Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof....
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Introduction to ADSL ModemsIntroduction to ADSL Modems
Prof. Brian L. Evans
Dept. of Electrical and Comp. Eng.The University of Texas at Austin
Graduate students:Ming Ding , Milos Milosevic (Schlumberger),Zukang Shen
Ex-graduate students:Güner Arslan (Cicada),Biao Lu (Schlumberger)
Ex-undergraduate students:Wade Berglund, Jerel Canales,David Love, Ketan Mandke, Scott Margo, Esther Resendiz, Jeff Wu
Other key collaborators:Lloyd Clark (Schlumberger),Sayfe Kiaei(ASU),Lucio Pessoa(Motorola),Arthur Redfern (Texas Instruments)
http://www.ece.utexas.edu/~bevans/projects/adsl
ADSL
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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
![Page 3: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/3.jpg)
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Residential Application Downstreamrate (kb/s)
Upstreamrate (kb/s)
Willing to pay DemandPotential
Database Access 384 9 High MediumOn-line directory; yellow pages 384 9 Low HighVideo Phone 1,500 1,500 High MediumHome Shopping 1,500 64 Low MediumVideo Games 1,500 1,500 Medium MediumInternet 3,000 384 High MediumBroadcast Video 6,000 0 Low HighHigh definition TV 24,000 0 High Medium
Business Application Downstreamrate (kb/s)
Upstreamrate (kb/s)
Willing to pay DemandPotential
On-line directory; yellow pages 384 9 Medium HighFinancial news 1,500 9 Medium LowVideo phone 1,500 1,500 High LowInternet 3,000 384 High HighVideo conference 3,000 3,000 High LowRemote office 6,000 1,500 High MediumLAN interconnection 10,000 10,000 Medium MediumSupercomputing, 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
CentralOffice
DSLAM
ADSLmodem
ADSLmodem
LPFLPF
PSTN
Internet
![Page 5: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/5.jpg)
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DSL Broadband Access StandardsDSL Broadband Access Standards
Courtesy of Shawn McCaslin (Cicada Semiconductor, Austin, TX)
xDSL Meaning Data Rate Mode ApplicationsISDN Integrated Services
Digital Network144 kbps Symmetric Internet Access, Voice,
Pair Gain (2 channels)T1 T-Carrier One
(requires two pairs)1.544 Mbps Symmetric Business, Internet
ServiceHDSL High-Speed Digital
Subscriber Line(requires two pairs)
1.544 Mbps Symmetric Pair Gain (12 channels),Internet Access, T1/E1replacement
SHDSL Single Line HDSL 1.544 Mbps Symmetric Same as HDSL exceptpair gain is 24 channels
SplitterlessADSL
SplitterlessAsymmetric DSL(G.Lite)
Up to 1.5 MbpsUp to 512 kbps
DownstreamUpstream
Internet Access, VideoPhone
Full-RateADSL
Asymmetric DSL(G.DMT)
Up to 10 MbpsUp to 1 Mbps
DownstreamUpstream
Internet Access, VideoConferencing,ÿRemoteLAN Access
VDSL Very High-SpeedDigital SubscriberLine (proposed)
Up to 22 MbpsUp to 3 MbpsUp to 6 Mbps
DownstreamUpstream
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
QAMdemod
decoder
invertchannel
=frequency
domainequalizer
S/P
quadratureamplitude
modulation(QAM)
encoder
mirrordataand
N-IFFT
addcyclicprefix
P/SD/A +
transmitfilter
N-FFTand
removemirrored
data
S/Premovecyclicprefix
TRANSMITTER
RECEIVER
N/2 subchannels N real samples
N real samplesN/2 subchannels
timedomain
equalizer(FIRfilter)
receivefilter
+A/D
channel
ADSL ModemADSL Modem
Bits
00110
![Page 8: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/8.jpg)
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Bit ManipulationsBit Manipulations• Serial-to-parallel
converter
• Example of one inputbit stream and twooutput words
• Parallel-to-serialconverter
• Example of two inputwords and one outputbit stream
S/P
Bits
00110110
00
Words
S/P
Words
00110
110
00
Bits
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( ) ( ) ( )
( ) ( ) ( ) ( )( )00
0
2
1
cos
ωωδωωδπωπ
ω
ω
−++∗=
=
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 acosine
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )000 ttxdtxttttx
txdtxttx
−=−−=−∗
=−=∗
ÿÿ
∞
∞−
∞
∞−
τττδδ
τττδδ
( ) ( ) ( )00 2
1
2
1 ωωωωω −++= FFY
![Page 10: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/10.jpg)
