ADSL TransceiversADSL Transceivers

Dr. A. Falahati BSc, C.Eng, MSc, MIC, PhD, MIEE

Dept. of Electrical & Electrical Eng.Iran University of Sceince & Technology

afalahati@iust.ac.ir

18 - 2

OutlineOutline• Introduction

• Modulation

• Asymmetric DSL (ADSL) Transceivers– Multicarrier Modulation in ADSL

– ADSL Transceiver Block Diagram

• Combating Inter-symbol Interference– Single-carrier communication systems

– Multicarrier communication systems

• Equalization in ADSL Transceivers– Time-Domain Equalization

– Frequency-Domain Equalization

• Conclusion

18 - 3

Digital Subscriber Line (DSL)Digital Subscriber Line (DSL) Broadband Access Broadband Access

Customer Premises

downstream

upstreamVoiceSwitch

Central Office

DSLAM

DSL modem

DSL modem

LPFLPF

Internet

DSLAM - Digital Subscriber Line Access Multiplexer

LPF – Low Pass Filter (passes voiceband frequencies)

Telephone Network

Introduction

18 - 4

Discrete Multitone (DMT) DSL StandardsDiscrete Multitone (DMT) DSL StandardsADSL – Asymmetric DSL

Maximum data rates supported in G.DMT standard (ideal case)Echo cancelled: 14.94 Mbps downstream, 1.56 Mbps upstreamFrequency division multiplexing: 13.38 Mbps downstream, 1.56 Mbps up

Widespread deployment in US, Canada, Western Europe, Hong KongCentral office providers only installing frequency-division multiplexed (FDM) ADSL:cable modem market 1:2

in US & 5:1 worldwide

ADSL+ 8 Mbps downstream min.

ADSL2 doubles analog bandwidth

VDSL – Very High Rate DSLAsymmetric

Faster G.DMT FDM ADSL2m subcarriers m [8, 12]

Symmetric: 13, 9, or 6 MbpsOptional 12-17 MHz band

G.DMT ADSL

Asymmetric DMT VDSL

Data band 0.025 – 1.1 MHz

0.138 – 12 MHz

Upstream subcarriers

32 256

Downstream subcarriers

256 2048/4096

Target up- stream rate

1 Mbps 3 Mbps

Target down- stream rate

8 Mbps 13/22 Mbps

Introduction

18 - 5

Spectral Compatibility of xDSLSpectral Compatibility of xDSL

10k 100k 1M 10M 100M

Plain Old Telephone Service

ISDN

ADSL - USA

ADSL - Europe

HDSL/SHDSL

HomePNA

VDSL

Upstream Downstream Mixed

Frequency (Hz)

1.1 MHz

12 MHz

Any overlap with the AM radio band?

Any overlap with the FM radio band?

Introduction

18 - 6

MessageSource

Modulator

Encoder

Channel Demodulator

DecoderMessage

SinkNoise

Transmitter Receiver

A Digital Communications SystemA Digital Communications System• Encoder maps a group of message bits to data symbols

• Modulator maps these symbols to analog waveforms

• Demodulator maps received waveforms back to symbols

• Decoder maps the symbols back to binary message bits

Modulation

18 - 7

Amplitude Modulation by Cosine FunctionAmplitude Modulation by Cosine Function

• Example: y(t) = f(t) cos(0 t)

f(t) is an ideal lowpass signal

Assume 1 << 0

Y() is real-valued if F() is real-valued

• Demodulation is modulation then lowpass filtering

• Similar derivation for modulation with sin(0 t)

0

1

-

F()

0

½

- - - +

- +

½F½F

00 2

1

2

1 FFY

Y()

Modulation

18 - 8

Amplitude Modulation by Sine FunctionAmplitude Modulation by Sine Function

• Example: y(t) = f(t) sin(0 t)

f(t) is an ideal lowpass signal

Assume 1 << 0

Y() is imaginary-valued ifF() is real-valued

• Demodulation is modulation then lowpass filtering

0

1

-

F()

j ½

- - - +

- +

-j ½Fj ½F

-j ½

00 22 F

jF

jY

Y()

