08/20/99 1 T1E1.4/99-333R1. Title: Soft Cancellation via Iterative Decoding to Mitigate the effect of Home-LANs on VDSL (333R1)

Transcription

1 08/0/99 TE.4/99-333R Project: TE.4: VDSL Ttle: Soft Cancellaton va Iteratve Decodng to Mtgate the effect of Home-LANs on VDSL (333R) Contact: Date: Dst'n: K. Cheong, J. Cho, J. Fan, R. Neg, N.Wu and J. Coff, Dept of EE, Stanford U., Stanford, CA , F: Thans to co-source research supporters: AMD, GTE (GS), IBM, Intel, Samsung AIT, SK Telecom, and TI August 3, 999 TE.4 Abstract: Prevous contrbutons [], [] have reported on the performance of a maxmum-lelhood based jont detecton of VDSL sgnals and Home LAN sgnals that share the frequency band between 5 and 0 MH. The methods descrbed were promsng n that they show t s possble to mtgate the effect of a Home LAN sgnal on VDSL almost entrely f a small fracton (3%) of the VDSL band was judcously slenced to assst the detector. These prevously presented optmum recevers for multuser crosstal were prohbtvely complex. Ths contrbuton ntroduces on a low-complexty teratve-decodng structure nown as "Soft Cancellaton" that can be used to obtan almost the same level of performance wth a recever complexty that s the same order as conventonal equalers. The method s very general and could be used on a number of dfferent types of crosstalers. Specfc nvestgaton nto the area of Home LAN nterference nto VDSL shows no mpact on VDSL of the Home LAN f Soft Cancellaton s used and the 3% band slencng s mantaned. NOTICE Ths contrbuton has been prepared to assst Standards Commttee T - Telecommuncatons. Ths document s offered to the Commttee as a bass for dscusson and s not a bndng on any of the companes lsted as authors. The requrements are subject to change after further study. The authors specfcally reserve the rght to add to, amend, or wthdraw the statements contaned heren.

2 08/0/99 TE.4/99-333R Soft Cancellaton va Iteratve Decodng to Mtgate the effect of Home-LANs on VDSL (333R) K. Cheong, J. Cho, J. Fan, R. Neg, N.Wu and J. Coff Department of Electrcal Engneerng Stanford Unversty, Stanford, CA Phone: Fax: Introducton: Spectrum management has come to be of paramount mportance n DSL employment as unbundlng and explotaton of the dormant enormous bandwdth of the twsted par have become a realty. Spectral crowdng of varous servces on the twsted par n terms of avalable bandwdth has been a consequence of severe crosstal-couplng penaltes between lnes. It s often a dffcult trade-off between bandwdth avalable for dfferent crosstalng servces, perhaps nowhere more pronounced than n the potental nterference of Home LANs nto VDSL. Averson of severe performance loss n VDSL s possble through the use of multuser detecton and nformaton theory concepts. The concepts requre advancement from the current state of DSL technology and understandng to encompass the code-dvson and advancedrecever archtecture concepts that have been successfully deployed n wreless communcatons. Full optmum detecton has often been used to demonstrate ultmate lmts of transmsson, only later to be followed by the observaton n mplementaton that a number of approxmatons can be used to obtan near optmum performance wth sgnfcantly less complexty. Multuser Detecton (MD) s one such recever technque that can be mplemented optmally at enormous complexty or can be approxmately optmum at low complexty. The reducton n complexty can be partcularly pronounced n MD f suboptmum teratve-decodng methods are used nstead of jont maxmum lelhood. The partcular concept used here s called "Soft Cancellaton" and s llustrated n Fgure for the smple case of detecton of ndependent messages that somehow collde on the nput to a sngle recever. Decoder attempts to compute the equvalent of a probablty for each of the possble values for the frst message. The resultant dstrbuton may be very easy to decode when t s narrowly centered on one value as very lely. However, the presence of the second data message may obscure the frst and thus the computed probablty dstrbuton may not heavly favor a partcular message value ntally. The reader wll recogne ntersymbol nterference as an example. However, the collson of messages can be nstead from multple sources and so the nterference between symbols may not correspond to a tme-doman convoluton wth a nown channel response and nstead can more generally be any lnear combnaton of the two message symbols. However, the ntal probablty dstrbuton for the frst user can be nput to a second decoder for the second user, whch n turn attempts to also compute the equvalent of a probablty dstrbuton for the second message. The dstrbuton on the frst message leads to a better dstrbuton for the second user's transmtted symbols than would be attanable wthout ths extraneous nformaton from the frst decoder. In turn, ths second dstrbuton can be returned to a second pass of the frst decoder that can now produce a better probablty dstrbuton than on ts frst executon. The process can proceed ether for a fxed number of teratons or untl there s no change n the symbols that would be decded by choosng the values wth maxmum probablty value. Whle ths process has no formal proof of convergence, a number of studes have found that under certan condtons ths process conforms to well nown convergent algorthms n artcfcal ntellgence [3]. Ths type of suboptmum decodng has been used successfully n the so-called "Turbo Codng" area, where one sees the reason for the name "Turbo" n the decoder. When ths process can be made to converge, the result s spectacular - codng gans approachng wthn epslon of the Shannon lmts for both sngle and multuser systems, essentally achevng the hgh performance of the optmum

