The Physical Layer

The Theoretical Basis for Data Communication

• Fourier analysis

• Niquist chriterium for bandwidth-limited channel

• Shannon maximum data rate of a noisy channel

Fourier Transform

• Periodic signals with period T=2π/w

• Non-periodic signals

dtnwttsT

bdtnwttsT

a

nwtbnwtats

T

n

T

n

nn

nn

)sin()(2

,)cos()(2

)sin()cos()(

00

00

dtetsjwS

dwejwSts

jwt

jwt

)()(

)(2

1)(

Bandwidth-Limited Signals

A binary signal and its root-mean-square Fourier amplitudes.

(b) – (c) Successive approximations to the original signal.

Bandwidth-Limited Signals

(d) – (e) Successive approximations to the original signal.

Bandwidth-Limited Signals

Relation between data rate and harmonics.

Band-Limited Channel• Fourier transform of a typical signal

00

0

)()2/(

)2/sin()(

)()(

nn

s

sjwt

nsn

jwt

nsn

nCawT

wTdtenTtga

dtenTtgajwS

1/Ts 2/Ts-1/Ts w

Niquist Theorem

• If the signal bandwidth has width of W, then it can be reconstructed by taking 2W samples per second.

• Maximum data rate is

where V is the number of different symbols

VWR 2log2

Niquist Chriterium

)2/(2

)2/(2sin

2)(

WntW

WntW

W

nXtX

Power Spectrum Density

• Autocorrelation function of signal or noise

• Power spectrum density

))()(()( tXtXE

dew jw)()(

Shannon Theorem

• If the signal bandwidth has width of W, and S/N is the signal-to-noise ratio, then the maximum data rate is

c

W

W

NN

W

W

SS

WNwNdwwNdnnpnN

dwwSdsspsS

NSWR

c

c

c

c

2/)(where,)()(||)0(

)()()0(

),/1(log

2

2

2

Filtering

• Channel behaves as a filter

• When the noise is white (uncorrelated) Gaussian optimum filter has transfer function H(w)=X*(w).

)()()(

),()()(

,)()()(

2wwHw

wXwHwY

xthty

XY

Modulation schemes

(a) QPSK.

(b) QAM-16.

(c) QAM-64.

Guided Transmission

• Twisted Pair

• Coaxial Cable

• Fiber Optics

Twisted Pair

(a) Category 3 UTP 16 MHz.(b) Category 5 UTP 100MHz.

Issues of Twisted-Pair Transmission

• Attenuation

• Distortion

• Cross-talk

• Impulse noise

Coaxial Cable

A coaxial cable 1GHz.

Fiber Optics

(a) Three examples of a light ray from inside a silica fiber impinging on the air/silica boundary at different angles.

(b) Light trapped by total internal reflection.

1211 sinsin nn

• From Maxwell equations:

• From boundary conditions:

Light Propagation

22

20

22221

20

2 ,

,,,

nkwnku

ewrBKrEeurAJrE jz

jz

20

22

2222

21 )(

1

)(

1

kwauajnjnkj wuwu

uaJua

uaJju

'

waKwa

waKkw

'

Light Propagation

22

21

22

210

2nn

annakV

Transmission of Light through Fiber

Attenuation of light through fiber in the infrared region.Bands 25-30THz, and last two bands have attenuation less than 5%/km

Fiber Cables

(a) Side view of a single fiber.(b) End view of a sheath with three fibers, diameter 8-10μm.

Transmission Devices

• Light emitting diode (LED)

• Semiconductor lasers

• Mach-Zehnder external modulator

• EDFA

• Photodiode

Optical Transmitters

A comparison of semiconductor diodes and LEDs as light sources.

Fiber Optic Networks

A fiber optic ring with active repeaters.

Fiber Optic Networks

A passive star connection in a fiber optics network.

Wireless Transmission

• The Electromagnetic Spectrum

• Radio Transmission

• Microwave Transmission

• Infrared and Millimeter Waves

• Lightwave Transmission

Wireless Transmission

• Relationship between wavelength and frequency:

• 100MHz waves are about 3m long, 1000MHz waves are 0.3m long.• An object distracts those waves, whose length is smaller or equal to the object dimension.

cf

The Electromagnetic Spectrum

The electromagnetic spectrum and its uses for communication.

