inductive logic baseband signaling and modulation eric l. michelsen part 1 of a 2-part presentation...

Inductive Logic

Baseband Signaling and Modulation

Eric L. Michelsen

Part 1 of a 2-part presentation

Part 1: Baseband Signaling

1/8/2003 2Inductive Logic

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

Transmitting data requires not only the signaling of bit values, but also bit timing.

time

1

or

0

sample here & here & here ...

If I could tell them a second sentence, it would be:

DC is bad.


Topics: Baseband Signaling (day 1)• On-Off signaling

• Antipodal signaling

• Timing recovery

• NRZI

• Multilevel: 2B1Q

• DS1 & DS3

• Manchester encoding

• 4B/5B encoding

• 8B/10B encoding

• Multi-Level Transition

• A modern line code

• Communication channels as filters

• Amplitude modulation

• Amplitude demodulation

• Quadrature multiplexing

• DMT ADSL

• Cosine review

• Sums of cosines

• Spectra

• Fourier transforms

• Baseband signaling

• Why cosine waves?

• Transfer functions

Topics: Modulation (day 2)


framing

5. Session

4. Transport

6. Presentation

framing framing framing framing

Where in the Stack?

signaling & modulation

• 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)

V.35, HSSI, SDSL

OSI stack

3. Network

7. Application

2. Link

1. Physical DS1 DS3 ADSL IDSL

bit serial (payload)

bit serial (line)

electrical

SONET

optical


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)

1 0 1 1 0 0

time

ampl

itude

bit period

1

0


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

time

sample times centered in data bits

data

cloc

ksample on rising edge

of clock


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.

interpolated sample times (bit centers)

transitions locate data

time

data


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


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

1 0 1 1 0 0

time

ampl

itude

bit period

distance 1

0


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

1 0 1 1 0 0time

ampl

itude

+0.5

0

-0.5distance

Can you say “tip-ring reversal?”


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

? 1 1 0 1 0time

+

0

-

? 1 1 0 1 0time

+

0

-

Equivalent NRZI signals


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.

11 10 01 00time

ampl

itude

+3

+1

-1

-3

Usually described as “distance 2”: -3, -1, +1, +3


AMI: Alternate Mark Inversion• Bipolar, tri-state (+, 0, and -)

• 50% duty cycle RTZ (Return To Zero)

• 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

time

- a

mpl

itude

+

1 0 1 1 0 0

UI = Unit Interval (bit period)

25% 25%50%

alternate polarity

idealized pulse

mark = 1space = 0


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

time

- a

mpl

itude

+

1 0 1 1 0 0 0 0 0 0

alternate polarity

Deliberate bipolar violation, substitutes for 3 zeros

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

X


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)

time

sign

al s

tate

A

B

1 0 1 1 0 0


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

• DC >> 0 (bad), but used with NRZI or MLT, DC ~= 0

• Checks line integrity by counting invalid codes

• Used in Ethernet 100BaseTX, FDDI

Data

0 1 1 1 1 0 1 0 1 0 0 12 1 0 1 0 03 1 0 1 0 14 0 1 0 1 05 0 1 0 1 16 0 1 1 1 07 0 1 1 1 18 1 0 0 1 09 1 0 0 1 1A 1 0 1 1 0B 1 0 1 1 1C 1 1 0 1 0D 1 1 0 1 1E 1 1 1 0 0F 1 1 1 0 1

Control

1 1 1 1 1 IDLE used as inter-stream fill code

1 1 0 0 0 J Start-of-Stream Delimiter, Part 1 of 2;always used in pairs with K

1 0 0 0 1 K Start-of-Stream Delimiter, Part 2 of 2;always used in pairs with J

0 1 1 0 1 T End-of-Stream Delimiter, Part 1 of 2;always used in pairs with R

0 0 1 1 1 R End-of-Stream Delimiter, Part 2 of 2;always used in pairs with T


Twice as Good: 8B/10B Encoding• Encodes 8 payload bits into 10 line bits

• Guarantees 3 to 8 transitions per 10-bit codeword

Code GroupName

OctetValue

Current RD –abcdei fghj

Current RD abcdei fghj

D0.0D1.0D2.0D3.0D4.0D5.0

:

000102030405:

100111 0100011101 0100101101 0100110001 1011110101 0100101001 1011

:

011000 1011100010 1011010010 1011110001 0100001010 1011101001 0100

:

Code GroupName

OctetValue

Current RD –abcdei fghj

Current RD abcdei fghj

Notes

K28.0K28.1K28.2K28.3K28.4K28.5K28.6K28.7

:

1C3C5C7C9CBCDCFC:

001111 0100001111 1001001111 0101001111 0011001111 0010001111 1010001111 0110001111 1000

:

110000 1011110000 0110110000 1010110000 1100110000 1101110000 0101110000 1001110000 0111

:

11,2111211,2

NOTE 1 — Reserved.NOTE 2 — Contains a comma.