3 08/0/99 3 TE.4/99-333R detector at a complexty that s both acceptable and at least bllons of tmes less complex than the optmum detector. Secton ntroduces channel models and basc algorthms, provdng nsght nto how teratve decodng wors and how t avods the error-propagaton problem that s nherent n exstng multuser detectors.. Secton 3 then shows the complete mtgaton of a home LAN on VDSL where the performance loss wth a conventonal VDSL recever would have been prohbtve.. Multuser Channels and Bascs The concept of multuser detecton s well summared n [4] where optmum detectors and varous suboptmum structures are nvestgated. The problem to date wth DSL channels and other dffcult channels s that the methods n [4] ether are too complcated n the case of optmum detectors or suffer catastrophc brea-down from error propagaton n the case of the sub-optmum structures. The latter brea-down led to the studes that provde the alternatve algorthms of ths paper that have complexty close to that of the prevous sub-optmum structures, but avod mang decsons and nstead teratvely propagate probablty dstrbutons that eventually lead to decsons, but also allow nterference cancellaton. Secton. models the multuser channel and provdes some motvaton examples of models n the context of the detaled Home LAN nto VDSL stuaton. Secton. presents the optmum ML detectors for both a sequence and a symbol and suggests ther performance s good, f some common bandwdth can be slenced by one of two users, but also ndcates complexty can be hgh. Secton.3 motvates soft cancellaton by showng the lower complexty of well-nown multuser recever archtectures, but also notes the error propagaton problem. Secton.4 then can easly follow for the reader wth the teratve-decodng fx to the error propagaton problem, allowng essentally performance of the optmum detector at vastly reduced complexty. Secton.5 dscusses ntalaton of algorthms.. Multuser Channel Modelng The nterference problem can be consdered abstractly for two users usng the followng framewor: y = H x + H x + where the vectors x and x correspond to vectors of sgnals from some dscrete sgnallng constellaton. The vector y contans the receved samples, the matrces descrbng the channel between the user nputs and the channel output are H and H respectvely, and n s a nose vector. The problem can be easly x or by consderng all "other generaled to any number of users by addng components le H x users" as part of a larger vector component. When dfferent users are not synchroned, the matrces H m can vary wth tme - ths analyss consders one bloc n tme only and thus need not propagate a tme-ndex notaton. Mutple phase-loc loops are need n the practcal case of unsynchroned clocs so that the proper H matrces at each bloc n tme can be used n the above model. Perfect nowledge of the matrces H and H s assumed. The goal s then to decode the vector x (and possbly the vector x also n the general case) based on the receved sgnal y. The sgnal H s sometmes treated as an nterferng sgnal, whch prevents the decodng of the sgnal component x. Rather than treatng ths sgnal component merely as nose, a recever can sgnfcantly mprove performance by jontly detectng the vectors x and x. x n H m m

