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DSL Spectrum Management

Dr. Jianwei Huang

Department of Electrical EngineeringPrinceton University

Guest Lecture of ELE539A

March 2007

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Acknowledgements

Collaborations: Raphael Cendrillon, Mung Chiang, Marc MoonenSponsorships: Alcatel, NSF

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Digitial Subscriber Line (DSL) Networks

Wireline communications networks based telephone copper lines

Cost-effective broadband access networkMore than 160 million users world-wide

crosstalk

TX

TX RX

RXCO

RT

(Remote Terminal)

(Central Office) Customer

Customer

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Digitial Subscriber Line (DSL) Networks

Wireline communications networks based telephone copper lines

Cost-effective broadband access networkMore than 160 million users world-wideSpeed is the bottleneck

crosstalk

TX

TX RX

RXCO

RT

(Remote Terminal)

(Central Office) Customer

Customer

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How DSL Works?

Copper line can support signal transmissions over a large bandwidthVoice transmission: up to 3.4 KHzDSL transmissions: up to 30 MHz

Multi-carrier transmissions: Discrete Multitone Modulation

Frequency (KHz)0 3.4

Voice DSL

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Network and Channel Model

crosstalk

TX

TX RX

RXCO

RT

(Remote Terminal)

(Central Office) Customer

Customer

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Mathematical model : multi-user multi-carrier interference channelEach telephone line is a user (transmitter-receiver pair)

Generate mutual crosstalks over multiple frequency tones

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Network and Channel Model

crosstalk

TX

TX RX

RXCO

RT

(Remote Terminal)

(Central Office) Customer

Customer

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Physical model : mixed CO/RT caseChannel attenuates with distance

Central Office (CO) connect customers who are reasonably closeRemote Terminal (RT) connect customers who are farther away

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Network and Channel Model

crosstalk

TX

TX RX

RXCO

RT

(Remote Terminal)

(Central Office) Customer

Customer

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Frequency-Dependent ChannelDirect channel gain decreases with frequency

Crosstalk channel gain increases with frequency

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Network and Channel Model

crosstalk

TX

TX RX

RXCO

RT

(Remote Terminal)

(Central Office) Customer

Customer

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Frequency-Dependent ChannelDirect channel gain decreases with frequency

Crosstalk channel gain increases with frequencyLead to near-far problem

RT generates strong crosstalk to CO line, especially inhigh tonesCO generates little crosstalk to RT in all tones

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Crosstalk System Model

N users (lines) and K tones (frequency bands)User ns achievable rate on tone k is

b k n = log 1 + SINRk n

whereSINR k n =

p k nm = n k n , m p k m + k n

Total data rate of user n

R n =k

b k n

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Network Objective: Maximize Rate Region

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Rate Region : set of all achievable rate vectors

1

R

Rate Region

2

R

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Network Objective: Maximize Rate Region

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Problem A: (Find One Point On the Rate Region Boundary)maximize

{pnP n }n nw n R n

User n chooses a power vector pn P n = k p k n P maxn , p k n 0 .

Rate Region : set of all achievable rate vectors

1

R

Rate Region

2

R

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Network Objective: Maximize Rate Region

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Problem A: (Find One Point On the Rate Region Boundary)maximize

{pnP n }n nw n R n

User n chooses a power vector pn P n = k p k n P maxn , p k n 0 .Changing different weights trace the entire rate region boundary

Rate Region : set of all achievable rate vectors

1

R

Rate Region

2

R

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Network Objective: Maximize Rate Region

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Problem A: (Find One Point On the Rate Region Boundary)maximize

{pnP n }n nw n R n

User n chooses a power vector pn P n = k p k n P maxn , p k n 0 .Changing different weights trace the entire rate region boundaryA suboptimal algorithm leads to a reduced rate region

Rate Region : set of all achievable rate vectors

R

Rate Region

2

R1

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Difficulties of Solving Problem A

Non-convexity: total weighted rate not concave in power.

Physically distributed: local channel information

Performance coupling: across users (interferences) and tones (powerconstraint)

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Dynamic Spectrum Management (DSM)State-of-art DSM algorithms:

IW: Iterative Water-lling [Yu, Ginis, Cioffi02]

IW

2

R 1

R

Algorithm Operation Complexity PerformanceIW Autonomous O (KN ) Suboptimal

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Dynamic Spectrum Management (DSM)State-of-art DSM algorithms:

IW: Iterative Water-lling [Yu, Ginis, Cioffi02]OSB: Optimal Spectrum Balancing [Cendrillon et al.04]ISB: Iterative Spectrum Balancing [Liu, Yu05] [Cendrillon, Moonen05]

