertio tetherless mobile/persol commuictio system developmet is fced with the coictig requiremets of providig both highest protectio gist oise/iterferece d keepig the trsmissio dely s low s possible. I this pper, ovel lgorithm for combied equliztio d of iterleved coded modultio is preseted. The ew M-CED lgorithm is extesio of the "covetiol" CED i two wys: i) per-survivor processig is used i the equlizer sectio i order to reduce the ltecy, d ii) M> equlizer sttes per code stte re kept i the survivor memory so s to further improve o the bit error performce. Results o simulted bit error rtes give isight ito the eect of vrious chel d receiver prmeters, i prticulr, iterlever legth (thus ltecy), umber of equlizer sttes, d the choice of trellis codes. The etire digitl receiver with feedforwrd syc, pproprite prelterig d M-CED equliztio/is show to combie the dvtges of beig robust gist fdig d yieldig good BER performce lso t low dely. Itroductio I the desig of mobile/persol commuictio systems, oe ttempts to chieve both high degree of protectio gist impirmets (oise, djcet- d co-chel iterferece) d s low ltecy s possible, prticulrly for speech trsmissio [5]. Obviously, these re coictig requiremets o fdig chels sice some kid of explicit or implicit time diversity, most ofte through bdwidth-eciet chel codig d iterlevig [6,7,8,6,9,2] must be provided for i order to bridge periods of deep chel fdes, especilly if te diversity is ot vilble. Here, we re cocered with dvced TDMA-bsed multiuser trsmissio of lierly modulted dt pckets over dispersive fdig chels. Ech pcket is ssumed to be heded by premble (P triig symbols) for sychroiztio d decoder iitiliztio purposes, followed by D trellis-ecoded d iterleved rdom dt symbols. If fster fdig must be hdled by the receiver, dditiol triig segmet oflegthp 2 my hve to be ppeded t the ed of the pcket so s to miti correct receiver syc [0]. Usig iterleved trellis codes with lrge eective code legth (ECL) combied with frequecy hoppig (FH) d feedforwrd receiver sychroiztio costitutes very eective tifdig techique [2]. Recetly, computtiolly-eciet combied equliztio d (CED) lgorithm hs bee proposed by Mehl [5] d developed further by the uthor [3,]. I the CED scheme, the block iterlever mtrix must hve specil structure tilored to the pcket legth F d the survivor depth S of the Viterbi decoder (Fig. 2 below) [5]. Sice S must be lrge w.r.t. the code costrit legth, the iterlever size d thus the ltecy must lso be lrge i order to chieve er-optiml decoder performce. For istce, survivor depth of S=20-30 leds to ltecy i excess of 00 ms if the pckets re trsferred i GSM-like time slot formt [4]. I the ew M-CED preseted here, the ltecy F J is reduced by fctor of Z by mes of per-survivor processig (PSP). The survivor depth S = Z J c be kept lrge by retrdig the l decoder decisios util Z rows i the deiterlever mtrix hve bee processed. The opertio of the covetiol CED c be iterpreted s joit equliztio d lgorithm tht cosiders oe equlizer stte per code stte. The equlizer portio therefore opertes i the mer of decisio-feedbck equlizer (DFE). I the cse of ucoded modultio, the soclled M -lgorithm is kow to improve o the DFE performce by keepig M>equlizer sttes i the survivor memory [,2,8]. Iterestigly, the performce of the optiml but much more complex Viterbi equlizer is pproched very quickly lredy for very smll M, provided tht suitble receiver prelterig is performed i frot of the equlizer [3,9]. Applyig the M-lgorithm cocept to combied equliztio d leds to turl extesio of the CED, termed M-CED lgorithm, where M equlizer sttes per code stte re kept i the survivor memory. Itroducig both per-survivor processig d the M-lgorithm cocept hs the potetil of reducig the ltecy d simulteously improvig the BER performce. 