Modulation

18 - 9

– Single carrier

– Single signal, occupying entire available bandwidth

– Symbol rate is bandwidth of signal being centered on carrier frequency

Quadrature Amplitude Modulation (QAM)Quadrature Amplitude Modulation (QAM)

Bits Constellation encoder Bandpass

Lowpassfilter

Lowpassfilter

I

Q

Transmit

cos(2fc t)

sin(2fc t)

-

Modulator

I

Q iX

00110

frequency

channel

mag

nitu

de

fc

Modulation

18 - 10

Multicarrier ModulationMulticarrier Modulation• Divide broadband channel into narrowband subchannels

– No ISI in subchannels if constant gain inevery subchannel and if ideal sampling

– Each subchannel has a different carrier

• Discrete multitone modulation– Based on fast Fourier transform

– Standardized for ADSL and VDSL

subchannel(QAM signal)

frequency

ma

gn

itude

carrier

DTFT-1pulse sinc

ncc

n

nc

sin

channel

Subchannels are 4.3 kHz wide in ADSL and VDSL

Modulation

18 - 11

Multicarrier Modulation by Inverse FFTMulticarrier Modulation by Inverse FFT

2/NX

x

tfje 12

1X

x

tfje 22

x

tfj Ne 2/2

+

g(t)

2X g(t)

g(t)

x

nN

je

12

1X

x

nN

je

22

x

nN

Nj

e2/

2

+2X

2/NX

Discretetime

g(t) : pulse shaping filter Xi : ith symbol from encoder

I

QiX

Modulation

18 - 12

Multicarrier Modulation in ADSLMulticarrier Modulation in ADSL

N-pointInverse

FastFourier

Transform(IFFT)

X1

X2

X1*

x0

x1

x2

xN-1X2

*

XN/2

XN/2-1*

X0

N real-valuedtime

samplesformsADSL

symbol

N/2 subchannels

(carriers)

QAM00101

I

QiX

Mirror complex data (in red) andtake conjugates:

)cos( 2 jj ee

ADSL Transceivers

18 - 13

Multicarrier Modulation in ADSLMulticarrier Modulation in ADSL

CP: Cyclic Prefix

N samplesv samples

CP CPs y m b o l ( i ) s y m b o l ( i+1)

copy copy

D/A + transmit filter

ADSL downstream upstream

CP 32 4 N 512 64

Inverse FFT

ADSL frame is an ADSL symbol plus cyclic prefix

ADSL Transceivers

18 - 14

Multicarrier Demodulation in ADSLMulticarrier Demodulation in ADSL

N-pointFast

FourierTransform

(FFT)

N time

samples

N/2 subchannels

(carriers)

S/P

*1

~X

*12

~NX

2

~NX

12

~NX

0

~X

0~x

1~x

2~x

1~

Nx

ADSL Transceivers

18 - 15

P/S QAM decoder

invert channel

=frequency

domainequalizer

S/P

quadrature amplitude

modulation (QAM) encoder

mirrordataand

N-IFFT

add cyclic prefix

P/SD/A +

transmit filter

N-FFTand

removemirrored

data

S/Premove

cyclic prefix

TRANSMITTER

RECEIVER

N/2 subchannels N real samples

N real samplesN/2 subchannels

time domain

equalizer (FIR filter)

receive filter

+A/D

channel

Data Transmission in an ADSL TransceiverData Transmission in an ADSL Transceiver

Bits

00110

P/S parallel-to-serial S/P serial-to-parallel FFT fast Fourier transform

ADSL Transceivers

18 - 16

Bit ManipulationsBit Manipulations• Serial-to-parallel

converter

• Example of one input bit stream and two output words

• Parallel-to-serialconverter

• Example of two input words and one output bit stream

S/P

Bits

0 0 1 1 01 1 0

0 0

Words

S/P

Words

0 0 1 1 0

1 1 0

0 0

Bits

ADSL Transceivers

18 - 17

Inter-symbol Interference (ISI)Inter-symbol Interference (ISI)• Ideal channel

– Impulse response is an impulse

– Frequency response is flat

• Non-ideal channelcauses ISI– Channel memory

– Magnitude and phase variation

• Received symbol is weighted sum of neighboring symbols– Weights are determined by

channel impulse response

1 1 1

-1

1.7

.4 .1

1

1.7

2.1

11 1 1

Channelimpulseresponse

Received signal

Thresholdat zero

Detected signal

* =

1 .7

1

Combating ISI

18 - 18

Single Carrier ModulationSingle Carrier Modulation• Ideal (non-distorting) channel over transmission band

