ATM QOS The Myth and the Legend

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ATM QOS The Myth and the Legend Powered By Docstoc
					Baseband Signaling and
     Modulation
      Part 1:
 Baseband Signaling
     Part 1 of a 2-part presentation

         Eric L. Michelsen

         Inductive Logic
           If You Could Tell Your Audience
                 Only One Sentence...

Transmitting data requires not only the
signaling of bit values, but also bit timing.
            1
            or
            0
                                                           time
                 sample here & here & here ...

    If I could tell them a second sentence, it would be:
                                        DC is bad.

1/8/2003                           Inductive Logic                2
       Topics: Baseband Signaling (day 1)
 •   On-Off signaling                 •   Manchester encoding
 •   Antipodal signaling              •   4B/5B encoding
 •   Timing recovery                  •   8B/10B encoding
 •   NRZI                             •   Multi-Level Transition
 •   Multilevel: 2B1Q                 •   A modern line code
 •   DS1 & DS3
                      Topics: Modulation (day 2)
 •   Cosine review                    •   Communication channels as
 •   Sums of cosines                      filters
 •   Spectra                          •   Amplitude modulation
 •   Fourier transforms               •   Amplitude demodulation
 •   Baseband signaling               •   Quadrature multiplexing
 •   Why cosine waves?                •   DMT ADSL
 •   Transfer functions

1/8/2003                   Inductive Logic                            3
                     Where in the Stack?
 •   Signaling and modulation are ways of transmitting data
 •   They are the lowest sublayers in Layer 1 (physical layer)
 •   In this context, “signaling” means “transmitting data”
                                         (not call setup/teardown)
 7. Application
                   OSI stack
 6. Presentation

 5. Session

 4. Transport
                                                                        bit serial
 3. Network                                                             (payload)

 2. Link                V.35, framing framing framing framing framing
                                                                        bit serial
                        HSSI,
                                                                        (line)
                        SDSL    DS1     DS3    ADSL IDSL SONET
 1. Physical
                                                                        signaling &
                                                                        modulation
                                     electrical               optical
1/8/2003                       Inductive Logic                                       4
                               A Matter of Values
 •   On-Off binary signaling
          simple
          indicates 1 (on) or 0 (off)
          by itself, does not explicitly convey timing
          works for electrical and optical signals
          Used by Ethernet 10Base5 and 10Base2 (w/ additional line coding)
               amplitude




                           1

                               1        0     1    1    0     0
                           0
                                                                  time
                           bit period



1/8/2003                                    Inductive Logic                   5
                       Time Is of the Essence
 •   With separate clock and data, the transmitter gives the receiver timing
     on one signal, and data on another
 •   Requires two signals (clock and data): can be expensive
 •   Data values are arbitrary (no restrictions)
 •   Used by local interfaces: V.35, (synchronous) EIA-232, HSSI, etc.
 •   As distance and/or speed increase, clock/data skew destroys timing
  sample on
               clock




 rising edge
   of clock

                                                      sample times
                                                      centered in data bits
               data




                                                                   time

1/8/2003                      Inductive Logic                                  6
                No Clock:
      Do You Know Where Your Data Is?
 •   Most long-distance or high speed signaling is self timed: it has no
     separate clock; the receiver recovers timing from the data itself
 •   Receiver knows the nominal data rate, but requires transitions in the
     signal to locate the bits, and interpolate the sample points
 •   Receiver tracks the timing continuously, to stay in synch
          Tracking requires sufficient transition density throughout the data stream
 •   Used in all DSLs, DS1, DS3, SONET, all Ethernets, etc.
                                 transitions locate data
                  data




                                                                   time
                         interpolated sample times
                                (bit centers)

1/8/2003                                Inductive Logic                                 7
                          Timing Recovery
 •   All self-timed line codes provide sufficient signal
     transitions for timing recovery. Some methods used:
          Scrambling
          Return to zero (RTZ)
          Zero substitution
          Manchester encoding
          4B/5B
          8B/10B
          Multi-level transition




1/8/2003                            Inductive Logic        8
                           All For One ... or Zero
 •   On-Off binary signaling: simple, but not energy efficient
     (SNR)
 •   At unit distance (A = 1), average energy = A2/2 = 0.5
 •   For balanced data, DC (Direct Current) ~= 0.5 (bad)
 •   Also known as Non-Return to Zero (NRZ)
 •   Requires sufficient data transition density, or scrambling
 •   Works for electrical and optical signals
           amplitude




