Crosstalk Mitigation in DMT VDSL with Impulse Noise *

Transcription

1 Crosstal Mtgato DMT VDSL wth Impulse Nose Huayu Da, Studet Member, IEEE, ad H Vcet Poor, Fellow, IEEE Departmet of Electrcal Egeerg, Prceto Uversty Prceto, NJ Tel: (609) Fax: (609) Emal: huayud@eeprcetoedu, poor@prcetoedu Abstract: Crosstal ad mpulse ose are two prcpal sources of degradato very-hgh-rate dgtal subscrber le (VDSL) trasmsso systems The tradtoal sgle-user data detector for such systems merges crosstal to the bacgroud ose, whch s assumed to be whte ad Gaussa Recet research has explored the ature of crosstal sgals ad show the potetal beefts of multuser detecto for VDSL sgals wth strog crosstalers Impulse ose s oe of the most dffcult trasmsso mparmets to suppress ad s poorly characterzed ad uderstood as well I DSL trasmsso mpulse ose s typcally combated wth terleaved forward error correcto However, recet data dcates that a sgfcat morty of mpulse ose evets are loger tha the maxmum error correctg capactes of the default terleaved forward error correcto (FEC) provded wth curret ANSI stadards Thus, t s of terest to cosder sgal processg methods that ca jotly mtgate crosstal ad mpulsve ose I ths paper, we explore such a techque based o a recetly developed robust M-detector structure for multuser detecto o-gaussa ambet ose Idex Terms Crosstal, DMT, DSL, Impulse ose, M-estmato, Multuser detecto Mauscrpt receved Jue 0, 000; revsed May 9, 001 Ths research was supported by the Natoal Scece Foudato uder Grat CCR

2 1 Itroducto Dgtal subscrber le (DSL) techology provdes trasport of hgh-bt-rate dgtal formato over telephoe subscrber les Phoe les, whch were orgally costructed to carry a sgle voce sgal wth a 34 Hz badwdth chael, are actually capable of carryg very hgh data rates f the arrowbad swtch the phoe compay cetral offce ca be avoded Varous DSL techques (basc rate tegrated servces dgtal etwors (ISDN), hgh-bt-rate DSL (HDSL), Asymmetrc DSL (ADSL), ad very-hghrate DSL (VDSL)) whch volve sophstcated dgtal trasmsso schemes ad extesve sgal processg have recetly become practcal due to advaces mcroelectrocs The latest DSL techology s VDSL, whch provdes tes of megabts per secod to those customers who desre broadbad etertamet or data servces Asymmetrc VDSL s vewed more as a resdetal servce, supportg up to 5 Mb/s dowstream ad 64 Mb/s upstream rates for delvery of dgtal TV ad hgh defto TV (HDTV) servces Symmetrc applcato of VDSL provdes two-way data rates up to 6Mb/s for data etwor or local area etwor (LAN) exteso, maly as a busess servce At such hgh rates, sgals o twsted pars ca be relably trasmtted at most to a few thousad feet Thus, VDSL wll prmarly be used for loops fed from a optcal etwor ut (ONU) or a cetral offce (CO) to a customer s premses, the socalled last mle problem The modulato scheme for VDSL ca ether be multcarrer-based or sgle carrer-based, typcally dscrete multtoe (DMT) ad carrerless ampltude/phase modulato (CAP)/quadrature ampltude modulato (QAM) The duplexg methods ca be ether tme-dvso duplexg (TDD) or frequecy-dvso duplexg (FDD) Typcal phoe les that carry VDSL sgals are 4- or 6-gauge ushelded twsted pars (UTP) Multple telephoe pars may share the same cable Normally VDSL sgals occupy from 300 Hz to 30 MHz of the twsted-par badwdth ad are separated from pla old telephoe system (POTS)/ISDN sgals by spltter devces Nose o phoe les ormally occurs because of mperfect balace of the twsted par There are may types of oses that couple through mperfect balace to phoe les, the most commo of whch Ths artcle s based o a paper preseted at the IEEE CAS-COM Worshop'99 o hgh speed data etwors held at Prceto Uversty o July 6-8,

