Transcript Combat Inter-Symbol Interference with Equalization
ADSL Transceivers
Dr. A. Falahati BSc, C.Eng, MSc, MIC, PhD, MIEE
Dept. of Electrical & Electrical Eng.
Iran University of Sceince & Technology
[email protected]
Outline
• • • • •
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 - 2
Interne t
Introduction
Digital Subscriber Line (DSL) Broadband Access
DSLAM
Central Office
DSL modem Voice Switch LPF Telephone Network
downstream upstream
DSL modem LPF
Customer Premises DSLAM - Digital Subscriber Line Access Multiplexer LPF – Low Pass Filter (passes voiceband frequencies)
18 - 3
Introduction
Discrete Multitone (DMT) DSL Standards
ADSL – Asymmetric DSL
Maximum data rates supported in G.DMT standard (
ideal case
) Echo cancelled: 14.94 Mbps downstream, 1.56 Mbps upstream Frequency division multiplexing: 13.38 Mbps downstream, 1.56 Mbps up Widespread deployment in US, Canada, Western Europe, Hong Kong Central 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
Data band G.DMT ADSL
0.025 – 1.1 MHz
Asymmetric DMT VDSL
0.138 – 12 MHz
VDSL – Very High Rate DSL
Asymmetric Faster G.DMT FDM ADSL 2
m
subcarriers
m
[8, 12] Symmetric: 13, 9, or 6 Mbps Optional 12-17 MHz band
Upstream subcarriers Downstream subcarriers Target up- stream rate Target down- stream rate
32 256 1 Mbps 256 2048/4096 3 Mbps
Introduction
Spectral Compatibility of xDSL
Plain Old Telephone Service 1.1 MHz ISDN ADSL - USA ADSL - Europe HDSL/SHDSL HomePNA VDSL
Any overlap with the AM radio band?
Any overlap with the FM radio band?
10k 100k 1M Frequency (Hz) 10M 100M 12 MHz Upstream Downstream Mixed 18 - 5
Modulation
A 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
Message Source Encoder Decoder Noise Modulator Transmitter Channel Demodulator Receiver Message Sink 18 - 6
Modulation
•
Amplitude Modulation by Cosine Function
Example:
y
(
t
) =
f
(
t
) cos( w 0
t
)
f
(
t
) is an ideal lowpass signal Assume w 1 << w 0
Y
( w ) is real-valued if
F
( w ) is real-valued
Y ½F
( w + w 0 ) 1 2
F
( w + w 0 ) + 1 2
F
( w w 0 )
Y
( w )
½F
( w - w 0 )
½
w 1
F
( w ) 0 1 w 1 w • • w 0 w 1 -w 0 w 0 + w 1 0 w 0 w 1 w 0 w 0 + w 1 w
Demodulation is modulation then lowpass filtering Similar derivation for modulation with
sin( w 0
t
) 18 - 7
•
Modulation
Amplitude Modulation by Sine Function
Example: y(t) = f(t) sin(
w
0 t)
f
(
t
) is an ideal lowpass signal Assume w 1 << w 0
Y
( w ) is imaginary-valued if
F
( w ) is real-valued w 1
Y
j ½F
( w + w 0 )
j
2
F
( w + w 0 ) -
j
2
F
( w
Y
( w ) w 0 )
-j ½F
( w - w 0 )
j ½
w 0 w 0 w 1 w 0 + w 1 w 0 w 1 w 0 + w 1 -w 0
-j ½ F
( w ) 0 1 w w 1 w •
Demodulation is modulation then lowpass filtering
18 - 8
Modulation
Quadrature Amplitude Modulation (QAM)
Q
X i
Bits
00110 I
Constellation encoder I Q
channel
Modulator Lowpass filter
cos(2 p
f c t
)
Bandpass
Transmit -
Lowpass filter
sin(2 p
f c t
) – Single carrier – Single signal, occupying entire available bandwidth – Symbol rate is bandwidth of signal being centered on carrier frequency f c frequency 18 - 9
• •
Modulation
Multicarrier Modulation
Divide broadband channel into narrowband subchannels
– No ISI in
subchannels
if constant gain in every subchannel and if ideal sampling – Each subchannel has a different carrier
pulse
DTFT -1
sinc
Discrete multitone modulation
– Based on fast Fourier transform – Standardized for ADSL and VDSL -w c w c w channel sin p ( )
n c n
carrier subchannel (QAM signal) Subchannels are 4.3 kHz wide in ADSL and VDSL frequency 18 - 10
X
1
X
2
Modulation
Multicarrier Modulation by Inverse FFT
e j
2 p
f
1
t
Q
X i e j
2 p 1
N n g
(
t
) x
e j
2 p
f
2
t
I
X
1 x
e j
2 p 2
N n g
(
t
) x + Discrete time
X
2 x +
e j
2 p
f N
/ 2
t X N
/ 2
g
(
t
) x
g
(
t
) :
pulse shaping filter
e j
2 p
N N
/ 2
n X N
/ 2 x
X i
:
i