                       1                           distance
                            1       0     1    1    0     0
                       0
                                                              time
                       bit period

1/8/2003                                Inductive Logic              9
                                Pluses and Minuses
 •   Antipodal binary signaling: energy efficient (SNR)
 •   At unit distance (A = 0.5), average energy = A2 = 0.25
     (3 dB better than on-off signaling)
 •   Requires sufficient data transition density, or scrambling
 •   For balanced (or scrambled) data, DC ~= 0 (good)
 •   For electrical signaling only (negative light?)
          Ethernet 10BaseT, EIA-232, V.35, V.36, HSSI

                         +0.5
             amplitude




                                1   0     1    1    0       0
                           0
                                                   distance          time
                         -0.5
                                                        Can you say “tip-ring reversal?”

1/8/2003                                Inductive Logic                                10
      NRZI (Non-Return to Zero Inverted)
 •   Data value coded as transition = 1, no transition = 0
 •   Used in combination with antipodal or on/off binary signaling
 •   With scrambling, DC ~= 0
 •   Why NRZI? Can you say “tip-ring reversal?”
 •   Requires sufficient data 1s (signal transition) density, or scrambling
                      +
                      0
                          ?      1     1    0      1     0
                                                                 time
                      -
      Equivalent
     NRZI signals
                      +
                      0   ?      1     1    0      1     0
                                                                 time
                      -

1/8/2003                      Inductive Logic                                 11
                          Multilevel Signaling: 2B1Q
 •   4 is better than 2:
     Encodes 2 Binary bits into 1 Quatenary (4-level) symbol
          A pair of bits in a single symbol is a dibit
 •   AKA 4-PAM (4-level Pulse Amplitude Modulation)
 •   Requires data transitions, or scrambling
 •   With scrambling, DC ~= 0
 •   Used in SDSL, IDSL, ISDN BRI
 •   Other PAMs exist: 16-PAM (G.shdsl), 256-PAM, etc.
              +3
              amplitude




                          +1
                               11 10    01    00
                          -1                                           time
                                                     Usually described as
                                                     “distance 2”: -3, -1, +1, +3
                          -3

1/8/2003                               Inductive Logic                              12
                         AMI: Alternate Mark Inversion
 •               Bipolar, tri-state (+, 0, and -)                           mark = 1
 •               50% duty cycle RTZ (Return To Zero)                        space = 0

 •               Pulses alternate polarity (DC = 0)
 •               Used by DS1 (Digital Service 1, ref. T1.107, T1.403): 2 pair (4 wire)
                    Line rate = 1.544 Mbps, including 8 kbps framing/OAM
                    Payload rate = 1.536 Mbps
                    Generic digital service, can carry T1, PRI, GR-303, Frame Relay, etc.
                    Timing recovery requires at least 2 pulses (ones) every 16 bits
                    B8ZS (Binary 8-Zero Substitution) provides transparency
 - amplitude +




                                                                             idealized
                                                                               pulse
                     1        0      1   1     0      0             25%          50%          25%
                                                          time
                         alternate
                         polarity                                    UI = Unit Interval (bit period)


1/8/2003                                     Inductive Logic                                           13
                                              AMI: DS3
 •           Digital Service 3 (ref. T1.107, T1.404): 2 coax, 75 
 •           RTZ (Return To Zero) pulse, very similar to DS1
 •           AMI (Alternate Mark Inversion), (DC = 0)
 •           Line rate = 44.736 Mbps, including ~530 kbps framing/OAM
 •           Payload rate = 44.736 x (84 / 85)  44.210 Mbps
 •           Generic digital service: can carry T3, Frame Relay, ATM, etc.
 •           Timing recovery requires at least one pulse every 3 bits
                    B3ZS (Binary 3-Zero Substitution) provides transparency
                                              Deliberate bipolar violation,
                                                substitutes for 3 zeros
     - amplitude +




                      1        0      1   1        0       0       0      0      0       0
                                                                          X                   time
                          alternate                            X bits inserted as needed to make BPVs
                          polarity                              alternate polarity, to maintain DC = 0