• Maximum run-length of 5

• 25% BW expansion (same as 4B/5B)

• 12 control codes (start of packet, end of packet, error, etc.)

• Alternately inverts non-zero-DC codewords to achieve zero DC (similar to AMI) Worst case codeword imbalance is

6/4

• Checks line integrity by counting invalid codes

• Used in Gigabit Ethernet, Fiber Channel (FC), some backplanes


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)

1 0 1 1 0 0 1 1time

- a

mpl

itude

+

distance


A Modern Line Code

ABCDEFGHIJKLM Interesting history of

pen and paper

NOPQRSTUVWXYZ

• Binary signaling (on and off, not dits and dahs)

• Pulse Width Modulated (PWM)• Return to zero coded (RTZ, vs.

NRZ or NRZI)• Variable rate• Self timed• Asynchronous at word level• Variable length encoding• Data compressed• Forward error corrected (English)


3

Just Do It

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

D O I T 7

minimum inter-word space

3

inter-letter space

inter-symbol space

dah size

1 1

dit size


Data Compression: English

A 8 .082.65

B 12 .014.17

C 14 .028.39

D 10 .038.38

E 4 .131.52

F 12 .029.35

G 12 .020.24

H 10 .053.53

I 6 .063.38

J 16 .001.02

K 12 .004.05

L 12 .034.41

M 10 .025.25

N 8 .071 .57

O 14 .0801.12

P 14 .020 .28

Q 16 .001 .02

R 10 .068 .68

S 8 .061 .49

T 6 .105 .63

U 10 .025 .25

V 12 .009 .11

W 12 .015 .18

X 14 .002 .02

Y 16 .020 .32

Z 14 .001 .01

Avg letter size:English weighted avg letter size:

Opt. Eng. weighted avg letter size:

11.2 units9.0(~20% savings)8.6(within 5%)

size frequency avg. size frequency avg.


Baseband SummaryInterface Signaling States Transition Coding

Ethernet 10Base5, 10Base2 on-off + DC bias Manchester

Morse Code on-off RTZ

Ethernet 10BaseT antipodal Manchester

EIA-232, V.35, HSSI antipodalnone (NRZ, separate clock and data)

Ethernet 100BaseTX, FDDI (electrical) MLT (3-level) 4B/5B, scrambled

SDSL, IDSL, ISDN BRI 2B1Q (= 4-PAM) scrambled

G.shdsl 16-PAM scrambled

DS1, DS3 AMI (3-level) RTZ, BxZSGigabit Ethernet (optical), Fiber Channel on-off (optical) 8B/10B

SONET on-off (optical) scrambled

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

on-o

ffan

tipo

dal

opti

cal

mul

ti-l

evel


Baseband Signaling and Modulation

Eric L. Michelsen

Part 2: Modulation


Another Day, Another Sentence

Modulation avoids baseband problems of signal overlap and DC error.

But first, a review of Fourier analysis...

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!


Topics: Modulation

• Communication channels as filters

• Amplitude modulation

• Amplitude demodulation

• Quadrature multiplexing

• DMT ADSL

• Cosine review

• Sums of cosines

• Spectra

• Fourier transforms

• Baseband signaling

• Why cosine waves?

• Transfer functions


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)


Cosine: A Function of Angle

• Basis function for frequency analysis and for modulation

angle (degrees)

- a

mpl

itude

+

90 180

270 360

450 540

630 720

one cycle

1 unit

0o

y

x

30oy

x

70o

y

x

120o

y

x

0o

30o

70o

120o


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 + )

time (sec)0.5 1

f = 2 Hz

t = 0

60o 204o132o

60o

t = 0.2

240o

t = 0.25t = 0.1

A

0.25

A = 10 V 10cos(360(2)t + 60o)


Sums of Cosiness(t) = A1cos(360f1t) + A2cos(360f2t) + A3cos(360f3t) + ...