– Flat magnitude response

– Linear phase response: delay is constant for all spectral components

– No intersymbol interference

• Impulse response for ideal channel over all frequencies– Continuous time:

– Discrete time:

• Equalizer– Shortens channel

impulse response(time domain)

– Compensates forfrequency distortion(frequency domain)

g[k-

Discretized Baseband System

g(t-

z-

h + w-

xk yk ekrk

nk

+

EqualizerChannel

g

Ideal Channel

+

Combating ISI

18 - 19

Combat ISI with EqualizationCombat ISI with Equalization• Problem: Channel frequency response is not flat• Solution: Use equalizer to flatten channel frequency response• Zero-forcing equalizer

– Inverts channel (impulseresponse forced to impulse)

– Flattens frequency response– Amplifies noise

• Minimum mean squarederror (MMSE) equalizer– Optimizes trade-off between

noise amplification and ISI

• Decision-feedbackequalizer– Increases complexity– Propagates error

Channel frequency response

Zero-forcing Equalizer frequency response

MMSEEqualizer frequency response

Combating ISI

18 - 20

Cyclic Prefix Helps in Fighting ISICyclic Prefix Helps in Fighting ISI

subsymbols to be transmitted

mirrored subsymbols

cyclic prefix

equal

to be removed

Combating ISI

18 - 21

Cyclic Prefix Helps in Fighting ISICyclic Prefix Helps in Fighting ISI

• Provide guard time between successive symbols– No ISI if channel length is shorter than +1 samples

• Choose guard time samples to be a copy of the beginning of the symbol – cyclic prefix– Cyclic prefix converts linear convolution into circular convolution

– Need circular convolution so that

symbol channel FFT(symbol) x FFT(channel)

– Then division by the FFT(channel) can undo channel distortion

N samplesv samples

CP CPs y m b o l ( i ) s y m b o l ( i+1)

copy copy

Combating ISI

18 - 22

Channel Impulse ResponseChannel Impulse Response

frequency (kHz)

Combating ISI

18 - 23

Channel Impulse ResponseChannel Impulse Response

frequency (kHz)

Combating ISI

18 - 24

Combat ISI with Time-Domain EqualizerCombat ISI with Time-Domain Equalizer• Channel length is usually longer than cyclic prefix

• Use finite impulse response (FIR) filter called a time-domain equalizer to shorten channel impulse response to be no longer than cyclic prefix length

channel impulse response

shortened channel impulse response

Combating ISI

18 - 25

Eliminating ISI in Discrete Multitone Eliminating ISI in Discrete Multitone ModulationModulation

• Time domain equalizer (TEQ)– Finite impulse response (FIR) filter

– Effective channel impulse response:convolution of TEQ impulse responsewith channel impulse response

• Frequency domain equalizer (FEQ)– Compensates magnitude/phase distortion

of equalized channel by dividing each FFTcoefficient by complex number

– Generally updated during data transmission

• ADSL G.DMT equalizer training– Reverb: same symbol sent 1,024 to 1,536 times

– Medley: aperiodic sequence of 16,384 symbols

– At 0.25 s after medley, receiver returns numberof bits on each subcarrier that can be supported

ADSL G.DMT Values Down

stream Up

stream 32 4

N 512 64

channel impulse response

effective channel impulse response

: transmission delay: cyclic prefix length

ADSL Equalization

18 - 26

Time-Domain Equalizer DesignTime-Domain Equalizer Design• Minimizing mean squared error

– Minimize mean squared error (MMSE) method [Chow & Cioffi, 1992]

– Geometric SNR method [Al-Dhahir & Cioffi, 1996]

