Introduction to ADSL Modems

1
Introduction to ADSL Modems

• Prof. Brian L. EvansDept. of Electrical and
  Comp. Eng.The University of Texas at
  Austinhttp//signal.ece.utexas.edu

Last modified August 27, 2005
UT graduate students Mr. Zukang Shen, Mr.
Daifeng Wang, Mr. Ian Wong UT Ph.D. graduates
Dr. Güner Arslan (Silicon Labs), Dr. Biao Lu
(Schlumberger), Dr. Ming Ding (Bandspeed), Dr.
Milos Milosevic (Schlumberger) UT senior design
students Wade Berglund, Jerel Canales, David J.
Love,Ketan Mandke, Scott Margo, Esther Resendiz,
Jeff Wu Other collaborators Dr. Lloyd D. Clark
(Schlumberger), Prof. C. Richard Johnson, Jr.
(Cornell), Prof. Sayfe Kiaei (ASU), Prof. Rick
Martin (AFIT),Prof. Marc Moonen (KU Leuven), Dr.
Lucio F. C. Pessoa (Motorola),Dr. Arthur J.
Redfern (Texas Instruments)
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Outline

• Broadband Access
• Applications
• Digital Subscriber Line (DSL) Standards
• ADSL Modulation Methods
• ADSL Transceiver Block Diagram
• Quadrature Amplitude Modulation
• Multicarrier Modulation
• ADSL Transceiver Design
• Inter-symbol Interference
• Time-Domain Equalization
• Frequency-Domain Equalization
• Conclusion

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Applications of Broadband Access
4
DSL Broadband Access
Internet
DSLAM
Central Office
ADSL modem
ADSL modem
Voice Switch
LPF
LPF
Customer Premises
PSTN
5
DSL Broadband Access Standards
Courtesy of Mr. Shawn McCaslin (National
Instruments, Austin, TX)
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Spectral Compatibility of xDSL
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ADSL Modem
N/2 subchannels
N real samples
S/P
quadrature amplitude modulation (QAM) encoder
mirror data and N-IFFT
add cyclic prefix
P/S
D/A transmit filter
Bits
00110
TRANSMITTER
channel
RECEIVER
N real samples
N/2 subchannels
P/S
time domain equalizer (FIR filter)
QAM demod decoder
N-FFT and remove mirrored data
S/P
remove cyclic prefix
receive filter A/D
invert channel frequency domain equalizer
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Bit 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
S/P
110
110
00110
00110
00
00
Words
Bits
Bits
Words
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Amplitude Modulation by Cosine Function

• Multiplication in time is convolution in Fourier
  domain
• Sifting property of the Dirac delta functional
• Fourier transform property for modulation by a
  cosine

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Amplitude Modulation by Cosine Function

• Example y(t) f(t) cos(w0 t)
• f(t) is an ideal lowpass signal
• Assume w1 ltlt w0
• Y(w) is real-valued if F(w) is real-valued
• Demodulation is modulation then lowpass filtering
• Similar derivation for modulation with sin(w0t)

Y(w)
w
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Amplitude Modulation by Sine Function

• Multiplication in time is convolution in Fourier
  domain
• Sifting property of the Dirac delta functional
• Fourier transform property for modulation by a
  sine

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Amplitude Modulation by Sine Function

• Example y(t) f(t) sin(w0 t)
• f(t) is an ideal lowpass signal
• Assume w1 ltlt w0
• Y(w) is imaginary-valued ifF(w) is real-valued
• Demodulation is modulation then lowpass filtering

F(w)
1
w
w1
-w1
0
Y(w)
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Quadrature Amplitude Modulation (QAM)

• One carrier
• Single signal, occupying the whole available
  bandwidth
• The symbol rate is the bandwidth of the signal
  being centered on carrier frequency

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Multicarrier Modulation

• Divide broadband channel into narrowband
  subchannels
• Discrete Multitone (DMT) modulation
• Based on fast Fourier transform (related to
  Fourier series)
• Standardized for ADSL
• Proposed for VDSL

every subchannel behaves like QAM
channel
carrier
magnitude
subchannel
frequency
Subchannels are 4.3 kHz wide in ADSL
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Multicarrier Modulation by Inverse FFT
Q
g(t)
x
x
I
Discrete time
g(t)
x
x


g(t)
x
x
g(t) pulse shaping filter Xi ith
symbol from encoder
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Multicarrier Modulation in ADSL
QAM
00101
N/2 subchannels (carriers)
N time samples
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Multicarrier Modulation in ADSL
Inverse FFT
D/A transmit filter
CP Cyclic Prefix
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Multicarrier Demodulation in ADSL
S/P
N-point FastFourierTransform(FFT)
N/2 subchannels (carriers)
N time samples
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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

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Channel Impulse Response
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Channel Impulse Response
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Cyclic Prefix Helps in Fighting ISI

• Provide guard time between successive symbols
• No ISI if channel length is shorter than n 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

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Cyclic Prefix Helps in Fighting ISI
Repeated symbol
cyclic prefix

to be removed

equal
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Combat 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

25
Convolution Review

• Discrete-timeconvolution
• For every k, we compute a new summation

• Continuous-time convolution
• For every value of t, we compute a new integral

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Finite Impulse Response (FIR) Filter

• Assuming that hk is causal and has
  finiteduration from k 0, , N-1
• Block diagram of an implementation (called a
  finite impulse response filter)

z-1
z-1
z-1

xk

h0
h1
h2
hN-1
S
yk
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Example Time-Domain Equalizer

• Minimize mean squared errorEek2 where ekbk-?
  - hkwk
• Chose length of bk to shorten length of hkwk
• Disadvantages
• Does not consider channel capacity
• Deep notches in equalizer frequency response

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Frequency Domain Equalizer in ADSL

• Problem FFT coefficients (constellation points)
  have been distorted by the channel.
• Solution Use Frequency-domain Equalizer (FEQ) to
  invert the channel.
• Implementation N/2 single-tap filters with
  complex coefficients.

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Frequency Domain Equalizer in ADSL
Y0
Y1
N/2 subchannels (carriers)
YN/2-1
Yi
QAM decoder
0101
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ADSL Modem
N/2 subchannels
N real samples
S/P
quadrature amplitude modulation (QAM) encoder
mirror data and N-IFFT
add cyclic prefix
P/S
D/A transmit filter
Bits
00110
TRANSMITTER
channel
RECEIVER
N real samples
N/2 subchannels
P/S
time domain equalizer (FIR filter)
QAM demod decoder
N-FFT and remove mirrored data
S/P
remove cyclic prefix
receive filter A/D
invert channel frequency domain equalizer
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Crosstalk and Near-End Echo
TX
TX
H
cable
H
RX
RX
TX
TX
H
cable
H
RX
RX
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ADSL vs. FEXT, NEXT, Near-end Echo

• ADSL with Freq. Division Multiplexing - FDM
• Near-End Echo filtered out
• Self-NEXT (NEXT from another ADSL) mostly
  filtered out
• FEXT and NEXT (from another type of DSL) are
  problems
• ADSL with overlapped spectrum (Echo Cancelled)
• Near-End Echo Eliminated using an echo canceller
• FEXT, NEXT and self-NEXT are a problem
• Larger Spectrum available for downstream higher
  data rate