5/1/2003 1 KU Leuven Department of Electrical Engineering R. Cendrillon and M. Moonen Optimal Spectrum Management

Optimal Spectrum Management

5/1/2003

1

KU Leuven Department of Electrical Engineering

R. Cendrillon and M. Moonen



5/1/2003

2R. Cendrillon and M. Moonen


ContentsContents• Optimal Spectrum Management

– Achieves maximum possible rates for modems within network– Up to 300% rate gains over IW

• Crosstalk Precompensation– Ginis’ QR Precompensator (requires modification of CPE)– Row-wise diagonal dominance– Linear Diagonalizing Precompensator (near optimal, no change of CPE)

• Partial Cancellation– Distributing compute power across frequency– Large run-time complexity reduction


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Optimal Spectrum ManagementOptimal Spectrum Management• Joint work together with Wei Yu (Uni. of Toronto), Alcatel Bell

• Goal: Characterise border of rate region– Find optimal operating points– Corresponding TX PSDs

• In DSL channels equivalent to maximising weighted rate-sum

transmit spectra of user n: sn = [ s1n...sK

n ]

• 2 user example to simplify discussion ( > 2 users straight-forward)

• Non-convex

• Cannot use convex optimisation techniques!

k kk k PsPs

RwwR

22

11

21,

,s.t.

)1(max21 ss


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Exhaustive SearchExhaustive Search• Limit sk

n to take d possible values e.g.

– Granularity of PSD scale (e.g. 0.5 dB in DSM Report, T1E1.4/2003-018R6)– PSDs corresponding to exact bitloadings

• (bmax + 1)N possible bitloading tuples (bk1,...,bk

N )

• Each bitloading tuple has corresponding PSD tuple (sk1,...,sk

N )

• Easy to convert (bk1,...,bk

N ) (sk1,...,sk

N ): O( N 3 ) complexity

• d = bmax + 1

• Exhaustive search– sn has dK possible values

– (s1, s2) has d 2K possible values

– Exhaustive search: O(d 2K ) complexity– ADSL K = 256, VDSL K = 4096

Computationally Intractable!Computationally Intractable!


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Per-tone SolutionPer-tone Solution• Consider original problem

• Can be rewritten

k kk k PsPs

RwwR

22

11

21,

,s.t.

)1(max21 ss

k kk k

k kkssss

PsPs

bwwbKK

22

11

21

),(),(

,s.t.

)1(max212

111


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ObjectiveObjective

k kkssss

bwwbKK

21

),(),()1(max

2121

11

• Exhaustive search O(dN) per tone -> O(KdN)• Computationally Tractable!

kbwwb kkss kk

,)1(max 21

, 21

• Could be solved independently on each tone


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ConstraintsConstraints

• But total power constraint couples optimisation between tones

• What to do?

k kk k

k kkssss

PsPs

bwwbKK

22

11

21

),(),(

,s.t.

)1(max212

111

Dual Decomposition!Dual Decomposition!


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• Standard technique in convex optimisation

• Our work shows can also be applied to non-convex problems

• Converts constrained opt. -> unconstrained opt.

• Constraints naturally enforced by maximisation of Lagrangian

22

11

21221121

21 ),()1(),(),,,( kkkkkkkkkkk ssssbwsswbssL

Dual DecompositionDual Decomposition

k kkkssss

k kk k

k kkssss

ssL

PsPs

bwwb

KK

KK

),,,(max

KKT

,s.t.

)1(max

2121

),(),(

22

11

21

),(),(

2121

11

2121

11

LagrangianLagrangian


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Dual DecompositionDual Decomposition• Standard technique in convex optimisation




k kkkssss

k kk k

k kkssss

ssL

PsPs

bwwb

KK

KK

),,,(max

KKT

,s.t.

)1(max

2121

),(),(

22

11

21

),(),(

2121

11

2121

11

22

11

21221121


ObjectiveObjective


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Dual DecompositionDual Decomposition• Standard technique in convex optimisation




k kkkssss

k kk k

k kkssss

ssL

PsPs

bwwb

KK

KK

),,,(max

KKT

,s.t.