2 Sigl Trsmissio d System Model The block digrm of the etire trsmissio system is outlied i Fig.. The iput bits b i re trellis-ecoded d mpped oto PSK or QAM dt symbols i (idex i: o-iterleved time scle) which re writte row-wise ito the block iterlever mtrix. After ddig triig segmets for sychroiztio, the chel symbols k (idex k: iterleved chel symbol time scle) re red out colum-wise d coverted to rte-2=t symbol strem which is ltered by thelowpss- equivlet physicl chel h(k) whose memory sps L symbol itervls. The received T=2-spced sigl r k is preltered i the detectio pth by the time-vrit chel mtched lter (MF) m(k), d, followig decimtio to rte =T, the whiteig lter (WF) w(k). Assumig idel lters, the cscde of rte coverter, chel h(k), MF m(k), rte decimtor d WF w(k) yields cusl, miimum phse equivlet T -spced
Trsmitter d Chel b i iput bits Trellis Ecoder / Modultor Block Iterlever Receiver (o te diversity) r k mtched filter (MF) m(k) m feedforwrd sychroiztio whiteig filter (WF) 2 w(k) w f v k equlizer iput sigl k k 2 h(k) r k chel symbols (M)-CED Algorithm physicl chel smpled received sigl b i decoded bits Figure : Trsmissio System d Receiver Structure chel impulse respose f(k) [7,9] so tht the resultig rte-=t sigl v k (see Fig. ) c be expressed s v k = l=0 f l (k) k + k = T (k) f(k)+ k () where k is the whiteed oise behid the WF. The chel ccess scheme d pcket durtio ssumed here re orieted t the GSM system [4]: throughput 270 kbit/s/crrier, 8 TDMA pckets per crrier, 4.65 ms spcig betwee pckets pertiig to user, pcket legth 577 s. However, here the dt bits re trellis-ecoded d lierly modulted. Sice ech symbol cotis two iformtio bits, the symbol rte is hlved to =T =35 kbd so tht F =74 symbols plus gurd time of 4.25 symbol itervls c be ccomodted i oe GSM time slot. The triig segmets re desiged for er-optiml feedforwrd receiver sychroiztio. Feedforwrd syc is most dvtgeous sice it elimites syc error propgtio preset i decisio-directed chel estimtors, ebles frequecy-hoppig, d is more robust gist fdig. Moreover, the premble c be used for iitiliztio of the decisio-directed ISI ccelltio procedure described below. Here, pcket of legth F =74 is ssumed to coti two triig segmets (pre- d postmble, Fig. 2) comprisig P =9 d P 2 =7 symbols, respectively. From these triig segmets, chel estimtes h(k) (here 0-dim. vectors spig L=4 symbol itervls) re computed for some positios k withi the dt block. The ^h(k) so obtied re the mpped oto MF-, WF- d equlizer coeciet sets m(k) w(k) f(k) [0]. As test simultios hve show, oly four chel/mf coeciet sets^h(k), m(k) d oly two WF/equlizer coeciet sets w(k) (9-dim.), f(k) (4-dim.) eed to be geerted per pcket to chieve qusi-optiml syc performce. For this study, two trellis codes hve bee selected tht re very eective i fdig eviromets due to their lrge eective code legths (ECL). The rst code ("8-PSK") is rte- 2/3, 6-stte, 8-PSK Ugerboeck code[20] with symptoticl gi (AWGN chel) 4. db d ECL 3. The secod code ("6-QAM") by Moher d Lodge [6] is 2rte-/2, 26-stte, 24-PAM (6-QAM) code with symptoticl gi 3.4 db d ECL 5. 