Part III – Wireline Multiuser Basics

1 Multiuser WondersMultiuser Wonders

Part III – Wireline Multiuser BasicsPart III – Wireline Multiuser Basics

March 31, 2001April 26 2001September 9, 2001September 9, 2001

Prof. John M. CioffiProf. John M. Cioffi

Dept of EEDept of EE

Stanford UniversityStanford University

[email protected]@stanford.edu


Parts 3 and 4: Outline/ScheduleParts 3 and 4: Outline/Schedule

2:00-2:452:00-2:45 MU TheoryMU Theory 2:45-3:302:45-3:30 channels for wirelinechannels for wireline 3:30-4:00 3:30-4:00 CoffeeCoffee 4:00-4:304:00-4:30 DSL and Ethernet archDSL and Ethernet arch 4:30-5:154:30-5:15 Multiuser improvementsMultiuser improvements 5:15-5:305:15-5:30 ZekeZeke


Part 3 OutlinePart 3 Outline

Levels of Coordination among Multi UsersLevels of Coordination among Multi Users GDFE TheoryGDFE Theory SolutionsSolutions

MUD – no coordinationMUD – no coordination Iterative Waterfilling – Interference ChanIterative Waterfilling – Interference Chan VectoringVectoring

ChannelsChannels


Goal: Best PHY signals for user sharing of channelGoal: Best PHY signals for user sharing of channel Set spectra/signals, optimization via controllerSet spectra/signals, optimization via controller

Wireline Multiuser BasicsWireline Multiuser Basics

RouterRouterDSLAMDSLAMSS

User 1User 1

User 2User 2

User KUser K

......

Controller ?Controller ?


Ultimate Goal: use of Rate RegionsUltimate Goal: use of Rate Regions

Plot of all possible rates of usersPlot of all possible rates of users Any point in region is possible, but each with different Any point in region is possible, but each with different

spectraspectra Varies for each channelVaries for each channel

RRshortshort

RRlonglong

Spectral pair 1Spectral pair 1



Wireline Coordination ?Wireline Coordination ?

How much coordination among lines is How much coordination among lines is allowed?allowed? NoneNone Spectra, all or someSpectra, all or some SignalsSignals

Answer: it depends on application (DSL, Answer: it depends on application (DSL, ethernet) and evolves with timeethernet) and evolves with time


No CoordinationNo Coordination

Multiuser Detectors only (MUD)Multiuser Detectors only (MUD) Different users could be competitive service providers (different DSLAMS, different modulation)Different users could be competitive service providers (different DSLAMS, different modulation) Unbundled state of artUnbundled state of art

Controller ?Controller ?

SharedSharedchannelchannel

User 1User 1User 1User 1

......

User 2User 2User 2User 2

User LUser L

User LUser L

NEXTNEXTFEXTFEXT


Coordinated Spectra (only)Coordinated Spectra (only)

““interference probleminterference problem” in Information Theory” in Information Theory Good, but not optimum, solution knownGood, but not optimum, solution known

Iterative waterfillingIterative waterfilling


User 1User 1

ControllerController

User 1User 1

User 2User 2

User LUser L

......

User 2User 2

User LUser L



Coordinated 1-sided Coordinated 1-sided SignalsSignals

Multiple access and Broadcast problemsMultiple access and Broadcast problems Monopoly Service ProviderMonopoly Service Provider



User 1User 1

User 2User 2

User LUser L

......



Coordinated 2-sided Coordinated 2-sided SignalsSignals

Full Vectoring Problem – private networks (cat 5)Full Vectoring Problem – private networks (cat 5) Highest data ratesHighest data rates







Coordination LevelsCoordination Levels GDFE TheoryGDFE Theory SolutionsSolutions


ChannelsChannels


Block/Packet Transmission channelBlock/Packet Transmission channel

Assumes NO NEXT (FDM used to separate up/downAssumes NO NEXT (FDM used to separate up/down X X is input vector ofis input vector of

One or up to L users’ data samplesOne or up to L users’ data samples Coordinated or not, L users x mN dimensionsCoordinated or not, L users x mN dimensions