1/8/2003                                      Inductive Logic                                            14
         Double Time: Manchester Encoding
 •   “Coding” in this sense is applicable to any binary (2-state) signal
     (on-off, antipodal, FSK, etc.)
 •   Provides a transition in the center of every bit
          no density requirement
          High information content: allows rapid timing recovery
 •   DC = 0, exactly (with antipodal signaling)
 •   Data bit is value in last half of bit (or could be first half)
 •   Used in Ethernet 10Base5, 10Base2, 10BaseT
 •   Equivalent to 1B/2B encoding
 •   Not spectrally efficient: requires transmitting 2 signal events for each
     bit (100% bandwidth expansion)
                             1   0    1    1      0     0
              signal state
                      B




                                                               time
                A




1/8/2003                             Inductive Logic                            15
      Enough is Enough: 4B/5B Encoding
 •   Encodes 4 payload bits into 5 line bits
 •   Guarantees transitions; no user data restrictions or scrambling needed
 •   Extra codewords available for control (Idle, SSD, ESD, ...)
 •   More BW efficient than Manchester: 25% expansion                 Data
 •   DC >> 0 (bad), but used with NRZI or MLT, DC ~= 0
 •
                                                                 0   1 1 1 1 0
     Checks line integrity by counting invalid codes             1   0 1 0 0 1

 •   Used in Ethernet 100BaseTX, FDDI
                                                                 2
                                                                 3
                                                                     1 0 1 0 0
                                                                     1 0 1 0 1
                                Control                                 4   0   1   0   1   0
                                                                        5   0   1   0   1   1
           1 1 1 1 1   IDLE   used as inter-stream fill code            6   0   1   1   1   0
                                                                        7   0   1   1   1   1
           1 1 0 0 0   J      Start-of-Stream Delimiter, Part 1 of 2;   8   1   0   0   1   0
                              always used in pairs with K               9   1   0   0   1   1
           1 0 0 0 1   K      Start-of-Stream Delimiter, Part 2 of 2;   A   1   0   1   1   0
                              always used in pairs with J               B   1   0   1   1   1
           0 1 1 0 1   T      End-of-Stream Delimiter, Part 1 of 2;     C   1   1   0   1   0
                              always used in pairs with R               D   1   1   0   1   1
           0 0 1 1 1   R      End-of-Stream Delimiter, Part 2 of 2;     E   1   1   1   0   0
                              always used in pairs with T               F   1   1   1   0   1



1/8/2003                        Inductive Logic                                             16
           Twice as Good: 8B/10B Encoding
 •   Encodes 8 payload bits into 10 line bits
 •   Guarantees 3 to 8 transitions per 10-bit codeword
 •   Maximum run-length of 5
 •   25% BW expansion (same as                  Code Group
                                                   Na me
                                                              Octet
                                                              Value
                                                                       Current RD – Current RD 
                                                                       abcdei fghj abcdei fghj
     4B/5B)                                         D0.0
                                                    D1.0
                                                                00
                                                                01
                                                                       100111 0100 011000 1011
                                                                       011101 0100 100010 1011

 •   12 control codes (start of packet,             D2.0
                                                    D3.0
                                                    D4.0
                                                                02
                                                                03
                                                                04
                                                                       101101 0100 010010 1011
                                                                       110001 1011 110001 0100
                                                                       110101 0100 001010 1011
     end of packet, error, etc.)                    D5.0        05     101001 1011 101001 0100

 •   Alternately inverts non-zero-DC
                                                      :          :           :            :


     codewords to achieve zero DC           Code Group    Octet    Current RD –    Current RD              Notes
     (similar to AMI)                         Na me
                                               K28.0
                                                          Value
                                                           1C
                                                                    abcdei fghj
                                                                    001111 0100
                                                                                   abcdei fghj
                                                                                   110000 1011              1
          Worst case codeword imbalance is               K28.1
                                                          K28.2
                                                                       3C
                                                                       5C
                                                                                001111 1001
                                                                                001111 0101
                                                                                              110000 0110
                                                                                              110000 1010
                                                                                                            1,2
                                                                                                            1
           6/4                                            K28.3        7C       001111 0011   110000 1100   1


 •
                                                          K28.4        9C       001111 0010   110000 1101   1

     Checks line integrity by counting                    K28.5
                                                          K28.6
                                                                       BC
                                                                       DC
                                                                                001111 1010
                                                                                001111 0110
                                                                                              110000 0101
                                                                                              110000 1001
                                                                                                            2
                                                                                                            1
     invalid codes                                        K28.7
                                                            :
                                                                       FC
                                                                        :
                                                                                001111 1000
                                                                                     :
                                                                                              110000 0111
                                                                                                   :
                                                                                                            1,2