3 The Covetiol CED Algorithm The structure of the block iterlever mtrix d the process of equliztio d s performed by Mehl's CED lgorithm [5] is illustrted i Fig. 2. Combied Equliztio/Decodig (CED) WF output umber of rows F=P+D v v v v v v v WF output sigl... fil symbol decisios vv v v v v v v =v - Σ f (k). l v v v v v v k-l v iterlever legth J = survivor depth S symbols i chel memory premble symb. i survivor memory directio of process sy. i survivor memory ISI compested symbol iterlever L... depth = D k k l= v postmble 2 Figure 2: CED Algorithm The frequecy-hopped TDMA pckets form the colums of the iterlever mtrix so tht the umber ofrows (icludig triig) is F = P +D where P deotes the totl umber of triig symbols per pcket (here P = P + P 2 =6, D=58). The iterlever depth is therefore the umber D of ecoded dt symbols i pcket. As soo s the deiterlever mtrix hs bee lled with J received d preprocessed pckets (smples v k, see Fig. 2), the row-wise equliztio d process begis. Ech itertio i ; ; i strts with DFE-like equliztio step where the ISI is cceled by subtrctig the ISI postcursors from v k : ^ k = k + f l (k) k;l + k ; f l (k) ~ k;l l= v k l= ISI estimte = k + k if ~ k;l = k;l (2) The ISI estimte is formed vi the l (thus more relible) symbol decisios ~ k;l (l = ::: L)"bove" the curret symbol k. Assumig idel prelterig d correct l
decisios, the ISI-cceled smple ^ k is just oisy replic of the trsmitted symbol k,sotht^ k c be pssed o to the Viterbi decoder. Switchig to decoder idexig k ; i d usig the ISIcceled smple ^ i =^ k, metric icremets m i ssocited with stte trsitios m ; re computed d dded to the previous pth metrics m i; so s to form "exteded" pth metrics m i.from the pths mergig i successor stte, the pth with the best metric is selected d its survivor bit sequece b i = fb i b i; :::g s wellsits survivor chel symbol sequece i = f i i; ::: g is stored i the survivor memory. I order to be ble to perform ISI ccelltio v k ; ^ k s described bove, the chel symbols k;l "bove" the curret smple v k, i prticulr k;,must be kow. Sice k; = i;j, the CED geertes l symbol decisio ~ i;j o survivor symbols i;j before metric computtio c be performed. Therefore, the survivor memory of the Viterbi decoder must be tructed to survivor depth S J ot lrger th the iterlever legth J. Ner-optiml decoder performce is obtied for survivor depths S tht re severl times lrger th the code costrit legth. If the GSM-like trsmissio formt d trellis codes described bove re used, survivor depths (umber of pckets per iterlever block) i the order of 20-30 led to ltecies i excess of 00 ms which is hrdly tolerble for speech trsmissio. Ltecies below 50 ms cll for tructig the survivor depth to o more th S=0 symbols. I Fig. 3, the simulted BER performce of the etire receiver with covetiol CED d frequecy-hopped pcket trsmissio over the GSM hilly-terri chel s specied by CEPT[4]isshow for the 8-PSK code. Curves re displyed for survivor depths of S=25 (er-optiml, 25 ms ltecy), 0 (50 ms) d 5 (25 ms), d for Doppler frequecies of 200 Hz (900/800 MHz: 250/25 km/h) d 400 Hz. Figure 3: BER Performce of CED, 8-PSK Code From the gure d similr results for the 6-QAM code (ot show here), oe observes the followig: The receiver is robust gist fdig up to Doppler frequecies of t lest 200 Hz (reltive Doppler :50 ;3 ). At higher Doppler, chel estimtio d thus receiver syc experieces degrdtio. Without frequecy hoppig, BER degrdtio results for Doppler below 50 Hz due to isuciet iterlevig. Uder idel coditios (S=25, Doppler 200Hz), the 6-QAM code with ECL 5 (8/2 db SNR re eeded to obti BER of 0 ;2 /0 ;4 ) performs better th the 8-PSK code with ECL 3 (9/3 db SNR for BER 0 ;2 /0 ;4 ). The BER degrdtio resultig from tructig the survivor depth is substtil due to its lrger costrit legth, the 6-QAM code is more sesitive th the 8-PSK code. These results reect trdeo betwee ltecy d performce which eeds to be improved upo if qusioptiml performce t lower delys is desired. 