Lecture IIntroduction to DigitalCommunications

1. Overview of comm. channels and digital links2. Signal propagation through baseband PAM Links• (ch. 1 – part 0 “Notes”)

Following Lecture II next week:2. …signal propagation through baseband PAM Links3. Finite Energy Signal Space representations4. Matched Filtering in AWGN for PAM antipodal linksRead-ahead: Ch. 2 – part 0 “Notes”

“The communication technology of a sufficiently advanced civilization is

indistinguishable from magic”

Defining communications 1. What does it mean to communicate?

• Derived from the Latin communicare: to share to impart or to transmit

Communication is the activity associated with transfering, distributing or exchanging information (usually

spanning a distance)

– One-way (one-to-one / one-to-many)

– Two-way (one-to-one / many-to-many)

• Interactive

• Simultaneous

What do we communicate (information/messages)?

• Data / Text / Graphics / Voice / Music / Video

How do we communicate? electro-magnetic signals carry the messages:

1. Analog signals (waveforms = continuous functions of time,

assuming any value)

2. Digital signals (discrete-time and discrete-valued)

• binary bit-streams (…10011011010111001…)

• symbol-streams (……)

analogmedium

TX RX

Transmitter Receiver

Data S(t) R(t)Data

N(t) Noise

Digital Communication Link

1. Transmitter (TX) משדר

2. Medium (Channel ערוץ) תווך

3. Receiver (RX) מקלט

DA AD

Medium (Channel ערוץ) תווך• Wireless (Free space - vacuum / air);

• Radio, microwave, satellite, cellular, Wireless LAN

• Wireline:• Telephone wires (twisted pairs)

• LAN (twisted pairs)

• RF cable (coaxial)

• Fiber optics

• May include active repeaters

• Satellite transponders

• Fiber optic repeaters

A digital Communications Link: bitstream-> TX->Analog Medium->RX > bitstream

• All media in Nature are analog – – A purely digital medium exists only in math.

• “Underneath every digital communications link there resides an

analog medium”

• The TX: Digital->Analog

• The RX: Analog->Digital

• The objective of a communication link:Receiving a bitstream at the TX and faithfully reproducing it at the RX

at maximum rate and with minimum power

Bitstream: a finite or possibly infinite sequence of random bits out of the set {0,1}, representing the information to be carried

(see Appendix to Lesson 1)

Two-way (full-duplex) links with modems

TX

RX

RX

TX

Modem Modem

D

D

D

D

A

A

A

ATwo-WayChannel

Telephony – Alexander Graham Bell receives a patent for the telephone (1876)

the earliest form of “analog electrical communications”

Telegraphy (1843)the earliest form of “digital electrical

communications”

26-ARY messageStream SourceHk {A,B,C,..Z}

A

B

Z...

S (t)S (t)

S (t)

(0)

(1)

(M-1)

......THIS COURSE IS FUN...

What’s wrong with this picture?

Data sources and pulse modulators

P-MOD example: QPSK transmittermapping pairs of bits to one of four signals

Bitstream

2 bitblocks

00 cos(2t/T)

01 -cos(2t/T)

10 sin(2t/T)

11 -sin(2t/T)

P-MODx(t)

S (t)(0)

S (t)(1)

S (t)(2)

S (t)(3)

Example QPSK TX

-

The transmitter’s most important block: P-MOD

Low-pass vs. Bandpass Media• LowPass – Passes DC and low freq.

– LowPass media: Telephone, LAN wires (RJ11/45)

• HighPass/Bandpass –Passes a passband of freq.

– Wireless media don’t carry low freq.

• radiation efficiency negligible at low freq.

