Multi-tone Signaling for High-speed Backplane Electrical Links

Transcription

1 Mult-tone Sgnalng for Hgh-speed Bacplane Electrcal Lns Amr Amrhany, Vladmr Stojanovć,, and Mar A. Horowtz Department of Electrcal Engneerng, Stanford Unversty, CA 9, USA Rambus, Inc., Los Altos, CA 9, USA Abstract A Mult-tone archtecture s proposed for hgh-speed bacplane seral lns. o lmt complexty, the lns use analog mult-tone rather than the more modern DM. he tradeoffs nvolved n the desgn of such a system are examned and the performance of a seral ln based on ths approach s compared to a baseband archtecture n terms of data rate and complexty usng a convex optmzaton framewor. Slghtly less than x mprovement n data rate at reasonable complexty s shown to be achevable wth the proposed archtecture. Keywords-hgh-speed; electrcal; lns; mult-tone; convex optmzaton I. IRODUCIO he requred bt rates for bacplane lns, lns that connect dfferent boards n a system, contnue to ncrease. Current systems use lns runnng at -.Gb/s, and components that provde -Gb/s have been demonstrated []. Although the transmsson meda n bacplane lns are copper traces that regularly do not exceed s of centmeters n length, sgnal reflectons orgnatng from mpedance msmatches at the va stubs and sgnal power loss due to sn effect and delectrc loss create a challengng envronment for sgnal transmsson at s of ggabts per second. As shown n Fg., whle from a dgtal communcaton perspectve lns channels have relatvely well behaved spectra, mplementaton constrants mae the desgn of these lns challengng. In partcular bacplane lns need to operate at Gsymbol/s rates and be both power and area effcent. As a result, producton lns only use baseband (BB) sgnalng wth lnear transmt precodng, whle the next generaton lns have recently started usng ether Decson Feedbac Equalzaton (DFE) or mult-level PAM constellatons [-] to mprove performance. However, as BB sgnalng extends to the regons of the channel wth hgh sgnal attenuaton, the margnal Research supported by the MARCO Interconnect Focus Center and Rambus, Inc. It s the ease of buldng hgh-speed dgtal to analog converters compared to analog to dgtal converters that causes the lns to use transmt precodng. db FR Channel Frequency Response ELCO 8 8 FR (a) Frequency (GHz) (b) me (ns) Fg. : Frequency Responses (a) and mpulse responses (b) of typcal ln channels. he notches n the frequency response of the FR channel and the reflecton taps towards the tal of ts mpulse response are the effects of va stubs. ncrease n rate wth ncreased complexty gets smaller and smaller. In fact, our recent results show that there s a large gap between the fundamental lmts of sgnalng on PCB traces and the rates achevable usng equalzaton-based BB communcaton technques []. Besdes ths fundamental lmt, as sgnalng rates approach the fundamental lmts of the avalable fabrcaton technology, BB processng becomes less effcent n terms of area and power. hs paper explores the feasblty of mult-tone (M) sgnalng to reduce the exstng performance gap. Snce both analog to dgtal converters (ADC) and sgnal processors that run at Gsample/Sec rates are expensve, we partcularly focus on a smple form of M, whch we call analog mult-tone (AM), a technque from the 9s []. However, as opposed to [], n order to be relatvely mmune to channel dstortons, we eep the overlap between the neghborng sub-channels to a mnmum and try to cancel the remanng nter-channel nterference (ICI). In partcular, we demonstrate that an AM system wth (matrx) precodng at the transmtter outperforms a BB ln wth transmt precodng by about a factor of two for a modest addtonal complexty. Better ICI cancellaton technques mght lead to even better performance whle mantanng a reasonable cost. AM was almost abandoned after the development of hghperformance DSP s and ntroducton of dscrete mult-tone. In... ELCO Channel Impulse Response Reflecton Globecom //$. IEEE