Y Y is output vector ofis output vector of One or more receivers output packetsOne or more receivers output packets Coordinated or not, L users x nN dimensionsCoordinated or not, L users x nN dimensions

H is linear coupling, Noise vector is H is linear coupling, Noise vector is nn

XXdata 1data 1

data 2data 2

data data LL

HH +

nn

YY rcvrrcvr


Generalized DFEGeneralized DFE

W and B are matrix operations on the packets Y and XW and B are matrix operations on the packets Y and X Traditional structures become matrices that do not Traditional structures become matrices that do not

necessarily correspond to convolutionnecessarily correspond to convolution Applies to all single-user and multiple-user situationsApplies to all single-user and multiple-user situations

WW ++decision sequencedecision sequence

for packetfor packet

BB

YY

SNRSNR

ZZXX


Finding the Equivalent ChannelFinding the Equivalent ChannelXX

HH

Y

N

+

““good part” - gets through channelgood part” - gets through channel

““null space” - blocked by channelnull space” - blocked by channel

““null space” - zeroed by designnull space” - zeroed by design

Input componentsInput components best are best are greengreen


GDFE SolutionsGDFE Solutions

Always can be combined with good AWGN transmit Always can be combined with good AWGN transmit codes and “green” signal optimization to get best codes and “green” signal optimization to get best performanceperformance b=c=log(1 +SNRb=c=log(1 +SNRGDFEGDFE))

Use good (turbo, LDPC) code on green componentsUse good (turbo, LDPC) code on green components

fundamental structure used to analyze (not fundamental structure used to analyze (not implement)implement)

Useful one way or another in all the multiple user Useful one way or another in all the multiple user problemsproblems

Introduced Cioffi/Forney, 1996 – see [5]Introduced Cioffi/Forney, 1996 – see [5]





ChannelsChannels


No coordination - MUDNo coordination - MUD

Similar to wireless caseSimilar to wireless case Various interference cancellation strategiesVarious interference cancellation strategies

LinearLinear Decision-aidedDecision-aided

Each receiver learns or estimates channel from all usersEach receiver learns or estimates channel from all users Each receiver attempts to reduce/eliminate signals from all other Each receiver attempts to reduce/eliminate signals from all other

users while estimating the signal it wantsusers while estimating the signal it wants Other signals may not be orthogonal for many reasonsOther signals may not be orthogonal for many reasons

Intersymbol interferenceIntersymbol interference Interchannel interference (crosstalk)Interchannel interference (crosstalk)

Wireline case differences (from wireless)Wireline case differences (from wireless) Crosstalkers may be very large or very small, and still significant in Crosstalkers may be very large or very small, and still significant in

all casesall cases Channel is relatively stationary (usually)Channel is relatively stationary (usually)


yy=H=Hxx + + n = n = HH11 xx11 + + HH22 x x22 …+ …+ nn H=[HH=[H11 H H22 … H … HL L ]]

MUD Channel ModelMUD Channel Model

Xtalk Xtalk filtering, filtering, HH22XmitXmit 2 2

((xx22 )) ++

..

Xtalk Xtalk filtering, filtering, HHLLXmit Xmit LL

((xxLL ))

..

..

Line channel, Line channel, HH11

Xmit Xmit 11((xx11 )) ++

Noise, Noise, 22, , nn

DSL DSL rcvrrcvr

HHHyyy


(L users) x (1N dimensions) –(L users) x (1N dimensions) –Generalized DFEGeneralized DFE

Tries to estimate all users, even if we don’t want them Tries to estimate all users, even if we don’t want them allall Helps estimate the user of interest in no-coordination problemHelps estimate the user of interest in no-coordination problem Best that can be done, given any input spectraBest that can be done, given any input spectra

Error propagation can be enormous degradationError propagation can be enormous degradation