 •   Used in Gigabit Ethernet, Fiber                  NOTE 1 — Reserved .
                                                      NOTE 2 — Conta ins a c omma .
     Channel (FC), some backplanes

1/8/2003                             Inductive Logic                                                        17
               Saving Bandwidth:
           MLT-3 (Multi-Level Transition)
 •   Bipolar, tri-state signal (+, 0, and -)
 •   Like a combination of NRZI and AMI
 •   Transition = data 1, no transition = 0
 •   Non-zero signals alternate polarity
 •   Cuts bandwidth in half (and SNR as well)
 •   Used by Ethernet 100BaseTX (with 4B/5B and
     scrambling)
           - amplitude +




                           1   0   1   1    0     0   1   1
                                       distance           time


1/8/2003                           Inductive Logic               18
           A Modern Line Code
 A          N            • Binary signaling (on and off, not
 B          O              dits and dahs)
 C          P            • Pulse Width Modulated (PWM)
 D          Q            • Return to zero coded (RTZ, vs.
 E          R              NRZ or NRZI)
 F          S            • Variable rate
 G          T            • Self timed
 H          U            • Asynchronous at word level
 I          V            • Variable length encoding
 J          W            • Data compressed
 K          X            • Forward error corrected (English)
 L          Y
 M          Z              Interesting history of
                               pen and paper

1/8/2003        Inductive Logic                           19
                              Just Do It
              D                O                 I T
            3 1 1 3                        7
           dah      dit
                                         minimum
           size size
                                        inter-word
              inter- inter-                space
            symbol letter
             space space


 •   Receiver recovers unit time interval from dits and inter-
     symbol spaces; extrapolates other intervals



1/8/2003                      Inductive Logic                    20
                Data Compression: English
   size    frequency   avg.                 size   frequency   avg.
 A 8         .082      .65                N 8        .071       .57
 B 12        .014      .17                O 14       .080      1.12
 C 14        .028      .39                P 14       .020       .28
 D 10        .038      .38                Q 16       .001       .02
 E 4         .131      .52                R 10       .068       .68
 F 12        .029      .35                S 8        .061       .49
 G 12        .020      .24                T 6        .105       .63
 H 10        .053      .53                U 10       .025       .25
 I 6         .063      .38                V 12       .009       .11
 J 16        .001      .02                W 12       .015       .18
 K 12        .004      .05                X 14       .002       .02
 L 12        .034      .41                Y 16       .020       .32
 M 10        .025      .25                Z 14       .001       .01
                             Avg letter size: 11.2      units
            English weighted avg letter size: 9.0 (~20% savings)
           Opt. Eng. weighted avg letter size: 8.6 (within 5%)

1/8/2003                       Inductive Logic                        21
                               Baseband Summary
                  Interface                           Signaling States   Transition Coding
    on-off

                  Ethernet 10Base5, 10Base2           on-off + DC bias   Manchester
                  Morse Code                          on-off             RTZ
                  Ethernet 10BaseT                    antipodal          Manchester
    antipodal




                                                                         none (NRZ,
                  EIA-232, V.35, HSSI                 antipodal          separate clock
                                                                         and data)
                  Ethernet 100BaseTX, FDDI
                                                      MLT (3-level)      4B/5B, scrambled
                  (electrical)
    multi-level




                  SDSL, IDSL, ISDN BRI                2B1Q (= 4-PAM)     scrambled
                  G.shdsl                             16-PAM             scrambled
                  DS1, DS3                            AMI (3-level)      RTZ, BxZS
                  Gigabit Ethernet (optical), Fiber
                                                      on-off (optical)   8B/10B
                  Channel
    optical




                  SONET                               on-off (optical)   scrambled
                  FDDI (optical)                      on-off (optical)   4B/5B, NRZI

1/8/2003                                 Inductive Logic                                     22
           Baseband Signaling and
                Modulation
                 Part 2:
                Modulation

                  Eric L. Michelsen


1/8/2003          Inductive Logic     23
           Another Day, Another Sentence

 Modulation avoids baseband problems of
 signal overlap and DC error.

    If I could tell them a second sentence, it would be:
                               Bandwidth is not capacity!
    If I could tell them a third sentence, it would be:
                               Bandwidth is not capacity!

    But first, a review of Fourier analysis...