Radio Transmission

(a) In the VLF, LF, and MF bands, radio waves follow the curvature of the earth.

(b) In the HF band, they bounce off the ionosphere.

Issues in Wireless Transmission

• Radio signals are omnidirectional, and penetrate through objects. Throughput is low.

• HF radio and microwave signals are directed. Suffer from multipath fading, and are reflected against the buildings.

• Above 4GHz, signals are absorbed by the rain.

Politics of the Electromagnetic Spectrum

The ISM bands in the United States.

• Goverments allocate frequencies, through contests, lottery, auctions.

• In ISM only the power is specified, used for household devices. Infrared is available.

Lightwave Transmission

Convection currents can interfere with laser communication systems.

A bidirectional system with two lasers is pictured here.

Fog and rain are disruptive too.

Communication Satellites

• Geostationary Satellites• Several kWs. 40 transponders with 80MHz.

TDMA.

• Medium-Earth Orbit Satellites• 24 GPS satellites.

• Low-Earth Orbit Satellites• Iridium project started by Motorola

Communication Satellites

Communication satellites and some of their properties, including altitude above the earth, round-trip delay time

and number of satellites needed for global coverage.

Communication Satellites

The principal satellite bands.

Geostationary Satellites

Very Small Aperature Terminals (VSATs) using a hub.

Low-Earth Orbit SatellitesIridium

(a) The Iridium satellites from six necklaces around the earth.(b) 66 satellites, 1628 moving cells cover the earth, 253000

channels.

Iridium and Globalstar

(a) Relaying in space (Iridium).(b) Relaying on the ground (Globstar).

Public Switched Telephone System• Structure of the Telephone System

• The Politics of Telephones

• The Local Loop: Modems, ADSL and Wireless

• Trunks and Multiplexing

• Switching

Structure of the Telephone System

(a) Fully-interconnected network.

(b) Centralized switch.

(c) Two-level hierarchy.

Structure of the Telephone System

A typical circuit route for a medium-distance call.

10kmCoax,

micorwave, fiber

Major Components of the Telephone System

• Local loops Twisted pairs going to houses and businesses

• Trunks Fiber optics connecting the switching offices

• Switching offices Where calls are moved from one trunk to another

The Politics of Telephones

The relationship of LATAs, LECs, and IXCs. All the circles are LEC switching offices. Each hexagon

belongs to the IXC whose number is on it.

164LATAs

The Local Loop: Modems, ADSL, and Wireless

The use of both analog and digital transmissions for a computer to computer call. Conversion is done by the modems and codecs.

Modems

(a) A binary signal

(b) Amplitude modulation(c) Frequency modulation

(d) Phase modulation

Modems

(a) V.32 for 9600 bps.

(b) V32 bis for 14,400 bps.

(a) (b)

Higher Bit-rate Modems

• 35kbps is the Shannon limit

• Line from a local office to an ISP is digitalized.

• V90 35kbps upstream, 56kbps downstream

• V92 48kbps upstream, 56kbps downstream

Digital Subscriber Lines

Bandwidth versus distanced over category 3 UTP for DSL.

Digital Subscriber Lines

Operation of ADSL using discrete multitone modulation.Up to 8Mbps downstream, and up to 1Mbps upstream

Digital Subscriber Lines

A typical ADSL equipment configuration.

Wireless Local Loops

Architecture of an LMDS system.

50km198MHz at

2.5GHz;2km

1.3GHz at 28GHz

Frequency Division Multiplexing

(a) The original bandwidths.

(b) The bandwidths raised in frequency.

(b) The multiplexed channel.

Wavelength Division Multiplexing

Wavelength division multiplexing.

Time Division Multiplexing

The T1 carrier (1.544 Mbps).

Time Division Multiplexing

Multiplexing T1 streams into higher carriers.

Time Division Multiplexing

Two back-to-back SONET frames.

Time Division Multiplexing

SONET and SDH multiplex rates.

Circuit Switching

(a) Circuit switching.

(b) Packet switching.

Message and Packet Switching

(a) Circuit switching (b) Message switching (c) Packet switching

Switching Comparison

A comparison of circuit switched and packet-switched networks.

? ?

The Mobile Telephone System

• First-generation mobile phones: Improved mobile telephone system (IMTS)

• 23 channels, 150-450MHz

• Second-generation mobile phones: Advanced mobile telephone system (AMTS)

• Cellular system

• Third-generation mobile phones: 3G• Voice and data

Advanced Mobile Phone System

(a) Frequencies are not reused in adjacent cells.

