Introduction to DSL

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Introduction to DSL

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Title: Introduction to DSL

1
Introduction toDSL

Yaakov J. Stein
Chief ScientistRAD Data Communications

2
PSTN
3
Original PSTN
UTP
UTP
Manual switching directly connected two local
loops Due to microphone technology, audio BW was
4 kHz
4
Analog switched PSTN

Invention of tube amplifier enabled long distance
Between central offices used FDM spaced at 4 kHz
(each cable carrying 1 group 12 channels)
Developed into hierarchical network of automatic
switches
(with supergroups, master groups, supermaster
groups)

5
Data supported viavoice-grade modems

To send data, it is converted into 4 kHz audio
(modem)
Data rate is determined by Shannon's capacity
theorem
there is a maximum data rate (bps) called the
"capacity"
that can be reliably sent through the
communications channel
the capacity depends on the BW and SNR
In Shannon's days it worked out to about 25 kbps
today it is about 35 kbps (V.34 modem - 33.6 kbps)

6
Digital PSTN
last mile
CO SWITCH
TDM
digital
analog
PSTN
TDM
last mile Subscriber Line
CO SWITCH
LP filter to 4 kHz at input to CO switch (before
A/D)
7
Digital PSTN

Sample 4 kHz audio at 8 kHz (Nyquist)
Need 8 bits per sample 64 kbps
Multiplexing 64 kbps channels leads to higher and
higher rates
Only the subscriber line (local loop) remains
analog
(too expensive to replace)
Can switch (cross connect) large number of
channels
Noise and distortion could be eliminated due to
Shannon's theorems
1. Separation theorem
2. Source coding theorem
3. Channel capacity theorem

8
Voice-grade modemsstill work over new PSTN
CO SWITCH
PSTN
UTP subscriber line
modem
CO SWITCH
But data rates do not increase ! Simulate analog
channel so can achieve Shannon rate lt native 64
kbps rate
modem
Internet
9
Where is the limitation ?

The digital network was developed incrementally
No forklift upgrades to telephones, subscriber
lines, etc.
Evolutionary deployment meant that the new
network needed to simulate pre-existing analog
network
So a 4 kHz analog channel is presented to
subscriber
The 4 kHz limitation is enforced by LP filter
at input to CO switch (before 8 kHz sampling)
The actual subscriber line is not limited to 4
kHz
Is there a better way
to use the subscriber line for digital
transmissions ?

10
UTP
11
What is UTP?

The achievable data rate is limited by physics of
the subscriber line
The subscriber line is an Unshielded Twisted Pair
of copper wires
Two plastic insulated copper wires
Two directions over single pair
Twisted to reduce crosstalk
Supplies DC power and audio signal
Physically, UTP is
distributed resistances in series
distributed inductances in series
distributed capacitances in parallel
so the attenuation increases with frequency
Various other problems exist (splices, loading
coils, etc.)

12
UTP characteristics

Resistance per unit distance
Capacitance per unit distance
Inductance per unit distance
Cross-admittance (assume pure reactive) per unit
distance

13
UTP resistance

Influenced by gauge, copper purity, temperature
Resistance is per unit distance
24 gauge 0.15 W/kft
26 gauge 0.195 W/kft
Skin effect Resistance increases with frequency
Theoretical result R f 1/2
In practice this is a good approximation

14
UTP capacitance

Capacitance depends on interconductor insulation
About 15.7 nF per kft
Only weakly dependent on gauge
Independent of frequency to high degree

15
UTP inductance

Higher for higher gauge
24 gauge 0.188 mH per kft
26 gauge 0.205 mH per kft
Constant below about 10 kHz
Drops slowly above

16
UTP admittance

Insulation good so no resistive admittance
Admittance due to capacitive and inductive
coupling
Self-admittance can usually be neglected
Cross admittance causes cross-talk!

