Techniques for Parameter Synchronization on Fading Channels

Transcription

1 echniques fo Pmete Synchoniztion on Fding Chnnels Stefn A. Fechtel, Achen Univesity of echnology, RWH-ISS, Pof. H. Mey, emplegben 55, 556 Achen, Gemny el , FAX , Intenet: Abstct In this ppe, we e concened with the clssifiction of eceive stuctues nd lgoithms fo sync pmete estimtion on both flt nd fequency-selective fding chnnels. he concept of synchonized detection, estblished vi the Byesin ppoch to optiml joint detection nd synchoniztion of messge busts, constitutes fily genel mthemticl fmewo nd lso pves the wy to implementble estimto-detecto type of eceives. he sync pmete estimtion stge cn be septed into the two tss of ML chnnel estimtion followed by MAP estimtion fom the ML estimte. When tining symbols e not vilble, online NA (non-dt-ided) estimtion is n effective mens of educing the complexity to n implementble level. he NA eceive pefoms 1 step chnnel pediction (one pedicto fo ech symbol suvivo) nd ecusive metic computtion bsed on the espective pedicto estimte. Retining only single suvivo leds to the simple (decision-diected) eceive stuctue. he chnnel pediction stge cn be bsed on eithe IIR Klmno FIR Wiene type filtes. Of pticul inteest e thei educed-complexity vints temed LMS-Klmn nd finite-length Wiene (flt fding) o LMS-Wiene (selective fding) lgoithms. When tining symbols e vilble, A (dtided) estimtion getly simplifies pmete synchoniztion. he estimto is esily sepble into tiningbsed ML chnnel snpshot cquisition nd finite-length Wiene filteing (intepoltion) of the snpshots. Fo the exmple of uncoded nd inteleved tellis-coded tnsmission ove flt fding chnnels, simultion esults demonstte the obust pefomnce of eceives using A pmete sync. 1 Intoduction With the dvent of vious pesonl nd mobile communiction systems, the theoy of optiml dt detection on ndomly fding chnnels hs gined enewed inteest. Bsic esults on optiml eceive stuctues hve ledy been obtined in the lte 5 s nd ely 6 s, see e.g. Kilth s ppe [9] fo good oveview. Although optiml detection on unnown o ndomly fding chnnels does not necessily equie explicit pmete synchoniztion, most pcticl eceive designs follow the concept of synchonized detection whee set of sync pmete estimtes is geneted (e.g. fme stt, timing, phse, fequency, fding tjectoy, etc.) nd then used in the detection pocess s if it wee the tue pmete set [14]. Amongst the mny possible epesenttions of the optiml eceive, we e theefoe inteested in those which explicity genete sync pmete estimtes nd subsequently pefom dt detection ming use of these estimtes [1]. As n impotnt step towds implementtion, the sync pmete estimtion stge of such estimtion-detection eceives my be septed into two distinct tss, viz. ML chnnel estimtion (ttempting to eliminte the dt modultion), nd MAP estimtion fom the ML estimte (ttempting to smooth the chnnel tjectoy). he Byesin ppoch to NA fding chnnel estimtion (non-dt-ided, no tining) usully entils n excessive computtionl lod. Some ecent ttempts to develop implementble lgoithms fo joint detection nd estimtion ssume slow fding so tht one my sech fo the dt sequence nd the chnnel tht yield the best (lest-sques) fit between hypotheticl chnnel output nd the eceived signl [16]. Recusive thus simplified nd suboptiml vints include the educed constelltion [17] o the quntized chnnel ppoch []. In this ppe, optiml nd educed-complexity vints of Byesin NA estimto detecto eceive stuctues e eviewed nd futhe developed fo the impotnt