Per-Tone Algorithms for ADSL Per-Tone Algorithms for ADSL TransceiversTransceivers

PhD-students: Koen Vanbleu, Geert Ysebaert

Supervisor: Marc Moonen

Email: {moonen, vanbleu, ysebaert}@esat.kuleuven.ac.be

Presentation: ftp://ftp.esat.kuleuven.ac.be/sista/ysebaert/presentations/

KULeuven, ESAT SCD-SISTA, BelgiumKULeuven, ESAT SCD-SISTA, Belgium

October 22, 2002

2

General OverviewGeneral Overview

• Basic Principles

• Per Tone Equalization

• Per Tone Echo Cancellation

• Per Tone Radio Frequency Interference (RFI) Mitigation

• Per Tone Crosstalk Mitigation

• Conclusions

3

OverviewOverview

• Basic Principles

� Introduction

� DMT

– Transmitter structure

– Receiver structure

– Cyclic Prefix trick

� Data Model

• Principles

• Equalization

• Echo

• RFI

• Crosstalk

• Conclusions

4

IntroductionIntroduction

• Communication at high rates towards customer

� telephone wire, cable, fiber, wireless

• Communication over telephone wire

� Evolution: ever increasing bitrates

� E.g. Time to download 10 Mbyte file

• Principles– Intro– DMT– Data

model

• Equalization

• Echo

• RFI

• Crosstalk

• ConclusionsModem Time

56 Kbps

Voice band modem

24 minutes

128 Kbps ISDN 10 minutes

6 Mbps ADSL 13 seconds

52 Mbps VDSL 1.5 seconds

5

IntroductionIntroduction

• Broadband communication over telephone line� ADSL (Asymmetric Digital Subscriber Line)

� VDSL (Very high bit rate Digital Subscriber Line)

� Bitrate is function of the line length

Upstream

Downstream

CustomerCentral

300 m6.4 Mbps52 MbpsVDSL

3 km640 Kbps6 MbpsADSL

Line lengthUpDown Frequency band

1.1 MHz

8.8 MHz

• Principles– Intro– DMT– Data

model

• Equalization

• Echo

• RFI

• Crosstalk

• Conclusions

6

• Traditional telephony (POTS) still available over the same wire.

DuplexingDuplexing

• Assign different frequency bins to up- and downstream directions� Frequency Division Duplexing (FDD)� Overlap: Echo Cancellation (EC)

f (kHz)

POTS UP DOWN POTS UP&DOWN

DOWN

4 25 138 1104 f (kHz)4 25 138 1104

e.g. ADSL

• Principles– Intro– DMT– Data

model

• Equalization

• Echo

• RFI

• Crosstalk

• Conclusions

7

Discrete Multi Tone: TransmitterDiscrete Multi Tone: Transmitter

00

11

10

01

Re

Im

2 bits

Re

Im

4 bits

bits Data symbols (QAM)

...

P/S

CP

kx

Cyclic Prefix

0

IFFT

N-point

.

.

.

.

.

.

...

IFFT modulation(Inverse Fast Fourier Transform)

N12/ N

• Principles– Intro– DMT– Data

model

• Equalization

• Echo

• RFI

• Crosstalk

• Conclusions

8

Discrete Multi Tone: ReceiverDiscrete Multi Tone: Receiver

00

11

10

01Re

Im

2 bits

Re

Im

4 bits

bits

Data symbols

ky...

S/P

CP

.

.

.

FFTN-point

FFT demodulation

.

.

.FEQ

1 tap / tone

.

.

.TEQ

tapsT

Time Domain

Equalizer

• Principles– Intro– DMT– Data

model

• Equalization

• Echo

• RFI

• Crosstalk

• Conclusions

9

Discrete Multi Tone: Cyclic PrefixDiscrete Multi Tone: Cyclic Prefix

To demodulator

`long’ channelCP

kkx

`short’ channel

kh

To demodulator

ky

• Principles– Intro– DMT– Data

model

• Equalization

• Echo

• RFI

• Crosstalk

• Conclusions

10

Discrete Multi Tone: InterferenceDiscrete Multi Tone: Interference

Influence of the channel behind the FFT:

• Short channel: amplitude- en phase change for each tone separately

Re

Im

Re

Im

Re

Im

iX iY iZ iH iH

• Long channel: interference between data symbols of different tones and different symbol periods)'( ii )'( kk