17
Propagation loss

Voltage decreases as travel along cable
Each new section of cable reduces voltage by a
factor
So the decrease is exponential
Va / Vb e -g x H(f,x)
where x is distance between points a and b
We can calculate g, and hence loss,
directly from RCLG model

1v
1/2 v
1/4 v
18
Attenuation vs. frequency
19
Why twisted?

from Alexander Graham Bells 1881 patent
To place the direct and return lines close
together.
To twist the direct and return lines around one
another so that they
should be absolutely equidistant from the
disturbing wires

n
a
V (an) - (bn)
b
20
Why twisted? - continued

So don't need shielding, at least for audio (low)
frequencies
But at higher frequencies UTP has cross-talk
George Cambell was the first to model (see
BSTJ 14(4) Oct 1935)
Cross-talk due to capacitive and/or inductive
mismatch
I2 Q f V1 where Q (Cbc-Cbd) or
Q(Lbc-Lad)

21
Loading coils

Long loops have loading coils to prevent voice
distortion
What does a loading coil do?
Flattens response in voice band
Attenuates strongly above voice frequencies
loops longer than 18 kft need loading coils
88 mH every 6kft starting 3kft

22
Bridge taps

There may also be bridged taps
Parallel run of unterminated UTP
unused piece left over from old installation
placed for subscriber flexibility
High frequency signals are reflected from the
open end
A bridged tap can act like a notch filter!

23
Other problems

Splices
Subscriber lines are seldom single runs of cable
In the US, UTP usually comes in 500 ft lengths
So splices must be made every 500 ft
Average line has gt20 splices
Splices are pressure connections that add to
attenuation
Over time they corrode and may spark, become
intermittent, etc.
Gauge changes
US binder groups typically start off at 26 AWG
Change to 24 AWG after 10 kft
In rural areas they may change to 19 AWG after
that

24
Binder groups

UTP are not placed under/over ground individually
In central offices they are in cable bundles
with 100s of other UTP
In the outside plant they are in binder groups
with 25 or 50 pairs per group
We will see that these pairs interfere with each
other
a phenomenon called cross-talk (XTALK)

25
CSA guidelines

1981 ATT Carrier Service Area guidelines
advise as follows for new deployments
No loading coils
Maximum of 9 kft of 26 gauge (including bridged
taps)
Maximum of 12 kft of 24 gauge (including bridged
taps)
Maximum of 2.5 kft bridged taps
Maximum single bridged tap 2 kft
Suggested no more than 2 gauges
In 1991 more than 60 of US lines met CSA
requirements

26
Present US PSTN

UTP only in the last mile (subscriber line)
70 unloaded lt 18kft
15 loaded gt 18kft
15 optical or digital to remote terminal DA
(distribution area)
PIC, 19, 22, 24, 26 gauge
Built for 2W 4 KHz audio bandwidth
DC used for powering
Above 100KHz
severe attenuation
cross-talk in binder groups (25 - 1000 UTP)
lack of intermanufacturer consistency

27
Present US PSTN - continued

We will see, that for DSL - basically four cases
Resistance design gt 18Kft loaded line - no DSL
possible
Resistance design unloaded lt18 Kft lt1300 W - ADSL
CSA reach - HDSL
DA (distribution area) 3-5 kft - VDSL
Higher rate - lower reach
(because of
attenuation and noise!)

28
xDSL
29
Alternatives for data services

Fiber, coax, HFC
COST 10k-20k / mile
TIME months to install
T1/E1
COST gt5k/mile for conditioning
TIME weeks to install
DSL
COST _at_ 0 (just equipment price)
TIME _at_ 0 (just setup time)

30
xDSL

Need higher speed digital connection to
subscribers
Not feasible to replace UTP in the last mile
Older voice grade modems assume 4kHz analog line
Newer (V.90) modems assume 64kbps digital line
DSL modems dont assume anything
Use whatever the physics of the UTP allows

31
xDSL System Reference Model
32
Splitter

Splitter separates POTS from DSL signals
Must guarantee lifeline POTS services!
Hence usually passive filter
Must block impulse noise (e.g. ring) from phone
into DSL
ADSLforum/T1E1.4 specified that splitter be
separate from modem
No interface specification (but can buy splitter
and modem from different vendors)
Splitter requires installation
Costly technician visit is the major impediment
to deployment
ADSL has splitterless versions to facilitate
residential deployment

33
Why is DSL better than a
voice-grade modem?

Analog telephony modems are limited to 4 KHz
bandwidth
Shannons channel capacity theorem
gives the maximum transfer rate
C BW log2 ( SNR 1 )
So by using more BW we can get higher transfer
rates!
But what is the BW of UTP?

for SNR gtgt 1
C(bits/Hz) ? SNR(dB) / 3

34
Maximum reach

To use Shannon's capacity theorem
we need to know how much noise there is
One type of noise that is always present
(above absolute zero temperature) is thermal
noise
Maximum reach is the length of cable for reliable
communications
ASSUMING ONLY THERMAL NOISE
Bellcore study in residential areas (NJ) found
-140 dBm / Hz
white (i.e. independent of frequency)
is a good approximation
We can compute the maximum reach from known UTP
attenuation