line Gussin cse. In pticul, we shll focus on online pocessing, i.e. ecusive decision metic computtion nd chnnel estimtion using only pst eceived smples. he online NA eceive stuctue is shown to encompss metic computtion nd suvivo selection unit which etins numbe of pomising cndidte sequences ( suvivos ), nd 1 step chnnel pedicto ssocited with ech suvivo. An impotnt membe of this eceive clss is the so-clled genelized Vitebi lgoithm [16] with pe-suvivo pocessing [1]. he simplest online NA eceive esults fom etining only single suvivo, i.e. ming instnt symbol decisions nd pefoming 1 step chnnel pediction (decision-diected) [8]. Fo optiml chnnel pediction, eithe Wiene o Klmn filtes cn be employed. We shll biefly discuss two of thei most inteesting educed- 1

2 complexity vints, viz. the finite-length Wiene (flt fding) o LMS-Wiene (selective fding) lgoithm nd the LMS-Klmn lgoithm, espectively. In the pesence of tining symbols (flt fding) o tining segments (selective fding), A chnnel estimtion (dt-ided) cn be employed wheeby pmete synchoniztion is entiely decoupled fom detection. Hence, eceive design is getly simplified, nd thee is much potentil fo pefomnce impovement though chnnel coding nd inteleving coss dt blocs. A popely designed messge fomt gin llows fo the seption of the estimto stge into ML snpshot cquisition fom the tining symbols (flt fding) o tining segments (selective fding) nd finite-length Wiene intepoltion of the snpshots. A pefomnce compison between eception of diffeentilly-encoded M PSK nd coheent A eception of uncoded M PSK shows tht both nd A eceptions e vible options in the cse of non-inteleved tnsmission. he ppe concludes with simultion esults on A eception of inteleved tellis-coded 8 PSK nd 16 QAM demonstting the potentil nd obust pefomnce of A pmete sync in the pesence of flt fding. Fding Chnnel nsmission Model We conside the tnsmission of bloc of N linely modulted, possibly encoded symbols = ( 1... N1), s it ises in MA-bsed (N finite) o qusi-continuous (N! 1) dt tnsmission. he flt fding chnnel weight pocess tjectoy is denoted by c = (c c 1... c N1 ), nd the set of selective chnnel impulse esponse (CIR) vectos by h = (h h 1... h N1 ). hen the tnsmission model fo the flt fding spced pulse mtched filte output signl z nd the model fo the selective fding = spced eceived signl become z = A 1 c + m (1) = A 1 h + n espectively, with ppopite dt mtices A. Moe genelly, let denote the obsevtion (eithe z o ), the unnown sync pmetes (eithe c o h), nd n the noise pocess (eithe m o n), so tht the geneic line tnsmission model cn be cst into the fom = A 1 + n () 3 he Byesin Appoch to Synchonized etection Optiml sequence detection [19] of clls fo mximizing the pobbility of, given the obsevtion ^ MAP = g mx P (j) (3) which collpses to ML detection ^ ML = g mx p(j) if ll e eqully liely. We conside the impotnt cse tht the sync pmetes of inteest e i) dynmic in the sense tht they e ten fom time vint (fding) ndom pocesses (hee c o h), nd ii) multivite complex Gussin ndom pocesses with nown men vecto nd covince mtix R, being dependent on the K fcto (Rice fding) nd the dynmics (opple spectum, opple cutoff fequency ) of the fding pocess, espectively. Assuming Gussin noise n with covince R n, the obsevtion = A 1 + n is line Gussin with men = E[] =A 1 nd covince R = E i h() 1 () H = AR A H + R n. hough lengthy nlysis, the loglielihood decision metic m () / log p(j) cn be efomulted [14] nd cst into the fom m () /() H R 1 () = ^ H () 1 61 () 