WW ++decision sequencedecision sequence

for packetfor packet

BB

YY

SNRSNR

ZZXX


Error Prop Fix: Iterative DecodingError Prop Fix: Iterative Decoding

Compute probabilities, rather than hard decisionsCompute probabilities, rather than hard decisions when done iterating, then do hard decisionwhen done iterating, then do hard decision Effectively achieves level of performance of no-error GDFE/capacityEffectively achieves level of performance of no-error GDFE/capacity

Decoder 1Decoder 1(prob of (prob of xx11 symbol) symbol)

ChannelChanneloutputoutput

Decoder 2Decoder 2(prob of (prob of xx22 symbol) symbol)

HardHardDecisonDecison

HardHardDecisonDecison

pp11

pp22(typically(typicallynot implemented)not implemented)

xx11

xx22

hh1,11,1

hh1,21,2

++ ++

nnnoisenoise

User 1User 1

User 2User 2


Soft vs Hard Canceller [18]Soft vs Hard Canceller [18]

is average value of is average value of xxii, computed from p.d., computed from p.d.

2x4x

1 2 4 Soft symbolsSoft symbols

Hard decisionsHard decisions

+ Soft or hardSoft or hardxx33

3y

1,3h

2,3h

4,3h

1x


3 step iteration3 step iteration

Compute new soft outputCompute new soft output compute probability distribution from soft compute probability distribution from soft

outputs for each output dimensionoutputs for each output dimension compute new soft symbol and variancecompute new soft symbol and variance Do it again and again, cycling through Do it again and again, cycling through

estimates of all users’ signals xestimates of all users’ signals x


Example for MUD: HPNA into VDSLExample for MUD: HPNA into VDSL

COCO

homehome

hpnahpnavdslvdsl

hpnahpna

telcotelco

vdslvdsl

No signal necessarily much larger than anotherNo signal necessarily much larger than another Error propagation would destroy GDFE aloneError propagation would destroy GDFE alone Iterative decoding with GDFE works at near optimum Iterative decoding with GDFE works at near optimum

levels (I.e., as if there were no error prop.)levels (I.e., as if there were no error prop.)


Optimum DetectorOptimum Detector

6 tones of 256 zeroed in 5-10 MHz band6 tones of 256 zeroed in 5-10 MHz band

26 Mbps]26 Mbps]VDSLVDSL

8 Mbps]8 Mbps]HLANHLAN


Example: DSL and HPNAExample: DSL and HPNA VDSL and HPNA both share 5-10 MHz on twisted pairVDSL and HPNA both share 5-10 MHz on twisted pair Use GDFE concept and soft-cancellation at rcvr for Use GDFE concept and soft-cancellation at rcvr for

VDSLVDSL Works like HPNA wasn’t there (mutliuser capacity on phone line Works like HPNA wasn’t there (mutliuser capacity on phone line

is 200 Mbps vs 20 Mbps when other user is Gaussian noise)is 200 Mbps vs 20 Mbps when other user is Gaussian noise)





ChannelsChannels


Interference Channel – Spectral BalancingInterference Channel – Spectral Balancing

No transmit or receive No transmit or receive signal signal coordinationcoordination Only spectra can be designed jointlyOnly spectra can be designed jointly Only cases for which opt. solution is known areOnly cases for which opt. solution is known are

1N dimensions by L users - broadcast1N dimensions by L users - broadcast L by 1N – multiple accessL by 1N – multiple access 1N by 1N – single user = “Water Filling”1N by 1N – single user = “Water Filling”

General case, a good (not nec opt) solution is General case, a good (not nec opt) solution is known as “iterative waterfilling”known as “iterative waterfilling”


Sub optimal SolutionSub optimal Solution

GDFE on each receiver for all L usersGDFE on each receiver for all L users Best for any given spectra of all usersBest for any given spectra of all users

Don’t know best spectra for set of usersDon’t know best spectra for set of users Try to optimize anyway using iterative waterfillingTry to optimize anyway using iterative waterfilling

GDFE 1GDFE 1


GDFE 1GDFE 1

GDFE 2GDFE 2

GDFE LGDFE L

......