35
xDSL - Maximum Reach
36
Other sources of noise

But real systems have other sources of noise,
and thus the SNR will be lower
and thus will have lower reach
There are three other commonly encountered types
of noise
RF ingress
Near End Cross Talk (NEXT)
Far End Cross Talk (FEXT)

37
Sources of Interference

XMTR RCVR
RCVR XMTR
FEXT
NEXT
RCVR XMTR
XMTR RCVR
RF INGRESS

38
Ungers discovery

What happens with multiple sources of cross-talk?
Unger (Bellcore) 1 worst case NEXT (T1D1.3
185-244)
50 pair binders
22 gauge PIC
18 Kft
Found empirically that cross-talk only increases
as N0.6
This is because extra interferers must be further
away

39
NEXT

Only close points are important
Distant points are twice attenuated by line
attenuation H(f,x)2
Unger dependence on number of interferers
Frequency dependence
Transfer function I2Campbell / R f 2 / f 1/2
f 3/2
Power spectrum of transmission
Total NEXT interference (noise power)
KNEXT N0.6 f 3/2 PSD(f)

40
FEXT

Entire parallel distance important
Thus there will be a linear dependence on L
Unger dependence on number of interferers
Frequency dependence
Transfer function I2Campbell f 2
Power spectrum of transmission
Total FEXT interference (noise power)
KFEXT N0.6 L f2 Hchannel(f)2
PSD(f)

41
Example - Interference spectrum
42
Examples of Realistic Reach

More realistic design goals (splices, some xtalk)
1.5 Mbps 18 Kft 5.5 km (80 US loops)
2 Mbps 16 Kft 5 km
6 Mbps 12 Kft 3.5 km (CSA 50 US loops)
10 Mbps 7 Kft 2 km
13 Mbps 4.5 Kft 1.4 km
26 Mbps 3 Kft 900 m
52 Mbps 1 Kft 300 m (SONET STS-1 1/3
STM-1)

43
Bonding (inverse mux)

If we need more BW than attainable by Shannon
bounds
we can use more than one UTP pair (although XT
may reduce)
This is called bonding or inverse multiplexing
There are many ways of using multiple pairs
ATM - extension of IMA (may be different rates
per pair)
ATM cells marked with SID and sent on any
pair
Ethernet - based on 802.3(EFM)
frames are fragmented, marked with SN, and
sent on many pairs
Time division inverse mux
Dynamic Spectral Management (Cioffi)
Ethernet link aggregation

44
Duplexing

Up to now we assumed that only one side transmits
Bidirectional (full duplex) transmission
requires some form of duplexing
For asymmetric applications we usually speak of
DS downstream and US upstream
Four methods are in common use
Half duplex mode (4W mode) (as in E1/T1)
Echo cancellation mode (ECH)
Time Domain Duplexing (requires syncing all
binder contents)
Frequency Domain Duplexing

45
Muxing, inverse muxing, duplexing

Duplexing 2 data streams in 2
directions on 1 physical line
Multiplexing N data streams in 1
direction on 1 physical line
Inverse multiplexing 1 data stream in 1
direction on N physical lines

46
(Adaptive) echo cancellation

Signal transmitted is known to transmitter
It is delayed, attenuated and distorted in the
round-trip
Using adaptive DSP algorithms we can
find the delay/attenuation/distortion
subtract

47
xDSL types and history
48
DSL Flavors

DSL is often called xDSL
since there are many varieties (different x)
e.g. ADSL, HDSL, SHDSL, VDSL, IDSL, etc.
There were once many unconnected types
but now we divide them into three main families
The differentiation is by means of the
application scenario
HDSL (symmetric, mainly business, data
telephony)
ADSL (asymmetric, mainly residential, Internet
access)
VDSL (very high rate, but short distance)

49
Some xDSL PSDs
PSD(dBm/Hz)
T1
IDSL
HDSL
HDSL2
ADSL

F(MHz)
50
ITU G.99x standards

G.991 HDSL (G.991.1 HDSL G.991.2 SHDSL)
G.992 ADSL (G.992.1 ADSL G.992.2
splitterless ADSL
G.992.3 ADSL2
G.992.4 splitterless ADSL2
G.992.5
ADSL2)
G.993 VDSL (G.993.1 VDSL G.993.2 VDSL2)
G.994 HANDSHAKE
G.995 GENERAL (INFO)
G.996 TEST
G.997 PLOAM
G.998 bonding (G.998.1 ATM G.998.2 Ethernet
G.998.3 TDIM)