4 08/0/99 4 TE.4/99-333R A generalaton s used n the followng where t s observed that all nputs can be decoded as part of gant detecton problem that s wrtten as x y = H x H [ H ] + n = x + n where all of the nputs n the vector x are detected. In such detecton, each dmenson can be consdered ndvdually wth all other dmensons beng alternate or "other" users n an teratve decodng scheme. Ths modelng s captured also n Fgure where perhaps the pcture maes the mathematcs less abstract. x H Xmt (x Lne channel, H ) + Nose, σ, n y DSL rcvr Xmt (x )... Xtal flterng, H + Xmt L (x L ) Xtal flterng, H L Fgure - Illustraton of crosstal stuaton. The set of crosstalers can all be consdered as havng one large nput vector x and a matrx channel H, the latter of whch usually has fewer output dmensons than nput dmensons. If the nose s small enough, and the matrx H s (as always n practce) -to- for the dscrete fnte set of possble nputs, then the recever can relably recover all the nput symbols. Some examples are provded here: DMT VDSL: In a DMT VDSL system wth H-wde tones (4 H symbol rate) spannng about 8.83 MH of bandwdth usng transmt bloc se of cyclc extenson, the matrx H would be a 048 (complex) dagonal matrx and x would be a (complex) 048-dmensonal nput vector wth the channel nput for each tone n the respectve dmensons. A maxmum-lelhood detector smply decodes each subchannel drectly by smple slcng after dvson by the correspondng dagonal element of H on each

5 08/0/99 5 TE.4/99-333R subchannel. If there s no crosstal, then H = 0. Ths s basc DMT and would have H = H = dag channel FFT 0. [ ( ) ] QAM LAN (or VDSL) In a 4-QAM transmsson system wth 4 MH symbol rate (data rate 8 Mbps) centered on 7.5 MH, the matrx H would be a Toeplt convoluton matrx (or f an equaler s appled, a dagonal matrx, but we do not use ths dagonalaton here). The matrx H over the perod of one 4 H DMT symbol n the above example would have exactly 000 samples at symbol spacng of the QAM system. H would be a 048 by 000+ν length complex convoluton matrx where ν s the length of the channel. Ths channel could be the twsted-par drect channel from transmtter to recever n a Home LAN or t could be the crosstal couplng channel between such a transmtter and a VDSL transmtter, dependng on the problem beng addressed. We assume the latter for the examples n ths paper. In ths case, the channel model s H = [ 0 H = FFT( Toeplt( xtal - channel FFT) )] wth no VDSL present. An optmum detector n ths case s too dffcult to mplement, but well-nown decson feedbac methods or other equalaton structures mght be used to decode x. Combnaton of both: In ths case of both sgnals n the prevous two examples present, the combned channel model s [ H = dag channel FFT) H FFT ( ( xtal - channel FFT) )] H = = ( Toeplt and the jont maxmum-lelhood detector wll be yet more complex. Smple equalaton or DFE structures wll not wor because the problem of whch symbol value n the DMT or QAM system to decde frst s dffcult, there are many choces, and lely none of those choces wll be correct. Ths s the area where soft-cancellaton s needed most n Secton.3.. Optmum Detecton The optmum detector [], [4] for the multuser channel selects (f nose s whte, f not prewhten the nose wth matrx transformaton, whch s typcally a dagonal scalng matrx n the DMT case llustrated n the above examples) that nput vector x that mnmes { mn y xˆ } x = arg H. xˆ Ths s the well-nown Maxmum Lelhood (ML) sequence (or bloc) detector and the probablty of mang an error n the bloc of symbols detected s mnmum. The soluton s easy n concept and straghtforward to wrte, but may nvolve a search of ncredble numbers of values for the jont nput and thus be not feasble. The soluton s called ML because the value chosen actually maxmes a "lelhood" functon that s the condtonal probablty dstrbuton of the channel output bloc y gven the nput bloc x. Ths lelhood functon s often wrtten n logarthmc form as ( ) L y / x = log p y / x. The performance s largely determned by a mnmum dstance that s found by the expresson mn = mn H x H xˆ d. xˆ x