GDFE 2GDFE 2

GDFE 3GDFE 3



WaterfillingWaterfilling

Waterfilling is known optimum on single-user channelWaterfilling is known optimum on single-user channel

/g(f)= /g(f)= |N(f)/H(f)| |N(f)/H(f)|22

NSR(f)NSR(f)

S(f)S(f)


Iterative Waterfilling [15],[16]Iterative Waterfilling [15],[16]

Each channel considers all others to have fixed spectra Each channel considers all others to have fixed spectra Can start with flat on allCan start with flat on all

Waterfilling executed for user 1Waterfilling executed for user 1 New spectrum for user 1 replaces oldNew spectrum for user 1 replaces old

Waterfilling executed for user 2 with new spectra for 1Waterfilling executed for user 2 with new spectra for 1 New spectra for user 2 replaces oldNew spectra for user 2 replaces old

… … user Nuser N Recycle a few timesRecycle a few times Converges – close to optimum solution for Inteference Converges – close to optimum solution for Inteference

channel – nearly maximizes sum of all rateschannel – nearly maximizes sum of all rates


Generation of Rate RegionsGeneration of Rate Regions

Each user has power limitEach user has power limit For each userFor each user

Lower the power limit in IterWater and get Lower the power limit in IterWater and get increased rates on othersincreased rates on others

Sketch N-dimensional rate region by running IterWater Sketch N-dimensional rate region by running IterWater for many different power combinationsfor many different power combinations Check if desired rate is in regionCheck if desired rate is in region

RRshortshort

RRlonglong







ChannelsChannels


Multiple Access – Up LinkMultiple Access – Up Link

GDFE at one side with H=[HGDFE at one side with H=[H11 H H22 … H … HLL]] Vector receiver, with synch-DMT, LxL GDFEVector receiver, with synch-DMT, LxL GDFE Best Solution now known – [15] Yu, Rhee, Cioffi (only FDM when there Best Solution now known – [15] Yu, Rhee, Cioffi (only FDM when there

is only one receiver [14] – more complicated than that here)is only one receiver [14] – more complicated than that here) May have all L users on each toneMay have all L users on each tone

GDFE separates them at DSLAMGDFE separates them at DSLAM May have error propagation, so iterative decoding necessary May have error propagation, so iterative decoding necessary

GDFEGDFEDSLAMDSLAM


User 1User 1

User 2User 2

User LUser L

......

SharedSharedChannelChannel

HHLN x LNLN x LN


Input SpectraInput Spectra

Can again be computed by iterative waterfilling Can again be computed by iterative waterfilling across N tonesacross N tones known optimum in this multiple-access caseknown optimum in this multiple-access case

Each tone is L x L GDFE receiver with DMT Each tone is L x L GDFE receiver with DMT modulation on channelmodulation on channel

Can approximately compute a lower bound on Can approximately compute a lower bound on rate region using iterative waterfilling and rate region using iterative waterfilling and varying powers on each channel as in spectral varying powers on each channel as in spectral balancingbalancing


Broadcast DownlinkBroadcast Downlink

Optimum known (solved after 30 yrs in 2001)Optimum known (solved after 30 yrs in 2001) More complicated version of IterWaterMore complicated version of IterWater See Wei Yu recent work [17] , iterative solution of Ricatti eqnSee Wei Yu recent work [17] , iterative solution of Ricatti eqn Achieves nearly same performance as multiple access for most Achieves nearly same performance as multiple access for most

wireline cases, but optimization occurs with precoder at transmit wireline cases, but optimization occurs with precoder at transmit side to leave each receiver independent – GDFE at each receiver side to leave each receiver independent – GDFE at each receiver is diagonal (no feedback) and is slicer for each user.is diagonal (no feedback) and is slicer for each user.

VectorVectorDSLAMDSLAM

Vector precoderVector precoder


simple 1simple 1

simple 2simple 2

simple Lsimple L

......