• Principles– Intro– DMT– Data

model

• Equalization

• Echo

• RFI

• Crosstalk

• Conclusions

11

Data modelData model

noisetransmitted data

symbols

IDFT-matrix

received samples add cyclic prefixFIR channel

synchronization

delay

nx

OO

OO

OO

sk

Tsk

kN

kN

kN

N

N

N

n

n

X

X

X

)1(

2

)1(:1

)(:1

)1(:1

ˆ

I

I

I

POO

OPO

OOP

O

h

h

O

y

0

0

)1(

2

sk

Tsk

y

y

1TN function of

Symbol lengthPrefix lengthEqualizer lengthSymbol period

NTk

• Principles– Intro– DMT– Data

model

• Equalization

• Echo

• RFI

• Crosstalk

• Conclusions

12

OverviewOverview

• Equalization

� “Pre FFT” Equalization– TEQ: several design algorithms

– See talk Prof. B. Evans

� “Post FFT” Equalization

– Equalization Per Tone

– Structure and Initialization

• Principles

• Equalization

• Echo

• RFI

• Crosstalk

• Conclusions

13

Time Domain Equalization (TEQ)Time Domain Equalization (TEQ)

Original structure of time domain equalizer + FEQs:

TEQ

kyS/P

CP

... FFT

FEQ

T taps

...

...

1 tap/tone

N-point

N

N

N

...N..

.- line with

down samplers

• Principles

• Equalization– TEQ– Per Tone

• Echo

• RFI

• Crosstalk

• Conclusions

14

TEQ: Channel ShorteningTEQ: Channel Shortening

• Channel Shortening [Al-Dhahir, Cioffi, Evans, Melsa, …]

⊖Finding `optimal’ TEQ leads to non-linear optimization

⊖Most channel shortening schemes are not equivalent to bitrate optimization

⊖Resulting bitrate is often sensitive to synchronization delay

⊖All tones are equalized in the same way limited capacity

⊕Limited memory: T-taps TEQ and 1-taps FEQ per used tone

• Principles

• Equalization– TEQ– Per Tone

• Echo

• RFI

• Crosstalk

• Conclusions

15

Per Tone Equalization (PTEQ)Per Tone Equalization (PTEQ)

y Y

• From TEQ to Equalization Per Tone [Van Acker]

)

TEQ

()(row

FEQtap1)( wY

NiiDk

iZ F

with Y an N x T Toeplitz matrix with received data samples

The received data symbol for tone i after equalization is given by

i

iD

TNi

ki

Z

w

wY

sFFT'

)(row)( F

After applying the associativity of the matrix product, we get

Equalization Per

Tone(PT-EQ)

• Principles

• Equalization– TEQ– Per Tone

• Echo

• RFI

• Crosstalk

• Conclusions

16

ky

S/P

N

N

N

...N

N

N

...1T

PT-EQ: StructurePT-EQ: Structure

• Efficient calculation with `sliding FFT’

• PTEQ-inputs: T successive FFT’s per DMT-symbol

• Cheap implementation using first FFT en T-1 real difference terms (t=2...T).

...

...

...

FFT

N-punt

T

FFTN-puntsliding

T –taps filter

w for each tone

PT-EQ ...

i

• Principles

• Equalization– TEQ– Per Tone

• Echo

• RFI

• Crosstalk

• Conclusions

17

PTEQ: StructurePTEQ: Structure

ky

N

N

N

...

N

... FFT

N-punt

...

1T

...

N N...

PTEQ ...

T –taps filter

v for each tonei

• PTEQ=linear combiner with T inputs per tone: 1 FFT-output and T-1 real difference terms

w vii

• Principles

• Equalization– TEQ– Per Tone

• Echo

• RFI

• Crosstalk

• Conclusions

18

PTEQ: ComplexityPTEQ: Complexity• Complexity during data transmission is comparable

with TEQ-complexity for the same T :

� TEQ

– 1 (real) T-taps TEQ @ sample frequency Fs

– 1 FFT operation @ symbol frequency Fs/(N+)

– (complex) 1-taps FEQ/used tone @ Fs/(N+)

� PTEQ

– 1 FFT operation @ Fs/(N+)

– (complex) T-taps PTEQ/used tone @ Fs/(N+)

(multiplications)

TEQ and FEQ PTEQ

O(Fs(T+1/2)+NlogN) O(Fs(T+1)+NlogN)

• Complexity reductions are possible by varying T per tone.