1 ^ (4) () whee ^ () = +R A H 11 AR A H +R n (A ) 6 () =R R A H 11 AR A H +R n AR (5) e the MAP (subscipt ) sync pmete estimte nd its estimtion eo covince, espectively. his fom suggests the two-stge optiml estimtion-detection eceive following the pinciple of synchonized detection: 1. n explicit MAP sync pmete estimte ^ () (eq. 5) is geneted fo ech possible symbol sequence hypothesis,. this estimte is used to fom the decision metic m () (eq. 4 o ny othe equivlent fom). As long s the opple fequency emins well below the symbol tnsmission te 1=, i.e. = =(1= ) 1, the ML (subscipt S) estimte ^ S () = A H R 1 1 n A1 1 A H R 1 n 1 (6) 6 S () = A H R 1 1 n A1 of the sync pmetes themselves (N dim. flt fding pocess S = c) o some elted quntities (set of N N chnnel snpshots S = h ;...; h of the N1 selective fding pocess h, see below) exists. hen lin between the ML nd MAP estimtes cn be estblished [14] to be of the fom ^ () =N() 1 ^ S () +M() 1 6 () =N() 1 6 S () (if N() sque) he mtix N() which incopotes pio nowledge on chnnel sttistics, i.e., R nd R n is seen to ply n impotnt ole; it lins the ML/MAP estimtes nd, if the ML estimte of the sync pmetes themselves (7)

3 exist (flt fding) so tht N() is sque, it lso lins thei espective eo covinces. his my be temed the seption popety of MAP dynmic pmete estimtion in the sense tht MAP estimtion, conditioned on the dt, cn be pefomed by the two-step pocedue of 1. computing n ML estimte ^ S () fom the obsevtion, disegding ny nowledge on sttisticl chnnel pmetes,. computing the MAP estimte ^ () fom the ML estimte ^ S (), ming use of pio nowledge on sttisticl chnnel pmetes. he second step cn be simplified by dopping the men M() 1 of eq. 7 bove; usully, this does not entil significnt pefomnce degdtion [14]. Both the estimto-detecto eceive stuctue nd the simplified two-step pmete synchoniztion pocedue e visulized in Fig. 1 below. with metic incement 1m ; ( ) 'jz ^c 1 j LX ^h n; 1 n t fding selective fding chnnel estimtion stge of estimtion-detection eceive Θ ( S ) Θ ( ) ML MAP N 1m ; ( ) ' n= (9) whee L is the spn of the selective chnnel memoy in symbol intevls. Concening selective fding, it is d Stuctue of Estimtion-etection Receive with MAP Sync Pmete Estimtion vi ML Estimtion H -1 ( A R n A) -1. A H -1 R. n ML pmete estimte θ ( ) S N( ) MAP pmete estimte θ ( ) two-step sync pmete estimtion stge θ H -1 Σ θ detection stge decision metic m ( ) online NA 1-step chnnel pediction -1-1 Θ S;-1 Θ ; ML MAP -1 N Figue 1 Estimto-etecto Receive Stuctue nd wo-step Pmete Synchoniztion 4 Online Non-t-Aided (NA) Fding Chnnel Estimtion he computtionl complexity of optiml NA eception ises exponentilly with the messge length N since ll possible Q N messges must be tested (Q denotes the size of the symbol lphbet Q = M of uncoded M PSK o M QAM, o the numbe of llowed encoded symbol tnsitions). Also, the effot necessy fo optiml ML nd MAP estimtion (uppe pt of Fig. below) becomes excessive with incesing N. In the bsence of tining, ntul woound consists in online NA pocessing whee only dt =( 1... ) nd eceived smples = ( 1... ) up to the pesent time index e consideed fo metic computtion, nd 1, 1 up to time 1 used fo chnnel estimtion (centl pt of Fig., eq. 1). Obseving this cuslity constint, the lielihood p( j ) my be expessed in tems of p( 1 j 1), which leds to the ecusive metic updte [14] (metic to be minimized) m ; ( )=m ;1( 1) +1m ; ( ) (8) A chnnel estimtion Θ S, Θ, ML 1 N-1 MAP Figue Optiml, Online NA, nd A Chnnel Estimtion