3 are crosstal ose, rado ose ad mpulse ose Crosstal s caused by electromagetc radato of other phoe les close proxmty, practce wth the same cable Such couplg creases wth frequecy ad ca be caused by sgals travelg the opposte drecto, called ear-ed crosstal (NEXT), ad by sgals travelg the same drecto, called far-ed crosstal (FEXT) Rado ose s the remat of wreless trasmsso sgals couplg to phoe les, partcularly AM rado broadcasts ad amateur (HAM) operator trasmssos Impulse ose s a ostatoary crosstal from temporary electromagetc evets (such as the rgg of phoes o les sharg the same bder, ad atmospherc electrcal surges) that ca be arrowbad or wdebad ad that occurs radomly Impulse oses ca be tes of mllvolts ampltude ad ca last as log as hudreds of mcrosecods [6], [16] Whle the rado ose problem ca be solved or at least allevated by restrctg the VDSL trasmsso rado bads, crosstal ad mpulse ose are two prcpal sources of degradato VDSL trasmsso systems The tradtoal sgle-user detector (SUD) for such systems merges crosstal to the bacgroud ose, whch s assumed to be whte ad Gaussa Actually, crosstal s the result of the sum of several fltered dscrete data sgals Its dstrbuto devates from Gaussa, ad ts power spectral desty (PSD) s also sgfcatly greater tha that of bacgroud added whte Gaussa ose (AWGN) Recet research has explored the ature of crosstal sgals ad has show the potetal beefts of multuser detecto for VDSL sgals wth strog crosstalers [], [3], [4] I DSL trasmsso mpulse ose s typcally combated wth terleaved forward error correcto (FEC) However, recet data dcates that a sgfcat morty of mpulse ose evets are loger tha the maxmum error correctg capactes of the default terleaved FEC provded wth curret ANSI stadards [9], [10] Thus, t s of terest to cosder sgal processg methods that ca jotly mtgate crosstal ad mpulsve ose Recet wor has examed multuser detecto (MUD) o-gaussa ambet evromets for wreless code-dvso multpleaccess (CDMA) systems [] I partcular, ths wor has show that stadard lear multuser detectors are ot robust to certa types of o-gaussa ambet ose (partcularly mpulsve ose), whereas lowcomplexty olear modfcatos provde excellet performace such evromets It s the purpose of ths paper to exame smlar techques for crosstal ad mpulse ose mtgato DMT VDSL systems Note that the crosstal sgals DSL trasmsso are of varous types ad caot be represeted

4 uder a uform framewor, to the best of the authors owledge I our applcato of MUD to sgal detecto DSL systems, we deal maly wth NEXT of other types ( cotrast to the self NEXT comg from the phoe les carryg the same VDSL servce) The reaso s gve as follows FEXT expereces the same le atteuato as the desred sgal whle NEXT does ot, whch maes NEXT the most detrmetal type of terferece, especally at hgh frequeces Self NEXT ca be largely allevated by duplexg methods that separate the upstream ad dowstream data tme or frequecy Therefore, the other-type NEXT provdes the best opportuty for performace ga However, the dea of multuser detecto s vald ad applcable to mtgato of crosstal of all types, although modfcatos of the techques proposed here may be ecessary for each specfc stuato Note that we do ot cosder codg ths paper, but ths ssue s treated a sequel [8] Ths paper s orgazed as follows I Secto a sgal model for the DMT VDSL commucato system, as well as the mpulse chael ose model, s descrbed I Secto 3 we propose a robust MUD-based scheme for DMT VDSL sgal detecto I order to reduce the recever complexty whle matag good performace, a suboptmum recever s troduced Secto 4, together wth ts robust verso Smulato results are gve Secto 5, ad Secto 6 cocludes the paper System Model Fgure 1 depcts a basc crosstalg chael wth oe desred VDSL sgal ad K-1 crosstalers The loop trasfer fucto H of the desred VDSL sgal ad the crosstal couplg fuctos are assumed to be ow At the chael output bacgroud ose s added, a model for whch wll be troduced shortly The VDSL sgal studed here uses a DMT trasmsso system, whose trasmtter ad recever are depcted Fg ad Fg 3, respectvely The typcal twsted par s a tersymbol-terferece (ISI) chael However, f the umber of subchaels s large eough, the cotuous trasfer fucto of the chael respose ca be approxmated by dscrete subchael gas, as llustrated Fg 4 The we ca 3