• PTEQ requires more memory than TEQ.

• Principles

• Equalization– TEQ– Per Tone

• Echo

• RFI

• Crosstalk

• Conclusions

19

PTEQ: InitializationPTEQ: Initialization

• Optimization of SNR with quadratic cost function per tone

• Direct initialization using channel and noise characteristics: Optimal MMSE solution per tone

Too expensive

• Adaptive initialization using training sequence minimization of the sum of quadratic errors

with LMS: convergence too slow with RLS: fast convergence, very complex with combination of RLS and LMS: fast convergence, lower complexity than full RLS [Ysebaert]

)(

1

2)()(T)( Ki

K

k

ki

kiii XJ vzvv

KkX ki 1,)(

• Principles

• Equalization– TEQ– Per Tone

• Echo

• RFI

• Crosstalk

• Conclusions

20

SimulationsSimulations

-40 -30 -20 -10 0 10 20 300

0.5

1

1.5

2

2.5

3

3.5x 10

6

Delay

Bit

rate

(bi

ts/s

)

32-taps PT-EQ8-taps PT-EQ32-taps TEQ8-taps TEQ

Comparison of PT-EQ and TEQ for 4km line, downstream

• Down: N=512, =32, Fs=2.2 MHz, tones 39-256

• Bitrate versus delay

• MMSE solution for PTEQ

• TEQ-init. with MMSE channel shortening with |b|=1

• Principles

• Equalization– TEQ– Per Tone

• Echo

• RFI

• Crosstalk

• Conclusions

21

SimulationsSimulations

Adaptive initialization T1.601#13line+24DSL NEXT, downstream

• Bitrate as a function of the number of training symbols for PT-EQ

• T=32, =-8

• Principles

• Equalization– TEQ– Per Tone

• Echo

• RFI

• Crosstalk

• Conclusions

22

OverviewOverview

• Echo cancellation (EC)

� Problem formulation

� Principles of EC

� Echo cancellation per tone (PTEC)

• Principles

• Equalization

• Echo

• RFI

• Crosstalk

• Conclusions

23

EC: Problem FormulationEC: Problem Formulation

• Hybrid couples transmitter and receiver to the same line

• Imperfectly balanced hybrid can cause leakage (echo) of the transmitted signal into the received signal.

• Solutions:

� Assign different frequencies for transmitted and received signal (FDD).

� Cancel the echo (EC).

DMT-tx

DMT-rx

hybrid echo-canceller

Echo

telephone line

• Principles

• Equalization

• Echo– Problem

formulation

– EC principle

– PTEC

• RFI

• Crosstalk

• Conclusions

24

Principle of Echo CancellationPrinciple of Echo Cancellation

• Echo canceller has 2 tasks:� Modeling the echo path (adaptively).� Remove the estimate of the echo signal

from the received signal.• Original approaches:

- time domain EC (TEC)

- mixed time/frequency EC [Ho, Cioffi]

FEQ

N-IFFT CP P/S

N-FFT

CP

S/P

TEC

TEQ

hybride

• Principles

• Equalization

• Echo– Problem

formulation

– EC principle

– PTEC

• RFI

• Crosstalk

• Conclusions

25

Per Tone Echo Cancellation Per Tone Echo Cancellation (PTEC)(PTEC)

• Structure [Van Acker]

Starting point: modem with equalization and echo cancellation in time domain (TEQ en TEC).

This structure is modified analogously to `TEQ to PT-EQ conversion’, i.e. TEQ and TEC are shifted behind FFT.

• Goal: bitrate optimization

)

TECTEQ

()(row

FEQtap1)(

ENiiDk

iZ wUwY

F

• Principles

• Equalization

• Echo– Problem

formulation

– EC principle

– PTEC

• RFI

• Crosstalk

• Conclusions

iE

iD

E

ET

Ni

i

iD

TNi

ki

Z

,sFFT'

)(row

sFFT'

)(row)(

w

wU

w

wY FF

26

Per Tone Echo Cancellation Per Tone Echo Cancellation (PTEC)(PTEC)

N-FFTPTEC -line withdownsamp.

-line withdownsamp.

N-IFFT CP P/S

N-FFTPTEQ -line withdownsamp.

-line withdownsamp.

