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

• If we knew which subset was transmitted,
• the decision would be easy
• So we transmit the subset and the point in the
  subset
• But we cant afford to make a mistake as to the
  subset
• So we protect the subset identifier bits with
  an ECC
• To decode use the Viterbi algorithm (example for
  4 states - 2 subsets)

130
OPTIS Overlapping PAM Transmission with
Interlocking Spectra

• An single pair HDSL replacement
• that is spectrally compatible with HDSL and T1
• 16 level PAM with 517K baud rate
• very strong (512 state, gt5 dB) TCM
• 1D for low (216 msec) latency (speech)
• strong DFE
• tailored spectra (fits between HDSL and T1)
• partially overlapped (interlocking) spectra
• folding (around fb/2) enhances SNR!
• upstream bump for spectral compatibility

131
OPTIS - continued
132
OPTIS - continued
133
DMT processing

• bit handling ((de)framer, CRC, (de)scrambler, RS,
  (de)interleaver)
• tone handling (bit load, gain scaling, tone
  ordering, bit swapping)
• QAM modem (symbolizer, slicer)
• signal handling (cyclic prefix insertion/deletion,
  (I)FFT,
• interpolation,
  PAR reduction)
• synchronization (clock recovery)
• channel handling (probing and training, echo
  cancelling, FEQ, TEQ)