th symbol from encoder 18 - 11
ADSL Transceivers
00101
QAM
Multicarrier Modulation in ADSL
Q
X i
I
N
/2 subchannels (carriers) Mirror complex data ( in red ) and take conjugates:
e j
+
e
-
j
2 cos( )
X 0 X
1
X
2
X N
/2
X N
/2-1
* X
2 *
X
1 *
N
-point Inverse Fast Fourier Transform (IFFT)
x
0
x
1
x
2
x N
-1
N
real valued time samples forms ADSL symbol 18 - 12
ADSL Transceivers
Multicarrier Modulation in ADSL
Inverse FFT
v
samples
N
samples
CP N ADSL
downstream upstream 32 4 512 64
CP s y m b o l ( i )
copy
CP s y m b o l ( i+1)
copy CP: Cyclic Prefix
D/A + transmit filter
ADSL frame is an ADSL symbol plus cyclic prefix 18 - 13
ADSL Transceivers
Multicarrier Demodulation in ADSL
S/P
N
/2 subchannels (carriers) ~
X
0 ~
X
~
X
~
X N N N
* 2 1 2 2 1 ~
X
1 *
N
-point Fast Fourier Transform (FFT) ~ 0 ~ 1 ~ 2
N
time samples
N
1 18 - 14
ADSL Transceivers
Data Transmission in an ADSL Transceiver
Bits
00110 S/P
TRANSMITTER
N
/2 subchannels quadrature amplitude modulation (QAM)
encoder
mirror data and
N
-IFFT
N
real samples add cyclic prefix P/S D/A + transmit filter channel
RECEIVER
P/S
N
/2 subchannels QAM decoder invert channel = frequency domain equalizer
N
real samples
N
-FFT and remove mirrored data S/P remove cyclic prefix time domain equalizer (FIR filter) receive filter + A/D 18 - 15 P/S parallel-to-serial S/P serial-to-parallel FFT fast Fourier transform
•
Serial-to-parallel converter
ADSL Transceivers
Bit Manipulations
•
Parallel-to-serial converter
1 1 0 0 0 1 1 0 S/P 0 0
Bits Words
•
Example of one input bit stream and two output words
1 1 0 S/P 0 0 1 1 0 0 0
Words Bits
•
Example of two input words and one output bit stream
18 - 16
1 1 1 1 -1
Combating ISI
*
Inter-symbol Interference (ISI)
2.1
1 .7
.4
Channel impulse response = 1 1.7
.1
.7
Received signal • •
Ideal channel
– Impulse response is an impulse – Frequency response is flat
Non-ideal channel causes ISI
– Channel memory – Magnitude and phase variation
Threshold at zero
1 1 1 1 1 •
Received symbol is weighted sum of neighboring symbols
– Weights are determined by channel impulse response Detected signal 18 - 17
Combating ISI
Single 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:
g g
d (
t-
T ) d [
k-
D ]
x k
Channel
n k y k
Equalizer
r k
Equalizer h
+
w
+ -
+ – Shortens channel impulse response (
time domain
) – Compensates for frequency distortion (
frequency domain
)
z
-
D
Ideal Channel g
Discretized Baseband System
e k
18 - 18
Combating ISI
Combat ISI with Equalization
• • • • •
Problem: Channel frequency response is not flat Solution: Use equalizer to flatten channel frequency response Zero-forcing equalizer
– Inverts channel (impulse response forced to impulse) – Flattens frequency response – Amplifies noise Zero-forcing Equalizer frequency response
MMSE Equalizer frequency response Minimum mean squared error (MMSE) equalizer
– Optimizes trade-off between noise amplification and ISI Channel frequency response
Decision-feedback equalizer
– Increases complexity – Propagates error 18 - 19
subsymbols to be transmitted
Combating ISI
Cyclic Prefix Helps in Fighting ISI
mirrored subsymbols cyclic prefix to be removed 18 - 20 equal
Combating ISI
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
v
samples
N
samples
CP s y m b o l ( i )
copy
CP s y m b o l ( i+1)
copy 18 - 21
Combating ISI
Channel Impulse Response
frequency (kHz) 18 - 22
Combating ISI
Channel Impulse Response
frequency (kHz) 18 - 23
Combating ISI
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
channel impulse response shortened channel impulse response D 18 - 24
• • •
ADSL Equalization
Eliminating ISI in Discrete Multitone Modulation
Time domain equalizer (TEQ)
– Finite impulse response (FIR) filter –
Effective channel impulse response