vntgeous to pefom pefilteing befoe pocessing the decision metic. Optimlly, the pefilte is the whitening mtched filte (WMF) [7, 11, 3], o equivlently, the cscde of mtched filte (MF), decimtion to symbol te, nd whitening filte (WF). he coesponding inne eceive is shown in Fig. 3; the extension to divesity eception is stightfowd [14]. he sync pmete set m (MF), w (WF) nd f (equivlent chnnel = cscde of CIR nd pefilte esponse) cn be computed fom the CIR h (hee: its estimte ^h ) nd the instntneous SNR pe symbol s;. In othe wods, the CIR estimte ^h nd the SNR constitute sufficient sttistics fo pmete synchoniztion, fct which undescoes the impotnce of chnnel estimtion. When pefilteing is employed, the metic incement is computed fom the WMF output v insted of, using the equivlent N 3

4 chnnel f n; in lieu of the physicl chnnel h n;, so tht LP 1m ; ( ) ' v f n; 1 n. Pefilteing is pticully effective when it comes to educing the numbe n= of suvivos which e etined t ny time instnt. he simplest such eceive etins single suvivo of instnt symbol decisions nd thus single ssocited (decision-diected) chnnel pedicto. Selective Fding Inne Receive (no ivesity) chnnel mtched filte (MF), decimto m ν; whitening filte (WF) iscete-equivlent nsmission System (including MF+WF pefilteing, without equlize) f v y w n; v h γs=1/n sync pmetes η (instnt. SNR γ s; ) equlize m w f Figue 3 Inne Receive using Pefilteing, nd Equivlent Selective Chnnel soft decisions (if possible) chnnel stte infomtion γ s; =E /N As bypoduct of the deivtion bove (leding to the ecusive metic) it lso follows tht the optiml online NA o chnnel estimte needed fo metic clcultion is given by the 1 step pedicto estimte [8, 14] (see lso Fig. ) ^c =^c j1 = E[c jz 1 ; 1 ] t fding ^h n; = ^h selective n;j1 = E[h n; j 1 ; 1 ] fding (1) In the flt fding cse, the ML estimte ^c S;1 = (^c S;... ^c S;1 ), i.e. the set of modultion-fee but noisy smples ^c S; =( 3=p )1z (whee p = j j )of the chnnel tjectoy exists, so tht the optiml MAP pedicto estimte is computed fom the ML estimte by length- Wiene filte w 1, i.e. ^c j1 = w 1 1 ^c S;1. he stightfowd method of simplifying the pedicto is to use n FIR Wiene filte of fixed length, i.e. ^c j1 = w 1 ^c S;1 (11) now with c S;1 =(c S;... c S;1 ) compising the ltest smples of the ML estimte. An ltentive ppoch is IIR-type line pediction. he optiml Klmn filte, howeve, is of high ode since the chnnel c is lso high-ode utoegessive pocess. By constining the Klmn filte to be fist-ode filte, one ends up with the LMS-Klmn lgoithm 1 ^c j1 =^c 1j + K 1 ^cs;1 ^c 1j (1) ttempting to smoothe the ML tjectoy pocess f^c S; g. he Klmn gin K cn be optimized s function of the eltive opple nd the noise powe [14]. Selective fding chnnel pediction cn liewise be chieved by IIR-type filteing; the coesponding fistode LMS-Klmn lgoithm is visulized in Fig. 4. Notice tht in ech filteing bnch the (nonexisting) ML Figue 4 LMS-Klmn Algoithm fo 1 Step Selective Fding Chnnel Pediction tp estimte hs been eplced by pseudo-ml tp estimte smples ^h S;n;1 which idelly epesent the modultionfee chnnel tp tjectoy fh n; g. A vint temed LMS- Wiene lgoithm cn be devised by eplcing ech of the IIR subfiltes of the LMS-Klmn by length- Wiene subfiltes w n ; this is illustted in Fig. 5. Both the set Figue 5 LMS-Wiene Algoithm fo 1 Step Selective Fding Chnnel Pediction of Klmn gins K n nd Wiene filtes w n cn be optimized s function of the eltive opple, the vege tp powe n = Efj h n; j g nd the noise powe. One finds tht, fo both flt nd selective chnnels, the LMS-Klmn lgoithm pefoms slightly bette fo vey low opple, while (LMS-)Wiene pediction is bette suited fo lge opple; the be-even point lies in the ode of =.3.1 (flt) nd.1.3 (selective chnnel) [14]. he BER pefomnce (nlysis nd simultion) of eceive with length-1 Wiene flt fding chnnel pediction is illustted in Fig. 6 fo low opple =.5 nd to 16 PSK. Chnnel pediction nd diffeentil encoding (in ode to be ble to tolete phse slips) e seen to cost few db s with espect to idel 4