4 The New M-CED Algorithm with Per-Survivor Processig I order to circumvet the dely limittios of the covetiol CED, the lgorithm is modied i two wys. As discussed bove, the symbols k;l "bove" the curret smple v k must be kow (see Fig. 2) i order to perform ISI ccelltio. Now isted of formig l decisios ~ k;l =~ i;lj by survivor memory tructio, the cocept of per-survivor-processig (PSP) is ivoked, i.e. the symbols k;l = i;lj cotied i the survivor memory i re used for survivor-depedet ISI ccelltio: ^ k = v k ; f l (k) k;l (3) l= survivor-depedet ISI estimte By such, the survivor memory my be exteded to more th oe row i the deiterlever mtrix. The process of equliztio d of the CED lgorithm with PSP is illustrted i Fig. 4. I the gure, the survivor memory is exteded to Z rows so tht the survivor depth becomes S = Z J. Therefore, J d thus the ltecy c be reduced without hvig to tructe the survivor memory. However, J must ot be smller th the code ECL i order to provide for suciet iterlevig remember tht the symbols k;l = i;lj i oe colum ted to fde simulteously sice they belog to the sme pcket. The secod modictio to the CED lgorithm is motivted by the fct tht lrge percetge of symbols k;l = i;lj i the chel memory "bove" v k my ifctbe wrog sice they belog to survivors edig i icorrect code stte. This is best explied vi exmple of survivors i the code trellis digrm s displyed i Fig. 5. Sice J is ow smller th the survivor depth S, my of the survivor pths pertiig to code sttes hve ot yet merged t istts i ; J, i ; 2J, ::: so tht their ssocited survivor symbols i, i prticulr k; = i;j k;2 = i;2j ::: i the chel memory "bove" v k,my dier from those of the correct pth. Usig these symbols k;l = i;lj for survivordepedet ISI ccelltio therefore yields icorrectly "compested" smples ^ i so tht the metrics computed from ^ i re likewise icorrect. A elegt remedy is foud by recogizig tht collectio of symbols k;l (l = ::: L) i the chel memory c be iterpreted s equlizer stte, just like i the cse of ucoded modultio. I this cotext, the ISI ccelltio mechism of the CED is ideticl to the opertio of decisio-feedbck equlizer (DFE) sice oly oe equlizer stte is kept per code stte. At the other ed of the complexity scle, the full-edged Viterbi equlizer (VE) [4] keeps
(M-)CED Algorithm with Per-Survivor- Processig WF output umber of rows F=P+D v v v v v v v v WF voutput v vsigl v v v... fil symbol decisios iterlever legth J survivor depth S=Z J symbols i chel memory sy. i survivor memory ISI compested symbol premble symb. i survivor memory directio of process L... iterlever =v - depth = D Σ f (k). v v,k v k l,k-l v v v v v l= postmble 2 Figure 4: The (M-)CED Algorithm with PSP Q L equlizer sttes per code stte, where Q is the crdility of the symbol lphbet (here 8 or 6) d L the chel memory (here 4). Fortutely, it is ot ecessry to implemet the VE sice it hs bee show tht keepig smll umber M of equlizer sttes lredy yields qusioptiml performce [,2,8]. Therefore, it seems resoble to exted this M-lgorithm cocept lso to joit equliztio d. This leds to the M-CED lgorithm where M survivors (equlizer sttes) re kept per code stte. At ech itertio i; ; i, the M survivors m i; (m = ::: M)ofechcodestte re used to perform M ssocited ISI ccelltios yieldig smples ^ m i.from these, M exteded pth metrics for ech possible stte trsitio re computed i the Viterbi decoder. Depedig o the code trellis, umber (8-PSK code: 4M, 6-QAM code: 2M) of pths merge i ech successor stte. Of these mergig pths, the M pths with best metrics re selected d their survivors stored for the ext itertio. 