5 effectvely decompose the orgal chael to a set of N parallel depedet chaels wth o ISI For each subchael the frequecy doma, the output s gve by Y = H X + K = C + N,, 1,, N =, (1) where H s the chael ga, X s the trasmtted (complex) DMT symbol, the th crosstaler, =,, K, ad N s the bacgroud ose at the th subchael [5] C, s the terferece from Impulse ose s a severe mparmet to DSL trasmsso, especally after log loop atteuato (at a resdetal locato) ad hgh frequeces (where the DSL sgal s more severely atteuated) However, the area of mpulse ose modelg remas usettled Coo preseted a aalytcal model [7] The ADSL stadard, however, uses stored represetatve mpulse waveforms, whch are measured emprcally Valet et al collected mpulse ose ad bacgroud ose data o ADSL loops at New Jersey resdeces ad dd aalyss o the data three ways: as power ad eergy spectral destes, as probablty desty fuctos of the tme waveform voltage ampltudes, ad as mpulse arrval ad terarrval tme statstcs [1], [18], [19] So far there are o such models for mpulse ose VDSL, but smlar results are atcpated [0] Our ey observato from these aalyses s: there are sgfcat mpulse spes the PSD of the measured wdebad ose, whch s otherwse essetally flat To model ths behavor of the mpulse ose we use a two-term Gaussa mxture model the frequecy doma The frst-order probablty desty fucto of ths ose model has the form ε ) (0, σ ) + ε (0, κσ ) (1 () wth σ > 0, 0 ε 1, ad κ 1 Here, the (0, σ ) term represets the omal bacgroud ose (Gaussa wth zero mea ad varace σ ), ad the (0, κσ ) term represets a mpulse compoet (Gaussa wth zero mea ad varace κσ ), wth ε represetg the probablty that mpulses occur [] It s assumed that ose samples dsjot frequecy bs are depedet 3 Robust Maxmum Lelhood Multuser Detecto Recever 4

6 As we metoed Secto 1, t s possble to apply multuser detecto to jotly detect the VDSL sgal ad the crosstal sgals ad thus greatly mprove the system performace For smplcty let us assume the bacgroud ose to be Gaussa (e () wth ε = 0 ) for the momet We wll retroduce the mpulse ose model below Accordg to the system model gve Fg 1, the optmal maxmum lelhood multuser detector (ML-MUD) for Gaussa ose s oe that estmates the VDSL put ad crosstaler puts uso so as to mmze the dstace betwee the chael output receved sgal ad all the possble dscrete waveform outcomes It s possble that the crosstal sgals are wrogly estmated, but the probablty of erroeous selecto of the desred VDSL sgal wll be less for such a detector tha whe the crosstal sgals are smply assumed to be Gaussa ose We wll expect a greater mprovemet performace f the dfferece betwee the PSD level of crosstal sgals ad bacgroud ose s larger Geerally speag, crosstal stregth creases wth frequecy: NEXT wth 15 f ad FEXT wth f Fortuately, FEXT expereces the same le atteuato as the desred sgal; but ufortuately, NEXT does ot For VDSL systems, hgh-frequecy NEXT s the most detrmetal type of crosstal, but wll also be most promsg for reducto va MUD The typcal bacgroud ose level of VDSL trasmsso s 140dbm, whle the typcal NEXT s 90~ 110dbm; thus we ca expect substatal ga from multuser detecto relatve to tradtoal sgle user detecto ths stuato Besdes, DMT VDSL subchaels where there are substatally stroger crosstal sgals (typcally hgh frequecy bads o log loops), the so-called "ear-far" problem wreless CDMA systems, SUD wll fal to wor properly whle optmal MUD should essetally acheve the sgle user lower boud Let us cosder the detecto problem for the data model gve (1) The tradtoal sgle user detector performs QAM demodulato ad detecto O the other had, jot maxmum-lelhood detecto of both VDSL ad crosstal sgals selects a set of N puts { X } ad the crosstal sequece ( ) ( ) ( ) ( ) { C1,, C,,, C }, =,, K, C = to satsfy N, X = arg{ m { X },{ C ( ), N Y H X } = 1 = K C ( ), }, = 1,, N, (3) 5

7 where the mmzato s searched over the DMT sgal alphabet ad all possble crosstal sequeces ( ) { C, = 1,, }, =,, K, C = C that ca occur wth the VDSL symbol perod of terest The sze C, =,, K, of the all possble crosstal sequeces set ca be large but s always fte whe all the crosstalers are dgtal sgals or are derved from dgtal sgals For whte Gaussa ose, maxmum lelhood detecto s the same as least-squares (LS) curve fttg, as ca be see from (3) It s well ow from the classc wor of Tuey [17] that least-squares estmates are very sestve to the tal behavor of the probablty desty of measuremet errors (represeted here by the addtve ose) Its performace depeds sgfcatly o the Gaussa assumpto, ad eve a slght devato of the ose desty from the Gaussa dstrbuto ca, prcple, cause a substatal degradato of the LS estmate The LS estmate correspodg to (3) ca be robustfed by usg the class of M-estmators proposed by Huber [11] Istead of mmzg over a sum of squared resduals, Huber proposed to use a less rapdly creasg pealty fucto ρ so as to allevate the effect of the mpulses X = arg{ m N ρ ( Y H X C )}, = 1,, N (4) ( ) { X },{ C, } = 1 = K ( ), The usual requremets for the pealty fucto ad ts dervatve ψ = ρ are: (1) ρ s sub-quadratc fucto for large values of resduals, order to de-emphasze the error caused by ose "outlers" ( ths case caused by mpulse ose); () ψ s bouded ad cotuous; (3) ψ ( x) x for small x, so as to acheve hgh effcecy the Gaussa case; (4) E{ ψ ( )} = 0 to get a cosstet estmate; ad for symmetrc ose destes ψ s usually odd N j symmetrc A good choce for Gaussa mxture ose s the Huber pealty ρ show Fg 5 together wth ts dervatve ψ These fuctos are gve explctly by 6

