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Introduction to ADSL ModemsIntroduction to ADSL Modems
Prof. Brian L. EvansDept. of Electrical and Comp. Eng.The University of Texas at Austin
http://signal.ece.utexas.edu
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)
Last modified August 27, 2005
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OutlineOutline• 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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Residential 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
Business 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
Applications of Broadband AccessApplications of Broadband Access
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DSL Broadband AccessDSL Broadband Access
Customer Premises
downstream
upstreamVoice
Switch
Central Office
DSLAM
ADSL modem
ADSL modem
LPFLPF
PSTN
Internet
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DSL Broadband Access StandardsDSL Broadband Access Standards
Courtesy of Mr. Shawn McCaslin (National Instruments, Austin, TX)
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
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Spectral Compatibility of xDSLSpectral Compatibility of xDSL
10k 100k 1M 10M 100M
POTS
ISDN
ADSL - USA
ADSL - Europe
HDSL/SHDSL
HomePNA
VDSL - FDD
Upstream Downstream Mixed
Frequency (Hz)
optional
1.1 MHz
12 MHz
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P/S
QAM demod
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
ADSL Modem ADSL Modem
Bits
00110
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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
00110110
00
Words
S/P
Words
00110
110
00
Bits
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00
0
2
1
cos
FY
ttfty
Amplitude Modulation by Cosine FunctionAmplitude 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
000 ttxdtxttttx
txdtxttx
00 2
1
2
1 FFY
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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(0t)
0
1
-
F()
0
½
- - - +
- +
½F½F
00 2
1
2
1 FFY
Y()
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00
0
2
1
sin
jFY
ttfty
Amplitude Modulation by Sine FunctionAmplitude 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
000 ttxdtxttttx
txdtxttx
00 22 F
jF
jY
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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()
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– One carrier – Single signal, occupying the
whole available bandwidth– The symbol rate is the
bandwidth of the signal being centered on carrier frequency
Quadrature Amplitude Modulation (QAM)Quadrature Amplitude Modulation (QAM)
frequency
channel
mag
nitu
de
fc
Bits Constellation encoder Bandpass
Lowpassfilter
Lowpassfilter
I
Q
TX
cos(2fct)
sin(2fct)
-
Modulator
I
Q iX
00110
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Multicarrier ModulationMulticarrier 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
subchannel
frequency
ma
gn
itude
carrier
channel
every subchannel behaves like QAM
Subchannels are 4.3 kHz wide in ADSL
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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
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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 time
samples
N/2 subchannels
(carriers)
QAM00101
I
QiX
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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
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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
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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
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Channel Impulse ResponseChannel Impulse Response
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Channel Impulse ResponseChannel Impulse Response
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Cyclic Prefix Helps in Fighting ISI Cyclic 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 distortionN samplesv samples
CP CPs y m b o l ( i ) s y m b o l ( i+1)
copy copy
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Cyclic Prefix Helps in Fighting ISICyclic Prefix Helps in Fighting ISI
cyclic prefix
equal
to be removed
Repeated symbol
*
=
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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
Shortened channel
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m
mkxmhky ][ ][ ][ dtxhty
h[k] y[k]x[k]Representedby its impulseresponse
h(t) y(t)x(t)Representedby its impulseresponse
Convolution ReviewConvolution Review• Discrete-time
convolution
• 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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1
0
][ ][ ][N
m
mkxmhky
z-1 z-1 z-1…
…
x[k]
y[k]
h[0] h[1] h[2] h[N-1]
Finite Impulse Response (FIR) FilterFinite Impulse Response (FIR) Filter• Assuming that h[k] is causal and has finite
duration from k = 0, …, N-1
• Block diagram of an implementation (called a finite impulse response filter)
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z-
h + w
b
-xk
yk ek
zk
rk
nk
+
• Minimize mean squared error
E{ek2} where ek=bk- - hk*wk
– Chose length of bk to shorten length of hk*wk
• Disadvantages– Does not consider channel capacity
– Deep notches in equalizer frequency response
Example Time-Domain EqualizerExample Time-Domain Equalizer
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Frequency Domain Equalizer in ADSLFrequency 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 ADSLFrequency Domain Equalizer in ADSL
YN/2-1
Y1
Y0
N/2 subchannels
(carriers)
QAM decoder
0101 Yi
1
~X
12
~NX
0
~X
FEQ
iii XcY~
iX~
Yi
Q
I
FEQ
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P/S
QAM demod
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
ADSL Modem ADSL Modem
Bits
00110
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Crosstalk and Near-End EchoCrosstalk and Near-End Echo
f
f f
TX
RX
H cable H
TX
RX
f f
TX
RX
H cable H
TX
RXfNEXT
FEXT
Near-End echo
Near-End echo
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ADSL vs. FEXT, NEXT, Near-end EchoADSL 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
US DS DSUS
f f
FDM EC