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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
  • 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)
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