8 ad x x σ ρ( x ) = σ (5) σ x x > σ ψ ( x) = x x σ σ, (6) sg( x) x > σ where, σ, ad ε (see ()) are related by φ( σ ) ε Q( σ ) =, (7) σ (1 ε ) 1 x wth φ ( x) e 1 x ad Q( t) e dx (see, [11], []) t π π I ths paper, we wll cosder ths partcular choce of ρ, ad the resultg DMT VDSL detector wll be called the robust maxmum lelhood multuser detecto recever (ML-MUD-R) The performace of ths detector wll be compared wth ML-MUD ad SUD Secto 5 4 A Iterferece Cacellato Multuser Detector ad Its Robust Verso Just as ts couterpart wreless CDMA, the maxmum lelhood multuser detector acheves optmum performace but suffers from very hgh complexty A full search the put doma requres approxmately N C M squared error computatos, where N s the umber of subchaels, C s the umber of possble crosstal sequeces, ad M s the average sze of the trasmtted alphabet I practce N ad especally C ca be very large, troducg prohbtve computatoal complexty The large umber of possble crosstal sequeces also meas a expoetally greater umber of states, mag dyamc programmg approprate So we eed to cosder a smplfed recever structure that matas satsfactory performace whle requrg far less computato complexty 7

9 Oe lower-complexty approach s to employ a lear multuser detecto techque, such as decorrelatg (zero forcg) or mmum-mea-square-error (MMSE) multuser detecto However, ule CDMA or space-dvso multple-access (SDMA) where lear detecto has bee effectve, there s o detfyg sgature such as the spreadg code for CDMA or the steerg vector for SDMA, to ad lear detecto VDSL Istead, desred sgals ad crosstal sgals are ofte of dfferet data format Aother popular approach s to employ terferece cacellato, e, to attempt removal of the crosstal from the receved sgal before mag the tradtoal DMT VDSL sgal detecto [1] Ths s the approach we adopt here To do so, we eed a scheme to detect the crosstal sgals frst As we metoed before, the crosstal sgals DSL trasmsso are of varous types ad caot be represeted uder a uform framewor The type we exame here s the domat ear-ed QAM-le crosstal (e g [3]) At frst glace, t seems qute dffcult to detect the crosstal correctly wth reduced computatoal complexty After all, t s the huge set of possble crosstal sequeces that complcates the computato (3) Let us cosder the power spectrum of the DMT VDSL sgal ad the crosstal sgals As we metoed before, each subchael has depedet trasmtted data ad added bacgroud ose, so the eergy s farly spread across the frequecy doma of terest, although t s ot equal everywhere sce dfferet bts may be assged to dfferet subchaels to acheve the optmum performace I cotrast, the PSD of the QAM-le crosstal sgals are ofte clustered aroud several relatvely arrow spectral compoets (called "toes" DMT modulato) A atural dea s to zero these toes DMT-VDSL trasmsso, e, do ot trasmt DMT VDSL sgals o these toes Ths s a form of CDMA where the DMT VDSL sgal s orthogoal to the crosstal sgals o these toes Because the data rates of the crosstal sgals are usually low compared to the VDSL sgal ad the SNRs are excellet (the crosstal sgals are treated as the sgals of terest here), oly a few zeroed toes are ecessary to detect the crosstal sgal farly well Thus the computato complexty s greatly reduced to N z C, where N z s the umber of zero toes (eg, N z = 5), addto to the early trval covetoal demodulato The choce of toes to be zeroed depeds o the owledge of where the eergy of crosstal sgals cocetrates, whch geerally s ow Advaces dgtal sgal processg mae toe zerog easy to mplemet Furthermore, spectral compatblty wth other DSL trasmsso ad rado broadcast ofte ecesstates 8