5 sync, but NA o synchoniztion emin to be vible options lso fo dense symbol constelltions. Figue 6 BER Pefomnce of Receive with Length-1 Wiene Flt Fding Chnnel Pediction 5 t-aided (A) Fding Chnnel Estimtion he ide of A synchoniztion is illustted in the lowe pt of Fig. bove. Chnnel estimtion is bsed on the set of tining symbols nd eceived tining segments. hee e plenty slient dvntges to A chnnel estimtion [1, 14], the most impotnt being the fct tht detection nd synchoniztion e now totlly decoupled so tht coding nd inteleving (even coss sevel messge blocs) is mde possible without the need fo pemtue symbol decisions. In the bsence of chnnel dispesion, numbe N of tining symbols ;K nd coesponding eceived smples z ;K = c ;K 1 ;K + m K t time instnts K (K = ;...; N 1) e used fo pmete sync. he ML estimte ^ S; ( )=^c S = ^c S;...^c S;N1, i.e. the set of N 1 modultion-fee but noisy smples ^c S;K = ( 3 ; K =p ;K )1z ;K of the chnnel tjectoy, e smoothed nd intepolted by mens of length-n Wiene filte w in ode to obtin the MAP chnnel estimte ^c = w 1 ^c S, vlid t time instnt (Fig. ). Agin, n FIR filte w of fixed length < N my be used. In the cse of continuous tnsmission with tining symbols being unifomly spced pt by F symbol intevls, only set of F Wiene filtes w ( = ;...; F 1) is needed fo filteing nd intepoltion. When the chnnel is selective, the isolted tining symbols nd eceived smples must be eplced by tining sequences K nd coesponding eceived blocs ;K = A ;K 1h K + n ;K. ML estimtes ( snpshots ) ^ S; ;K ( )=^h S;K = ^h S;;K...^h S;L;K 11 = A H ; K R 1 n; K A ;K A H ; K R 1 n; K 1 ;K (13) exist s long s the tining sequences ;K hve minimum length L1. ML snpshot cquisition mes sense only when the fding is slow with espect to this bloc length L1 ( snpshot ssumption [4], i.e. the chnnel must be well undesped with sped fcto L1 1); this is stisfied fo ll elevnt chnnels nd dt tes consideed fo mobile dio nd PCS/PCN. Fom the set of N snpshots f^h S;K g, the MAP chnnel estimte is gin obtined vi Wiene filteing. Assuming tht the tining sequences ;K e pefect (o ne-pefect) sequences [4], the chnnel tps cn be pocessed individully, so tht the MAP tp estimtes t time instnt become (n =;...;L) ^h n; = wn; 1 ^h S;n;... ^h S;n;N1 (14) Get svings in computtionl complexity nd stoge esult fom using length- FIR filtes w n; nd pefoming MAP estimtion only fo set of some selected time instnts nd then use line intepoltion to obtin the othe estimtes, if necessy. In fct, the sme method should be pplied to pmete synchoniztion s well, i.e. the sync pmete set m (MF), w (WF) nd f (equivlent chnnel) of Fig. 3 bove e lso computed fom h only fo some time instnts nd then linely intepolted. 