Upload
diella
View
42
Download
0
Embed Size (px)
DESCRIPTION
Part III – Wireline Multiuser Basics. Prof. John M. Cioffi Dept of EE Stanford University [email protected]. September 9, 2001. March 31, 2001. April 26 2001. Parts 3 and 4: Outline/Schedule. 2:00-2:45MU Theory 2:45-3:30channels for wireline 3:30-4:00 Coffee - PowerPoint PPT Presentation
Citation preview
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
2 Multiuser WondersMultiuser Wonders
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
3 Multiuser WondersMultiuser Wonders
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
4 Multiuser WondersMultiuser Wonders
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 ?
5 Multiuser WondersMultiuser Wonders
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
Spectral pair 2Spectral pair 2
6 Multiuser WondersMultiuser Wonders
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
7 Multiuser WondersMultiuser Wonders
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
8 Multiuser WondersMultiuser Wonders
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
SharedSharedchannelchannel
User 1User 1
ControllerController
User 1User 1
User 2User 2
User LUser L
......
User 2User 2
User LUser L
9 Multiuser WondersMultiuser Wonders
SharedSharedchannelchannel
Coordinated 1-sided Coordinated 1-sided SignalsSignals
Multiple access and Broadcast problemsMultiple access and Broadcast problems Monopoly Service ProviderMonopoly Service Provider
RouterRouterDSLAMDSLAMSS
ControllerController
User 1User 1
User 2User 2
User LUser L
......
10 Multiuser WondersMultiuser Wonders
SharedSharedchannelchannel
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
RouterRouterDSLAMDSLAMSS
ControllerController
RouterRouterDSLAMDSLAMSS
ControllerController
11 Multiuser WondersMultiuser Wonders
Part 3 OutlinePart 3 Outline
Coordination LevelsCoordination Levels GDFE TheoryGDFE Theory SolutionsSolutions
MUD – no coordinationMUD – no coordination Iterative Waterfilling – Interference ChanIterative Waterfilling – Interference Chan VectoringVectoring
ChannelsChannels
12 Multiuser WondersMultiuser Wonders
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
13 Multiuser WondersMultiuser Wonders
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
14 Multiuser WondersMultiuser Wonders
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
15 Multiuser WondersMultiuser Wonders
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]
16 Multiuser WondersMultiuser Wonders
Part 3 OutlinePart 3 Outline
Coordination LevelsCoordination Levels GDFE TheoryGDFE Theory SolutionsSolutions
MUD – no coordinationMUD – no coordination Iterative Waterfilling – Interference ChanIterative Waterfilling – Interference Chan VectoringVectoring
ChannelsChannels
17 Multiuser WondersMultiuser Wonders
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)
18 Multiuser WondersMultiuser Wonders
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
19 Multiuser WondersMultiuser Wonders
(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
20 Multiuser WondersMultiuser Wonders
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
21 Multiuser WondersMultiuser Wonders
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
22 Multiuser WondersMultiuser Wonders
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
23 Multiuser WondersMultiuser Wonders
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.)
24 Multiuser WondersMultiuser Wonders
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
25 Multiuser WondersMultiuser Wonders
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)
26 Multiuser WondersMultiuser Wonders
Part 3 OutlinePart 3 Outline
Coordination LevelsCoordination Levels GDFE TheoryGDFE Theory SolutionsSolutions
MUD – no coordinationMUD – no coordination Iterative Waterfilling – Interference ChanIterative Waterfilling – Interference Chan VectoringVectoring
ChannelsChannels
27 Multiuser WondersMultiuser Wonders
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”
28 Multiuser WondersMultiuser Wonders
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
ControllerController
GDFE 1GDFE 1
GDFE 2GDFE 2
GDFE LGDFE L
......
GDFE 2GDFE 2
GDFE 3GDFE 3
SharedSharedchannelchannel
29 Multiuser WondersMultiuser Wonders
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)
30 Multiuser WondersMultiuser Wonders
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
31 Multiuser WondersMultiuser Wonders
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
Spectral pair 1Spectral pair 1
Spectral pair 2Spectral pair 2
32 Multiuser WondersMultiuser Wonders
Part 3 OutlinePart 3 Outline
Coordination LevelsCoordination Levels GDFE TheoryGDFE Theory SolutionsSolutions
MUD – no coordinationMUD – no coordination Iterative Waterfilling – Interference ChanIterative Waterfilling – Interference Chan VectoringVectoring
ChannelsChannels
33 Multiuser WondersMultiuser Wonders
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
ControllerController
User 1User 1
User 2User 2
User LUser L
......
SharedSharedChannelChannel
HHLN x LNLN x LN
34 Multiuser WondersMultiuser Wonders
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
35 Multiuser WondersMultiuser Wonders
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
ControllerController
simple 1simple 1
simple 2simple 2
simple Lsimple L
......
SharedSharedChannelChannel
HHLN x LNLN x LN
36 Multiuser WondersMultiuser Wonders
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
37 Multiuser WondersMultiuser Wonders
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
38 Multiuser WondersMultiuser Wonders
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
39 Multiuser WondersMultiuser Wonders
Part 3 OutlinePart 3 Outline
Coordination LevelsCoordination Levels GDFE TheoryGDFE Theory SolutionsSolutions
MUD – no coordinationMUD – no coordination Iterative Waterfilling – Interference ChanIterative Waterfilling – Interference Chan Vectoring – MA, BroadcastVectoring – MA, Broadcast Full Vectoring solutionFull Vectoring solution
ChannelsChannels
40 Multiuser WondersMultiuser Wonders
ADSL LoopsADSL Loops
d d
3-5 mile loops3-5 mile loops loops with bridge tapsloops with bridge taps
41 Multiuser WondersMultiuser Wonders
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
42 Multiuser WondersMultiuser Wonders
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)
43 Multiuser WondersMultiuser Wonders
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
44 Multiuser WondersMultiuser Wonders
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
45 Multiuser WondersMultiuser Wonders
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
46 Multiuser WondersMultiuser Wonders
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
47 Multiuser WondersMultiuser Wonders
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
++
++
++
--
48 Multiuser WondersMultiuser Wonders
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
49 Multiuser WondersMultiuser Wonders
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
50 Multiuser WondersMultiuser Wonders
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
51 Multiuser WondersMultiuser Wonders
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)
52 Multiuser WondersMultiuser Wonders
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
53 Multiuser WondersMultiuser Wonders
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
54 Multiuser WondersMultiuser Wonders
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)
55 Multiuser WondersMultiuser Wonders
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
56 Multiuser WondersMultiuser Wonders
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
57 Multiuser WondersMultiuser Wonders
Cross-correlationCross-correlation
58 Multiuser WondersMultiuser Wonders
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
59 Multiuser WondersMultiuser Wonders
NEXTs and FEXTsNEXTs and FEXTs
NEXTsNEXTs FEXTsFEXTs
60 Multiuser WondersMultiuser Wonders
HDSL NEXT, time responseHDSL NEXT, time response
61 Multiuser WondersMultiuser Wonders
Estimation ErrorEstimation Error
62 Multiuser WondersMultiuser Wonders
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
63 Multiuser WondersMultiuser Wonders
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
64 Multiuser WondersMultiuser Wonders
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
65 Multiuser WondersMultiuser Wonders
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
66 Multiuser WondersMultiuser Wonders
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)
67 Multiuser WondersMultiuser Wonders
EM Simulation ResultsEM Simulation Results
68 Multiuser WondersMultiuser Wonders
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]
69 Multiuser WondersMultiuser Wonders
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