)1(max

2121

),(),(

22

11

21

),(),(

2121

11

2121

11

22

11

21221121


Total Power ConstraintsTotal Power Constraints


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KKT ConditionsKKT Conditions• Lagrangian multipliers 1, 2 chosen such that either

• Then maximising Lagrangian is equivalent to constrained optimisation

k nnkn

k nnkn

Ps

Ps

,0

,0


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The Big PictureThe Big Picture

nPsRwwR k nnk ,s.t.)1(max 21

, 21 ss

)()()1(max 222

111

21

),(),( 2121

11

k kk kk kkssss

sPsPbwwbKK

Dual Decomposition

kssssbwsswb kkkkkkkkss kk

,),()1(),(max 22

11

212211

, 21

Lagrangian can be decoupledacross frequency


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, 21 ss


• Original problem– Non-convex optimisation with KN dimensions– O(dKN)

– Computationally intractable


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, 21 ss


• Equivalent optimization– K decoupled non-convex optimisations with N dimensions each– O(KdN)

– Computationally tractable!

kssssbwsswb kkkkkkkkss kk

,),()1(),(max 22

11

212211

, 21


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end

decrease else ; increase if

end

decreaseelse; increase if

end


,)1(maxarg),(

0 and while

0 and while

while

target11

1111

2222

22

11

21

,

21

222

111

target11

21

wwRR

Ps

Ps

kssbwwbss

Ps

Ps

RR

k k

k k

kkkkss

kk

k k

k k

kk

The OSM AlgorithmThe OSM Algorithm

Adjust total power of user 2



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end


end


end


,)1(maxarg),(

0 and while

0 and while

while

target11

1111

2222

22

11

21

,

21

222

111

target11

21

wwRR

Ps

Ps

kssbwwbss

Ps

Ps

RR

k k

k k

kkkkss

kk

k k

k k

kk





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end


end


end


,)1(maxarg),(

0 and while

0 and while

while

target11

1111

2222

22

11

21

,

21

222

111

target11

21

wwRR

Ps

Ps

kssbwwbss

Ps

Ps

RR

k k

k k

kkkkss

kk

k k

k k

kk


Adjust rate of user 1

Adjust rate of user 1


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PerformancePerformance• We compare performance of OSM against Iterative Waterfilling (IW)

– CO distributed ADSL– Mix of CO/RT distributed ADSL– Upstream VDSL

• Also include comparisons with techniques used in today’s modems– ADSL: Margin Adaptive (MA) mode

• CO ADSLs TX flat PSD at -40 dBm/Hz

• RT ADSLs TX flat PSD at -52 dBm/Hz

– VDSL: Reference PSD method• Long lines at -60 dBm/Hz

• Power back-off on short lines such that RX PSD = Ref. PSD

• Simulation parameters:– 998 Bandplan – 26 AWG lines– 12.9 dB SNR-gap – TX power ADSL: 20.4 dBm, VDSL: 11.5 dBm– ANSI noise model A– Continuous bitloading (similar results with discrete)


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ADSL - CO DistributedADSL - CO Distributed• Evaluated over a range of line lengths

• Gains of IW typically 100-300% over MA

• PSDs from IW virtually identical to those found with OSM

• IW achieves same gains as OSM

• IW effectively optimal

• Found this to be case in general for all CO distributed ADSLs

Iterative Waterfilling optimal for CO distributed ADSL

Iterative Waterfilling optimal for CO distributed ADSL


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ADSL - CO/RT MixADSL - CO/RT Mix• CO ADSL of 4km + RT ADSL of 3km

• RT located 3km from CO

• Leads to following rate regions

CO RT3 km

4 km

3 km

0 1 2 3 4 50

0.5

1

1.5

CO

AD

SL

(M

bp

s)

RT ADSL (Mbps)