(b) To add more users, smaller cells can be used.

10km

Channel Categories The 832 30kHz channels in bands 824-

849MHz and 869-894Mhz (45 per cell), are divided into four categories:

• Control (base to mobile) to manage the system

• Paging (base to mobile) to alert users to calls for them

• Access (bidirectional) for call setup and channel assignment

• Data (bidirectional) for voice, fax, or data

D-AMPS Digital Advanced Mobile Phone System

(a) A D-AMPS channel with three users.

(b) A D-AMPS channel with six users.

Bands 1850-1910, and 1930-1990MHz

GSMGlobal System for Mobile Communications

GSM uses 124 200kHz frequency channels, each of which uses an eight-slot TDM system

GSM

A portion of the GSM framing structure.

CDMA – Code Division Multiple AccessIS-95

X t

dt0

)(

g1(t) r1(t)

X t

dt0

)(

g2(t) r2(t)

X t

dt0

)(

gK(t) rK(t)

r(t)

Walsh-Hadamard Sequences

MMMM

M

M

aaa

aaa

aaa

M

...

............

...

...

21

22221

11211

MM

MMM HH

HHHH 22 11

11

M Sequences and Gold Code

• Autocorrelation function of m-sequence

• Gold sequence is a sum of two m-sequences such that it has cross-correlation values {-1,-2(m+2-mod(m,2))+1,2(m+2-mod(m,2))-1)

111

0)(

nj

jnj

z -1z -1

X X

z -1 z -1

X X

+

a0am-1a1am-2

CDMA – Code Division Multiple AccessIS-95

(a) Binary chip sequences for four stations(b) Bipolar chip sequences (c) Six examples of transmissions(d) Recovery of station C’s signal

Multiuser Detection

X t

dt0

)(

g1(t) r1(t)

X t

dt0

)(

g2(t) r2(t)

X t

dt0

)(

gK(t) rK(t)

r(t) Maximize MetricsC(rk,bk)

Decorrelating Detector

• Information is detected according to the formula:

T

jiKxKijs

KsK

dttgtgr0

1

)()(}{

),sgn(ˆ

R

rRb

Decorrelating Detector, K=2• Information is detected according to the formula:

)1/()(

)1/()(

)()()()(

)()(,1

1

1

1

21222

22111

21

22211

122112

222111

0

2121

nnbE

nnbE

nbEbE

nbEbE

tntgbEtgbEtr

dttgtgR

s

T

s

rR

r

Third-Generation Mobile Phones:Digital Voice and Data

Basic services an IMT-2000 network should provide

• High-quality voice transmission

• Messaging (replace e-mail, fax, SMS, chat, etc.)

• Multimedia (music, videos, films, TV, etc.)

• Internet access (web surfing, w/multimedia.)

3G

• W-CDMA or universal mobile telecommunication system (UMTS) compatible with GSM, uses 5MHz.

• CDMA2000 extension of IS-95 uses 5Mhz

• Enhanced data rates for GSM evolution (EDGE) uses more bits per baud

• General radio packet servise (GPRS) is overlay packet network over D-AMPS or GSM

Cable Television

• Community Antenna Television

• Internet over Cable

• Spectrum Allocation

• Cable Modems

• ADSL versus Cable

Community Antenna Television

An early cable television system.

Internet over Cable

Cable television

Internet over Cable

The fixed telephone system.

Spectrum Allocation

Frequency allocation in a typical cable TV system used for Internet access

Cable Modems

Typical details of the upstream and downstream channels in North America.

Community Antenna Television (CATV)

antenna

HEADEND

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o o

o o o o

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HOME

RF Spectrum:

55 MHz 350 MHz

AM-VSB signals Long chains of RF amplifiers: limited bandwidth, poor reliability.

Sheryl Woodward, AT&T Labs-Research

Linear Lightwave Revolution

55 (E 85)MHz 350 MHz 550 (E 606)MHz

RF Spectrum: 80 AM-VSB channels

HEADEND

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o o

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o o

HOME

Fiber Node

o oo o

Hybrid-Fiber-Coax Architecture: Improved reliability and performance, BUT to transmit 80 channels of AM-VSB, an optical link must operate near fundamental limits.