N1T

ky

ku

• Principles

• Equalization

• Echo– Problem

formulation

– EC principle

– PTEC

• RFI

• Crosstalk

• Conclusions

27

PT-EC: ComplexityPT-EC: Complexity

• Complexity of PT-EC filtering

� Similar to time domain EC (for same filter length)

� Optimization of filter length per tone

� Extra FFT-operation on echo reference signal

• Cost function

� Cost function contains optimal joint shortening per tone

� SNR per tone is maximized

2)()(,

)(, ),( k

ik

iiEk

iiiEi XJ uvzvvv E

PT-ECPT-EQ

• Principles

• Equalization

• Echo– Problem

formulation

– EC principle

– PTEC

• RFI

• Crosstalk

• Conclusions

28

SimulationsSimulations

Echo cancellation per tone for 4 km line, downstream

• FDM with tx- and rx-filters of low order

• Bitrate as a function of the length of the echo filter (PT-EC)

• Comparable with 400 taps time domain EC

02

2.2

2.4

2.6

2.8

3

3.2

3.4x 106

50 100 150 200 250T E

Bit

rate

(bi

ts/s

)

32-taps PTEQ2*16-taps PTEQ

32-taps PTEQ, no echo2*16-taps PTEQ, no echo

• Principles

• Equalization

• Echo– Problem

formulation

– EC principle

– PTEC

• RFI

• Crosstalk

• Conclusions

29

OverviewOverview

• Radio frequency interference mitigation

� Problem definition

� Receiver structure (in brief)

Window incorporated PTEQ (WI-PTEQ)

� Simulation results

• Principles

• Equalization

• Echo

• RFI

• Crosstalk

• Conclusions

30

RFI interference problemRFI interference problem• Downstream band overlaps with e.g.

AM broadcast bands which causes narrowband interference.

� Contrary to popular belief: affects lots of tones

� Reason? High DFT filter bank side lobes.

� Solution? Windowing functions.

• Principles

• Equalization

• Echo

• RFI– Problem

formulation

– WI-PTEQ

• Crosstalk

• Conclusions

31

PTEQ + windowing: Structure PTEQ + windowing: Structure [Cuypers]

• Principles

• Equalization

• Echo

• RFI– Problem

formulation

– WI-PTEQ

• Crosstalk

• Conclusions

32

Simulation resultsSimulation results

• Nice gain for low number of tapsADSL T1.601#13 standard loop

RFI at 630, 740, 800, 980, 1100, 1160, 308 kHz

• Principles

• Equalization

• Echo

• RFI– Problem

formulation

– WI-PTEQ

• Crosstalk

• Conclusions

33

OverviewOverview

• Per tone alien crosstalk mitigation

� Problem definition

� Principles of cyclostationarity

� Receiver structure

PTEQ combined with FRESH filtering

� Simulation results

• Principles

• Equalization

• Echo

• RFI

• Crosstalk

• Conclusions

34

Problem Formulation: Problem Formulation: Per-tone Per-tone Alien Alien Crosstalk Crosstalk

MitigationMitigation• Crosstalk (XT)

Desired

Remote terminals

Central office

Binder

TX

RXRX

TX

TX TX

RX RX

User 1

User 2

Far-end XT

Near-end XT

• Principles

• Equalization

• Echo

• RFI

• Crosstalk– Problem

formulation

– Principle– Receiver

structure

• Conclusions

35

Problem FormulationProblem Formulation

• Crosstalk (XT): reduces the SNR in each frequency bin

• Crosstalk types:� Self XT: caused by other ADSL systems

� Alien XT: caused by copper wire transmission systems with different modulation scheme occupying (partially) same frequency band

• Alien crosstalk examples:� in ADSL: HDSL and SDSL XT (baseband)

� in VDSL: HPNA (QAM passband)

• Principles

• Equalization

• Echo

• RFI

• Crosstalk– Problem

formulation

– Principle– Receiver

structure

• Conclusions

36

kDSL symbol blocks

XT symbols

k+1 k+2

Non-integer relation between DSL and XT symbol rate

Principles of CyclostationarityPrinciples of Cyclostationarity

• What makes alien XT particular?