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Amplitude Modulation by Cosine FunctionAmplitude Modulation by Cosine Function
• Example: y(t) = f(t) cos(ω0 t)– f(t) is an ideal lowpass signal
– Assumeω1 << ω0
– Y(ω) is real-valued ifF(ω) is real-valued
• Demodulation is modulation then lowpass filtering
• Similar derivation for modulation with sin(ω0t)
0
1
ω1-ω1ω
F(ω)
ω0
½
-ω0 - ω1 -ω0 + ω1−ω0
ω0 - ω1 ω0 + ω1ω0
½F(ω − ω0)½F(ω + ω0)
( ) ( ) ( )00 2
1
2
1 ωωωωω −++= FFY
Y(ω)
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( ) ( ) ( )
( ) ( ) ( ) ( )( )00
0
2
1
sin
ωωδωωδπωπ
ω
ω
−−+∗=
=
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 asine
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )000 ttxdtxttttx
txdtxttx
−=−−=−∗
=−=∗
ÿÿ
∞
∞−
∞
∞−
τττδδ
τττδδ
( ) ( ) ( )00 22ωωωωω −−+= F
jF
jY
![Page 12: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/12.jpg)
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Amplitude Modulation by Sine FunctionAmplitude Modulation by Sine Function
• Example: y(t) = f(t) sin(ωωωω0 t)– f(t) is an ideal lowpass signal
– Assumeω1 << ω0
– Y(ω) is imaginary-valued ifF(ω) is real-valued
• Demodulation is modulation then lowpass filtering
0
1
ω1-ω1ω
F(ω)
ω
j ½
-ω0 - ω1 -ω0 + ω1−ω0
ω0 - ω1 ω0 + ω1
ω0
-j ½F(ω − ω0)j ½F(ω + ω0)
-j ½
( ) ( ) ( )00 22ωωωωω −−+= F
jF
jY
Y(ω)
![Page 13: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/13.jpg)
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– One carrier– Single signal, occupying the
whole available bandwidth– The symbol rate is the
bandwidth of the signal beingcentered on carrier frequency
QuadratureQuadratureAmplitude Modulation (QAM)Amplitude Modulation (QAM)
frequency
channel
mag
nitu
de
fc
Bits Constellationencoder Bandpass
Lowpassfilter
Lowpassfilter
I
Q
TX
cos(2πfct)
sin(2πfct)
-
ModulatorI
Q iX
00110
![Page 14: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/14.jpg)
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Multicarrier ModulationMulticarrier Modulation
• Divide broadband channel into narrowbandsubchannels
• Discrete Multitone (DMT) modulation– Based on fast Fourier transform (related to Fourier series)
– Standardized for ADSL
– Proposed for VDSL
subchannel
frequency
mag
nitu
de
carrier
channel
every subchannelbehaves like QAM
Subchannels are 4.3 kHz wide in ADSL
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MulticarrierMulticarrier Modulation by Inverse FFTModulation by Inverse FFT
2/NX
x
tfje 12π
1X
x
tfje 22π
x
tfj Ne 2/2π
+
g(t)
2X g(t)
g(t)
x
nN
je
12π
1X
x
nN
je
22π
x
nN
Nj
e2/
2π
+2X
2/NX
Discretetime
g(t) : pulse shaping filter Xi : i th symbol from encoder
I
QiX
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MulticarrierMulticarrier Modulation in ADSLModulation 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/2subchannels
(carriers)
QAM00101
I
QiX
![Page 17: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/17.jpg)
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MulticarrierMulticarrier Modulation in ADSLModulation 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
ADSLdownstream upstream
CP 32 4N 512 64
Inverse FFT
![Page 18: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/18.jpg)
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MulticarrierMulticarrier Demodulation in ADSLDemodulation in ADSL
N-pointFast
FourierTransform
(FFT)
N time
samples
N/2subchannels
(carriers)
S/P
*1
~X
*12
~−NX
2
~NX
12
~−NX
0
~X
0~x
1~x
2~x
1~
−Nx
![Page 19: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/19.jpg)
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InterInter--symbol Interference (ISI)symbol Interference (ISI)• Ideal channel
– Impulse response is animpulse
– Frequency response is flat
• Non-ideal channelcauses ISI– Channel memory– Magnitude and phase
variation
• Received symbol isweighted sum ofneighboring symbols– Weights are determined by
channel impulse response
1 1 1
-1
1.7
.4 .1
1
1.7
2.1
11 11
Channelimpulseresponse
Receivedsignal
Thresholdat zero
Detectedsignal
* =
1 .7
1
![Page 20: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/20.jpg)
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Channel Impulse ResponseChannel Impulse Response