10 some partcular toes beg zeroed Fally, zerog of these toes also leads to a reducto FEXT o these toes Fgure 6 gves the structure of ths terferece cacellato multuser detector (IC-MUD) The detal of the IC-MUD algorthm s gve as follows 1 Choose the toes to be zeroed based o the owledge of a specfc crosstal sgal; The crosstal sgal s detected ad recostructed these DMT-symbol-free chaels; eg, for a home phoe etwor of Amerca (HPNA) sgal (see [3]), t ca be detected va C = arg{m Y Cˆ C }, = 1,, N, (8), { C, } T < z,, where { C ˆ,} are formerly detected crosstal sgals, ad T z s the set of toes beg zeroed; 3 The recostructed crosstal s subtracted from receved sgal all subchaels; 4 Repeat the above process utl all crosstal sgals ˆ = [ Cˆ, = K] C,, are estmated, recostructed, ad subtracted (dfferet crosstal sgals may be detected through dfferet methods accordg to ther characterstcs); 5 SUD s used for DMT sgal detecto, X = arg{m Y { X } H X K = Cˆ, }, = 1,, N ad Tz (9) If the Huber pealty fucto (5) s used crosstal sgal decodg for combatg the mpulse ose, the resultg detector s called the robust terferece cacellato multuser detector (IC-MUD-R) Ie, stead of (8), ths detector uses C arg{ m ( ˆ, = ρ Y C, C, )}, = 1,, N (10) { C, } Tz < The terferece cacellato scheme s suboptmal sce errors may arse crosstal detecto However, t s partcularly sutable for hgh SNR chaels wth power mbalaces Aother shortcomg for ths suboptmum recever s the capacty loss due to toe zerog Noetheless, we wll show the followg secto that t provdes a favorable tradeoff of performace ad complexty 9

11 5 Smulato Results I ths secto we exame the behavor ad the performace of the proposed multuser detecto recevers for DMT-VDSL sgals wth crosstal ad mpulse ose va computer smulatos Bt-error-rate (BER) s adopted as the performace measure wth respect to the average sgal-to-ose rato (SNR), whch s defed as N H X = 1 SNR = (11) N = 1 N I the smulato, the DMT VDSL sgal s assumed to occupy 0-56 MHz wth 56 subchaels a frequecy-dvso multplexed (FDM) desg The symbol rate for each VDSL subchael s 100 Hz I each subchael, bts are assged so the sgals are 4-QAM No bt allocato algorthms are used here, although exteso to ths case s straghtforward The trasfer fucto of the DMT VDSL sgal s smulated by 4e e e e jω jω jω 3 H ( e ) = 10 (1) jω jω We assume oe NEXT crosstal sgal wth a ow couplg fucto gve as ω 3/ 4 F( e j ) = K ω, (13) where K s a costat used to adjust the PSD of the crosstal sgal These settgs are made to roughly approach the PSD shapes dcated [1] We assume that these trasfer fuctos stay fxed for the whole smulato terval, whch s reasoable for wrele commucatos evromets The crosstal sgal s BPSK modulated o 8 MHz carrer frequecy wth a 1M symbol-per-secod rate Such a stuato would arse, for example, due to the coexstece of home-phoe LANs ad asymmetrc DMT VDSL sgals the same cable the customer premses Thus, there are 10 possble crosstal sequeces oe VDSL symbol Ths umber s chose for smulato smplcty I realty, ths umber could be much larger For IC-MUD ad IC-MUD-R, the fve zeroed toes are T = {78, 79, 80, 81, 8} MHz, aroud whch most of the z crosstal eergy s cocetrated The mpulse ose s assumed to have parameters ε = 0 1ad κ = 100, 10

12 whch meas the mpulse spe s 0 db hgher tha the bacgroud ose floor The average PSD levels of the crosstal sgal ad bacgroud ose floor are fxed whle that of the desred sgal s vared, correspodg to dfferet le legth (the sgal atteuato s creasg wth the le legth) I our smulato, the average PSD of the crosstal s 7 db hgher tha that of the bacgroud ose floor ad the pea PSD of the crosstal s 40 db hgher These settgs seem to agree roughly wth emprcal measuremets I the DSL evromet, BER values as low as 10-7 are ofte requred For Mote Carlo (MC) smulato, approxmately 10 / P smulato trals are requred to have a 95 percet cofdece terval of e [ e e P / 5, 8 P / 5] [13] To alevate ths computatoal burde, we use mportace samplg (IS) [13], [14], [15] The basc dea of mportace samplg s to bas the probablty desty fucto (pdf) from whch the data are geerated so that errors of detecto are more lely to happe, the weght each error such that a ubased BER estmate s obtaed Assume a error occurs whe the receved data R falls wth some rego Z The the BER s gve by P = 1 ( r) f ( r dr, (14) e Z R ) where 1Z ( ) s the dcator fucto over Z ad f R ( ) s the pdf of R The MC estmator of Pe s gve by M Pˆ 1 MC = 1Z ( R ), (15) M = 1 where M s the umber of trals of the smulato ad the R s deote data samples Whe the data samples are depedet ad detcal dstrbuted (d), Pˆ MC s a ubased estmator wth varace The IS estmator of Pe s gve by wth var( Pˆ MC Pe (1 Pe ) ) = (16) M M Pˆ 1 IS = 1Z ( R ) W ( R ) (17) M = 1 11