Sheryl Woodward, AT&T Labs-Research

challenge: HFC plant is HYBRID Coax -limited bandwidth, -good SNR.

Fiber -huge bandwidth, -difficult to maintain high SNR.

M-QAM standard digital transmission format.

On-Off Keying is the preferred transmission format.

On/Off keying:

>40 Gbps / λ >1Tbps on a single fiber.

256-QAM:5 Gbps / λ requires RIN<-135 dB/Hz.Fiber non-linearities limit

number of λ per fiber.

Quick optical transmission format comparison.

Sheryl Woodward, AT&T Labs-Research

Compressed Digital Video

a) MPEG-3 compresses a video channel to <5 Mbps.

b) Quadrature Amplitude Modulation (QAM) can be used to transmit multiple television channels in a single 6 (E 8)MHz RF channel. Around 38Mbps can be transmitted through this channel.

c) A much lower Carrier-to-Noise Ratio (CNR) is required to transmit these QAM signals than is required by AM-VSB.

d) A set top box is required to receive these channels.

55 (E 85)MHz 350 MHz 550 (E 603)MHz 750 (E 862)MHz

RF Spectrum: 80 AM-VSB channels 30 QAM channels

(~150 video channels)

Sheryl Woodward, AT&T Labs-Research

10

100

1000

10000

20 25 30 35 40 45 50

SNR (dB)

Ma

x. N

um

be

r o

f C

ha

nn

els

QAM capacity limitations

C.F. Lam, "A Simplified Model for Estimating the Capacity Limit of an Optical Link in Transporting Multi-channel M-QAM Singals," to appear in IEEE Photonics Technology Letters, Nov. 2000

From top to bottom RIN = -140dB/Hz -135dB/Hz -130dB/Hz64-QAM

256-QAM

5MHz per channel

616

123

RIN= -135dB/Hz

18.5 Gbps

4.9 Gbps

Sheryl Woodward, AT&T Labs-Research

Upstream Transmission

5-40 (E 65)MHz 350 MHz 550 (E 603)MHz 750 (E 862)MHz

RF Spectrum: 80 AM-VSB channels 30 QAM channels

(~150 video channels)

HEADEND

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Fiber Node

o oo o

a) Can now offer interactive services

Sheryl Woodward, AT&T Labs-Research

Upstream Transmissiona) RF band is 5-42 (E 65)MHz, this band can carry multiple RF channels.

Modulation schemes are QPSK or 16QAM

b) 5-15 MHz is plagued with ingress noise.

c) All frequencies suffer from the funnel effect.

d) Up to 10 Mbps transmission per RF channel is provided in the standard, but a peak rate of ~3 Mbps is more realistic.

e) Bandwidth is shared.

f) Services can be segregated by RF frequency.

g) For data the standard is DOCSIS (Data Over Cable Service Interface Specification).

h) Telephony can be carried over DOCSIS 1.1.

i) A cable modem or set top box resides in the home, a CMTS, which coordinates traffic, resides in the headend.

Sheryl Woodward, AT&T Labs-Research

Upstream Transmission-Frequency Stacking

HEADEND

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o oo o

5-40 MHz 300 MHz

RF Spectrum on upstream fiber:

1 2 3 4

Fiber Node1

2 3

4

To improve upstream capacitydivide the fiber node serving area into quadrants. Frequency stack these signals, then transmit them to the HE.

Sheryl Woodward, AT&T Labs-Research

Scientific Atlanta’s Baseband Digital Return

To avoid needing analog links, digitization (not demodulation) is performed at the Fiber Node.RF transparency is preserved.

HEADEND

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o oo o o o

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A-DA-D

Fiber Node

digital Tx

Mux

Sheryl Woodward, AT&T Labs-Research

A Sample HFC System

Secondary Hub

o o o o o oo o

o o o o

o o

HOME

o oo o

5-42 MHz 550 MHz 750 MHz

RF Spectrum on coax:return 80 broadcast channels 30 QAM channels

(~150 video channels)

Downstream: 500 MHz shared by ~50,000 (broadcast) 200 MHz by 1200 (narrowcast)

Upstream: ~37 MHz shared by 300

broadcast narrowcastnarrowcast

Fiber Node

up

b

n (4n/fiber)

Sheryl Woodward, AT&T Labs-Research