SharedSharedChannelChannel

HHLN x LNLN x LN


Ginis/Negi QR Simplification of Ginis/Negi QR Simplification of Vectored GDFEVectored GDFE

ZF-GDFE close to MMSE-GDFE on wireline channels (max rate ZF-GDFE close to MMSE-GDFE on wireline channels (max rate sum)sum) FEXT from any source is less than on-line signal from that sourceFEXT from any source is less than on-line signal from that source

H=QR (orthogonal, triangular) H=QR (orthogonal, triangular) Applies directly to Multiple Access Applies directly to Multiple Access UplinkUplink Problem for each tone Problem for each tone

W=Q’W=Q’ ++decision sequencedecision sequence

for packetfor packetYY

SNRSNR

ZZXX

B=RB=R


Vectored Transmitter - downlinkVectored Transmitter - downlink

Q’Q’++

I-RI-R

modmodXX xx

X’X’

Vector version of Tomlinson precoder, done Vector version of Tomlinson precoder, done for each tone independentlyfor each tone independently

Prewarps transmitted signal to avert FEXTPrewarps transmitted signal to avert FEXT


Full Vectoring Solution – SVDFull Vectoring Solution – SVD

H=H=MM’’FF (M,F orthogonal, (M,F orthogonal, diagonal) diagonal) Singular value decompositionSingular value decomposition

Vectored VDSL or VDMTVectored VDSL or VDMT Always gets max rate-sum capacityAlways gets max rate-sum capacity

QR is close on DSL channels, but not in all situationsQR is close on DSL channels, but not in all situations Easy to implement on per-tone basisEasy to implement on per-tone basis

MIMO Echo cancellation possible (so full band)MIMO Echo cancellation possible (so full band)

W=F’W=F’ decision sequencedecision sequencefor packetfor packet

YY

XXHHMMXX




MUD – no coordinationMUD – no coordination Iterative Waterfilling – Interference ChanIterative Waterfilling – Interference Chan Vectoring – MA, BroadcastVectoring – MA, Broadcast Full Vectoring solutionFull Vectoring solution

ChannelsChannels


ADSL LoopsADSL Loops

d d

3-5 mile loops3-5 mile loops loops with bridge tapsloops with bridge taps


CrosstalkCrosstalk

phone line 1phone line 1

phone line 2phone line 2

NEXTNEXT FEXTFEXT

Dominant noises, increased coupling at higherDominant noises, increased coupling at higherfrequencies - must be mitigated in designfrequencies - must be mitigated in designNEXT - 10NEXT - 10-13-13 f f1.5 1.5 ; FEXT - 10; FEXT - 10-19 -19 d |H(f)|d |H(f)|22 f f22


Other NoisesOther Noises Radio Noise, AM, HAMRadio Noise, AM, HAM

1 mW differential into rcvr1 mW differential into rcvr must reject HAM by 70-90 dB (VDSL) and AM must reject HAM by 70-90 dB (VDSL) and AM

by 20-40 dB (ADSL)by 20-40 dB (ADSL)

Impulse NoiseImpulse Noise 10’s millivolts10’s millivolts 100’s microseconds100’s microseconds narrowband (high amplitude)narrowband (high amplitude) broadband (low amplitude)broadband (low amplitude)


Radio EmissionsRadio Emissions like crosstalk, except into radio receiverslike crosstalk, except into radio receivers VDSL amateur (HAM) bands Public Safety bandsVDSL amateur (HAM) bands Public Safety bands transmit in discontinuous bandstransmit in discontinuous bands

2 MHz2 MHz 3.5 MHz3.5 MHz

no signalno signalallowedallowed

signalsignalallowedallowed

10 MHz10 MHz

frequency

7 MHz7 MHz-60 dBm/Hz-60 dBm/Hz

-80 dBm/Hz-80 dBm/Hz


MIMO Line Quantities [3]MIMO Line Quantities [3]

Matrix Channel XferMatrix Channel Xfer

Individual lines i=jIndividual lines i=j Magnitude profiles (i.e., no phase information)Magnitude profiles (i.e., no phase information)

Virtual Binder GroupVirtual Binder Group

KKjjKKiiij fHf

,...,,...,11;;,...,,...,11 HH

iijf

i fHJ max


Noises [3],[4]Noises [3],[4]

