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Optimal Spectrum Management
5/1/2003
1
KU Leuven Department of Electrical Engineering
R. Cendrillon and M. Moonen
Optimal Spectrum Management
Optimal Spectrum Management
5/1/2003
2R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
3R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
4R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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!
Optimal Spectrum Management
5/1/2003
5R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
6R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
7R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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!
Optimal Spectrum Management
5/1/2003
8R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
• 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
Optimal Spectrum Management
5/1/2003
9R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
Dual DecompositionDual Decomposition• 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
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
21 ),()1(),(),,,( kkkkkkkkkkk ssssbwsswbssL
ObjectiveObjective
Optimal Spectrum Management
5/1/2003
10R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
Dual DecompositionDual Decomposition• 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
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
21 ),()1(),(),,,( kkkkkkkkkkk ssssbwsswbssL
Total Power ConstraintsTotal Power Constraints
Optimal Spectrum Management
5/1/2003
11R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
12R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
13R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
nPsRwwR k nnk ,s.t.)1(max 21
, 21 ss
The Big PictureThe Big Picture
• Original problem– Non-convex optimisation with KN dimensions– O(dKN)
– Computationally intractable
Optimal Spectrum Management
5/1/2003
14R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
nPsRwwR k nnk ,s.t.)1(max 21
, 21 ss
The Big PictureThe Big Picture
• Equivalent optimization– K decoupled non-convex optimisations with N dimensions each– O(KdN)
– Computationally tractable!
kssssbwsswb kkkkkkkkss kk
,),()1(),(max 22
11
212211
, 21
Optimal Spectrum Management
5/1/2003
15R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
end
decrease else ; increase if
end
decreaseelse; increase if
end
decreaseelse; increase if
,)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
Adjust total power of user 2
Optimal Spectrum Management
5/1/2003
16R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
end
decrease else ; increase if
end
decreaseelse; increase if
end
decreaseelse; increase if
,)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 1
Adjust total power of user 1
Optimal Spectrum Management
5/1/2003
17R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
end
decrease else ; increase if
end
decreaseelse; increase if
end
decreaseelse; increase if
,)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 rate of user 1
Adjust rate of user 1
Optimal Spectrum Management
5/1/2003
18R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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)
Optimal Spectrum Management
5/1/2003
19R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
20R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
21R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
22R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
ADSL - CO/RT MixADSL - CO/RT Mix
Optimal Spectrum Management
5/1/2003
23R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
• IW: Achieves 1 Mbps on both
ADSL - CO/RT MixADSL - CO/RT Mix
Optimal Spectrum Management
5/1/2003
24R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
ADSL - CO/RT MixADSL - CO/RT Mix
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
• IW: Achieves 1 Mbps on both
• OSM: CO at 1 MbpsIncreases RT to 3.3 Mbps! (+230%)
Optimal Spectrum Management
5/1/2003
25R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
ADSL - CO/RT MixADSL - CO/RT Mix• Where do gains of OSM come from?
Optimal Spectrum Management
5/1/2003
26R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
27R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
28R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
29R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
30R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
31R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
32R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
• 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
• For example: Target rate of 1 Mbps on both lines
ADSL - CO/RT MixADSL - CO/RT Mix
Technique CO ASDL (Mbps) RT ADSL (Mbps)MA 0.5 1.9IW 1.0 1.0OSM 1.0 3.3 (+230%)
Optimal Spectrum Management
5/1/2003
33R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
• 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
• For example: Target rate of 1 Mbps on both lines
• With MA 1 Mbps service not possible on both lines
• Possible with IW
• OSM increases RT rate to 3.3 Mbps (video capable!)
ADSL - CO/RT MixADSL - CO/RT Mix
Technique CO ASDL (Mbps) RT ADSL (Mbps)MA 0.5 1.9IW 1.0 1.0OSM 1.0 3.3 (+230%)
Optimal Spectrum Management
5/1/2003
34R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
35R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
36R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
37R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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)
Optimal Spectrum Management
5/1/2003
38R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
39R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
• Leads to improved performance over IW
• 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%)
Optimal Spectrum Management
5/1/2003
40R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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)
Optimal Spectrum Management
5/1/2003
41R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
DSM EvolutionDSM Evolution• Phase 1: CO Distributed ADSL
– Most commonly deployed system today– IW optimal (DSM Level 1)– Large gains (100 - 300%)
Right Now
Optimal Spectrum Management
5/1/2003
42R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
DSM EvolutionDSM Evolution• Phase 1: CO Distributed ADSL
– Most commonly deployed system today– IW optimal (DSM Level 1)– Large gains (100 - 300%)
• 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
Optimal Spectrum Management
5/1/2003
43R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
DSM EvolutionDSM Evolution• Phase 1: CO Distributed ADSL
– Most commonly deployed system today– IW optimal (DSM Level 1)– Large gains (100 - 300%)
• 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
• Phase 3: Vectored DSL– DSM Level 3– 100 Mbps+ symmetric service
Right Now
Next 1-2 Years
3 – 5 years
Optimal Spectrum Management
5/1/2003
44R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
DSM EvolutionDSM Evolution• Phase 1: CO Distributed ADSL
– Most commonly deployed system today– IW optimal (DSM Level 1)– Large gains (100 - 300%)
• 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
• 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?
Optimal Spectrum Management
5/1/2003
45R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
ContentsContents Optimal Spectrum Management
– Achieves maximum possible rates for modems within network– Up to 300% rate gains over IW
• Crosstalk Precompensation– Ginis’ QR Precompensator (modification of CPE)– Row-wise diagonal dominance– Linear Diagonalizing Precompensator (no change of CPE)
• Partial Cancellation– Distributing compute power across frequency– Large run-time complexity reduction
Optimal Spectrum Management
5/1/2003
46R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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!
Optimal Spectrum Management
5/1/2003
47R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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)
Optimal Spectrum Management
5/1/2003
48R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
49R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
50R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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{
Optimal Spectrum Management
5/1/2003
51R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
52R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
53R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
54R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
55R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
. . . . . .
Optimal Spectrum Management
5/1/2003
56R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
57R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
58R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
59R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
60R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
PerformancePerformance• DP:
300 400 500 600 700 800 900 100020
30
40
50
60
70
80
Line Length (m)
Ra
te (
Mb
ps
)
ZFQRDP
Optimal Spectrum Management
5/1/2003
61R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
62R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
63R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
ContentsContents Optimal Spectrum Management
– Achieves maximum possible rates for modems within network– Up to 300% rate gains over IW
Crosstalk Precompensation– Ginis’ QR Precompensator (modification of CPE)– Row-wise diagonal dominance– Linear Diagonalizing Precompensator (no change of CPE)
• Partial Cancellation– Distributing compute power across frequency– Large run-time complexity reduction
Optimal Spectrum Management
5/1/2003
64R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
65R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
66R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
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
Optimal Spectrum Management
5/1/2003
67R. Cendrillon and M. Moonen
KU Leuven Department of Electrical Engineering
Questions?Questions?
Papers available online at www.geocities.com/raphael_cendrillon