51
ITU xDSL layer model

Transport protocol (ATM, STM, PTM)
Transport Protocol Specific - Transmission
Convergence (TPS-TC)
Physical Medium Specific - Transmission
Convergence (PMS-TC)
Physical Medium Dependent (PMD)
Physical medium

52
More xDSL flavors

53
More xDSL flavors (cont.)

54
T1 service (not DSL)

1963 Coax deployment of T1
2 groups in digital TDM
AMI line code
Beyond CSA range should use DLC (direct loop
carrier)
Repeaters every 6 Kft
Made possible by Bell Labs invention of the
transistor
1971 UTP deployment of T1 (but still not DSL)
Bring 1.544 Mbps to customer private lines
Use two UTP in half duplex mode
Requires expensive line conditioning
One T1 per binder group

55
T1 line conditioning

In order for a subscribers line to carry T1
Single gauge
CSA range
No loading coils
No bridged taps
Repeaters every 6 Kft (starting 3 Kft)
One T1 per binder group
Labor intensive (expensive) process
Need something better (DSL)

56
The first true xDSL!

1984,88 IDSL
BRI access for ISDN
4B3T (3 level PAM) or 2B1Q (4 level PAM)
modulation
Prevalent in Europe, never really caught on in US
144 Kbps over CSA range
ITU-T G.961 describes IDSL
There are 4 appendices
Appendix I - 4B3T (AKA MMS43)
Appendix II - 2B1Q
Appendix III - AMI Time Compression Multiplex
(TDD)
Appendix IV - SU32 (3B2T ECH)

57
HDSL - NA improved copy of IDSL

1991 HDSL
Replaced T1/E1 service, but
full CSA distance w/o line conditioning /
repeaters
AMI line code replaced with IDSL's 2B1Q line code
Use 2 UTP pairs, but in ECH mode (DFE)
For T1 784 kbps on each pair
For E1, 1, 2, 3 and 4 pair modes (all ECH)
Requires DSP for echo cancellation
Mature DSL technology, now becoming obsolete

58
HDSL2

With the success of HDSL,
customers requested HDSL service that would
require only a single UTP HDSL
attain at least full CSA reach
be spectrally compatible w/ HDSL, T1, ADSL, etc.
The result, based on high order PAM, was called
HDSL2 (ANSI)
SDSL Symmetric DSL (ETSI)
and is now called
SHDSL Single pair HDSL (ITU)

59
SHDSL

Uses Trellis Coded 16-PAM with various shaping
options
Does not co-exist with POTS service on UTP
Can uses regenerators for extended reach
single-pair operation
192 kbps to 2.312 Mbps in steps of 8 kbps
2.3 Mbps should be achieved for reaches up to 3.5
km
dual-pair operation (4-wire mode)
384 kbps to 4.608 Mbps in steps of 16 kbps
line rate is the same on both pairs
Latest standard (G.shdsl.bis - G.991.2 2003
version)
bonding up to 4 pairs
rates up to 5696 kbps
optional 32-PAM (instead of 16-PAM)
dynamic rate repartitioning

60
ADSL

Asymmetric - high rate DS, lower rate US
Originally designed for video on demand
New modulation type - Discrete MultiTone
FDD and ECH modes
Almost retired due to lack of interest
but then came the Internet
Studies - DSUS for both applications can be
about 101
Some say ADSL could mean
All Data Subscribers Living

61
Why asymmetry?

NEXT is the worst interferer stops HDSL from
achieving higher rates
FEXT much less (attenuated by line)
FDD eliminates NEXT
All modems must transmit in the SAME direction
A reversal would bring all ADSL modems down
Upstream(US) at lower frequencies and power
density
Downstream (DS) at high frequencies and power

62
ADSL Duplexing

US uses low DMT tones (e.g. 8 - 32)
If over POTS / ISDN lowest frequencies reserved
DS uses higher tones
If FDD no overlap
If ECH DS overlaps US

63
Why asymmetry? - continued
PSD (dBm/Hz)
US
DS
F(MHz)
64
Echo cancelled ADSL

FDD gives sweet low frequencies to US only
and the sharp filters enhance ISI
By overlapping DS on US
we can use low frequencies and so increase reach
Power spectral density chart