6 08/0/99 6 TE.4/99-333R Ths mnmum dstance (or dstances very close to t) domnate the well-nown probablty of error approxmaton where e P d N mn e e, Q σ N s the number of nearest neghbors at (or near) the mnmum dstance. The probablty of error mnmed, however, s not the mnmum for each symbol value, a fact often gnored wthout penalty n detecton theory, but whch surfaces as more mportant n soft-cancellaton methods. To mnme the probablty of error for a partcular symbol value (when all symbol values are equally lely), nstead the recever should maxme ( p ) L y / x = log y / x that corresponds to the same channel output vector, but condtons only upon the symbol of nterest. Ths better probablty dstrbuton s derved from the full bloc condtonal channel dstrbuton by averagng the effects of all the other nputs. A detector may try to approxmate the above probablty or lelhood functon pror to mang a decson on whch symbol value maxmes t, whch then s the symbol most lely to have been transmtted (and thus least lely to be n error). The soft canceller wll try to teratvely approxmate ths probablty, whch s actually easer to approxmate than the bloc-level probablty..3 Lnear Multuser Detectors Verdu and others (see [4] and references theren) have studed multuser detecton at length and have extended the basc lnear equaler structures often found for ntersymbol ntereference n sngle-user detecton to the multuser case. The lnear flters become matrces, but the concepts are dentcal to those famlar wth varous equalaton structures. Decson-feedbac s the best-performng of these lnear equaler structures, but s predcated upon correct decsons beng used for subsequent decsons. For lnear sngle-user channels, sometmes ths assumpton breas down and error propagaton effects force the use of precoders, devces that essentally move the process of subtracton of prevous decsons nterference on the current decson to the transmtter. These precoders cannot be used n the multuser case n practce because the transmtters for dfferent sgnals are not co-located. Varous orderng schemes for decsons have been studed, but franly, none really wor. Error propagaton defeats multuser decson feedbac n practce and magnfes the problems slghtly present n sngle-user detecton, but overwhelmngly present n the multuser case. If one s prepared to observe the whole bloc frst, t s possble to subtract the nterference from all other symbols f decsons for those symbols somehow exst from some prelmnary recever. Ths s called "Lnear Cancellaton" for the sngle-user case and was studed by Gersho and Lm [5]. Lnear cancellaton has a theory that predcts t actually wors better than optmum when all decsons are correct, so clearly error propagaton s a major effect and lnear cancellers have not been used because of ths effect. However, havng acnowledged all the error propagaton problems wth DFE's and Lnear Cancellers, the basc concept may llustrate a drecton to proceed. The basc equaton n the multuser case can be rewrtten for each channel output dmenson as y j = L = h where j s an ndex for the channel output (whch we can thn here as the DMT tone ndex) and s an ndex for the channel nput vector (whch we can thn here as runnng frst over all the the DMT channel nputs for VDSL and then over the 000 QAM nputs for the Home LAN, yeldng a maxmum of x + n j

7 08/0/99 7 TE.4/99-333R L=3048+ν possble entres n each sum). A recever that had all the other decsons except for subtract the nterference to determne: Then, a decson for ( lcan) = y j xˆ. x easly follows by computng h x could, xˆ = usng only the j= channel output h, dmenson. Other channel output dmensons could be used f x s nown to affect these dmensons, and then the decson generales to testng all the values for x and selectng that closest n dstance to the vector of correspondng j, 's. Clearly, f any of the other decsons s wrong, catastrophc propagaton of errors s possble dependng on the h, values. One s left wth tryng to decde whch nput to decde frst. Furthermore, the concept of j causalty and mnmum phase desred n sngle-user DFE's may be very dffcult to establsh wth multple users. However, suppose nstead of computng only the probablty dstrbuton of j, j, based on a decson that the recever computed and then used that probablty dstrbuton n turn to compute the probablty dstrbuton of the other channel nputs. The result s ntroduced here under the ttle of "soft cancellaton," and of whch there are many forms and approxmatons that can reduce error propagaton so much that the detector performs almost as well as the optmum ML detector for each symbol value..4 Soft Cancellaton For soft cancellaton, the recever needs two quanttes that can be computed from a dstrbuton (n ths case a condtonal dstrbuton of x based on the observaton of the entre sequence y, the average value or soft symbol χ = Ex / y ( x ) and the correspondng varance about ths mean value ε = y x χ. E x / ( ) Ths dstrbuton, or equvalently the two quanttes above, can be approxmated by usng the mean value for other symbols n the lnear-canceller expresson above nstead of decded values, thus avertng most of the negatves of error propagaton. The ndependence assumpton: Each of the channel output dmensons clearly are not ndependent unless the matrx H s dagonal. Nonetheless, snce soft-caneceller algorthms wll approxmate lelhood functons and probablty denstes n any case, ths analyss assumes they are ndependent only n so far as the decomposton of the overall Lelhood functon as N L y / x ( a) = L ( a). (L) j= Ths expresson denotes the possble values for the th symbol as a. A more complcated expresson nvolvng the channel matrces and couplng would otherwse have to be approxmated wthout ths ndependence assumpton. Our experments repeatedly show that ths ndependence assumpton does not prevent the convergence of the soft canceller. Note many of the entres for the j h, wll be small or ero so there are often only a relatvely small number of entres n each sum that matter.