13 f R ( r) W ( r) =, (18) f ( ) R r where R s the th data sample from based desty f ( ) ad W ( ) s the weght fucto If the ew R geerated data are d, Pˆ IS s a ubased estmator wth varace where W s defed as var( Pˆ IS W Pe ) =, (19) M W = W ( r) f ( r) dr (0) Z R Whe f ( ) s approprately selected, the varace of the IS estmator wll be far less tha that of the MC R estmator Thus the umber of trals eeded for a gve estmator varace s greatly reduced for the IS estmator compared to the MC estmator The optmal bas dstrbuto s gve by 1Z ( r) f R( r) f ( r) =, (1) Ropt P e whch acheves zero estmato varace but s degeeratve sce t requres the owledge of P e A wdely used method of desgg suboptmal f ( ) s mea traslato (MT) Ths class of based desty fuctos s of the form R f ( r ) = f ( r T ), () R R + where T s chose to be the mode (at whch maxmum value of a pdf s acheved) of f ( ) For the R opt multuser commucato system of (1), let ρ = X, C,, C ), mpose the restrcto f ( ) = f ( ) ad codtoally shft the mea of the ose ρ ρ f ( K ( ) = f N ( + m( ρ )) = f N ( + H X + N ρ The IS estmator of BER s the gve by K = C ) (3) Pˆ IS = 1 M M Ι( Xˆ X = 1 M 1 f N ( N ) ) W ( ρ, N ) = Ι( Xˆ X ), (4) M = 1 f ( N ) ρ N 1

14 where we assume the depedece of ρ ad N, ˆ X s the detected data of X wth the orgal decso rule, ad 1 x > 0 Ι( x ) = (5) 0 x 0 Whe the ear-far problem occurs, e, we eed to adjust the IS error estmator as follows: Pˆ IS = 1 M sg( m( ρ )) = sg( H X ), (6) M f N ( N ) Ι( Xˆ X ) + (1 Ι( Xˆ X ))(1 ) = 1 f ρ N ( N ) (7) Note that ths stuato, the IS techque s used to cout correct detectos (whch happe wth small probablty), whch the gves (see (4)) Pˆ IS correct = 1 M M = 1 Ι( Xˆ X ) f f N N ( N ) (8) ( N ) ρ The quatty of (7) s the obtaed through Pˆ = 1 ˆ IS P IS correct I our smulatos, the IS techque s uformly better tha the MC techque It acheves great varace reducto for optmal detecto (maxmum lelhood) methods ad also gets substatal gas for others Fgure 7 shows the performace of varous detectors for DMT VDSL systems wth oe crosstaler ad mpulse ose As we ca see, there s a sgfcat gap betwee the performace of the tradtoal sgle user detector ad the sgle user lower boud (correspodg to a crosstal-free chael), dcatg the effectveess of the sgle-user detector Whle the maxmum lelhood multuser detector essetally acheves the sgle user lower boud, t suffers from prohbtve complexty The terferece cacellato multuser detector offers a favorable performace ad complexty tradeoff compared wth the sgle-user ad ML multuser detectors 13