Sampling offset between DSL and XT changes from DSL block to block XT “nonstationary”, i.e. time varying, w.r.t. DSL symbol rate Processing varies from DSL block to block? No: exploit XT cyclostationarity(*) in “frequency domain” ((*) with large period: e.g. 100s of symbols)

• Principles

• Equalization

• Echo

• RFI

• Crosstalk– Problem

formulation

– Principle– Receiver

structure

• Conclusions

37

Principles of CyclostationarityPrinciples of Cyclostationarity

• Received PSD of cyclostationary signals with excess bandwidth (EBW)

• E.g. SDSL XT, symbol rate of fs=1.04MHz, 100% EBW

• Principles

• Equalization

• Echo

• RFI

• Crosstalk– Problem

formulation

– Principle– Receiver

structure

• Conclusionsf

PSD(f)

fs/2 fs-fs/2-fs

EBWEBW

Same information about signal!

Determined by pulse shapeand channel

38

Principles of CyclostationarityPrinciples of Cyclostationarity

• Mitigate the cyclostationary SDSL from a received signal y

f

PSD(f)

fs/2 fs

EBW + ADSL

by optimal combined filtering of y and frequency shifted version y’ (shift = fs) [Gardner]

y =

f

PSD(f)

fs/2 fs

EBW + shifted ADSLy’ =

uncorrelatedcorrelated

• Principles

• Equalization

• Echo

• RFI

• Crosstalk– Problem

formulation

– Principle– Receiver

structure

• Conclusions

39

Receiver StructureReceiver Structure

• From classical TEQ to TEQ with alien crosstalk mitigation:

TEQyS/P

CP

... FFT FE

Q

...

...

1 tap/tone

N-points

)2exp( kfj s

XTcanceller'y

time invariant filtersOverall structure= time varying

• Principles

• Equalization

• Echo

• RFI

• Crosstalk– Problem

formulation

– Principle– Receiver

structure

• Conclusions

• Only prior knowledge required: fs=crosstalker symbol rate

40

Per-Tone Receiver for Per-Tone Receiver for AlienAlien Crosstalk Mitigation Crosstalk Mitigation

• From “pre-FFT” to “post-FFT” (cfr. from TEQ to PTEQ)

N-FFT PTEQ-line withdownsamp.

-line withdownsamp.

N1T

y

)2exp( kfj s N-FFTXT

canceller

-line withdownsamp.

N

-line withdownsamp.

1T

• Principles

• Equalization

• Echo

• RFI

• Crosstalk– Problem

formulation

– Principle– Receiver

structure

• Conclusions

41

Simulation ResultsSimulation Results

• Bitrate as a function of loop length (26AWG loops)

• SDSL crosstalker

• Up to 100 % gain around 3000m

• Principles

• Equalization

• Echo

• RFI

• Crosstalk– Problem

formulation

– Principle– Receiver

structure

• Conclusions

42

ConclusionsConclusions

• Evolution in equalization

� TEQ: Simple initialization, low memory requirements, little relation with bit rate, unpredictable behaviour

� PTEQ: Optimize SNR per tone, comparable complexity, high memory requirements

• Per tone echo canceling

� PTEC: Optimize SNR per tone, apply the same trick as for PTEQ

• Radio frequency interference

� Solution based on PTEQ + windowing (WI-PTEQ)

• Crosstalk mitigation

� Solution based on PTEQ + FREquency SHift PTEQ (FRESH)

• Principles

• Equalization

•Echo

• RFI

• Crosstalk

• Conclusions

43

Time-/frequency domain ECTime-/frequency domain EC

• Time-/frequency domain EC [Ho, Cioffi]

� Adaptation of EC filter: in frequency domain

� Removing echo: partially in time- and frequency domain

� Efficient implementation of time domain EC

N-IFFT

hybrid

freq. dom. EC

CP P/S

N-FFT CPS/P

Time dom. EC

TEQFEQ

• Principles

• Equalization

• Echo– Problem

formulation

– EC principle

– PTEC

• RFI

• Crosstalk

• Conclusions

44

Double talk problemDouble talk problem

N-IFFT

hybrid

C P

N-FFT CP

CES

TEQFEQ

• Far end signal causes excess MSE in EC coefficient update

• LMS step size has to be lowered to average out far end signal reduced convergence speed = double talk problem

• Solution: cancellation of far end signal prior to EC update [Ysebaert]

Freq. ECUpdate1/FEQ

N-IFFT

• Principles

• Equalization

• Echo– Problem

formulation

– EC principle

– PTEC

• RFI

• Crosstalk

• Conclusions