65
ADSL - continued

ADSL system design criterion BER 10-12 (1 error
every 2 days at 6 Mbps)
Raw modem can not attain this low a BER!
For video on demand
RS and interleaving can deliver (error bursts of
500 msec)
but add 17 msec delay
For Internet
TCP can deliver
high raw delay problematic
So the G.992.1 standard defines TWO framers
fast (noninterleaved ) and slow (interleaved)
buffers

66
ADSL standard

ITU (G.dmt) G.992.1, ANSI T1.413i2 standard
DS - 6.144 Mbps (minimum)
US- 640 kbps
First ADSL data implementations were CAP (QAM)
ITU/ANSI/ETSI standards are DMT with spacing of
4.3125 kHz
DMT allows approaching water pouring capacity
DMT is robust
DMT requires more complex processing
DMT may require more power

67
Splitterless ADSL

Splitterless ADSL, UAWG, G.lite, G.992.2, G.992.4
Splitterless operation
fast retrain
power management to eliminate clipping
initialization includes probing telephone sets
for power level
microfilters
modems usually store environment parameters
G.992.2 - cost reduction features
G.992.1 compatible DMT compatible using only 128
tones
512 Kbps US / 1.5 Mbps DS (still gtgt V.34 or V.90
modems)
features removed for simplicity
simpler implementation (only 500 MIPS lt 2000 MIPS
for full rate)

68
ADSL2

ADSL uses BW from 20 kHz to 1.1 MHz
ADSL2 Increases rate/reach of ADSL by using 20
kHz - 4.4 MHz
Also numerous efficiency improvements
better modulation
reduced framing overhead
more flexible format (see next slide)
stronger FEC
reduced power mode
misc. algorithmic improvements
for given rate, reach improved by 200 m
3 user data types - STM, ATM and packet
(Ethernet)
ADSL2 dramatically increased rate at short
distances

69
More ADSL2 features

Dynamic training features
Bit Swapping (dynamic change of DMT bin bit/power
allocations)
Seamless Rate Adaptation (dynamic change of
overall rate)
Frame bearers
Multiple (up to 4) frame bearers (data flows)
Multiple latencies for different frame bearers
(FEC/interleave lengths)
Dynamic rate repartitioning (between different
latencies)

70
ADSL annexes (G.992.1/3)

Annex A ADSL over POTS
Annex B ADSL over 2B1Q/4B3T ISDN
Annex C ADSL over TDD ISDN
Annex D State diagrams (state machine for idle,
(re)training, etc)
Annex E Splitters (POTS and ISDN)
Annex F North America - classification and
performance
Annex G Europe - classification (interop options)
and performance
Annex H Synchronized Symmetric DSL with TDD ISDN
in binder

71
ADSL annexes (G.992.3)

Annex I All digital ADSL (i.e. alone on UTP)
with POTS in binder
Annex J All digital ADSL with ISDN in binder
Annex K Transmission Protocol Specific functions
(STM, ATM, PTM)
Annex L Reach Extended ADSL2 over POTS
Annex M Extended US BW over POTS

72
VDSL

Optical network expanding (getting closer to
subscriber)
Optical Network Unit ONU at curb or basement
cabinet
FTTC (curb), FTTB (building)
These scenarios usually dictates low power
Rates can be very high since required reach is
minimal!
Proposed standard has multiple rates and reaches

73
VDSL - rate goals

Symmetric rates
6.5 4.5Kft (1.4 Km)
13 3 Kft (900 m)
26 1 Kft (300 m)
Asymmetric rates (US/DS)
0.8/ 6.5 6 Kft (1.8 Km)
1.6/13 4.5 Kft (1.4Km)
3.2/26 3 Kft (900 m)
6.4/52 1 Kft (300 m)

74
VDSL - Power issues

Basic template is -60 dBm/Hz from 1.1MHz to 20
MHz
Notches reduce certain frequencies to -80 dBm/Hz
Power boost on increase power to -50 dBm/Hz
Power back-off reduces VTU-R power so that wont
block another user
ADSL compatibility off use spectrum down to 300
KHz