8 08/0/99 8 TE.4/99-333R Assumng a set of ntal soft symbol values exstng, the soft canceller then frst executes the cancellaton step = y h χ j, where the decson on other symbols s replaced by the soft symbol value. The objectve s to compute an estmate of L ( a) from j,. For each possble symbol value a for x, the recever can also compute for each tone w ( a) h a =, whch s an estmate of the nose on the j th output dmenson. The quantty w s dstrbuton-le n that t assumes a value for each a. The value of a for whch w has mnmum magntude s the most lely decson. If one assumes ths nose estmate s Gaussan (because the nose s Gaussan and t approxmates the nose), then the varance of ths term can be computed (the mean s assumed ero) to specfy the Gaussan dstrbuton as σ = σ j + h h Ths varance and the values for a allow approxmaton of the true dstrbuton. The subchannel lehood functon s then [ w j ( a) ] L ( a) = log π σ e ε, σ j, for a complex Gaussan random varable. The subchannel terms can be summed over j for each nput symbol value to form the overall lelhood functon as n (L). Equvalently, one can form the product of the ndvdual probablty dstrbutons to get the overall probablty dstrbuton. p / x Snce the overall probablty dstrbuton y s proportonal to the probablty dstrbuton x / y by terms that only depend on the value of y, and snce the nput dstrbuton for each symbol s unform, the new soft symbol value for a subsequent teraton s then computed accordng to and the varance about ths mean value s then a p a = p a y / x y / x ( a) χ (La) ( a) ( a χ ) p ( a) ( a) a ε =. (Lb) p a y / x Havng computed these two quanttes, the soft symbol and ts varance, for each symbol value x, the algorthm can proceed to a subsequent nteraton, where, w, and L values are agan computed. At some pont n tme the teratons can be stopped (n practce 6-0 teratons s enough) and hard decsons made from the lelhood functons on all symbols. An excepton procedure s used to delete lelhoods that may falsely contrbute too much to the overall lelhood. If the denomnator above n (L) s below a threshold and too close to ero, the probablty of y y / x, p

9 08/0/99 9 TE.4/99-333R s small, meanng the nformaton s unrelable and so the soft value s eroed for the next teraton. We found ths smple chec to have a sgnfcant mprovement on the convergence of the algorthm..5 Intalaton of Soft Symbol The authors have found the psuedonverse to provde a good ntal soft bt nformaton for the teratve decodng process, whch s computed accordng to ( * ) = H * HH y and then computng = + f f f < χ. > The matrx H s nown and often sparse so the nverson can be low complexty n practce..6 Synchronaton and Channel Identfcaton Most home LAN sgnals are pacet based and have synchronaton and tranng patterns at the begnnng of each pacet. If the LAN sgnal s sgnfcantly hgher than the bacground nose, then t s of concern to VDSL. Further, f t s ths large, then synchronaton and dentfcaton of the crosstalng channel can be acheved. Phase locng s acheved perhaps most smply by bandpass flterng the result of nonlnear operatons on the receved sgnal at 4 MH baseband. In the presence of VDSL, a more sophstcated and relable method s to cross-correlate the nown synchronaton pattern n baseband aganst a complex demodulated verson of the channel output for several conjectured phase offsets. The maxmum offset s then nput to a dgtal phase loc loop for use n nterpolaton receved sample values n formaton of a matrx H, whose rows are also determned by the result of the cross-correlaton sequence (dvded by the nown QAM nput channel energy). In the presence of VDSL, the channel ID and synchronaton can be readly acheved, but a symbol perod or two of DMT delay s necessary so that these corrupted VDSL DMT pacets can use the soft canceller wth χ replaced by the nown tranng values. Thus, teratve decodng s not necessary when the Home LAN sgnal s tranng, but some of the dormant computng power needed for nteratve decodng needs to be appled to cloc extracton and channel ID. 3. Some results for Home LAN nterference nto VDSL The followng smulatons show the performance of the proposed teratve decoder when copng wth Home LAN nterference nto VDSL. Fgure 3a and 3b show the VDSL channel response for varous VDSL lne lengths, and the Home LAN spectrum mas used. Smulatons were performed for VDSL lne lengths rangng from 00m to 700m. Fgure 3 shows the Home LAN cross-tal channel that nterferes wth VDSL. The Home LAN sgnal s 4Mbaud, 4QAM occupyng the bandwdth 4 to 0MH. VDSL s 56 tones, wth a 69H tone spacng. In the band affected by Home LAN cross-tal, the constellaton se for VDSL s 4QAM. In the smulaton, only whte gaussan nose of PSD -40dBm/H s consdered. The transmt power for Home LAN s about -70dBm/H whle that for VDSL s -60dBm/H. Frst an ML chec s used wth 6 tones slenced (about 3% bandwdth loss) where the crosstal s largest and the result s llustrated n Fgures 4 and 5 for 4 Mbps and 8 Mbps Home LANS respectvely. The ML detector has essentally no loss wth respect to performance f no home LAN sgnal were present n ths practcal stuaton.