MAIWOSM


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0 1 2 3 4 50

0.5

1

1.5

CO

AD

SL

(M

bp

s)

RT ADSL (Mbps)

MAIWOSM

• For example: Target rate of 1 Mbps on both lines

ADSL - CO/RT MixADSL - CO/RT Mix


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0 1 2 3 4 50

0.5

1

1.5

CO

AD

SL

(M

bp

s)

RT ADSL (Mbps)

MAIWOSM

• MA: Only achieves 0.5 Mbps on 4km



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0 1 2 3 4 50

0.5

1

1.5

CO

AD

SL

(M

bp

s)

RT ADSL (Mbps)

MAIWOSM


• IW: Achieves 1 Mbps on both



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0 1 2 3 4 50

0.5

1

1.5

CO

AD

SL

(M

bp

s)

RT ADSL (Mbps)

MAIWOSM


• IW: Achieves 1 Mbps on both

• OSM: CO at 1 MbpsIncreases RT to 3.3 Mbps! (+230%)


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ADSL - CO/RT MixADSL - CO/RT Mix• Where do gains of OSM come from?


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ADSL - CO/RT MixADSL - CO/RT Mix• Examine RT ADSL PSD

0 0.2 0.4 0.6 0.8 1-80

-70

-60

-50

-40

-30

-20

PS

D (

dB

m/H

z)

Frequency (MHz)

RT ADSL PSD

MAIWOSM


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ADSL - CO/RT MixADSL - CO/RT Mix• Crosstalk coupling minimal at low frequencies

0 0.2 0.4 0.6 0.8 1-80

-70

-60

-50

-40

-30

-20

PS

D (

dB

m/H

z)

Frequency (MHz)

RT ADSL PSD

MAIWOSM


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ADSL - CO/RT MixADSL - CO/RT Mix• Crosstalk coupling minimal at low frequencies

• RT ADSL can transmit at high PSD with little degradation to CO ADSL

0 0.2 0.4 0.6 0.8 1-80

-70

-60

-50

-40

-30

-20

PS

D (

dB

m/H

z)

Frequency (MHz)

RT ADSL PSD

MAIWOSM


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ADSL - CO/RT MixADSL - CO/RT Mix• Examine CO ADSL PSD

0 0.2 0.4 0.6 0.8 1-80

-70

-60

-50

-40

-30

-20

PS

D (

dB

m/H

z)

Frequency (MHz)

CO ADSL PSD

MAIWOSM


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ADSL - CO/RT MixADSL - CO/RT Mix• CO ADSL not active in high frequencies (large channel attenuation)

0 0.2 0.4 0.6 0.8 1-80

-70

-60

-50

-40

-30

-20

PS

D (

dB

m/H

z)

Frequency (MHz)

CO ADSL PSD

MAIWOSM


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ADSL - CO/RT MixADSL - CO/RT Mix• CO ADSL not active in high frequencies (large channel attenuation)

• RT ADSL can transmit at high PSD with little degradation to CO ADSL

0 0.2 0.4 0.6 0.8 1-80

-70

-60

-50

-40

-30

-20

PS

D (

dB

m/H

z)

Frequency (MHz)

RT ADSL PSD

MAIWOSM


5/1/2003



• Where do gains of OSM come from?– RT ADSL can transmit in low frequencies with little degradation to CO ADSL– RT ADSL can transmit in high frequencies with little degradation to CO ADSL

• Leads to improved performance over IW



Technique CO ASDL (Mbps) RT ADSL (Mbps)MA 0.5 1.9IW 1.0 1.0OSM 1.0 3.3 (+230%)


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• Where do gains of OSM come from?– RT ADSL can transmit in low frequencies with little degradation to CO ADSL– RT ADSL can transmit in high frequencies with little degradation to CO ADSL



• With MA 1 Mbps service not possible on both lines

• Possible with IW

• OSM increases RT rate to 3.3 Mbps (video capable!)