75
VDSL2

DMT line code (same 4.3125 kHz spacing as ADSL)
VDSL uses BW of 1.1 MHz - 12 MHz (spectrally
compatible with ADSL)
VDSL2 can use 20 kHz - 30 MHz
new band-plans (up to 12 MHz, and 12-30 MHz)
increased DS transmit power
various algorithmic improvements
borrowed improvements from ADSL2
3 user data types - STM, ATM and PTM

76
VDSL2 band plans

North American bandplan
US0 (if present) starts between 4 kHz - 25 kHz
and ends between 138-276 kHz
Europe - six band plans (2 A and 4 B)
A (998) US0 from 25 DS1 from 138 or 276
US1 3750-5200 DS2 5200-8500
B (997) US0 from 25 or 120 or nonexistent
DS1 from 138 or 276
US1 3000-5100 DS2 5100-7050

77
HPNA (G.PNT)

Studies show that about 50 of US homes have a PC
30 have Internet access, 20 have more than
one PC!
Average consumer has trouble with cabling
HomePNA de facto industry standard for home
networking
Computers, peripherals interconnect (and connect
to Internet?)
using internal phone wiring (user side of
splitter)
Does not interrupt lifeline POTS services
Does not require costly or messy LAN wiring of
the home
Presently 1 Mbps, soon 10 Mbps, eventually 100
Mbps!

78
Shannon Theory
79
Shannon - Game plan

Claude Shannon (Bell Labs) 1948
Digital communications never worse than analog
and frequently better !
Basic idea
Analog signals become contaminated by noise
Amplification doesn't help - noise is amplified
too
Bits can not be degraded in a minor way - either
0 or 1
When bit flip - Error Correcting Codes can fix
Rigorous proof
Source - channel separation theorem
Source encoding theorems
Channel capacity theorems

80
Shannon - Separation Theorem

Source channel separation theorem
Separate source coding from channel coding
No efficiency loss
The following are NOT optimal !!!
OSI layers
Separation of line code from ECC

81
Shannon - Channel Capacity

Every bandlimited noisy channel has a capacity
Below capacity errorless information reception
Above capacity errors
Shocking news to analog engineers
Previously thought
only increasing power decreases error rate
But Shannon didnt explain HOW!

82
Channel Capacity (continued)

Shannons channel capacity theorem
If no noise (even if narrow BW)
Infinite information transferred instantaneously
Just send very precise level
If infinite bandwidth (even if high noise)
No limitation on how fast switch between bits
If both limitations
C BW log2 ( SNR 1 )

83
Channel Capacity (continued)

The forgotten part
All correlations introduce redundancy
Maximal information means nonredundant
The signal that attains channel capacity
looks like white noise filtered to the BW

84
Channel Capacity (continued)

That was for an ideal low-pass channel
What about a real channel (like DSL)?
Shannon says ...
Simply divide channel into subchannels and
integrate
each
bandpass channel
obeys
regular Shannon law
S log2 (SNR(f) 1) BW ? log2 (SNR(f)
1) df
Only SNR(f) is important !

85
Water pouring (Gallager) theorem

Given total amount of energy, N(f) and A(F)
how can we maximize the capacity?

86
Line Codes
87
How do modems work?

The simplest attempt is to simply transmit 1 or 0
(volts?)
This is called NRZ (short serial cables, e.g.
RS232)
Information rate number of bits transmitted per
second (bps)

88
The simplest modem - DC

So what about transmitting -1/1?
This is better, but not perfect!
DC isnt exactly zero
Still can have a long run of 1 OR -1 that will
decay
Even without decay, long runs ruin timing
recovery (see below)

89
The simplest modem - DC

What about RZ?
No long 1 runs, so DC decay not important
Still there is DC
Half width pulses means twice bandwidth!

90
The simplest modem - DC

T1 uses AMI (Alternate Mark Inversion)
Absolutely no DC!
No bandwidth increase!

91
NRZ - Bandwidth

The PSD (Power Spectral Density) of NRZ is a sinc
( sinc(x) sin(x) )
The first zero is at the bit rate (uncertainty
principle)
So channel bandwidth limits bit rate
DC depends on levels (may be zero or spike)

x
92
From NRZ to n-PAM

NRZ
4-PAM
(2B1Q)
8-PAM
Each level is called a symbol or baud
Bit rate number of bits per symbol baud rate

GRAY CODE 10 gt 3 11 gt 1 01 gt -1 00 gt -3
GRAY CODE 100 gt 7 101 gt 5 111 gt 3 110 gt
1 010 gt -1 011 gt -3 001 gt -5 000 gt -7
111
001
010
011
010
000
110
93
PAM - Bandwidth

BW (actually the entire PSD) doesnt change with
n !
So we should use many bits per symbol
But then noise becomes more important
(Shannon strikes again!)