• Minimizing energy outside of shortened channel response– Maximum Shortening SNR method [Melsa, Younce & Rohrs, 1996]

– Minimum ISI method [Arslan, Evans & Kiaei, 2000]

• Maximizing achievable bit rate– Maximum bit rate method [Arslan, Evans, Kiaei, 2000]

– Maximum data rate method [Milosevic, Pessoa, Evans, Baldick, 2002]

– Bit rate maximization [Vanblue, Ysebaert, Cuypers, Moonen & Van Acker, 2003]

• Other equalizer architectures– Dual-path (DP) design uses two TEQs [Ming, Redfern & Evans, 2002]

– TEQ filter bank design [Milosevic, Pessoa, Evans, Baldick, 2002]

– Per tone equalization [Acker, Leus, Moonen, van der Wiel, Pollet, 2001]

ADSL Equalization

18 - 27

• Minimize E{ek2} [Chow & Cioffi, 1992]

– Chose length of b (e.g. in ADSL) to shorten length of h * w– b is eigenvector of minimum eigenvalue of channel-dependent matrix

– Minimum MSE achieved when where

• Disadvantages– Does not consider bit rate

– Deep notches in equalizer frequency response (zeros out low SNR bands)

– Infinite length TEQ case: zeros of b on unit circle (kills subchannels)

Minimum Mean Squared Error TEQ DesignMinimum Mean Squared Error TEQ Design

1 yyxyRRbw TT 0w

z-

h + w

b

-xk

yk ekrk

nk

+

bk-

TEQChannel

Amenable to real-time fixed-point DSP implementation

ADSL Equalization

18 - 28

Maximum Shortening SNR SolutionMaximum Shortening SNR Solution• Minimize energy leakage outside shortened channel length

• For each possible position of a window of +1 samples,

• Disadvantages– Does not consider channel capacity

– Requires Cholesky decomposition andeigenvector calculation

– Does not consider channel noise

• Amenable to real-time fixed-point DSP realization

TEQafter windowoutsideenergy

TEQafter windowinsideenergy log10 maxdBin SSNRmax 10

ww

h w

ADSL Equalization

18 - 29

Maximum Shortening SNR SolutionMaximum Shortening SNR Solution

hwin, hwall : equalized channel within and outside the window

• Objective function is shortening SNR (SSNR)

h + wxk

ykrk

nk

BwwwHHwhh

AwwwHHwhhT

winTwin

Twin

Twin

Twall

Twall

Twall

Twall

• Choose w to minimize energy outside window of desired length– Locate window to capture maximum channel impulse response energy

1 subject to log10 maxSSNRmax 10

Bww

Aww

Bwwww

TT

T

CqqBw of eigenvalue min ofr eigenvecto : minmin

1 T

opt

11 TBABC

ADSL Equalization

18 - 30

Simulation Results for 17-Tap TEQsSimulation Results for 17-Tap TEQs

ParametersCyclic prefix length 32FFT size (N) 512Coding gain (dB) 4.2Margin (dB) 6Input power (dBm) 23Noise power (dBm/Hz) -140Crosstalk noise 24 ISDN disturbers

Figure 1 in [Martin, Vanbleu, Ding, Ysebaert, Milosevic, Evans, Moonen & Johnson, submitted]

Downstream transmission

ADSL Equalization

18 - 31

Simulation Results for 17-Tap TEQs (con’t)Simulation Results for 17-Tap TEQs (con’t)

ParametersCyclic prefix length 32FFT size (N) 512Coding gain (dB) 4.2Margin (dB) 6Input power (dBm) 23Noise power (dBm/Hz) -140Crosstalk noise 24 ISDN disturbers

Figure 3 in [Martin, Vanbleu, Ding, Ysebaert, Milosevic, Evans, Moonen & Johnson, submitted]

Downstream transmission

ADSL Equalization

18 - 32

• Single-path, dual-path, per-tone & TEQ filter bank equalizersAvailable at http://www.ece.utexas.edu/~bevans/projects/adsl/dmtteq/