5 Receiver Performce The bit error performce results reported here re of prelimiry ture s yet, oly few trsmissio scerios hve bee ivestigted i simultio experimets. Simultios hve bee coducted for the GSM hilly terri chel [4] (mild ISI spig L=4 symbol itervls) oly. Also, the simultio of referece curves for idel chel estimtio will hve to be completed i the er future. Nevertheless, the beets of the M-CED lgorithm with PSP d the impct of some importt prmeters do become ppret from the results lredy obtied. Here, BER results re show for the etire digitl receiver with feedforwrd syc d M-CED joit equliztio d Exmple of Survivor Pths i Code Trellis,k-3 i-3j,k-2 i-2j survivor depth S,k- i-j iterlever legth J,k i code stte time idex i Figure 5: Exmple of Survivors i the Code Trellis Digrm. Iterlever legths of J=5, 0 d 25 hve bee tested the survivor depth S is xed t 25. The BER curves for the 8-PSK code (ECL 3) re give i Figs. 6 d 7 for Doppler frequecies of (up to) 200 d for 400 Hz, respectively. Figure 6: M-CED, 8-PSK Code, 200 Hz Agi, the receiver is see to be robust gist fdig up to Doppler frequecies of t lest 200 Hz (reltive Doppler :5 0 ;3 ). The BER degrdtio t fster fdig (Doppler 400 Hz) is etirely due to the compromized qulity of receiver sychroiztio. Cocerig the 8-PSK code (ECL 3), oe observes the followig: The use of per-survivor processig (PSP) lredy yields substtil gis w.r.t. the covetiol CED, especilly for smll iterlever depths J. Applyig the M-lgorithm cocept yields dditiol gis, d the BER curves "coverge" rpidly: beyod M =4, further performce gis re very mrgil so tht M =4 is the best compromize betwee complexity
Figure 7: M-CED, 8-PSK Code, 400 Hz d performce. The M-CED yields gis ot oly for smll J but lso for lrge J = S=25 For J = S=25, 8-PSK d Doppler 200 Hz, the M-CED (Fig. 6) is see to be superior to the CED by bout db. The M-CED with J=5 performs pproximtely s well s the CED with J=0, d the M-CED with J=0 s well s the CED with J=25 so tht, by virtue of the M-CED, the ltecy c be reduced by fctor of 2 to 2.5 without scricig the BER performce. The results (ot show here) for the 6-QAM code (ECL 5) revel the followig: The gis obtied by virtue of PSP re oticeble (especilly for J=0) but re smller th for the 8-PSK code. The dditiol M-CED gis (M ) re lso smller th for 8-PSK, but the BER curves "coverge" eve fster here, M=2 is the best compromize betwee complexity d performce. The ltecy reductio fctors re smller (usully 2) th for the 8-PSK code. Oly t 400 Hz Doppler d with J=0, the ltecy c be reduced by fctor of 2 without compromizig BER performce (the M-CED [J=0] performs lmost s well s the CED [J=25]). I summry, the M-CED lgorithm sigictly improves o the trdeo betwee ltecy d performce whereby qusioptiml performce c be chieved t lower delys. Iterestigly, the results revel other trdeo, viz. betwee ltecy d eective code legth (ECL). Without dely limittios, codes with lrge ECL re kow to yield the best performce o fdig chels due to their high degree of iheret time diversity. However, lrge ECL's c become couterproductive whe it comes to miimizig the ltecy. The results obtied so fr clerly idicte tht, uder severe dely costrits, the 8-PSK code with smller ECL ( smller costrit legth) should be preferred to the 6-QAM code. 6 Coclusios A digitl receiver icludig feedforwrd syc, receiver pre- lterig d M-CED processig hs bee studied. BER simultio results give isight ito the eect of the iterlever legth J (thus ltecy), umber M of equlizer sttes, d the choice of trellis codes with dieret ECL's. I summry, the receiver with