BAUD RATE
94
The simplest modem - OOK

Even better - use OOK (On Off Keying)
Absolutely no DC!
Based on sinusoid (carrier)
Can hear it (morse code)

95
OOK - Bandwidth

PSD of -1/1 NRZ is the same, except there is no
DC component
If we use OOK the sinc is mixed up to the carrier
frequency
(The spike helps in carrier recovery)

96
ASK

What about Amplitude Shift Keying - ASK ?
2 bits / symbol
Generalizes OOK like multilevel PAM did to NRZ
Not widely used since hard to differentiate
between levels
Is FSK better?

97
FSK

FSK is based on orthogonality of sinusoids of
different frequencies
Make decision only if there is energy at f1 but
not at f2
Uncertainty theorem says this requires a long
time
So FSK is robust but slow (Shannon strikes
again!)

98
PSK

Even better to use sinusoids with different
phases!
BPSK
1 bit / symbol
or QPSK
2 bits /
symbol
Bell 212 2W 1200 bps
V.22

99
QAM

Finally, best to use different phases and
amplitudes
2 bits per symbol
V.22bis 2W full duplex 2400 bps used 16 QAM (4
bits/symbol)
This is getting confusing

100
The secret math behind it all

The instantaneous representation
x(t) A(t) cos ( 2 p fc t f(t) )
A(t) is the instantaneous amplitude
f(t) is the instantaneous phase
This obviously includes ASK and PSK as special
cases
Actually all bandwidth limited signals can be
written this way
Analog AM, FM and PM
FSK changes the derivative of f(t)
The way we defined them A(t) and f(t) are not
unique
The canonical pair (Hilbert transform)

101
The secret math - continued

How can we find the amplitude and phase?
The Hilbert transform is a 90 degree phase
shifterH cos(f(t) ) sin(f(t) )
Hence
x(t) A(t) cos ( 2 p fc t f(t) )
y(t) H x(t) A(t) sin ( 2 p fc t f(t) )
A(t) x2(t) y2(t)
f(t) arctan( y(t) x(t) )

102
Star watching

For QAM we can draw a diagram with
x and y as axes
A is the radius, f the angle
For example, QPSK can be drawn (rotations are
time shifts)
Each point represents 2 bits!

103
QAM constellations

16 QAM V.29 (4W 9600
bps)
V.22bis 2400 bps Codex
9600 (V.29)
2W
first non-Bell modem
(Carterphone decision)
Adaptive equalizer
Reduced PAR constellation
Today - 9600 fax!
8PSK
V.27
Received symbols are not points
due to noise and Inter
Symbol Interference
4W
(ISI removed by equalizer)
4800bps

104
QAM constellations (cont)
1664 points
105
Multicarrier Modulation

NRZ, RZ, etc. have NO carrier
PSK, QAM have ONE carrier
MCM has MANY carriers
Each is essentially an independent, standalone
modem
Achieve maximum capacity by direct water pouring!
PROBLEM
Basic FDM requires has Inter Channel Interference
To reduce effect require guard frequencies
Squanders good bandwidth

106
OFDM

Subsignals are orthogonal if spaced precisely by
the baud rate
Sinc function has zero at center of nearby modem
This implies that the signals are orthogonal - no
ICI
No guard frequencies are needed
Dont need N independent modems
efficient digital implementation by FFT algorithm

107
DMT

Measure SNR(f) during initialization
Water pour QAM signals according to SNR(f)
Each individual signal narrowband --- no ISI
Symbol duration gt channel impulse response time
--- no ISI
No equalizer required

108
DMT - continued

frequency
time
109
Summary of xDSL Line Codes

PAM
IDSL (2B1Q)
HDSL
SHDSL/HDSL2 (with TCM and optionally OPTIS)
SDSL
QAM/CAP
proprietary HDSL/ADSL/VDSL
DMT
ADSL
ADSL2, ADSL2
G.lite
VDSL2

110
Misc. Topics in DSL Modem Theory
111
Bit scrambling

We can get rid of long runs that cause DC at the
bit level
Bits randomized for better spectral properties
Self synchronizing
Original bits can be recovered by descrambler
Still not perfect! (one to one transformation)