2 Secton II, we wll revew and compare the general class of dscrete mult-tone technques wth the AM approach based on ln-specfc desgn constrants and pont out the mportant mplementaton ssues nvolved n the desgn of both systems. An AM system essentally creates a number of baseband channels that are frequency dvson multplexed on the same wre. In Secton III we wll extend our convex optmzaton framewor for baseband channels [] to AM systems wth matrx transmt precodng. Snce many lns must run at very low BER, we use accurate nose models, and not ther Gaussan approxmatons, n our analyss. here are many desgn parameters n the mplementaton of an AM system that sgnfcantly affect the performance, and the analyss of such a system s not possble wthout good understandng of those effects. Besdes, the large number of parameters nvolved allows for many tradeoffs that the desgner can use to advantage. Secton IV enumerates the desgn parameters and ponts out the possble tradeoffs n some detal. Usng the optmzaton framewor from Secton III and the nsght from Secton IV, the performance and complexty of an AM system wth matrx precodng s compared wth a BB system wth lnear precodng n Secton V and fnal concludng remars are presented n Secton VI. Snce the purpose of ths paper s to demonstrate the feasblty of the M approach and perform a far comparson wth BB rather than maxmzng the throughput, we wll mostly favor smplcty n our analyss and n the choce of system confguratons. We wll, however, occasonally comment on some of the opportuntes to further boost performance. II. MULI-OE APPROACHES FOR HIGH-SPEED LIKS A. Dscrete Mult-tone Dscrete Mult-tone (DM) [] and other DF-based M technques, le Fltered M (FM) [7], perform the necessary frequency up-converson and down-converson for M operaton n dgtal doman usng nverse Dscrete Fourer ransform (IDF) at the transmtter (x) and DF at the recever (Rx). For ths reason, all such technques share the requrement for hgh resoluton, hgh bandwdth (BW) ADC s at the Rx front-end. Unfortunately, buldng hgh resoluton ADC s at several ggahertz frequency s a major challenge, and f the ADC does not have enough samplng resoluton, quantzaton nose becomes a serous lmtng factor. o estmate the requred ADC bandwdth and resoluton, we use the capacty results from Stojanovc []. He shows that the channels n Fg. have about GHz of usable bandwdth for sgnal transmsson. herefore, a regular dscrete mplementaton would requre a Gsamples/Sec ADC at the recever. hermal nose resultng from a Ω termnaton resstor at the recever s about nv Hz and assumng about db nose fgure for the recever sampler, a typcal number for a BB ln, gves a nose sgma of.mv. Further assumng that the output transmtter swng s V, the ADC should at least have -bt resoluton n order to have nondomnant quantzaton nose at the recever. A few addtonal bts mght be requred as well to push quantzaton nose well below thermal nose level. A state of the art ADC only supports 8-bt quantzaton at Gsamples/Sec [8] and s far too complex for a seral ln. DF-based M technques preserve the orthogonalty of the sub-channels by addng a cyclc prefx to the tme-doman DF bloc, le DM, or by avodng spectral overlap between the sub-channels, le the so called non-crtcally sampled FM. For ln systems, due to the long mpulse response caused by the reflectons, Fg. (b), the overhead for addng a cyclc prefx would be huge unless channel shortenng flters are used. However, an FM approach smlar to [9], wth relatvely small number of sub-channels and per sub-channel precodng, shares many advantages of the AM, as descrbed n the followng secton, and could have been feasble f the ADC requrements dd not exst. B. Analog Mult-tone A dfferent approach to M s to create several parallel BB streams of data and up-convert and down-convert them to the sub-channel frequences usng mxers. Regular BB equalzaton technques can then be appled to each subchannel to compensate for the remanng dsperson. We wll refer to ths