15 Fgure 8 shows the performace of the M-estmator-based robust detectors the crosstal ad mpulse ose evromet Whle there s ot much dfferece betwee the ML multuser detector ad ts robust verso, both of whch approxmate the sgle user lower boud, there s sgfcat mprovemet for the robust terferece cacellato multuser detecto compared wth ts Gaussa-based couterpart The crosstal detecto errors are for IC-MUD, for IC-MUD-R ad almost 0 for ML- MUD ad ML-MUD-R It should be oted that the expected mprovemet from usg M-estmators s due to better estmato of the crosstal sgals the DMT VDSL case The desred DMT VDSL sgals dfferet subchaels are depedet whle the crosstal sgals are correlated the frequecy doma, whch meas that M-estmators are especally applcable to mpulse-ose-cotamated DMT VDSL systems wth crosstal sgals strogly correlated the frequecy doma However, more crosstal errors do ot ecessarly mea worse performace, especally for the ML jot detecto scheme Ths s because the whole set of possble crosstal sequeces s usually dvded to may small subsets Whle the correspodg sequeces of a subset ca be largely dfferet, ther spectral compoets are smlar I fact, we foud from our smulatos that the IC scheme s much more sestve to crosstal detecto errors tha s the ML scheme For example, f we lower the power of the crosstal by 15 db (whch ca be thought of as a FEXT) whle eepg the other settgs uchaged, the crosstal detecto errors are for IC-MUD, for IC-MUD-R, for ML-MUD ad for ML-MUD-R But ML- 4 MUD stll almost approaches the sgle user lower boud, whch ca be see from Fg 9 Sce the crosstal sgals are estmated frst oly a few toe-free subchaels for IC-MUD, more ga of IC- MUD-R over IC-MUD s acheved as compared wth the ga of ML-MUD-R over ML-MUD Fally, Fg 10 shows that, for the terferece cacellato multuser detector, strog crosstal actually mproves the stuato We lower the stregth of the crosstal 1dB ad compare the performaces of the tradtoal sgle user detector ad robust terferece cacellato multuser detector appled to the two dfferet crosstal evromets The mpulse ose settgs rema uchaged It s see that IC-MUD-R performs better wth the stroger crosstal Ths s o surprse, sce for successve cacellato, strog terferece s almost as good as o terferece These results also dcate that for crosstal wthout 14

16 sgfcatly greater PSD level tha that of the bacgroud ose, at hgh SNR, the IC scheme does ot get much ga over SUD 6 Coclusos I ths paper we have show the potetal beefts of multuser detecto for crosstal mtgato DMT VDSL systems subject to mpulse ose We see that ML-MUD ca essetally elmate crosstal sgals DMT systems at a cost of hgh complexty As a tradeoff, IC-MUD ca sgfcatly outperform SUD, wth lower complexty tha ML-MUD We have also show the effectveess of the M-estmator combatg the mpulse ose There are some ssues overlooed ths paper, whch mght be of terest for further study For example, we have assumed owledge of the le trasfer fucto ad the crosstal couplg fuctos I realty, however, chael detfcato s eeded Also, we have ot cosdered the ssue of optmal bt allocato to subchaels wth dfferet SNRs Fally, our smulato, oly oe crosstal sgal s assumed The treatmet of multple crosstal sgals follows straghtforward, although hgher complexty s evtable I future wor, we pla to study other crosstal applcatos where multuser detecto techques ca be appled more drectly (eg combatg self-fext) We admt that realty crosstal sgals vary wdely modulato formats ad data rates ad so far there s o uform framewor for mtgato of crosstal DSL What we address here s the combatg of a specal class of crosstal sgal (QAM-modulated sgals), but we beleve that the geeral dea of multuser detecto s a promsg techque for crosstal mtgato DSL Also, teratve (Turbo style) jot decodg ad multuser detecto (see [3]) s a attractve techque whose applcato o DSL s of terest 15

17 Refereces [1] J Bgham, Sychroous DMT for low-complexty VDSL, ANSI T1E14/96-081, 1996 [] K W Cheog ad J M Coff, "Coexstece of 1 Mbps HPNA ad DMT VDSL va multuser detecto ad code dvso multplexg, ANSI T1E14/99-10,1999 [3] K W Cheog ad J M Coff, "Coexstece of -10 Mbps Home-Phoe LANS ad DMT VDSL va multuser detecto, ANSI T1E14/99-333, 1999 [4] J M Coff, K Cheog, J Lauer, ad A Salvear, "Mtgato of DSL crosstal va multuser detecto ad code-dvso multple access, ANSI T1E14/98-53, 1998 [5] J M Coff, A multcarrer prmer, upublshed otes, Staford Uversty [6] J M Coff, et al, Very-hgh speed dgtal subscrber les, IEEE Commu Mag, pp 7-79, Apr 1999 [7] J W Coo, Wdebad mpulse ose survey of the access etwor, BT Techcal Joural, Vol 11, No 3, pp , July 1993 [8] H Da ad H V Poor, Iteratve multuser detecto ad decodg for DMT VDSL systems, Proc 001 Cof Iform Sceces ad Systems, The Johs Hops Uversty, Baltmore, MD, Mar [9] S Daves, et al, Impulse ose evets of relatvely log durato, ANSI T1E14/94-10, 1994 [10] S Daves, et al, Australa wdebad mpulse ose survey data, ANSI T1E14/95-15, 1995 [11] P J Huber, Robust Statstcs, New Yor: Wley, 1981 [1] K J Kerpez ad C F Valet, Impulse ose testg for ADSL trascevers, ANSI T1E14/93-034, 1993 [13] G Orsa ad B Aazhag, O the theory of mportace samplg appled to the aalyss of detecto systems, IEEE Tras Commu, vol 37, o 4, pp , Apr 1989 [14] G Orsa ad B Aazhag, Effcet mportace samplg techques for smulato of multuser commucato systems, IEEE Tras Commu, vol 40, o 6, pp , Jue 199 [15] P J Smth, M Shaf ad H Gao, Quc smulato: A revew of mportace samplg techques commucatos systems, IEEE J Select Areas Commu, vol 15, o 4, pp , May