1/8/2003                          Inductive Logic           24
                   Topics: Modulation
 •   Cosine review                   •   Communication channels as
 •   Sums of cosines                     filters
 •   Spectra                         •   Amplitude modulation
 •   Fourier transforms              •   Amplitude demodulation
 •   Baseband signaling              •   Quadrature multiplexing
 •   Why cosine waves?               •   DMT ADSL
 •   Transfer functions




1/8/2003                  Inductive Logic                            25
                               Definitions
 •   Baseband signaling
          Communicating a signal in its original form for a given medium
           (e.g., audio)
              or
          Communicating a signal with components down to DC (or almost
           DC)
 •   Carrier modulation
          Communication based on modifying (modulating) a cosine wave
           signal
          Other forms of modulation exist (non-carrier modulation, e.g.,
           PAM, PWM, PCM(?), but that‟s another story)




1/8/2003                        Inductive Logic                             26
                                Cosine: A Function of Angle
 •   Basis function for frequency analysis and for modulation

                               0o
           - amplitude +


                                    30o o
                                     70
                                        90    180                450 540                   angle
                                                       270 360                 630 720   (degrees)
                                    120o

                                           one cycle

                           y                           y                   y                   y
                                                           30o                                  120o
                                    0o                                         70o
                                         x                   x                       x                 x
                           1 unit


1/8/2003                                               Inductive Logic                                 27
           Cosine Wave: A Function of Time
 •   Fully characterized by 3 parameters:
            A           Amplitude (e.g., 10 V)
            f           Frequency (e.g., 2 Hz)      cosine wave = A cos(f*360t + )
                       Phase    (e.g., 60)                    = A cos(360ft + )
                                  A = 10 V                        10cos(360(2)t + 60o)

            60o                                                               time
                          0.25           0.5                       1          (sec)

                                     f = 2 Hz

                                    132o         204o
                  60o                                                  240o

             t=0                   t = 0.1              t = 0.2                 t = 0.25


1/8/2003                          Inductive Logic                                        28
                                         Sums of Cosines
 s(t) = A1cos(360f1t) + A2cos(360f2t) + A3cos(360f3t) + ...
                  1
             0.8
             0.6
             0.4
             0.2
                  0
                        0    0.1    0.2    0.3     0.4   0.5   0.6   0.7   0.8   0.9    1
            -0.2
            -0.4
            -0.6
            -0.8
                  -1
              1

           0.8

           0.6

           0.4

           0.2

             0
                  0.0       0.1    0.2    0.3      0.4   0.5   0.6   0.7   0.8    0.9   1.0
           -0.2

           -0.4

           -0.6

           -0.8

             -1




1/8/2003                                        Inductive Logic                               29
           Spectrum: A Bar Chart of Cosines
 •   Progressively denser bar charts give way to a simple graph
A




                                   A
                f                                 f
A




                                   A


                f                                 f

1/8/2003                 Inductive Logic                      30
                        Why Cosine Waves?
 •   Cosines are the only basis functions (aka eigenfunctions) of
     Time Invariant Linear Systems
          System: produces output from input
          Linear: if Ia  Oa, then kIa  kOa
              and if Ib  Ob, then (Ia + Ib)  Oa + Ob
          Time invariant: it does the same thing all the time
 •   If input is a cosine, then output is a cosine of same frequency,
     but different amplitude and phase
 •   Linear  Cosine components of input don‟t interact
                 input is                               output is cosine of exactly
                any cosine                                the same frequency...
                                         TILS                                      ...but different
                                                                                   amplitude and
                                                                                        phase


                                time                                                   time



1/8/2003                            Inductive Logic                                           31
              Triangles Are Not Cosines
 •   If input is not a cosine, output is not a multiple of the input
 •   Single triangle wave input produces complex output
 •   What a mess!



              input is a                         output is NOT a
           triangle wave                          triangle wave
                                   TILS


                           time                                        time




1/8/2003                      Inductive Logic                      32
                                 Transfer Functions
 •   A TILS multiplies each input frequency amplitude (& shifts its phase)
 •   The multiplier (and phase-shift) are functions of frequency
                                              TILS
                                          H(f ) = Aout / Ain
                                                 or
                     Ain                  Aout = H(f )Ain                 Aout                time
                                   time
               at frequency, f                                       at same frequency, f

 •   We can graph the amplitude multiplier as a function of frequency,
     the amplitude transfer function, H(f ):

                                                                   We can graph the phase-
                                                                   shift as a function of
       H(f )




                                                                   frequency: the phase
                                                                   transfer function, (f )
                                                                   (but we won‟t)
                                                               f

1/8/2003                              Inductive Logic                                         33
                Transfer Functions at Work
 •   Since cosine components of the input signal do not interact, each
     cosine is multiplied by the transfer function at its frequency
 •   Thus, the output spectrum is the input spectrum multiplied by the
     transfer function, at each frequency
 •   Every TILS has a transfer function, and
     a transfer function defines a TILS.