approach as Analog M (AM). Fg. shows a general bloc dagram of such a system. Dependng on the archtecture, addtonal mxers or bandpass flters (BPF) mght exst n the actual mplementaton, but the lowpass flters are archtecture-ndependent and are referred to as channel-select flters. he sgnal processng blocs n the transmtter and the recever are also archtecture dependent and mght not exst. One clear advantage of AM s that sgnal-processng rate n each sub-channel s a fracton of the overall sgnalng rate. Fg. : General bloc dagram of an AM transmtter (top) and recever (bottom). Some blocs mght not exst n a specfc archtecture. Globecom //$. IEEE

3 herefore, more sophstcated algorthms can be mplemented compared to BB. he second advantage s that all exstng experence n BB ln desgn s readly applcable to each subchannel; an appealng property for the ndustry. AM also fts very well to the characterstcs of ln channels. Due to the smooth roll-off of ln channels, t s expected that not many sub-channels are necessary to acheve the desred low equalzaton loss. Consequently, the overall complexty overhead due to the Rado Frequency (RF) components n each sub-channel could be tolerable. onetheless, some challengng mplementaton constrants exst as well. One man ssue n mplementng an AM system s to deal wth nter-channel nterference (ICI). Even though t s theoretcally possble to elmnate ICI over an deal channel f channel-select flters follow certan orthogonalty condtons, due to channel dstortons and bad tolerance of analog on-chp flters the actual ICI level mght become ntolerable f sgnfcant overlap s allowed between the sub-channels []. On the other hand, buldng several sharp on-chp analog flters that would allow non-overlappng sub-channels wthout loss of spectral effcency s not easy as well, due to the bad qualty of on-chp nductors and the large sze of on-chp capactors. A compromse s, therefore, to allow suffcent guard-band between the sub-channels so that the overlap s small and try to cancel the remanng ICI wth sgnal processng. One good ICI cancellaton method whch s a natural extenson of transmt precodng n BB lns s matrx transmt precodng. Besdes ICI cancellaton, mplementaton of good qualty low nose lnear gan elements and mxers s also mportant. he followng secton establshes an approprate framewor that helps us quantfy the requrements on the analog front-end as well as the channel-select flters. III. COVEX OPIMIZAIO FRAMEWORK We recently derved a convex optmzaton framewor for mnmzng the Bt Error Rato (BER) n BB lns that too nto account accurate models for ln-specfc nose sources []. Snce an AM system s essentally a set of nteractng BB lns, we can easly extend that framewor to AM by wrtng the problem n vector form. However, we frst need to model the system. A. Sgnal ransmsson Model he baseband equvalent of the M system wth transmt matrx precodng s shown n Fg.. he model conssts of a matrx precoder wth fnte length dagonal and cross precoders and a matrx channel. he matrx channel models the subchannels n the system and the nterference between them. We wll refer to the sub-channels as dagonal channels and to the nterference channels as cross channels n the followng dscusson. At the recever, data s sampled at sub-channel symbol rate and a decson s made mmedately. he formulaton we wll use n ths paper s based on the x case of a system presented n []. Maxmum ISI spread for all dagonal and cross channels, p lj, s assumed to be ν, and Fg. : Baseband equvalent of an AM system wth matrx precodng. the length of all dagonal and cross precoders, w lj, s L. he response of the system from nput to output l at sample tme n can be expressed as: xˆ (n) x (n) P w P w P w () ( ) l = l lj j l x (n) = x(n)... x(n L ν + ) (L+ where [ ] s the data vector at nput, w [ ] j(n) = wj( )... wj(l ) L s the precoder from data nput to transmtter output j, and the channel convoluton matrx P lj s defned as: plj( )... plj( P = plj( )... plj( () lj plj( )... plj( (L+ L he system s fully descrbed by: xˆ (n) = X(n) Ψ W (n) () (L (L L L where the channel matrx Ψ s defned as: P Ψ... = P P P = [ ] (L+ L (L+ L wth P = [ P P ], defned as: [ w = ] W =... w L P (), and the precoder flter W s w = w... w (), [ ] L and the nput data matrx X(n) s defned as: [ X ] (n)... X (L X (n) = (n) + x(n) X(n) =... x (n) (L+ he vector (n) represents several nose terms ncludng thermal nose, samplng jtter and carrer phase nose. he spectral densty of thermal nose orgnatng from a Ω termnaton resstor s ( nv ) Hz and the nose fgure of all modules n the recever data path ncludng the sampler, gan elements, mxers and flters add to ths value. Carrer phase nose s the result of the random varatons n the phase of the up/down convertng oscllators at the x/rx. Phase nose manfests tself as a voltage nose at the slcer nput through the mxng of the real and magnary parts of the QAM sgnal. he varance of the phase nose-nduced voltage nose on the real/magnary part of the sgnal,, can be C (7) Globecom //$. IEEE

4 descrbed as: = + E (8) C ( carrer x carrer Rx ) y where E y s receved sgnal energy per dmenson, and s the varance of phase varatons at the x/rx carrer _ x / Rx relatve to the oscllator perod. Samplng jtter models the random varatons n the phase of the sgnalng cloc at the x and the samplng cloc at the Rx. Ignorng the second order effects from the cross channels and cross precoders, we can drectly use jtter expressons from Stojanovc [] for the dagonal channels: J_x/Rx, = w x/rx S w, ( j ) ( j ) sbe sbe R X R X h x,,, S = E x, I j[ h, j h, j ] ( j+ ) ( j ) j= sbs = sbs R X R X h,,, sbe sbe Rx h, S = E x, R RX () I [ h, j h,, j ] j j= sbs = sbs h, (9) where J_x/Rx, s the jtter-nduced voltage nose varance at the th x/ Rx x / Rx sub-channel slcer nput, R x / Rx ( m) = E( + m ) s the m th sample of jtter correlaton functon, I n s the dentty matrx shfted rght by n places, and h,j s the j th sample of the mpulse response of the th dagonal channel. E x, s the th subchannel x sgnal energy per dmenson, and sbs and sbe are start and end ndces of the correspondng mpulse response sequences. B. Optmzaton Framewor Extendng the convex optmzaton framewor of [] to a M system wth matrx transmt precodng as descrbed n the prevous secton, we can obtan the followng combnatoral optmzaton problem on the nteger bt loadng of the subchannels, b = [ b b... b ], whch reduces to a convex feasblty problem on W ( b ) for a gven b : MaxmzeDataRate= s b = Subject to: BER b target Q ( ) b b s ( ) ΨW b s w Vpea, = b j + = PD ΨW + offset, = () In the above nequaltes s a vector of length (L+ that has all zero entres except at ts (+)(-)(L++ + poston where t s unty, s a vector of the same sze that PD has unty entres at the postons correspondng to the taps that are to be consdered for pea dstorton, and Varables represented wth a bar are all per dmenson,.e. per real/magnary part of the sgnal. = W Ψ Carrer, D = = E s ( D ) x_ Carrer,+ ΨW+ Rx_ Carrer,, Carrer,W Ψ DΨW Jtter, = S x_ Jtter, ( X X) = dag ( s s... s ) s S + S + W S Jtter, Rx_ Jtter, W + hermal, () s the man tap delay of the th sub-channel and s s for the BB sub-channel and for the PB sub-channels. Fnally, offset s the total slcer senstvty for the th sub-channel. We have also set E(x (n)) = (=,,,) for all sub-channels, absorbng all the gan coeffcents nto the precoder. he frst set of nequaltes n the feasblty problem are bt error rato constrants for the sub-channels and the second set are pea voltage constrants at the x. Pea voltage constrant orgnates from the headroom requrement of the transmtter crcuts, such that they mantan lnearty of operaton wthout ntroducng non-lnear dstorton. In the AM archtecture, the last ponts n the x data path where transstors are used are potentally the mxers, and therefore, t s essental that the pea voltages at the nput to the mxers reman wthn the allowed range. However, the pea voltage expanson