6 Pefomnce of nd A Reception fo Flt Fding he BER pefomnce (nlysis nd simultion) of coheent eceive with length-1 Wiene A flt fding chnnel estimtion bsed on tining symbols with unifom spcing F =11 is illustted in Fig. 7 fo low opple =.5 nd uncoded to 16 PSK. Simil esults hve lso been obtined fo lge opple =.5, spcing F =4, nd dul divesity eception. A comptive study of eceives with nd A selective chnnel estimtion is cuently unde wy; the esults obtined so f coobote the findings nd conclusions pesented hee fo the flt fding cse. Genelly, the pefomnce of A sync is compomized by the insetion of tining symbols; the powe nd bndwidth efficiency eduction fcto of (F 1)=F (hee = 1/11) hs been included in Fig. 7. Nevetheless, A eception hs been found to be supeio in tems of powe efficiency (simulted SNR) fo ll of the scenios investigted. Also, nlysis nd simultion gee much bette thn fo chnnel estimtion; this cn be ttibuted to detimentl 5

6 effects (such s eo popgtion) of sync not coveed by the nlysis. As mentioned befoe, A pmete sync is pticully well suited to suppot inteleved chnnel coding. Conside, fo exmple, the system of Fig. 9 employing tellis coded modultion with bloc inteleving. he Flt Fding nsmission System with Inteleved CM b i ellis Encode, Modulto F I*F S n z c bloc inteleve flt fding chnnel z inne eceive soft decisions CSI F I*F CSI Vitebi ecode b i finl bit decisions q feedfowd A sync bloc deinteleve Figue 7 BER Pefomnce of Receive with Length-1 Wiene A Flt Fding Chnnel Estimtion Fig. 8 compes nd A eception in tems of both powe nd bndwidth efficiency, bsed on the SNR (pe bit nd chnnel) needed fo (simulted) BER of.1. Fo low opple ( =.5), nd lso fo high opple ( =.5) without divesity, A eception emins to be supeio, while eception cn become supeio fo high opple nd dul divesity. Figue 8 BER Pefomnce of Receive with Length-1 Wiene A Flt Fding Chnnel Estimtion Figue 9 nsmission System with Inteleved CM Chnnel Coding nd A Reception input bits b i (index i: non-inteleved time scle) e tellis-encoded nd mpped onto PSK o QAM dt symbols which e witten ow-wise into the bloc inteleve mtix. Afte dding tining symbols fo A chnnel estimtion, the chnnel symbols (index : inteleved time scle) e ed out column-wise fo tnsmission. In the eceive, both the soft decisions ^ nd the CSI s; e deinteleved nd used fo Vitebi decoding. he inteleve depth, being multiple IF of the fme length F, should be sufficiently lge so s to effectute neidel inteleving. Also, the inteleve length is equl to the suvivo depth of the Vitebi decode. his choice is lso dvntgeous in the context of combined decoding nd equliztion [5, 13] of selective chnnels. wo tellis codes with lge effective code length (ECL) hve been selected. Both codes convey two infomtion bits pe symbol nd e theefoe compble (in tems of bndwidth efficiency) with uncoded 4 PSK. he fist code ( 8 PSK ) is te-/3, 16 stte 8 PSK Ungeboec code [18] with ECL 3. he second code ( 16 QAM ) by Mohe nd Lodge [15] is te-1/, 16 stte, 4 PAM (16 QAM) code with ECL 5. Fig. 1 shows the BER simultion esults fo 8 PSK nd 16 QAM tellis coded tnsmission ove flt Ryleigh chnnels with =(.5.5) nd A eception with unifom smpling nd F =(11 4), long with the symptotic mtched filte lowe bounds (MFB) fo these codes [, 6]. he 16 QAM code is most effective, especilly when ntenn divesity is not vilble. hns to the lge ECL of 5, the BER decys s fst s one decde pe db SNR, nd BER of 1 is chievble t (8. 9.9) db SNR pe bit ( =(.5.5)), which is supeio to the 8 PSK code by bout 1.5 db. With dul divesity, the 16 QAM code emins to be supeio to the 8 PSK code (by bout.7 db), nd BER of 1 is 6