Noises are “unknown” crosstalkers and Noises are “unknown” crosstalkers and thermal/radiothermal/radio Psd Psd N(f)N(f) Frequency bandwidth of measurementFrequency bandwidth of measurement Time interval for measurementTime interval for measurement Requisite accuracyRequisite accuracy


Source Information [3],[5]Source Information [3],[5]

Clock offsets – can be determined at various Clock offsets – can be determined at various points for virtual binder linespoints for virtual binder lines

Transmit power level – needs reportingTransmit power level – needs reporting


Channel ID 1Channel ID 1

Estimate gains at several frequenciesEstimate gains at several frequencies Estimate noise variances at same freqsEstimate noise variances at same freqs

XXnn

Size-NSize-NIFFTIFFT

(with prefix)(with prefix)ppkk

++

nnkk

Size-NSize-NFFTFFT

++PPnnEEnn

++

++

++

--


Gain EstimationGain Estimation

Divide/average channel-out by known inDivide/average channel-out by known in

Need about Need about L=40L=40 symbols of training to symbols of training to reduce gain estimation error to .1 dBreduce gain estimation error to .1 dB

LL

ll nnll

nnllnn

XX

YY

LLPP

11 ,,

,,11ˆ̂


Noise EstimationNoise Estimation

Use Errors from Gain estimationUse Errors from Gain estimation

Need Need L=4000 L=4000 for .1 dB errorfor .1 dB error SNR is then gain-squared/noise SNR is then gain-squared/noise

estimateestimate

LL

llnnnn EE

LL 11

22

,,1122 11

ˆ̂


MIMO ComplicationsMIMO Complications

Training may not be availableTraining may not be available Use actual dataUse actual data

Different systems may not have same Different systems may not have same clockclock Interpolation problemInterpolation problem


Transmitter User i

Receiver User j

NEXT FEXT

Basic MIMO crosstalk ID [4]Basic MIMO crosstalk ID [4]

NEXTs and FEXTSNEXTs and FEXTS Difference services (ADSL, HDSL ,…)Difference services (ADSL, HDSL ,…) Different operators (unbundling)Different operators (unbundling)


Generic Crosstalk ModelGeneric Crosstalk Model

Channel hChannel h00

CrosstalkCrosstalkchannel hchannel h11

CrosstalkCrosstalkchannel hchannel hkk

Xmit 0Xmit 0

Xmit 1Xmit 1

Xmit KXmit K

noise n

+ Rcvr 0yxx00

xx11

xxKK

• Mathematical modelMathematical model

K

iiii mndmxmhmy

0

)()()()(

• ObjectivesObjectives find hfind hii(m)(m)If each solely excited If each solely excited with training sequence, with training sequence, then previous method then previous method applies directly for eachapplies directly for eachRare if ever occurrenceRare if ever occurrence


Step 1: Data AcquisitionStep 1: Data Acquisition

Modem 0

Modem k

COCustomerPremises

Modem 0

Modem k

NMCNMCSNMPSNMP

• Network Maintenance Center (NMC) Acquire data during a pre-defined time period


Step 2: ResamplingStep 2: Resampling

Different servicesDifferent services Different sampling rateDifferent sampling rate Time-varying crosstalk functionTime-varying crosstalk function

Resample the transmitted input dataResample the transmitted input data Stationary crosstalk functionStationary crosstalk function

Tx FilterTx Filterp(t)p(t)

xTalkxTalkhhii(t)(t)

Rcvr FilterRcvr Filterhhlplp(t)(t)1/T 1/T1/T''

yxc(t)x(n)


Timing differenceTiming difference

Different modems Different modems Different time stamps Different time stamps Pre-defined periods do not align perfectlyPre-defined periods do not align perfectly

Modem 0

Modem i

Modem k

DSLAM

DSLAM

NMCNMC


Step 3: Timing Difference EstimationStep 3: Timing Difference Estimation

Example of timing differenceExample of timing difference Cross-correlationCross-correlation

Calculate cross-correlation between xCalculate cross-correlation between x ii and and y, y, RxRxiiy(l)y(l)