feedforwrd sychroiztio d the ew M-CED lgorithm hs bee show to be good cdidte for 3-rd geertio digitl mobile/persol rdio sice, prt from beig robust gist fdig, it combies the dvtges of good BER performce with low dely d moderte cost of implemettio. Refereces [] Aderso, J.B. d Moh, S. Sequetil Codig Algorithms: Survey d Cost Alysis. IEEE Trs. Commu., Vol. COM-32, No. 2, pp. 69{76, Feb. 984. [2] Bier, A. d Heirich, G. Performce of M-Algorithm MLSE Equlizers i Frequecy-Selective Fdig Mobile Rdio Chels. I Proc. ICC, pp. 28{284, 989. [3] Bergms, J.W.M., Rjput, S.A., d v de Lr, F.A.M. O the Use of Decisio Feedbck for Simplifyig the Viterbi Detector. Philips J. Res., Vol. 42, No. 4, pp. 399{428, 987. [4] CEPT/ETSI. GSM recommedtios 5.x, 988. [5] Chi, S. The Uiversl Mobile Telecommuictio System. IEEE Commuictios Mgzie, Vol. 30, No. 2, pp. 54{62, Dec. 992. [6] Divslr, D d Simo, M.K. The Desig of Trellis Coded MPSK for Fdig Chels: Performce Criteri. IEEE Trs. Commu., Vol. 36, No. 9, pp. 004{0, Sep. 988. [7] Divslr, D d Simo, M.K. The Desig of Trellis Coded MPSK for Fdig Chels: Set Prtitioig for Optimum Code Desig. IEEE Trs. Commu., Vol. 36, No. 9, pp. 03{02, Sep. 988. [8] Du, J. dvucetic, B. Trellis Coded 6-QAM for Fdig Chels. Europe Trs. Telecommu., Vol. 4, No. 3, pp. 335{34, My-Ju. 993. [9] Fechtel, S.A. d Meyr, H. A Ivestigtio of Ner-Optiml Receiver Structures Usig the M-Algorithm for Equliztio of Dispersive Fdig Chels. I Proc. EUSIPCO'92, pp. 603{606, Brussels, Belgium, Aug. 992. [0] Fechtel, S.A. d Meyr, H. Optiml Prmetric Feedforwrd Estimtio of Frequecy-Selective Fdig Rdio Chels. IEEE Trs. Commu., Vol. 42, No. 2/3/4, pp. 639{650, Feb./Mr./Apr. 994. [] Fechtel, S.A. d Meyr, H. Combied Equliztio, Decodig d Ate Diversity Combiig for Mobile / Persol Digitl Rdio Trsmissio usig Feedforwrd Sychroiztio. I Proc. IEEE It. Cof. Vehicul. Techol., VTC'93, pp. 633{636, Secucus, NJ, USA, My 993. [2] Fechtel, S.A. d Meyr, H. Mtched Filter Boud for Trellis-Coded Trsmissio over Frequecy-Selective Fdig Chels with Diversity. Europe Trs. Telecomm., Vol. 4, No. 3, pp. 09{20, My-Jue 993. [3] Fechtel, S.A. d Meyr, H. A ew Mobile Digitl Rdio Trsceiver Cocept usig Low-Complexity Combied Equliztio / Trellis Decodig d Ner-Optiml Receiver Syc Strtegy. I Proc. IEEE It. Cof. Persol, Idoor d Mobile Rdio Comm., PIMRC'92, pp. 382{386, Bosto, MA, USA, Oct. 992. [4] Forey, G.D. Mximum-Likelihood Sequece Estimtio of Digitl Sequeces i the Presece of Itersymbol Iterferece. IEEE Trs. Iform. Theory, Vol. IT-8, No. 3, pp. 363{378, My 972. [5] Mehl, R. d Meyr, H. Combied Equliztio / Decodig of Trellis Coded Modultio o Frequecy Selective Fdig Chels. I Coded Modultio d Bdwidth-Eciet Trsmissio, pp. 34{352, Tirrei, Itly, Sep. 99. [6] Moher, M.L. d Lodge, J.H. TCMP- A Modultio d Codig Strtegy for Rici Fdig Chels. IEEE J. Sel. Ares Commu., Vol. 7, No. 9, pp. 347{355, Dec. 989. [7] Prokis, J.G. Digitl Commuictios. McGrw-Hill, 989. [8] Suer-Gre, W. Optimle ud suboptimle Empfger fur verzerrte ud gestorte Dtesigle uter besoderer Berucksichtigug der ufwdsreduzierte Detektio mittels M-Algorithmus. PhD thesis, Kisersluter Uiversity, My 989. [9] Schlegel, C. d Costello, D.J. Bdwidth Eciet Codig for Fdig Chels: Code Costructio d Performce Alysis. IEEE J. Sel. Ares Commu., Vol. 7, No. 9, pp. 356{368, Dec. 989. [20] Ugerboeck, G. Chel Codig with Multilevel/Phse Sigls. IEEE Trs. Iform. Theory, Vol. IT-28, pp. 55{67, J. 982. [2] Vucetic, B. d Du, J. Performce Bouds d New 6-QAM Trellis Codes for Fdig Chels. I Coded Modultio d Bdwidth-Eciet Trsmissio, pp. 353{363, Tirrei, Itly, Sep. 99.