of the fxed analog LPF s precedng the mxers n the x data path s fxed and nown through smulaton. herefore, the pea voltage constrant can alternatvely be appled at the nput to those analog LPF s. Although the optmzaton problem s combnatoral, t s possble to obtan a tght upper bound for the b s by upper boundng the ndvdual sub-channels n solaton when ICI does not exst. In a practcal stuaton, due to complexty constrants, number of sub-channels s small and t s desred that ICI does not have a sgnfcant effect on the performance of the sub-channels. Consequently, startng from the upper bound, the maxmum achevable bt loadng can be obtaned n reasonably small number of teratons. Agan followng Stojanovc s procedure n [], we can readly add per sub-channel DFE to the optmzaton framewor; however, snce the goal of ths paper s to demonstrate the fundamental advantages of AM to BB, we wll only focus on lnear transmt precodng n the subsequent sectons. IV. SYSEM PARAMEERS AD DESIG RADEOFFS An AM system has many desgn parameters that have to be determned before an optmzaton s performed. hese parameters nclude the bandwdth of the sub-channels, channel-select flter type, order and bandwdth, and the guard bandwdth between the sub-channels. Due to the combnatoral nature of the optmzaton framewor, a smple sweep of all these parameters s vrtually mpossble and provdes lttle nsght to the tradeoffs nvolved. An alternatve s to try to quantfy the effect of all the parameters n solaton and n a progressve manner. hs s the procedure we wll tae on n ths secton. Sgnal to ose Rato (SR) s generally very hgh n ln Globecom //$. IEEE

5 channels, at least n the low frequency range. Snce n a M mplementaton a large fracton of the overall data rate comes from the hgh-sr portons of the channel, t s essental that the channel-select flters do not change the qualty of the subchannels by nducng ISI. Unfortunately regular analog flters are not yqust flters n general and can potentally affect the performance. Analog flters follow a general tradeoff between the sharpness of ther stopband fall-off and the lnearty of ther passband phase. he sharper the fall-off, the more nonlnear the phase, and consequently, the more ISI the flter can nduce. here s also a general tradeoff between the bandwdth of a flter and the amount of ISI t can nduce. Roughly speang, the larger the BW, the shorter the tme doman response of the flter, and the less ISI t creates when convolved wth the channel. Smple Sgnal to Interference Rato (SIR) analyss reveals that channel-select flters wth moderate phase propertes, le Butterworth (maxmally flat) flters, nduce less ISI compared to lnear phase flters, le Bessel, or very sharp flters, le Chebyshev, when compared at same stopband rolloff. Consequently, we wll focus on analog Butterworth flters to llustrate the tradeoffs. Fg. (a) llustrates the tradeoff between flter characterstcs and flter nduced ISI. In order to have a quanttatve measure for ISI, ths fgure plots the mnmum number of requred dagonal equalzer taps to acheve certan performance level versus flter excess bandwdth, where excess bandwdth s measured wth respect to the yqust bandwdth. o generate the curves optmzaton s performed on a sngle passband channel and target performance s set to bts per dmenson by settng the nose level. Clearly, as the sgnal attenuaton ncreases n hgher frequency sub-channels and thermal nose becomes more domnant, more levels of ISI can be tolerated and therefore, the requrements we have obtaned for bts/dmenson performance level serve as an upper bound for hgh frequency sub-channels. here s also a tradeoff between guard bandwdth and number of requred cross equalzer taps to acheve a target performance. Fg. (b) llustrates ths tradeoff. In order to generate the curves, optmzaton s performed on three adjacent sub-channels. he sub-channels each support bts 8 Mn. Req. Dag. Precoder aps 7 % Excess Bandwdth % Guard Bandwdth (a) (b) Fg. : Mnmum number of dagonal equalzer tap per dmenson for target performances of bts/dmenson (a) and Mnmum number of cross equalzer taps per Hgher dmenson performance per neghbor levels for for the target PB sub-channels performances requre of bts/dmenson unacceptable (b). excess Butterworth bandwdth flters and are guard used bandwdth both at the to x brng and the down Rx and ISI deal and ICI channel to the s assumed requred for level. both fgures. 