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Channel Impulse ResponseChannel Impulse Response
![Page 22: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/22.jpg)
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Cyclic Prefix Helps in Fighting ISICyclic Prefix Helps in Fighting ISI
• Provide guard time between successive symbols– No ISI if channel length is shorter thanν +1 samples
• Choose guard time samples to be a copy of thebeginning 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
![Page 23: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/23.jpg)
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Cyclic Prefix Helps in Fighting ISICyclic Prefix Helps in Fighting ISI
cyclicprefix
equal
to beremoved
Repeatedsymbol
*
=
![Page 24: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/24.jpg)
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Combat ISI with TimeCombat ISI with Time--Domain EqualizerDomain Equalizer
• Channel length is usually longer than cyclic prefix• Use finite impulse response (FIR) filter called a
time-domain equalizer to shorten channel impulseresponse to be no longer than cyclic prefix length
∆
channel
Shortenedchannel
![Page 25: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/25.jpg)
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�∞
−∞=
−=m
mkxmhky ][][][ ( ) ( ) ( ) τττ dtxhty −= ÿ∞
∞−
h[k] y[k]x[k]Representedby its impulseresponse
h(t) y(t)x(t)Representedby its impulseresponse
Convolution ReviewConvolution Review
• Discrete-timeconvolution
• For every k, wecompute a newsummation
• Continuous-timeconvolution
• For every value of t,we compute a newintegral
![Page 26: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/26.jpg)
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�−
=
−=1
0
][][][N
m
mkxmhky
z-1 z-1 z-1…
…
x[k]
Σ 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 finiteduration from k = 0, …,N-1
• Block diagram of an implementation (called afinite impulse response filter)
![Page 27: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/27.jpg)
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z-∆∆∆∆
h + w
b
-xk
yk ek
zk
rk
nk
+
• Minimize mean squared error
E{ek2} whereek=bk-∆ - hk*wk
– Chose length ofbk to shorten length ofhk*wk
• Disadvantages– Does not considerchannel capacity
– Deep notches in equalizer frequency response
Example TimeExample Time--Domain EqualizerDomain Equalizer
![Page 28: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/28.jpg)
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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 withcomplex coefficients.
![Page 29: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/29.jpg)
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Frequency Domain Equalizer in ADSLFrequency Domain Equalizer in ADSL
YN/2-1
Y1
Y0
N/2subchannels
(carriers)
QAMdecoder
0101 Yi
1
~X
12
~−NX
0
~X
FEQ
iii XcY~=
iX~
Yi
Q
I
FEQ
![Page 30: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/30.jpg)
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P/S
QAMdemod
decoder
invertchannel
=frequency
domainequalizer
S/P
quadratureamplitude
modulation(QAM)
encoder
mirrordataand
N-IFFT
addcyclicprefix
P/SD/A +
transmitfilter
N-FFTand
removemirrored
data
S/Premovecyclicprefix
TRANSMITTER
RECEIVER
N/2 subchannels N real samples
N real samplesN/2 subchannels
timedomain
equalizer(FIRfilter)
receivefilter
+A/D
channel
ADSL ModemADSL Modem
Bits
00110
![Page 31: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/31.jpg)
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CrosstalkCrosstalkand Nearand Near--End EchoEnd 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
![Page 32: Introduction to ADSL Modems - Kryzkryz.org/docs/lecture25.pdf · Introduction to ADSL Modems Prof. Brian L. Evans Dept. of Electrical and Comp. Eng. The University of Texas at Austin](https://reader030.fdocuments.us/reader030/viewer/2022040119/5e6d647c3608315969232637/html5/thumbnails/32.jpg)
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ADSL vs. FEXT, NEXT, NearADSL vs. FEXT, NEXT, Near--end Echoend 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