Matlab DMT TEQ Design Toolbox 3.1Matlab DMT TEQ Design Toolbox 3.1

variousperformance

measures

default parameters

from G.DMT ADSL

standard

different graphical

views

-140

23

ADSL Equalization

18 - 33

Multicarrier ModulationMulticarrier Modulation• Advantages

– Efficient use of bandwidth without full channel equalization

– Robust against impulsive noise and narrowband interference

– Dynamic rate adaptation

• Disadvantages– Transmitter: High signal peak-to-average power ratio

– Receiver: Sensitive to frequency and phase offset in carriers

• Open issues for point-to-point connections– Pulse shapes of subchannels (orthogonal, efficient realization)

– Channel equalizer design (increase bit rate, reduce complexity)

– Synchronization (timing recovery, symbol synchronization)

– Bit loading (allocation of bits in each subchannel)

• Open issues for coordinating multiple connections

18 - 34

Application Downstream rate (kb/s)

Upstream rate (kb/s)

Willing to pay Demand Potential

Database Access 384 9 High Medium On-line directory; yellow pages 384 9 Low High Video Phone 1,500 1,500 High Medium Home Shopping 1,500 64 Low Medium Video Games 1,500 1,500 Medium Medium Internet 3,000 384 High Medium Broadcast Video 6,000 0 Low High High definition TV 24,000 0 High Medium

Application Downstream rate (kb/s)

Upstream rate (kb/s)

Willing to pay Demand Potential

On-line directory; yellow pages 384 9 Medium High Financial news 1,500 9 Medium Low Video phone 1,500 1,500 High Low Internet 3,000 384 High High Video conference 3,000 3,000 High Low Remote office 6,000 1,500 High Medium LAN interconnection 10,000 10,000 Medium Medium Supercomputing, CAD 45,000 45,000 High Low

Residential

Business

Applications of Broadband AccessApplications of Broadband AccessNotes

18 - 35

DSL Broadband Access StandardsDSL Broadband Access Standards

Courtesy of Mr. Shawn McCaslin

xDSL Meaning Data Rate Mode Applications ISDN Integrated Services

Digital Network 144 kbps Symmetric Internet Access, Voice,

Pair Gain (2 channels) T1 T-Carrier One

(requires two pairs) 1.544 Mbps Symmetric Business, Internet

Service HDSL High-Speed Digital

Subscriber Line (requires two pairs)

1.544 Mbps Symmetric

Pair Gain (12 channels), Internet Access, T1/E1 replacement

SHDSL Single Line HDSL 1.544 Mbps Symmetric Same as HDSL except pair gain is 24 channels

Splitterless ADSL

Splitterless Asymmetric DSL (G.Lite)

Up to 1.5 Mbps Up to 512 kbps

Downstream Upstream

Internet Access, Video Phone

Full-Rate ADSL

Asymmetric DSL (G.DMT)

Up to 10 Mbps Up to 1 Mbps

Downstream Upstream

Internet Access, Video Conferencing, Remote LAN Access

VDSL Very High-Speed Digital Subscriber Line (proposed)

Up to 22 Mbps Up to 3 Mbps Up to 6 Mbps

Downstream Upstream Symmetric

Internet Access, Video-on-demand, ATM, Fiber to the Hood

Notes

18 - 36

ADSL and Cable ModemsADSL and Cable Modems• Need for high-speed (broadband) data access

– Voiceband data modems can yield 53 kbps (kilobits per second) – Telephone voice channel capacity ois 64 kbps (the Central Office samples

voice signals at 8 kHz using 8 bits/sample)– Integrated Services Digital Network (ISDN) modems deliver 128 kbps– New modem standards are necessary to meet the demand for higher

bandwidth access for telecommuting, videoconferencing, video-on-demand, Internet service providers, Internet access, etc.

• Two standards tested in 1998 and now widely available– Cable modems– Asymmetric Digital Subscriber Line (ADSL) modems

• Cable Modems– Always connected to the Internet– Your neighbors on the same local area network share the bit rate– Local area network provides either 27 or 36 Mbps downstream, and

between 320 kbps and 10 Mbps upstream.