8 7 Mn. Req. Cross Precoder aps per dmenson f they operate n solaton. Mnmum number of requred cross equalzer taps s thus obtaned so that same performance s acheved when they operate together. As could be observed, even when a th order flter s used, the matrx precoder wth only a few number of taps s able to cancel ICI to the desred level f moderate guard bandwdth s allowed between the sub-channels. It s clear from Fg. that although sharper flters need less cross precoder taps, they create more ISI, and hence, need more dagonal precoder taps, and a tradeoff exsts. Usng the data presented n Fg., t s possble to plot the mnmum overall requred precoder taps (cross plus dagonal) versus the overall BW penalty (excess plus guard). Results ndcate that for overall precoder complexty of to taps, th order flter nduces the least BW penalty (between % to %). An overall complexty of taps corresponds to % excess BW and % guard BW, and ths s the confguraton we choose for our analyss. he approprate bandwdth for the sub-channels very much depends on the channel characterstcs and mplementaton constrants. For ln channels smlar to Fg., ISI cancellaton loss over.7ghz wde sub-channels s neglgble and sgnal processng rate s low enough that allows usng sophstcated algorthms f desred. Consequently reducng sub-channel bandwdth beyond.7ghz does not boost the performance whle t ncreases the complexty overhead due to the RF frontend. On the other hand, ncreasng sub-channel BW beyond.ghz leads to poor performance due to the deep notches n the channels. A notch n the channel can affect two neghborng sub-channels and when the sub-channels are wde, the resultng loss n the overall data rate could be sgnfcant. herefore, for the analyss n ths paper, we wll set subchannel BW to GHz ndependent of the channel beng analyzed. V. PERFORMACE AD COMPLEXIY COMPARISO WIH BB We are now n a poston to perform a performance evaluaton and complexty analyss on an AM system. Snce ln performance s very mplementaton dependent, we wll have to mae some reasonable assumptons. For comparson, we wll assume that the nose fgure (F) from the crcutry n each sub-channel n the M system, and the F n the BB system are the same and equal to db. We wll assume dedcated rng oscllators wth rms jtter for up/down converson n each sub-channel. In practce better performance s achevable at hgher cost f tuned oscllators are used, or f the low frequency clocs are derved from a sngle hgh-frequency cloc. he cloc used for samplng n all sub-channels s derved from the hghest frequency oscllator n the system, and consequently, the samplng cloc jtter s a percentage of the hgh-frequency cloc perod. Snce nsertng gan elements n the data path can Globecom //$. IEEE

6 Bts/Dm Gan (db) # Req. Pre. aps Bt Rate (Gbps) ELCO Bt Rate (Gbps) (a) 8 (b) 8 (c) proportonally reduce the effect of slcer senstvty, we wll assume neglgble senstvty for the slcers, but nstead, wll fnd the mnmum requred gan necessary for that assumpton to hold f the actual senstvty of the slcers was mv. Fg. (b) shows sub-channel bt loadng for the two channels n Fg. when thermal nose, samplng jtter and carrer phase nose exst all together. Plotted n same fgures are the bt loadngs for BB systems operatng at ther optmum sgnalngrates. he overall bt rates are shown n Fg. (a). Slghtly less than x ncrease n data rate s acheved wth M over BB mplementaton. As expected, over both channels carrer phase nose has mtgated the gan of M n low frequency