                                    TILS




     Input signal              Transfer function             Output signal
      spectrum                 of linear system               spectrum

1/8/2003                     Inductive Logic                                 34
     The Communication Channel as Filter
 •   Any communication channel is imperfect
 •   A time invariant linear channel is described by its transfer function
 •   A filter is a TILS that passes some frequencies, and blocks others

       Transfer function



                              H(f )
       for a copper loop
                                                                       f

       Transfer function
                              H(f )
       for a copper loop
         with a splitter
                                                                       f


     Transfer function for
                              H(f )




     a transistor amplifier           This is why
                                      DC is bad.                       f

1/8/2003                      Inductive Logic                                35
           The Spectrum of Square Wave
                Antipodal Signaling
 •   90+% of energy is in the first lobe
 •   Part of the first, and all of the other lobes can be discarded without
     much degradation
 •   This is also the spectrum of 2B1Q, and all PAMs




                                   A
                           time

                           square wave
                                   A             fsym         2fsym           3fsym




                           time

                      filtered square wave       fsym         2fsym           3fsym

1/8/2003                       Inductive Logic                                   36
                         Amplitude Modulation
 •     Given a signal, i(t)
 •     And a carrier, cos(360ct)
 •     We modulate the signal onto the carrier by multiplying the two at each
       instant in time: i(t)cos(360ct)
                                                                cos(360ct)


                              i(t)
                                     x
           modulator
i(t)


            cos(360ct)
                                     =
                                                            i(t)cos(360ct)
1/8/2003                       Inductive Logic                              37
                    Know Your Identity
 1. cos(-a) = cos(a)
 2. cos(90-a) = -cos(90+a)
 3. cos(a+b) = cos(a)cos(b) - cos(90-a)cos(90-b)
                    cos(a - b) + cos(a + b)
 4. cos(a)cos(b) =             2                 cos(90-a)cos(90-b)
                                                      90-b
                                   Demonstration
                                   of identity #3                      cos(90-a)
                                                           90-a
                                                                  b

   Recall that
   for any right
   triangle:


                                      a
     a                               b
     H•cos(a)
                                           cos(a+b)                   cos(90-a)cos(90-b)
                                            cos(a)cos(b)

1/8/2003                     Inductive Logic                                          38
  Spectral View of Amplitude Modulation
 •   Modulating a baseband cosine onto a carrier

           i(t) = cos(360wt)                (simple) baseband spectrum:
A




                                            a cosine of frequency „w‟
       w                                f

                         cos(360ct)
                                            carrier spectrum:
A




                                            a cosine of frequency „c‟
                               c        f
                                            Modulated signal spectrum:
                                            Using identity #4:
A




                                            cos(360wt)cos(360ct) =
                                            cos[360(c-w)t] + cos[360(c+w)t]
                                        f
                        c-w c c+w            Pop Quiz: Is a modulator a TILS?

1/8/2003                           Inductive Logic                              39
      Deja View of Amplitude Modulation
 •   Modulating a complicated baseband signal onto a carrier

            i(t)                         complicated
A




                                         baseband spectrum
                                         (AM radio BW = 5 kHz)
      bandwidth
                                     f

                   cos(360ct)
                                         carrier spectrum
A




                                         (AM radio carrier = 540 - 1600 kHz)

                        c            f
                                         Modulated signal spectrum;
                                         using identity #4 for each
A




                                         frequency component
                                     f   Notice that the modulated bandwidth is
                        c                twice the baseband signal bandwidth
                    bandwidth            (AM radio BW = 10 kHz)

1/8/2003                        Inductive Logic                                   40
                  Demodulation: Getting It Back
              •    Given a modulated signal:            i(t)cos(360ct)
              •    Multiply by the carrier again:       i(t)cos(360ct)cos(360ct)
                                                        = i(t)[cos(0) + cos(360(2ct))]
      modulated                                         = i(t) + i(t)cos[360(2ct)]
      spectrum
A