Notes

18 - 37

ADSL ModemsADSL Modems

• ADSL modems– Always connected to the Internet

– Call central office using a dedicated telephone line which also supports a conventional Plain Old Telephone Service (POTS) line for voice

– Connection time is 5-10 seconds

– ADSL modems are capable of delivering 1-10 Mbps from the central office to the customer (downstream) and 0.5-1 Mbps from the customer to the central office (upstream)

– Although ADSL lines have been available from Southwestern Bell since the Fall of 1997, ADSL modems were not commercially available until Fall of 1999.

Notes

18 - 38

Discrete Multitone (DMT) ModulationDiscrete Multitone (DMT) Modulation

• DMT uses multiple harmonically related carriers– Implemented as inverse Fast Fourier Transform (FFT) in transmitter

– Implemented using forward FFT in receiver

• Transmission bandwidth– 1.1 MHz downstream and 256 kHz upstream

– Limit of 1.1 MHz is due to power constraints imposed by the FCC

– For 18 kft telephone lines, the attenuation at 1.1 MHz is -120 dBm.

• Frequency domain is divided into 256 4.3-kHz bins– Channel 0 is dedicated to voice

– Channels 1-5 are not used due to compatibility with ISDN services.

Notes

18 - 39

Two Types of TransmissionTwo Types of Transmission

• Two versions of ADSL1. Frequency Division Multiplexing: the upstream and downstream

channels do not overlap: the upstream uses channels 6-31 and the downstream uses channels 32-255.

2. Echo Cancelled: the upstream and downstream channels overlap: the upstream uses channels 6-31 and the downstream uses channels 6-255.

• According to available SNR in each bin, bin carries– QAM signal whose constellation varies from 2-15 bits or

– no signal if SNR is less than 12 dB in that subchannel

• Constellations chosen so that overall bit error rate < 10-7

• Maximum transmission rate with symbol rate of 4 kHz– Downstream: 248 channels x 15 bits/channel x 4 kHz = 14.88 Mbps

– Upstream: 24 channels x 15 bits/channel x 4 kHz = 1.440 Mbps

Notes

18 - 40

Channel AttenuationChannel Attenuation• Reliable transmission of high-frequency information over a

telephone line is wrought with several challenges.– Telephone lines are unshielded and bundled 50 wires to a trunk. The

other lines in the bundle can cause severe crosstalk– Telephone lines attenuate signals. The attenuation increases with

increasing frequency. At 1.1 MHz, which is the highest transmitted frequency, the attenuation of a 24 gauge wire is

10 kft -70 dBm/Hz 16 kft -110 dBm/Hz 12 kft -90 dBm/Hz 18 kft -120 dBm/Hz 14 kft -100 dBm/Hz

• Because of severe effects in the channel, the ADSL standard defines channel coding using cyclic prefixes and employs error correcting codes

Notes

18 - 41

Bridge TapsBridge Taps

• Bridge Taps are unterminated lines– During modem initialization, effect of bridge taps is included in

channel estimate. Their effect would be to lower the possible channel capacity.

– During data transmission, bridge taps may saturate the front-end and at a least will be unpleasant for the echo canceller. The echo canceller should have an estimate of the echo channel including the bridge taps. Given that the reflected echo is almost instantaneous than the echo canceller channel estimate should capture them too.

• In G.lite, echo cancellation is optional– Modems who use it can still use it

– A bigger problem in G.lite is the phone due to the splitterless environment

– Transmitters that do not have an echo canceller system can rely on their receive filters to reduce the echo.

Notes

18 - 42

ADSL ModemsADSL Modems

• ADSL modem consists of a line driver plus 3 subsystems: 1. analog front end (15 V)

2. digital interface (3 V)

3. discrete multitone processor (3 V)

• Analog front end provides the analog-to-digital and digital-to-analog interfaces to the telephone line.

• Digital interace manages the input and output digital message streams.

• Discrete multitone processor implements the digital communications and signal processing to support the ADSL standard. An ADSL modem requires much greater than 200 Digital Signal Processor MIPS.