10 08/0/99 0 TE.4/99-333R Fgure 3(a) - Inserton loss of loops used n study. Fgure 3b - Spectrum of Home LAN sgnal.

11 08/0/99 TE.4/99-333R Fgure 4 - Coexstence of 4 Mbps, MH-symbol-rate QAM home LAN wth DMT Fgure 5 - Coexstence of 8 Mbps, 4 MH-symbol rate QAM HPL wth DMT VDSL.

12 08/0/99 TE.4/99-333R The teratve decoder wors on ndvdual VDSL blocs. It consders 88 tones of VDSL for each bloc. Ths produces 88 VDSL DMT tone subsymbols and 58 Home LAN QAM symbol ponts n a bloc. Ths jont set of samples consttutes the sgnal x. Also, a certan number m of VDSL tones are nulled wthn these 88 tones. For m= nulled tones, tones 3 and 3 are nulled; for 4 nulled tones, tones 30:33 are nulled; for 6 nulled tones, tones 9:34 are nulled; for 8 nulled tones, tones 8:35 are nulled. The home LAN affects tones 59 to 46. In general for arbtrary crosstalng functons, the tones wth the largest amount of crosstal nose should be nulled and these may not correspond to consecutve tone frequences n / 49 0 f 3. 5 general. In ths wor, we assumed the Amercan crosstalng model of ( ) wth lnear phase for the couplng channel. The wor s not very senstve to the choce of crosstalng functon's shape as long as ths shape s nown. Besdes the teratve decoder descrbed n Secton, another varant of the decoder s used, whch can be called bloc ML soft canceller. Ths s smlar to the soft canceller except that a lelhood functon s calculated for blocs of or more symbols nstead of a sngle symbol. The cancellaton s stll done wth the soft bts. Thus t s a compromse between a full-blown maxmum lelhood and soft cancellaton. Another feature s the ncluson of a smple error detecton scheme. If the lelhoods for all the possble transmtted sequences n a bloc are below a set threshold, ths ndcates that the nterference estmaton s naccurate. In ths case, the soft bt s set to ero for the next teraton. In the smulatons, a bloc se of s used. The number of teratons used for the teratve decodng ranges from 6 to 0. About 5000 VDSL blocs were transmtted for the smulatons presented. Fgure 5 shows the bt error rates obtaned when the soft canceller teratve decoder s used for varous VDSL lne lengths and varous number of nulled tones m. Ths plot does not assume any FEC. Fgure 6 shows the same result when a (00,84) RS code s appled. Fgure 7 shows the bt error rates obtaned when the bloc ML soft canceller teratve decoder s used for varous VDSL lne lengths and varous number of nulled tones m. Ths plot does not assume any FEC. Fgure 8 shows the same result when a (00,84) RS code s appled. For small lne lengths (00m) or large lne lengths (700m), there s a large dfference between the VDSL and HPNA sgnal powers, and so the teratve decoder performs excellently, gvng very low error rates. However, even n the dffcult case of lne length 500m, where the two sgnal powers are roughly equal, the teratve decoder gves low error rates. The bloc ML soft canceller performs better than the standard soft canceller. For purposes of ths contrbuton, the mportant ssue of synchronaton s not addressed and the VDSL sgnal pacet boundary wth respect to the 58 QAM-symbol pacet s not drectly addressed, however the mathematcs s suffcently general to encompass the stuaton of the phase rotaton of the crosstalng channel that would correspond to an offset n the clocs of the two systems.

13 08/0/99 3 TE.4/99-333R Fgure 6 - Bt error rate canceller for soft canceller wthout FEC. Fgure 7 - Bt error rate for soft canceller wth FEC.

14 08/0/99 4 TE.4/99-333R Fgure 8 - Four dmensonal soft canceller wthout FEC. Fgure 9 - Four-dmensonal Soft Canceller wth FEC.