– Certain wireline media are bandpass

• e.g. coaxial amplifiers are AC coupled

LTI systemb(t) Impulse responseB() freq. response

+b(t) x s(t) R(t)

N(t) noise

s(t)

Model for LTI-AWGN medium

analogmedium

S(t) R(t)

N(t) Noise

AdditiveWhiteGaussianNoise

DelayT0 +

S(t) R(t)

N(t)

Ideal Medium

B0

Model for zero-distortion idealized AWGN medium

Bo

|B()|

"flat"

B()

Linear Phase

Frequency responseB

B

Ideal Medium

End2end digital communication link

Data Source CoderPulse

Modulator

Decoder DetectorData

Destination

TX

RX

Medium

Analogpulses

Symbols(coded bits)

uncoded bits (messages)

Symbols(coded bits)

uncoded bits (messages)

Analogwaveforms

bits2symbols

symbols2bits

symbols2pulses

waveforms2symbols

Complete digital communication link (more detail)

Data SourcePulse

Modulator

DataDestination

TX

RX

Medium

SourceCoder

ChannelCoder

Coder

SufficientStatisticsExtractor

Detector

SlicerSource

DecoderChannelDecoder

Coder

MessageStream

Symbol StreamAK

S(t)

R(t)

WaveformRecognition

Sufficient StatisticsVector Stream

EstimatedSymbol Stream

KA

A/DQUANTIZATION

Datacompression

Redundant check-bitsinsertion

analogmedium

DataSource

Coder PulseModulator

Datasink

DecoderPulseDemodulator

bitstream...0111.0100.1010.1111....

symbols/indexes

...74AF055BA... S(t) R(t)

Analog link

Message link

TX RX

s(t)=...p7(t)+p4(t-T)+p10(t-2T)+p15(t-3T)+...

bitstream...0111.0100.1010.1111....

symbols/indexes

...74AF055BA...

4bit 4bit

DATA LINK EXAMPLE

16 QAM waveform code

Digital transmission formats for a binary stream

ASK, PSK, FSKAmp./Phase/Freq. Shift-Keying

PSK FSK

ASK

t

0f

1f

t

0 ( )p t

1( )p t

pulsegenerator

0 ( )p t

pulsegenerator

1( )p t

+

"0"

"1"

trigger

trigger

bitstream 1 0 1 1 0 0 0 1

Pulse modulation

1 0 1 1 0( ) ( ) ( 2 ) ( 3 ) ( 4 ) ...p t p t T p t T p t T p t T

1 0 1 1 0

FSK transmitter

FSK ReceiverFSK receiver

BPF f0

f

BPF f1

ff1

f0

Choose indexof largest

signal

101100

energydet

energydet

Sufficientstatistics extractor

slicer

PAM – Pulse Amplitude Modulation

P-MOD:

PAM:

4-level PAM transmission

2 - BitSerial toParralel

b1 b2 A

0 1 -11 0 11 1 3

0 0 -3 Ak2 S(t)Input

Bits

A

0 T

PAM

0 T 2T 3T 4T 5T

1

2

3

-1

-2

-3

b0b1: 00 10 10 01 11Ak: -3 1 1 -1 3

S(t)

Pulse Amplitude Modulation (PAM)

tt

PAM

P(t)AK KA P(t KT)k

k

Figure 1.12:

PAM modulator output waveform

“Single shot” @ t=0 – Isolated Pulse Amplitude Modulation

t

PAM

P(t)A0

LTIA0

t

P(t)( )t

0 ( )A p t

0 ( )A p t

t

General PAM Link Analysis

SlicerAK S(t)CODER

PAM

g(t)

SAMP [T]Bits CH. Filter

b(t)

N(t)

RX Filter

f(t)

r(t) q(t) qK

TX Medium/Channel RX

Figure 1.17:

(“multiple shots” analysis in TA classes…)

מועד א'מערכת תקשורת ספרתית משדרת אחת מצורות הגל

cos 2

cos2

cos2 2

cos2 3

cos2 63

o

o

o

o

o

A f t

A f f t

A f f t

A f f t

A f f t

0למשך זמן t T T נמדד מחדש בתחילת כל קטע של t שניות )הזמן T , כל

שניות(.קצב הסיביות )מספר הביטים לשניה( המשודר ע"י המערכת הוא:

64

64 /

8

8/

6

6 /

4

4 /

a T

b T

c T

d T

e T

f T

g T

h T

הפקולטה להנדסת חשמל 8.7.2003)044115כיוונים בהנדסת חשמל (