: convolution of TEQ impulse response with channel impulse response n+1
Frequency domain equalizer (FEQ)
– Compensates magnitude/phase distortion of equalized channel by dividing each FFT coefficient by complex number – Generally updated during data transmission D channel impulse response effective channel impulse response D :
transmission delay
n
: cyclic prefix length
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 number of bits on each subcarrier that can be supported
ADSL G.DMT Values
Down stream Up stream n 32 4
N
512 64 18 - 25
ADSL Equalization
Time-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] 18 - 26
ADSL Equalization x k
Minimum Mean Squared Error TEQ Design
Channel
n k y k
TEQ
r k e k
h
+
w
-
+ • •
z
-
D
b
b k-
D
Minimize
E
{
e k 2
} [Chow & Cioffi, 1992] – Chose length of
b
–
b
(e.g. n in ADSL) to shorten length of
h * w
is eigenvector of minimum eigenvalue of channel-dependent matrix
w
b R R w
0 Disadvantages Amenable to real-time fixed-
– Does not consider
bit rate
point DSP implementation
– Deep notches in equalizer frequency response (zeros out low SNR bands) – Infinite length TEQ case: zeros of
b
on unit circle (kills n subchannels) 18 - 27
ADSL Equalization
Maximum Shortening SNR Solution
• •
Minimize energy leakage outside shortened channel length For each possible position of a window of
n
+1 samples
, max
w
( SSNR in dB ) max
w
10 log 10 energy inside energy outside window window after TEQ after TEQ
h w
• •
Disadvantages
– Does not consider
channel capacity
– Requires Cholesky decomposition and eigenvector calculation – Does not consider channel noise D
Amenable to real-time fixed-point DSP realization
18 - 28
ADSL Equalization
Maximum Shortening SNR Solution
•
x k
Choose w to minimize energy outside window of desired length
– Locate window to capture maximum channel impulse response energy
n k
h
+
y k
w
r k
h
T wall
h
wall
h
T win
h
win
w
T
H
T wall
H
wall
w w
T
H
T win
H
win
w
w
T
w
T
Aw Bw
•
h win, h wall
: equalized channel within and outside the window Objective function is shortening SNR (SSNR)
max
w w
opt
( SSNR ) ( ) 1
q
max
w
min 10
q
min log 10
w
T
w
T
Bw Aw
: eigenvecto
C
subject to r of ( ) 1
A
( ) 1 min
w
T
Bw
eigenvalue 1 of
C
18 - 29
ADSL Equalization
Simulation Results for 17-Tap TEQs
Parameters
Cyclic prefix length 32 FFT size (
N
) 512 Coding gain (dB) 4.2
Margin (dB) 6 Input power (dBm) 23 Noise power (dBm/Hz) -140 Crosstalk noise 24 ISDN disturbers
Downstream transmission
Figure 1 in [Martin, Vanbleu, Ding, Ysebaert, Milosevic, Evans, Moonen & Johnson, submitted] 18 - 30
ADSL Equalization
Simulation Results for 17-Tap TEQs (con’t)
Parameters
Cyclic prefix length 32 FFT size (
N
) 512 Coding gain (dB) 4.2
Margin (dB) 6 Input power (dBm) 23 Noise power (dBm/Hz) -140 Crosstalk noise 24 ISDN disturbers
Downstream transmission
Figure 3 in [Martin, Vanbleu, Ding, Ysebaert, Milosevic, Evans, Moonen & Johnson, submitted] 18 - 31
ADSL Equalization
Matlab DMT TEQ Design Toolbox 3.1
•
Single-path, dual-path, per-tone & TEQ filter bank equalizers
Available at http://www.ece.utexas.edu/~bevans/projects/adsl/dmtteq/
default parameters from G.DMT ADSL standard
23 -140
various performance measures different graphical views
18 - 32
Multicarrier 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 - 33
Notes
Applications of Broadband Access
Application Database Access On-line directory; yellow pages Video Phone Home Shopping Video Games Internet Broadcast Video High definition TV
Residential
Downstream rate (kb/s)
384 384 1,500 1,500 1,500 3,000 6,000 24,000
Upstream rate (kb/s)
9 9 1,500 64 1,500
Willing to pay Demand Potential
High Low High Medium High Medium Low Medium Medium Medium 384 0 0 High Low High Medium High Medium