15 08/0/99 5 TE.4/99-333R 3.. Complexty The complexty of the technque descrbed and used here depends on the matrx H and the crosstal couplng channel, but s usually on the order of lnear n the pacet se per symbol. Ths s the same complexty assocated wth equalers n detecton. The length of the equaler depends on H and can lead to computatonal requrements that are on the order of the complexty of the FFT n practce. More precse calculaton of compexty s hghly vendor/algorthm dependent, but bascally ths technque s n the range of mmedate practce for VDSL, unle the ML methods n [] that were used to justfy and motvate the search for suboptmum methods as studed here. 4. Concluson QAM Home LAN sgnals and DMT VDSL sgnals are fundamentally separable wth lttle loss n VDSL performance. Iteratve decodng methods for the smultaneous detecton of both sgnals where approprate leads to acceptable complexty for the beneft of renderng VDSL essentally mmune to Home LANS, thus smplfyng spectral management. The authors hope that these results can assst the process of spectrum management n SG5/Q4 studes relatng to G.vdsl and G.pnt. The methods dscussed here are not restrcted necessarly to DMT VDSL and QAM Home LANs and other cancellaton methods may be possble for other crosstalng systems. However, two aspects of the transmsson code are mportant - the use of suffcent powerful and thus consequently orthogonal codes and the ablty of at least one of the coded systems to sense common dmensons where nterference s relatvely strong or wea. Annex A : FEC wth Reed-Solomon Codes Usng the teratve soft nterference cancellaton, t s possble to detect the VDSL sgnal n spte of the nterference from HPNA, wth a reduced error rate. Erroneous blocs may stll occur, so that t s necessary to ntroduce error-correcton to handle these errors. In partcular, forward error correcton (FEC) n the form of byte-orented Reed-Solomon codes can be used. In ths example, a sngle DMT symbol for VDSL s assumed to correspond to 400 bts. Then puttng four VDSL symbols together gves 00 bytes, whch s a reasonable length for a byte-orented Reed-Solomon codeword, whch must be less than 55 bytes n total. It s assumed that the FEC s appled over the entre DMT symbol, although the prmary cause of errors wll be nterference from HPNA n the 88 tones (of 56 tones). For smplcty, t wll be assumed that 4-QAM sgnallng was used on all 88 of these bands, for a total of 76 affected bts, or affected bytes. In ths analyss, errors from Gaussan nose are assumed to be neglgble. Snce the errors occurs n bursts, due to the nature of the nterference cancellaton, t s necessary to nterleave Reed-Solomon words n order to spread the bursts, decreasng the lelhood that a sngle Reed- Solmon codeword s ht wth an uncorrectable number of errors. If we assume that the nterleaver s long enough, so that the bt errors are..d., then we can calculate the byte error rate as 8 p = P byte = ( P ). bt Suppose that the Reed-Solomon code has bloc length n = 00 bytes. Then f the number of redunances s t, the number of byte errors that can be corrected s t. If the nput byte error rate s p, then the error rate of the Reed-Solomon decoder s then gven by ( ) ( n ) decoder = = t+ n p p P.

16 08/0/99 6 TE.4/99-333R References [] J. Coff et al, "Mgtaton of DSL Crosstal va Multuser Detecton and Code-Dvson Multple Access," ANSI Contrbuton TE.4/98-53, San Antono, TX, September 998. [] K.W. Cheong and J. Coff, "Coexstence of Mbps HPNA and DMT VDSL va Multuser Detecton and Code Dvson Multple Access," ITU SG5/Q4 Contrbuton MA-033, Melbourne, Australa, March 3, 999. [3] R. McElece, D. McKay, and J. Cheng, "Turbo Decodng as an Instance of Pearl's 'Belef Propagaton' Algorthm," IEEE Journal on Selected Areas n Communcatons, Vol. 6, No., February 999, pp [4] S. Verdu, Multuser Detecton, Cambrdge Press, UK, 998. [5] A. Gersho and T.L.\ Lm, Adaptve cancellaton of ntersymbol nterference for data transmsson, Bell Syst. Tech. J., vol. 60, no., Nov. 98., pp [6] D.J.C. MacKay, Good Error-Correctng Codes Based on Very Sparse Matrces, IEEE Trans. Inform Theory, vol. 45, No., March 999, pp [7] Z.-N. Wu, J.M. Coff, Decson-Aded Equalaton, submtted to Globecom '99.