Technique CO ASDL (Mbps) RT ADSL (Mbps)MA 0.5 1.9IW 1.0 1.0OSM 1.0 3.3 (+230%)


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VDSL - UpstreamVDSL - Upstream• 4 x VDSL of 600m + 4 x VDSL of 900m

• Leads to following rate regions

CO/ONU CP600 m

900 m

44

0 5 10 15 200

1

2

3

4

5

6

7

90

0m

(M

bp

s)

600m (Mbps)

Ref. PSDIWOSM


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VDSL - UpstreamVDSL - Upstream• Where do gains of OSM come from?

4 5 6 7 8 9 10 11 12-100

-90

-80

-70

-60

-50

-40

-30

PS

D (

dB

m/H

z)

Frequency (MHz)

900m PSD

Ref. PSDIWOSM


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VDSL - UpstreamVDSL - Upstream• Examine PSD on 900m lines

4 5 6 7 8 9 10 11 12-100

-90

-80

-70

-60

-50

-40

-30

PS

D (

dB

m/H

z)

Frequency (MHz)

900m PSD

Ref. PSDIWOSM


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4 5 6 7 8 9 10 11 12-100

-90

-80

-70

-60

-50

-40

-30

PS

D (

dB

m/H

z)

Frequency (MHz)

900m PSD

Ref. PSDIWOSM

VDSL - UpstreamVDSL - Upstream• 900m not active in 2nd US band (high attenuation)


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VDSL - UpstreamVDSL - Upstream• 900m not active in 2nd US band (high attenuation)

• 600m can TX at high PSD with little degradation to 900m

4 5 6 7 8 9 10 11 12-100

-90

-80

-70

-60

-50

-40

-30

PS

D (

dB

m/H

z)

Frequency (MHz)

600m PSD

Ref. PSDIWOSM


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• For example: Target rate of 6 Mbps on 900m

• Not possible with Ref. PSD

• Possible with IW only by decreasing 600m to 4.5 Mbps

• OSM allows 6 Mbps on 900m + enhanced 14 Mbps service on 600m (211% gain)

• Enables high-speed services: Web-hosting, Virtual Private LAN

VDSL - UpstreamVDSL - Upstream

Technique 900m (Mbps) 600m (Mbps) Ref. PSD 3.9 12.0 IW 6.0 4.5 OSM 6.0 14.0 (+211%)


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OSM - ConclusionsOSM - Conclusions• IW: Optimal for CO distributed ADSL

• OSM: Large gains over IW in RT ADSL and VDSL– Based on Dual Decomposition method from Optimisation Theory– Gives maximum possible performance– Typical gains 200 - 300%– Exploits minimal crosstalk coupling at low freq. to boost near-end PSD– Exploits weak channel of far-end at high freq. to boost near-end PSD– More centralised than IW: Requires PSDs to be remotely set, not just rates– Higher complexity than IW

• Ultimately may want to combine best aspects of OSM and IW

• Goal:– Simple Algorithm (IW)– Semi-autonomous (IW)– Near-optimal performance (OSM)


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DSM EvolutionDSM Evolution• Phase 1: CO Distributed ADSL

– Most commonly deployed system today– IW optimal (DSM Level 1)– Large gains (100 - 300%)

Right Now


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• Phase 2: RT Distributed ADSL + VDSL– Implement combination of OSM and IW (DSM Level 2)– Adds 200 - 300% on top of already spectacular gains of IW– Offer high-speed services (video, virtual private LAN, P2P filesharing) to

maximum number of people

Right Now

Next 1-2 Years


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• Phase 3: Vectored DSL– DSM Level 3– 100 Mbps+ symmetric service

Right Now

Next 1-2 Years

3 – 5 years


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• Phase 3: Vectored DSL– DSM Level 3– 100 Mbps+ symmetric service

• Phase 4: Fiber to the Home

– Retirement?

Right Now

Next 1-2 Years

3 – 5 years

20 years?