112
Timing

Proper timing
Provided by separated transmission
uses BW or another UTP
Improper timing
causes extra or missed bits, and bit errors

113
Timing (baudrate) recovery

How do we recover timing (baud rate) for an NRZ
signal?
For clean NRZ - find the GCF of observed time
intervals
For noisy signals need to filter b T / t
t a t (1-a) T/b
PLL
How can we recover the timing for a PSK signal?
The amplitude is NOT really constant (energy
cut-off)
Contains a component at baud rate
Sharp filter and appropriate delay
Similarly for QAM
BUT as constellation gets rounder
recovery gets harder

114
Carrier recovery

Need carrier recovery for PSK / QAM signals
How can we recover the carrier of a PSK signal?
X(t) A(t) cos ( 2 p fc t ) where A(t)
/- 1
So X2(t) cos2 ( 2 p fc t )
For QPSK X4(t) eliminates the data and emphasizes
the carrier!
Old saying
square for baud, to the fourth for carrier

115
Constellation rotation recovery

How can we recover the rotation of the
constellation?
Simply change phase for best match to the
expected constellation!
How do we get rid of 90 degree ambiguity?
We cant! We have to live with it!
And the easiest way is to use differential
coding!
DPSK NPSK Gray code
000 100 110 010 011 111 101 001 000
QAM put the bits on the transitions!

00
10
01
11
116
ISI - BW reduction
117
QAM ISI

The symbols overlap and interfere
Constellations become clouds
Only
previous symbol
Moderate ISI
Severe ISI

118
Equalizers

ISI is caused by the channel acting like a
low-pass filter
Can correct by filtering with inverse filter
This is called a linear equalizer
Can use compromise (ideal low-pass) equalizer
plus an adaptive equalizer
Usually assume the channel is all-pole
so the equalizer is all-zero (FIR)
How do we find the equalizer coefficients?

119
Training equalizers

Basically a system identification problem
Initialize during training using known data
(can be reduced to solving linear algebraic
equations)
Update using decision directed technique (e.g.
LMS algorithm)
once decisions are reliable
Sometimes can also use blind equalization
e e (ai)

e
120
Equalizers - continued

Noise enhancement
This is a basic consequence of using a linear
filter
But we want to get as close to the band edges as
possible
There are two different ways to fix this problem!

noise
channel
modulator
equalizer
demodulator
filter
121
Equalizers - DFE

ISI is previous symbols interfering with
subsequent ones
Once we know a symbol (decision directed) we can
use it
to directly subtract the ISI!
Slicer is non-linear and so breaks the noise
enchancement problem
But, there is an error propogation problem!

linear
slicer
out
equalizer
feedback
filter
122
Equalizers - Tomlinson precoding

Tomlinson equalizes before the noise is added
Needs nonlinear modulo operation
Needs results of channel probe or DFE
coefficients
to be forwarded

noise
Tomlinson precoder
channel
modulator
demodulator
filter
123
More on QAM constellations

What is important in a constellation?
The number of points
N
The minimum distance between points
dmin
The average squared distance from the center E
ltr2gt
The maximum distance from the center
R
Usually
Maximum E and R are given
bits/symbol log2 N
PAR R/r
Perr is determined mainly by dmin

124
QAM constellations - slicers

How do we use the constellation plot?
Received point classified to nearest
constellation point
Each point has associated bits (well thats a
lie, but hold on)
Sum of errors is the PDSNR

125
Multidimensional constellations

PAM and PSK constellations are 1D
QAM constellations are 2D (use two parameters of
signal)
By combining A and f of two time instants ...
we can create a 4D constellation
From N times we can make 2N dimensional
constellation!
Why would we want to?
There is more room in higher dimensions!
1D 2 nearest neighbors 2D 4 nearest
neighbors
ND 2N nearest neighbors!

How do I draw this?
126
Trellis coding

Modems still make mistakes
Traditionally these were corrected by ECCs (e.g.
Reed Solomon)
This separation is not optimal
Proof incorrect hard decisions - not obvious
where to correct
soft decisions - correct symbols
with largest error
How can we efficiently integrate demodulation and
ECC?
This was a hard problem since very few people
were expert
in ECCs and signal processing
The key is set partitioning

127
Set Partitioning - 8PAM
Final step
First step
Original
Subset 0
Subset 1
00
01
10
11
128
Set Partitioning - 8PSK
129
Trellis coding - continued