sub-channels. In other words, as long as both M and BB systems are affected by sgnal dependent nose of the same order, there s no Bts/Dm Gan (db) # Req. Pre. aps FR Frequency (GHz) Frequency (GHz) (d) Fg. : (a) otal bt rate for M and BB systems over ELCO (left) and FR (rght) channels. (b) Bt loadng over same channels. (c) Mnmum requred voltage gan per sub-channel. (d) Mnmum number of requred precoder taps (real and magnary, dagonal and cross) per sub-channel. advantage n swtchng to M. However, a notch n the channel, FR, prevents further ncrease n BB sgnalng rate wthout sgnfcant loss n performance whle t has lttle effect on M. Even f the channel does not have any notches, ELCO, as BB sgnalng rate ncreases, channel attenuaton becomes so hgh that thermal nose becomes domnant, and therefore, M prevals by sufferng less from equalzaton loss. Fg. (c) shows the mnmum requred voltage gan n each sub-channel so that our neglgble slcer senstvty assumpton holds. For most sub-channels less than db gan over a GHz bandwdth s suffcent to acheve the target performance. Part of ths gan has to occur before the mxer so that the target F of db s realzed, but the rest can occur at BB or any other convenent place n the data path. Part of the gan can also be absorbed n slcer senstvty f ADC s wth senstvtes less than mv can be desgned at GHz data rate. he requred voltage gans for BB mplementatons are db and db over about.ghz and 7.GHz bandwdth for FR and ELCO respectvely. Fg. (d) shows the approxmate mnmum number of requred precoder taps per sub-channel to acheve the performance shown n Fg. (b). Both real and magnary dmensons for PB channels are counted. Overall, the two M systems over FR and ELCO requre about and precoder taps operatng at GHz respectvely. he subchannels n the ELCO channels operate at hgher rates compared to ther counterparts n the FR channel, and therefore, requre more ICI cancellaton, and consequently, more cross precoder taps. he BB systems over same channels requre and 77 taps operatng at.ghz and 7.GHz respectvely. Snce power approxmately scales wth frequency, M has a slght advantage over BB n terms of precoder complexty. Fnally, the M system requres ADC s operatng at GHz whle BB requres a sngle ADC operatng at. GHz (7.GHz) over FR (ELCO) channel. In order to better understand the effect of thermal nose and carrer phase nose on the performance of a M system, we now eep the same confguraton as used for Fg. and change thermal nose level and carrer phase nose ndependently. Fg. (a) shows the bt loadngs for a M system when F s changed by ±db. Carrer phase nose has not changed. Fg. (b) shows same data for the case when carrer phase nose s changed by a factor of (correspondng to ±db voltage nose) whle F s ept the same as n Fg.. o be exact, snce nterference contrbutes to both carrer phase nose and samplng jtter, M would be affected less by these mparments, but the dfference s not sgnfcant as long as nterference s suffcently canceled. In other words, requred gan of g for one sub-channels means that the rato of slcer senstvty and sgnal gan n that sub-channel should be smaller than mv/g. Excessve number of precoder taps or requred gan for some sub-channels ndcates that they (or ther neghborng sub-channels) are operatng very close to the target BER, and therefore, requre sgnfcant nterference cancellaton or gan. In general ths can be fxed by assgnng one less bt to those subchannels (or ther neghbors). Globecom //$. IEEE