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ContentsContents Optimal Spectrum Management


• Crosstalk Precompensation– Ginis’ QR Precompensator (modification of CPE)– Row-wise diagonal dominance– Linear Diagonalizing Precompensator (no change of CPE)



5/1/2003



Crosstalk PrecompensationCrosstalk Precompensation• Joint work together with George Ginis (Texas Inst.), Alcatel Bell

• In downstream (DS) TXs co-located

• Facilitates crosstalk precompensation– Pre-distort TX signals such that:– Distortion and crosstalk annihilate– RXs see crosstalk free signal

• Ginis’ QR Precoder– Multi-user version of Tomlinson-Harashima precoder– Removes all crosstalk– Large performance gains – Achieves close to theoretical capacity in DSL channels– Uses modulo operations at TX to ensure TX power not increased– Modulo operation at RX makes modulo at TX transparent

Requires modification of CPE!Requires modification of CPE!


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Crosstalk PrecompensationCrosstalk Precompensation• Modification of CPE

– Highly undesirable– Legacy issues: Potentially millions of CPEs already (soon to be) in place– All owned an operated by different customers!– CPE / COE often manufactured by different vendors (interoperability issues)

• Our Work: Diagonalizing Precompensator– Linear– Achieves close to theoretical capacity in DSL channels– No modification of CPE required

• First look at optimal linear pre/post filtering (SVD)


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Optimal Linear Pre/Post FilteringOptimal Linear Pre/Post Filtering• SVD of channel matrix Hk

• Pre-filter applied prior to TX

• Post-filter applied after RX

• Estimate of (scaled) transmitted symbol

Hkkkk VUH

kk VP

Hkk UW

kHkkk

kkkkkk

zUx

zxPHWx

)(ˆ


5/1/2003



Optimal Linear Pre/Post FilteringOptimal Linear Pre/Post Filtering• Crosstalk perfectly removed

• Pre-filter does not increase TX power

• Post-filter does not cause noise enhancement

• Achieves channel capacity

• But application of Wk requires co-located RXs

• Not the case since RXs at different CPs

• Only usefull in bonded DSL


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Row-wise Diagonal DominanceRow-wise Diagonal Dominance• Precompensation: TXs must be co-located

• Co-located TXs Hk row-wise diagonal dominant (RWDD)

• Implies rows of Hk orthogonal

• In terms of SVD

nmhh mnk

nnk ,,,

Hkkkk VUH

RWDD kNN

kkHk

NNkkk

Nk

hh

hh

HV

IU

1,1,1

,1,1

},,diag{

},,diag{


5/1/2003



Simplified Pre/Post FilteringSimplified Pre/Post Filtering• Recall optimal pre/post filter

• Using RWDD approximations:

• Simplified Pre-filter

• RX side co-ordination not required!

NHkk IUW


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Simplified Pre/Post FilteringSimplified Pre/Post Filtering• Recall optimal pre/post filter

• Using RWDD approximations:

• Simplified Post-filter

• Application of Pk diagonalises Hk

• Term this: Diagonalizing Precompensator (DP)

• All users see original direct channel

• Crosstalk perfectly removed

},,diag{ ,1,11 NNkkk

Hkkk

hh

H

VVP


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Pre-filter NormalisationPre-filter Normalisation• DP must be normalised

• Ensure TX power not increased on any line

• RWDD ensures that Pk orthogonal

• So k 1

• Capacity of user n

kkk PP 1

nkn

k row ][max P

)1(log

)1(log

1,

2,2

1,

2,12

nknk

nnk

nknk

nnkk

nk

sh

shc Crosstalk free capacity


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Pre-filter NormalisationPre-filter Normalisation• DP must be normalised• Ensure TX power not increased on any line

• RWDD ensures that Pk orthogonal

• So k 1

• Capacity of user n

• Further details: Can bound capacity loss as function of degree of RWDD

kkk PP 1

nkn

k row ][max P

)1(log

)1(log

1,

2,2

1,

2,12

nknk

nnk

nknk

nnkk

nk

sh

shc Crosstalk free capacity


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PerformancePerformance• Compare Zero Forcing (ZF) precompensator, DP and QR precoder

• Scenario consists of 8 lines of length 300,400,...,1000 m.