18 [16] T Starr, J M Coff ad P J Sverma, Uderstadg Dgtal Subscrber Le Techology, Pretce Hall, 1999 [17] J W Tuey, "A survey of samplg from cotamated dstrbutos," Cotrbutos to Probablty ad Statstcs (Harold Hotellg Volume), I Ol, et al, eds Staford Uversty Press: Staford, CA, 1960 [18] C F Valet, K J Kerpez ad B Blae, Aalyss of loop ad sde wre bacgroud ose measured at two New Jersey resdetal locatos, ANSI T1E14/9-7, 199 [19] C F Valet ad K J Kerpez, Aalyss of wdebad ose measuremets ad mplcatos for sgal processg ADSL systems, Proc 1994 IEEE Iteratoal Cof o Commucatos, pp 86-83, May 1994 [0] C F Valet, Survey pla for characterzato of mpulse ose ad bacgroud ose at VDSL frequeces, ANSI T1E14/97-95, 1997 [1] S Verdú, Multuser Detecto, Cambrdge, UK: Cambrdge Uversty Press, 1998 [] X Wag ad H V Poor, "Robust multuser detecto o-gaussa chaels, IEEE Tras Commu, vol 47, o, pp , Feb 1999 [3] X Wag ad H V Poor, Iteratve (Turbo) soft terferece cacellato ad decodg for coded CDMA, IEEE Tras Commu, vol 47, o 7, pp , July

19 (t) DMT Sgal x 1 ( t) VDSL le chael H y(t) { Crosstal Sgals x ( t ) x K (t) crosstal couplg crosstal couplg C ( t) C K (t) Fg 1 System model for DMT VDSL X 1 x 1 X x Iput bt Stream Ecoder IFFT N = N Parallel To Seral Coverter DMT sgal x(t) X N x N Fg DMT trasmtter 18

20 y 1 Y 1 y Y Seral To Chael Output Parallel y(t) Coverter FFT N = N Decoder Detected data y N Y N Fg 3 DMT recever H(f) Trasfer fucto of chael respose H3 H1 H H 4 H N H N 1 H 0 f1 f f3 4 f f f N N 1 f N f Fg 4 Multchael decomposto of a chael respose 19

21 Fg 5 Huber pealty fucto ad ts dervatve for the Gaussa mxture model used ths paper = ε = 01, κ = 100, σ 1, = 1 14 y(t) FFT Y Ĉ + + Ĉ K DMT Decoder X Crosstal Detector Ecoder Crosstal Detector Ecoder Fg 6 Iterferece cacellato multuser detector for DMT VDSL system wth crosstals 0

22 R E B SNR Fg 7 Bt error rate (BER) versus sgal-to-ose rato (SNR) for dfferet detectors (x-mar: SUD, crcle: IC-MUD, damod: ML-MUD, dashed: sgle user lower boud) 1

23 R E B SNR Fg 8 Bt error rate (BER) versus sgal-to-ose rato (SNR) for dfferet detectors (x-mar: SUD, crcle: IC-MUD, plus: IC-MUD-R, damod: ML-MUD, star: ML-MUD-R, dashed: sgle user lower boud)

24 R E B SNR Fg 9 Bt error rate (BER) versus sgal-to-ose rato (SNR) for dfferet detectors wth 15 db weaer crosstal (crcle: IC-MUD, plus: IC-MUD-R, damod: ML-MUD, star: ML-MUD-R, dashed: sgle user lower boud) 3

25 R E B R E B SNR SNR Fg 10 Effect of crosstal stregth for tradtoal ad robust terferece cacellato multuser detecto left: SUD; rght: IC-MUD-R (sold: stroger crosstal; dash dot: (1 db) weaer crosstal) 4