7 chievble ledy t ( ) db SNR pe bit nd chnnel. Comped with uncoded 4 PSK see lso Fig. 8 bove whee the powe nd bndwidth efficiencies of uncoded M PSK nd CM 16 QAM e comped, the 16 QAM code yields gins s lge s 7 db without divesity nd still bout 3 db with dul divesity. Hence, t the expense of complexity nd some ltency, well-designed tellis coded modultion, combined with A pmete sync, cn considebly impove on the powe efficiency. Figue 1 BER Pefomnce of nsmission System with A Reception nd CM Chnnel Coding 7 Conclusions Pmete synchoniztion fo eceives following the concept of synchonized detection hve been discussed, in pticul, optiml MAP estimtion, nd online NA,, nd A chnnel estimtion fo both flt nd selective fding chnnels. Both nd A eception e vible options fo uncoded M PSK tnsmission, lthough the ltte hs n dvntge in most cses of inteest. A pmete sync is the method of choice when it comes to inteleved chnnel coding. Bibliogphy [1] Cves, J.K. nd Vldi, J. Cochnnel Intefeence nd Pilot Symbol Assisted Modultion. IEEE ns. Vehicul echnol., 4(4):47 413, Sept [] Cl, M.V. et l. Mtched Filte Pefomnce Bounds fo ivesity Combining Receives in igitl Mobile Rdio. In Poc. Globecom, pges , ec [3] Fechtel, S.A. nd Mey, H. An Investigtion of Ne- Optiml Receive Stuctues Using the M-Algoithm fo Equliztion of ispesive Fding Chnnels. In Poc. EUSIPCO 9, pges , Bussels, Belgium, Aug [4] Fechtel, S.A. nd Mey, H. Optiml Pmetic Feedfowd Estimtion of Fequency-Selective Fding Rdio Chnnels. IEEE ns. Commun., 4(/3/4): , Feb./M./Ap [5] Fechtel, S.A. nd Mey, H. Combined Equliztion, ecoding nd Antenn ivesity Combining fo Mobile / Pesonl igitl Rdio nsmission using Feedfowd Synchoniztion. In Poc. IEEE Int. Conf. Vehicul. echnol., VC 93, pges , Secucus, NJ, USA, My [6] Fechtel, S.A. nd Mey, H. Mtched Filte Bound fo ellis-coded nsmission ove Fequency-Selective Fding Chnnels with ivesity. Euopen ns. elecomm., 4(3):19 1, My-June [7] Foney, G.. Mximum-Lielihood Sequence Estimtion of igitl Sequences in the Pesence of Intesymbol Intefeence. IEEE ns. Infom. heoy, I-18(3): , My 197. [8] Häb, R. nd Mey, H. A Systemtic Appoch to Cie Recovey nd etection of igitlly Phse-Modulted Signls on Fding Chnnels. IEEE ns. Commun., 37(7): , Jul [9] Kilth,. Optimum Receives fo Rndomly Vying Chnnels. In Poc. 4-th London Symposium on Infomtion heoy, Buttewoth Scientific Pess, London, pges 19 1, [1] Kilth,. A Genel Lielihood Fomul fo Rndom Signls in Gussin Noise. IEEE ns. Infom. heoy, I-15, My [11] Lee, E.A. nd Messeschmitt,.G. igitl Communiction. Kluwe Acdemic Publishes, [1] Lin, J., Ling, F., nd Pois, J.G. Joint t nd Chnnel Estimtion fo MA Mobile Chnnels. In Poc. PIMRC, pges 35 39, Oct [13] Mehln, R. nd Mey, H. Combined Equliztion / ecoding of ellis Coded Modultion on Fequency Selective Fding Chnnels. In Coded Modultion nd Bndwidth- Efficient nsmission, pges , ieni, Itly, Sep [14] Mey, H., Moenecley, M., nd Fechtel, S.A. igitl Communiction Receives Synchoniztion nd Chnnel Estimtion Algoithms. John Wiley. to be published [15] Mohe, M.L. nd Lodge, J.H. CMP- A Modultion nd Coding Sttegy fo Ricin Fding Chnnels. IEEE J. Sel. Aes Commun., 7(9): , ec [16] Seshdi, N. Joint t nd Chnnel Estimtion using fst blind ellis Sech echniques. In Poc. Globecom, pges , ec [17] Seshdi, N. Joint t nd Chnnel Estimtion Using Blind ellis Sech echniques. IEEE ns. Commun., 4(/3/4):1 111, M./Ap./My [18] Ungeboec, G. Chnnel Coding with Multilevel/Phse Signls. IEEE ns. Infom. heoy, I-8:55 67, Jn [19] vn ees, H.L. etection, Estimtion, nd Modultion heoy Pt I. John Wiley, [] Zevs, E., Pois, J., nd Eyuboglu, V. A Quntized Chnnel Appoch to Blind Equliztion. In Poc. ICC, pges , Jun