CO/ONU CP300 m

400 m

900 m

1000 m

. . . . . .


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PerformancePerformance• ZF precompensator:

300 400 500 600 700 800 900 100020

30

40

50

60

70

80

Line Length (m)

Ra

te (

Mb

ps

)

ZFQRDP


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PerformancePerformance• ZF precompensator: All lines see direct channel of worst line (1 km)

300 400 500 600 700 800 900 100020

30

40

50

60

70

80

Line Length (m)

Ra

te (

Mb

ps

)

ZFQRDP


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PerformancePerformance• QR precoder:

300 400 500 600 700 800 900 100020

30

40

50

60

70

80

Line Length (m)

Ra

te (

Mb

ps

)

ZFQRDP


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PerformancePerformance• QR precoder: Near-optimal, but requires modification of CPE!

300 400 500 600 700 800 900 100020

30

40

50

60

70

80

Line Length (m)

Ra

te (

Mb

ps

)

ZFQRDP


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PerformancePerformance• DP:

300 400 500 600 700 800 900 100020

30

40

50

60

70

80

Line Length (m)

Ra

te (

Mb

ps

)

ZFQRDP


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PerformancePerformance• DP: Near-optimal, No modification of CPE!

300 400 500 600 700 800 900 100020

30

40

50

60

70

80

Line Length (m)

Ra

te (

Mb

ps

)

ZFQRDP


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Remark: Upstream CancellationRemark: Upstream Cancellation• In US: crosstalk cancellation• RXs co-located• Channel is column-wise diagonal dominant (CWDD)• No TX co-ordination required

• ZF canceller near-optimal

Nkk IVP

11 kHkkk HUW

Direction TechniqueUpstream ZFDownstream DPBonded Either


5/1/2003



ContentsContents Optimal Spectrum Management


Crosstalk Precompensation– Ginis’ QR Precompensator (modification of CPE)– Row-wise diagonal dominance– Linear Diagonalizing Precompensator (no change of CPE)



5/1/2003



Partial CancellationPartial Cancellation• Joint work with George Ginis (Texas Inst.), Alcatel Bell

• Well known that most crosstalk caused by surrounding 4-5 pairs

• “Space-selectivity of crosstalk”

• Partial cancellation: Reduce complexity by only cancelling largest xtalkers

• Crosstalk coupling also varies with frequency

• “Frequency-selectivity of crosstalk”

• Crosstalk coupling minimal at low freq. ( f 2 )– No point in doing cancellation

• Direct channel gains weak at high freq.– Minimal bitloading even in absence of crosstalk– No point in doing cancellation

• Our Work: Develop partial cancellers which vary complexity on each tone

• Exploit frequency-selectivity of crosstalk


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Partial CancellationPartial Cancellation• Define bk

n(v) as rate on tone k with v largest crosstalkers cancelled

• Goal: Maximise data-rate under total complexity constraint

• Exhaustive search: Complexity N K Intractable

• Our Work:– Modified greedy algorithm

– Finds optimal solution with complexity KN 2 Tractable

Vvvb knkk

nk

nk

vv nK

n s.t.)(max

),,( 1

Think of it as waterfilling, but we distribute compute-power instead of TX-power

Think of it as waterfilling, but we distribute compute-power instead of TX-power


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Partial CancellationPartial Cancellation• Result: Majority of gains of full cancellation, Fraction of the complexity

0 10 20 30 40 50 60 700

1

2

3

4

5

6

7

300m (Mbps)

12

00

m

(Mb

ps

)

No Cancellation

Partial Canc10% complexity

Partial Canc20% complexity

Full Cancellation


5/1/2003



Questions?Questions?

Papers available online at www.geocities.com/raphael_cendrillon

Documents

5/1/2003 1 KU Leuven Department of Electrical Engineering R. Cendrillon and M. Moonen Optimal Spectrum Management