Detect the peak of Detect the peak of |Rx|Rxiiy(l)|y(l)|

timetimeddii LLtt+1+1

xxii(0)(0) xxii(d(dii)) xxii(L(Ltt))

y(0)y(0) y(Ly(Ltt))

3:00:003:00:00 3:01:003:01:00


Cross-correlationCross-correlation


Step 4: Crosstalk Functions Estimation Step 4: Crosstalk Functions Estimation

Modified mathematical modelModified mathematical model

K

iiii

K

iiii

iiiiii

mnmzmh

mnmzmhmy

dmxmzdd

1

1

~~

)()()(

)()()()(

)()( ,

• Vector formVector form

nhZ

n

h

h

h

] Z ZZ[y

K

2

1

K 21


NEXTs and FEXTsNEXTs and FEXTs

NEXTsNEXTs FEXTsFEXTs


HDSL NEXT, time responseHDSL NEXT, time response


Estimation ErrorEstimation Error


MIMO Channel ID Method with MIMO Channel ID Method with training packetstraining packets

Correlate to rough timing alignmentCorrelate to rough timing alignment I/O packets stored around time stamp on I/O packets stored around time stamp on

lines and reported to maintenance centerlines and reported to maintenance center Determination of exact timing offsetDetermination of exact timing offset Interpolation of inputs to common timing Interpolation of inputs to common timing

phasephase Least-Squares fittingLeast-Squares fitting

See JSAC or [4], C. Zeng for DSLSee JSAC or [4], C. Zeng for DSL


EM (Blind) TrainingEM (Blind) Training

NXHY

A block of received data can be collected to form:A block of received data can be collected to form:

!unknown! is but , and Find XH


ML and EM SolutionsML and EM Solutions

Maximum Likelihood (complex)Maximum Likelihood (complex)

Matrix inversion for each possible sequenceMatrix inversion for each possible sequence Expectation Maximization (easier)Expectation Maximization (easier)

No training – 1 matrix inversionNo training – 1 matrix inversion

),|(logmax,

XHYpXH

),|(logmax XHYpEXH


Block EM channel estimationBlock EM channel estimation

],,|[ 2_____________

kkTET HYXXXX

nkk

nL

n

nnL

n

nT YYEY ],,|[ 2

11

HXXYX

),,|(

),,|(],,|[

2

,,|

2

,,|2

2

2

kknn

Y

kknn

Y

n

kknn

Yf

YfYE

HX

HXXHX

HX

HX

k

TTk

TTk

Tk

TTk

LHXXHYXHYY

YXXXH

ˆˆˆ21

ˆ

ˆ

21

1

1. Compute and invert.1. Compute and invert.

2. Compute2. Compute

usingusing

3. Channel and noise variance estimate is given by 3. Channel and noise variance estimate is given by


Simulation SetupSimulation Setup

ADSL-DBM modemADSL-DBM modem 1 NEXT (SSDSL) and 1 NEXT (SSDSL) and 1 FEXT (ADSL)1 FEXT (ADSL)

Initial condition acquired from sync symbol or Initial condition acquired from sync symbol or from network maintenance center from network maintenance center

500 m line FEXT source500 m line FEXT source 10 ms of data (L=40)10 ms of data (L=40)


EM Simulation ResultsEM Simulation Results


MotivationMotivation

Eliminates delayEliminates delay Reduces storageReduces storage Track time-variant parameters or locally Track time-variant parameters or locally

stationary processes in an adaptive stationary processes in an adaptive mannermanner

Block stationary assumption no longer Block stationary assumption no longer neededneeded

See [3]See [3]


Parts 3 and 4: Outline/ScheduleParts 3 and 4: Outline/Schedule

2:00-2:452:00-2:45 MU TheoryMU Theory 2:45-3:302:45-3:30 channels for wirelinechannels for wireline 3:30-4:00 3:30-4:00 CoffeeCoffee 4:00-4:304:00-4:30 DSL and Ethernet archDSL and Ethernet arch 4:30-5:154:30-5:15 Multiuser improvementsMultiuser improvements

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Part III – Wireline Multiuser Basics