7 Bts/Dm F = 7dB F = 9dB Bts/Dm Ph =.7% Ph =.8% could be bult n CMOS technology. ACKOWLEDGME A. Amrhany and V. Stojanovć than B. ezamfar and I. Stojanovć for full-hearted help on the paper and techncal dscussons. 8 (a) Frequency (GHz) 8 (b) Frequency (GHz) Fg. : Bt loadngs for M over FR channel when nose fgure s changed by ±db, phase nose = (a) and when carrer phase nose s changed by a factor of, nose fgure = db (b). Comparson of the bt loadngs n Fg. wth those n Fg. reveals that the performance we obtaned for M n Fg. s not very dependent on our assumptons about phase nose and nose fgure. Furthermore, the bt loadngs n Fg. ndcate that the change n the level of thermal nose only affects the hgh frequency sub-channels of the system whle the change n carrer phase nose only affects the performance n the low frequency sub-channels. he reason s that the power of the voltage nose nduced by carrer phase nose s proportonal to receved sgnal power whle thermal nose power s sgnal ndependent. herefore, n the low-frequency sub-channels where sgnal attenuaton s low, thermal nose s much smaller than the nose nduced by carrer phase nose. However, snce for these sub-channels ICI power also depends on the strong neghborng sub-channels, reducng carrer phase nose mproves the performance only as long as ICI s not domnant. Further analyss ndcates that the performance of the nd subchannel n Fg. could have been mproved by addtonal one bts/dmenson f ICI was not present. As sgnal attenuaton ncreases n hgh frequency sub-channels, both phase nose nduced voltage nose and ICI scale wth sgnal strength and thermal nose becomes domnant. A practcal mplcaton of ths observaton s that mplementaton constrants on cloc qualty are relaxed n the hgh frequency sub-channels where buldng hgh-qualty crcuts s dffcult. However, RF frontend for same sub-channels should have good nose propertes. REFERECES [] J. Zerbe, C. Werner, V. Stojanovć, F. Chen, J. We, G. sang, D. Km, W. Stonecypher, A. Ho,. hrush, R. Kollpara, M. Horowtz, K. Donnelly, "Equalzaton and Cloc Recovery for a. - Gb/s - PAM/-PAM Bacplane ranscever Cell," IEEE Journal of Sold-State Crcuts, vol. 8, no., pp. -, Dec.. [] S. Wu, S. Ramaswamy, B. Bhata, P. Landman, R. Payne, V. Gupta, B. Parthasarathy, S. Deshpande, W. Lee, Desgn of.-gbps Bacplane SerDes wth op-down Desgn Methodology, DesgnCon. [] J.. Stonc et al, "An adaptve pam- -Gb/s bacplane transcever n.-µm CMOS," IEEE J. Sold-State Crcuts, vol. 8, no., pp. -, March. [] V. Stojanovć, A. Amrhany and M.A. Horowtz, Optmal lnear precodng wth theoretcal and practcal data rates n hgh-speed seral-ln bacplane communcaton, IEEE Internatonal Conference on Communcatons, June. [] B. Saltzberg, Performance of an effcent parallel data transmsson system, IEEE ransactons on Communcatons, vol., ssue, pp 8-, Dec. 97. [] S. B. Wensten and P. M. Ebert, Data transmsson by frequency dvson multplexng usng the Dscrete Fourer ransform, IEEE ransactons on Communcatons, vol. 9, ssue, pp 8-, Oct. 97. [7] B. Hrosa, An orthogonally multplexed QAM system usng the Dscrete Fourer ransform, IEEE ransactons on Communcatons, vol. 9, ssue, pp 98-89, July 98. [8] K. Poulton et al, A GS/s 8b ADC wth a MB memory n.8µm CMOS, IEEE Internatonal Sold-State Crcuts Conference, Feb., San Francsco. [9] G. Cherubn, E. Eleftherou, S. Oer and J. M. Coff, Flter ban modulaton technques for very hgh speed dgtal subscrber lnes, IEEE Communcatons Magazne, Vol. 8, ssue, pp. 98-, May. [] P. A. elson, F. O-Bustamante and H. Hamada, Inverse flter desgn and equalzaton zones n multchannel sound reproducton, IEEE ransactons on Speech and Audo Processng, vol., no., pp.8-9, May 99. VI. COCLUSIO Analog Mult-tone has the potental to sgnfcantly mprove the performance of hgh-speed seral lns beyond the lmts acheved by baseband processng. he superorty of AM orgnates from ts fundamental capablty to deal wth ISI, as well as ts nherent parallel structure that enables buldng better crcut components at lower frequences. In fact, t s expected that better ICI cancellaton technques, when combned wth better crcut components, lead to a lot better performance. Due to the exstence of RF components, mplementaton of an AM system s a challengng tas, however, our analyss ndcates that the requrements are modest and far from beng mpossble. herefore, the next man step would be to prove that RF crcuts wth the characterstcs specfed n ths paper Globecom //$. IEEE