                                           f
                            c
                                           i(t)cos[360(2ct)]
           i(t)                                                 almost
                                                                demodulated
A




                                                                spectrum
                                                                      f
                            c                      2c
                                                                filtered and fully
                         filter transfer                        demodulated
A




                         function                               spectrum
                                                                      f
                            c                      2c
1/8/2003                            Inductive Logic                                      41
              All Together Now




                         A
                  time

           Energy Efficient Signaling fsym   2fsym   3fsym




                         A
                  time
           Filtered Baseband Signal fsym
                         A                   2fsym   3fsym




              Modulated Carrier               c

1/8/2003             Inductive Logic                    42
                 Comparison of Modulated and
                    Unmodulated Carrier
             +
             -




 unmodulated
 carrier
 modulated
 carrier




1/8/2003           Inductive Logic        43
             Quadrature Multiplexing:
           Two for the Bandwidth of One
 •   Consider a signal modulated with the wrong carrier phase, off by 90.
     We attempt to demodulate (recall identity #4):
                                          i(t)cos(360ct + 90)cos(360ct)
         modulated                        = i(t)[cos(90) + cos(360(2ct) + 90)]
         spectrum                         = i(t)cos[360(2ct) + 90]
A




                                         f
                         c
                             i(t)cos[360(2ct) + 90]        attempted
                                                           demodulated
A




                                                           spectrum
                                                                  f
                         c                            2c
                    filter transfer                        filtered signal
A




                    function                               spectrum
                                                                  f

1/8/2003                         Inductive Logic                             44
       Quadrature Multiplexing: Part Deux
 •   Consider two signals, i(t) and q(t), modulated with two carriers of the
     same frequency, but different by 90:
                i(t)cos(360ct) + q(t)cos(360ct + 90)

                   i(t)                   q(t)            baseband spectra
           A




                                  A
                            f                         f


                                                  modulated signal spectrum:
                                                  generally not symmetric
               A




                                                  f
                                      c


1/8/2003                        Inductive Logic                                45
               Quadrature Demodulation
 •   Given a quadrature multiplexed modulated signal:
            i(t)cos(360ct) + q(t)cos(360ct + 90)
 •   Demodulate each channel separately, each with its own carrier:
                                                                 carrier for i(t)
              [ i(t)cos(360ct) + q(t)cos(360ct + 90) ]cos(360ct)
              = i(t)cos(360ct)cos(360ct) + q(t)cos(360ct+90)cos(360ct)
                                                                             i(t)
                                                                             demodulated
       A




                                                                             spectrum

                                                                                      f
                                   c                          2c          carrier for q(t)
                [ i(t)cos(360ct) + q(t)cos(360ct + 90) ]cos(360ct + 90)
                = i(t)cos(360ct)cos(360ct+90) + q(t)cos(360ct+90)cos(360ct+90)

                                                                                q(t)
       A




                                                                                demodulated
                                   c                          2c                spectrum
                                                                                      f
1/8/2003                        Inductive Logic                                              46
                              DMT ADSL
 •   Discrete Multi-Tone
 •   Up to 255 “separate” carriers,
          Each carrier is quadrature multiplexed multi-level PAM
          Two to 15 bits per symbol per carrier (2 - 256 PAM per I/Q axis)
          Optimum filling of data into the carriers for maximum total SNR
          All share the same time, frequency, and phase references
          Lower carriers omitted for baseband voice
 •   Carrier spacing is 4312.5 Hz
                          upstream              downstream
A




      baseband
        voice
                                                                              f
 300 Hz        3600 Hz      N x 4312.5 Hz



1/8/2003                         Inductive Logic                                  47
                                  DMT ADSL
 •   Two kinds of FEC:
          “Fast” path (low latency): Trellis Coded Modulation (TCM)
          “Interleaved” path (higher latency): Reed-Solomon block interleaved
 •   Framing structure built into the modulation
 •   Integral number of bytes per frame, 4000 user data frames per second
     = N x 32 kbps data rates
 •   G992.1 defines two services: STM and ATM
          The industry standard is ATM over STM (HEC delineation)
          No one uses G992.1‟s ATM mode
                                  Superframe: 17 ms
            frame frame frame frame           ...   frame frame synch
               0      1       2       3               66    67 symbol


           over                       over         over                       over
           head      Fast bytes       head   FEC   head   Interleaved bytes   head



1/8/2003                          Inductive Logic                                    48

				
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