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1


Spectrum: A Bar Chart of Cosines

• Progressively denser bar charts give way to a simple graph

f

A

f

A

f

A

f

A


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

TILS

time time

input is any cosine

output is cosine of exactly the same frequency...

...but different amplitude and

phase


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!

TILS

time time

input is a triangle wave

output is NOT a triangle wave


Transfer Functions• A TILS multiplies each input frequency amplitude (& shifts its phase)

• The multiplier (and phase-shift) are functions of frequency

f

H(f

)

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

TILS

time time

at frequency, f

Ain Aout

at same frequency, f

H(f ) = Aout / Ain

orAout = H(f )Ain

We can graph the phase-shift as a function of frequency: the phase transfer function, (f ) (but we won’t)


Input signal spectrum

Transfer function of linear system

Output signal spectrum

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


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

H(f

)H

(f )

Transfer function for a copper loop

f

f

Transfer function for a copper loop

with a splitter

H(f

)Transfer function for a transistor amplifier

fThis is why DC is bad.


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

fsym 2fsym 3fsymA

time

fsym 2fsym 3fsym

A

time

square wave

filtered square wave


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)

i(t)

cos(360ct)

i(t)cos(360ct)

x

= modulator

i(t)

cos(360ct)


Know Your Identity

a

b

b

1 un

it

cos(a)

cos(90-a)

cos(90-a)cos(90-b)

cos(90-a)cos(90-b)cos(a)cos(b)

cos(a+b)

90-a

H

aH•cos(a)

Recall that for any right triangle:

Demonstration of identity #3

90-b

4. cos(a)cos(b) =

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)

2


Spectral View of Amplitude Modulation• Modulating a baseband cosine onto a carrier

Pop Quiz: Is a modulator a TILS?

f

A

i(t) = cos(360wt)

w

f

A

cos(360ct)

c

(simple) baseband spectrum: a cosine of frequency ‘w’

carrier spectrum:a cosine of frequency ‘c’

f

A

c-w c c+w

Modulated signal spectrum:Using identity #4: cos(360wt)cos(360ct) = cos[360(c-w)t] + cos[360(c+w)t]


Deja View of Amplitude Modulation• Modulating a complicated baseband signal onto a carrier

f

A

i(t)

f

A

cos(360ct)

c

complicatedbaseband spectrum (AM radio BW = 5 kHz)

carrier spectrum (AM radio carrier = 540 - 1600 kHz)

f

A

c

Modulated signal spectrum;using identity #4 for each frequency component

bandwidth

bandwidth

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


Demodulation: Getting It Back• Given a modulated signal: i(t)cos(360ct)

• Multiply by the carrier again:

f

A

i(t)

f

A

c

i(t)cos(360ct)cos(360ct)= i(t)[cos(0) + cos(360(2ct))]= i(t) + i(t)cos[360(2ct)]

2c

modulated spectrum

almost demodulated spectrum

f

A

2c

filtered and fully demodulated spectrum

filter transfer function

i(t)cos[360(2ct)]

c

c


All Together Now

fsym 2fsym 3fsym

A

time

fsym 2fsym 3fsymA

time

Energy Efficient Signaling

Filtered Baseband Signal

c

A

Modulated Carrier


Comparison of Modulated and Unmodulated Carrier

modulated carrier

unmodulated carrier

-

+


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)= i(t)[cos(90) + cos(360(2ct) + 90)]= i(t)cos[360(2ct) + 90]

f

A

f

A

c

2c

modulated spectrum

attempted demodulated spectrum

f

A

filtered signal spectrum

filter transfer function

i(t)cos[360(2ct) + 90]

c


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)

f

A

i(t)

f

A

q(t) baseband spectra

f

A

c

modulated signal spectrum:

generally not symmetric


Quadrature Demodulation• Given a quadrature multiplexed modulated signal:

• Demodulate each channel separately, each with its own carrier:

i(t)cos(360ct) + q(t)cos(360ct + 90)

[ 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)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)

carrier for i(t)

f

A

2c

i(t) demodulated spectrum

carrier for q(t)

f

A

2c

q(t) demodulated spectrum

c

c


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

f

A

upstream downstream

baseband voice

300 Hz 3600 Hz N x 4312.5 Hz


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

frame 1

synch symbol

frame 2

frame 3 ... frame

66frame

67frame

0

Superframe: 17 ms

frame 0

Fast bytes Interleaved bytesover head

over head FEC over

headover head

inductive logic baseband signaling and modulation eric l. michelsen part 1 of a 2-part presentation...

Documents