Notes

18 - 43

Motorola CopperGold ADSL ChipMotorola CopperGold ADSL Chip

• Announced March 1998

• 5 million transistors, 144 pins, clocked at 55 MHz

• 1.5 W power consumption

• DMT processor contains – Motorola MC56300 DSP core

– Several application specific ICs

• 512-point FFT

• 17-tap FIR filter for time-domain channel equalization based on MMSE method (20 bits precision per tap)

• DSP core and memory occupies about 1/3 of chip area

• It gives up to 8 Mbps upstream and 1 Mbps downstream

Notes

18 - 44

Motorola Copper Gold ADSL TransceiverMotorola Copper Gold ADSL Transceiver• Contains all 3 ADSL modem subsystems on a single chip.

– Has programmable bit to tell it whether it is at customer's or central office site

– Analog front end operates at a sampling rate of 2.208 MHz and gives 16 bits/sample of resolution. It uses sigma-delta modulation with an oversampling factor of 55 / 2.208 = 25.

• Discrete multitone processor consists of a Motorola MC56300 DSP Onyx core and several application-specific digital VLSI circuits to implement – 256-point FFT for downstream transmission or 512-point FFT for

downstream reception if it is at the central office or customer's site, respectively

– 17-tap adaptive FIR filter for channel equalization (20 bits of precision per tap) running at 2.208 MHz

– DSP core computes the 32-point FFT for the downstream transmission or the 64-point FFT for the downstream reception.

Notes

18 - 45

Minimum Mean Squared Error TEQMinimum Mean Squared Error TEQ

TNb

bbb ] [ 10 b

TNw

www ] [ 10 w

wRwwRbbRb yyxyxxTTT

ke 2}{MSE 2

ifonly achieved is MSE minimum

bRbbRRRRb y|xyxyyxyxxTT MSE 1

bRb ΔTMSE

Matrix O selects the proper part out of Rx|y corresponding to the delay

then Define OROR y|xT

yyxy RwRb TT

z-

h + w

b

-xk

yk ek

zk

rk

nk

+

Notes

18 - 46

Simulation Results for 17-Tap TEQSimulation Results for 17-Tap TEQ Achievable percentage of upper bound on bit rate

ADSL CSA Loop

Minimum

MSE

Maximum Geometric

SNR

Maximum Shortening

SNR

Minimum

ISI

Maximum

Bit Rate

Upper Bound

(Mbps) 1 43% 84% 62% 99% 99% 9.059

2 70% 73% 75% 98% 99% 10.344

3 64% 94% 82% 99% 99% 8.698

4 70% 68% 61% 98% 99% 8.695

5 61% 84% 72% 98% 99% 9.184

6 62% 93% 80% 99% 99% 8.407

7 57% 78% 74% 99% 99% 8.362

8 66% 90% 71% 99% 100% 7.394

Cyclic prefix length 32FFT size (N) 512Coding gain 4.2 dBMargin 6 dB

Input power 23 dBmNoise power -140 dBm/HzCrosstalk noise 8 ADSL disturbersPOTS splitter 5th order Chebyshev

Notes

18 - 47

Simulation Results for Three-Tap TEQSimulation Results for Three-Tap TEQ Achievable percentage of upper bound on bit rate

ADSL CSA Loop

Minimum

MSE

Maximum Geometric

SNR

Maximum Shortening

SNR

Minimum

ISI

Maximum

Bit Rate

Upper Bound

(Mbps) 1 54% 70% 96% 97% 98% 9.059

2 47% 71% 96% 96% 97% 10.344

3 57% 69% 92% 98% 99% 8.698

4 46% 66% 97% 97% 98% 8.695

5 52% 65% 96% 97% 98% 9.184

6 60% 71% 95% 98% 99% 8.407

7 46% 63% 93% 96% 97% 8.362

8 55% 61% 94% 98% 99% 7.394

Cyclic prefix length 32FFT size (N) 512Coding gain 4.2 dBMargin 6 dB

Input power 23 dBmNoise power -140 dBm/HzCrosstalk noise 8 ADSL disturbersPOTS splitter 5th order Chebyshev

Notes