Application On-line directory; yellow pages Financial news Video phone Internet Video conference Remote office LAN interconnection Supercomputing, CAD
Business
Downstream rate (kb/s)
384 1,500 1,500 3,000 3,000 6,000 10,000 45,000
Upstream rate (kb/s)
9 9 1,500 384 3,000 1,500 10,000 45,000
Willing to pay Demand Potential
Medium Medium High Low High High Low High High High Medium High Low Medium Medium Low 18 - 34
Notes
DSL Broadband Access Standards
xDSL ISDN T1 HDSL SHDSL Splitterless ADSL Full-Rate ADSL VDSL Meaning
Integrated Services Digital Network T-Carrier One (requires two pairs) High-Speed Digital Subscriber Line (requires two pairs) Single Line HDSL Splitterless Asymmetric DSL (
G.Lite)
Asymmetric DSL (
G.DMT)
Very High-Speed Digital Subscriber Line (proposed)
Data Rate Mode Applications
144 kbps Symmetric Internet Access, Voice, Pair Gain (2 channels) 1.544 Mbps Symmetric Business, Internet Service 1.544 Mbps Symmetric Pair Gain (12 channels), Internet Access, T1/E1 replacement 1.544 Mbps Symmetric Same as HDSL except pair gain is 24 channels Up to 1.5 Mbps Up to 512 kbps Downstream Upstream Internet Access, Video Phone Up to 10 Mbps Up to 1 Mbps Up to 22 Mbps Up to 3 Mbps Up to 6 Mbps Downstream Upstream Downstream Upstream Symmetric Internet Access, Video Conferencing, Remote LAN Access Internet Access, Video on-demand, ATM, Fiber to the Hood 18 - 35 Courtesy of Mr. Shawn McCaslin
Notes
ADSL 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.
18 - 36
Notes
ADSL 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.
18 - 37
Notes
Discrete 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.
18 - 38
• • • •
Notes
Two Types of Transmission
Two versions of ADSL
1. 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 18 - 39
Notes
Channel 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
18 - 40
Notes
Bridge 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.
18 - 41
Notes
ADSL 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.
18 - 42
Notes
Motorola 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
18 - 43
Notes
Motorola 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.
18 - 44
Notes
Minimum Mean Squared Error TEQ
x k n k
h
+
y k
w
r k
+
e k
b
[
b
0
b
1
b N b
]
T -
w
[
w
0
w
1
w N w
]
T
z -
D
b
z k
MSE {
e k
2 }
b
T
R xx b
2
b
T
R xy w
+
w
T
R yy w
minimum MSE MSE is
b
T
R xx
achieved
R R
only
R yx
]
b xy
1
yy
if
b
T
b
T
R R x | y xy b
w
T
R yy
Define
R
D
O
T
R x | y O
then MSE
b
T
R Δ b Matrix O selects the proper part out of
R x|y
corresponding to the delay
D 18 - 45
Notes
Simulation Results for 17-Tap TEQ
Achievable percentage of upper bound on bit rate
ADSL CSA Loop Minimum MSE
1
43% Maximum Maximum Geometric SNR Shortening SNR 84% 62% Minimum ISI Maximum Bit Rate 99% 99%
2
70% 73% 75% 98% 99%
3
64%
4
70%
5
61%
6 7
62% 57%
8
66% Cyclic prefix length FFT size (
N
) Coding gain Margin 94% 68% 84% 93% 78% 90% 32 512 4.2 dB 6 dB 82% 61% 72% 80% 74% 71% 99% 98% 98% 99% 99% 99% Input power Noise power Crosstalk noise POTS splitter 5 th 99% 99% 99% 99% 99% 100% 23 dBm Upper Bound (Mbps) 9.059 10.344 -140 dBm/Hz 8.698 8.695 9.184 8.407 8.362 7.394 8 ADSL disturbers order Chebyshev 18 - 46
Notes
Simulation Results for Three-Tap TEQ
Achievable percentage of upper bound on bit rate
ADSL CSA Loop Minimum MSE
1
54% Maximum Maximum Geometric SNR Shortening SNR 70% 96% Minimum ISI Maximum Bit Rate 97% 98%
2
47% 71% 96% 96% 97%
3
57%
4
46%
5
52%
6 7
60% 46%
8
55% Cyclic prefix length FFT size (
N
) Coding gain Margin 69% 66% 65% 71% 63% 61% 32 512 4.2 dB 6 dB 92% 97% 96% 95% 93% 94% 98% 97% 97% 98% 96% 98% Input power Noise power Crosstalk noise POTS splitter 5 th 99% 98% 98% 99% 97% 99% 23 dBm Upper Bound (Mbps) 9.059 10.344 -140 dBm/Hz 8.698 8.695 9.184 8.407 8.362 7.394 8 ADSL disturbers order Chebyshev 18 - 47