OSB/ISB

IW

2

R 1

R

Algorithm Operation Complexity PerformanceIW Autonomous O (KN ) SuboptimalOSB Centralized O Ke N OptimalISB Centralized O KN 2 Near Optimal

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Dynamic Spectrum Management (DSM)State-of-art DSM algorithms:

IW: Iterative Water-lling [Yu, Ginis, Cioffi02]OSB: Optimal Spectrum Balancing [Cendrillon et al.04]ISB: Iterative Spectrum Balancing [Liu, Yu05] [Cendrillon, Moonen05]ASB: Autonomous Spectrum Balancing [Huang et al.06]

/ASBOSB/ISB

IW

R

1 R

2

Algorithm Operation Complexity PerformanceIW Autonomous O (KN ) SuboptimalOSB Centralized O Ke N OptimalISB Centralized O KN 2 Near OptimalASB Autonomous O (KN ) Near Optimal

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Optimal Spectrum Balancing

Global optimization based on dual decomposition

Key: the duality gap is asymptotically zero under frequency-sharingproperty

R2

1R

1R

target

A

C

B

E L l

l

D

w = 0

w = 1

w =

w = +

XYX Y

c Cendrillon et. al., ICC, 2004

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l l

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Optimal Spectrum Balancing

Partial Lagrangian:

L (p1 ,..., pN ) =n

w nk

log 1 + SINR k n n

nk

p k n P maxn

Decompose K nonconvex subproblems, one for each tone k :

maximize{p k n }

n 0 n

w n log 1 + SINR k n n

n p k n

Joint exhaustive search of optimal transmission power of all usersOptimal values of 1 ,..., N can be found using bisection orsubgradient search

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Iterative Water lling

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Iterative Water-lling

ProsAutonomous: no explicit communication among users (interferenceplus noise can be locally measured)Low computational complexity of O (KN ): separable across users andtonesAchieve better performance than the current practice

ConsSelsh optimizationNo consideration for damages to other users

Highly suboptimal in the mixed CO/RT case

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Autonomous Spectrum Balancing

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Autonomous Spectrum Balancing

Key idea: reference line - static pricing for static channelA virtual line representative of the typical victim in the networkGood choice: the longest CO lineParameters (power, noise, crosstalk) are publicly known

Each user will choose its transmit power to protect the reference line

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Reference Line

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Reference Line

CP

RT

RT

RT

CP

CO CP

CP

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Reference Line

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Reference Line

Actual Line

Reference Line

CO

CPCO

RT CP

RT

RT

CP

CP

CP

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Reference Lines Rate

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Reference Line s Rate

User ns obtains the reference line parameters locally

Length & Location Reference Crosstalk:Reference Noise:

Reference Power:OperatorReference LineDatabase

pk,ref

k,ref

k,ref n

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Reference Lines Rate

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Reference Line s Rate

User ns obtains the reference line parameters locally

Length & Location Reference Crosstalk:Reference Noise:

Reference Power:OperatorReference LineDatabase

pk,ref

k,ref

k,ref n

The reference line rate

R ref n =k

log 1 +p k , ref

k , ref n p k n + k , ref

Interference only depends on user ns transmit power p k nLocally computable without explicit message passing

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Frequency Selective Water-lling

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Frequency Selective Water llingUnder high SNR approximation of the reference line

Bk n p n = w n n + k , ref n / k , ref 1{p k , ref > 0}

m = n

k n , m p k m k n

+

Reference line isnot active in high frequency tones

Special case: traditional water-lling (ignore k , ref n / k

, ref )

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Frequency Selective Water-lling

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Frequency Selective Water llingUnder high SNR approximation of the reference line

Bk n p n = w n n + k , ref n / k , ref 1{p k , ref > 0}

m = n

k n , m p k m k n

+

Reference line isnot active in high frequency tones

Special case: traditional water-lling (ignore k , ref n / k

, ref )

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Power

Traditional WaterFilling

Frequency

Interference & Noise

Frequency Selective Water-lling

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Frequency Selective Water llingUnder high SNR approximation of the reference line

Bk n p n = w n n + k , ref n / k , ref 1{p k , ref > 0}

m = n

k n , m p k m k n

+

Reference line isnot active in high frequency tones

Special case: traditional water-lling (ignore k , ref n / k

, ref )

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Power

Active Reference Line

FrequencySelective WaterFilling

Frequency

Interference & Noise

Convergence of ASB Algorithm

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Convergence of ASB Algorithm

ASB Algorithm: users update their individual power allocationaccording to best responses either sequentially or in parallel

TheoremASB algorithm globally and geometrically converges to the unique N.E. if the crosstalk channel is small , i.e.,

maxn , m , k

k n , m