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.


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


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

Power Spectrum Density

• Autocorrelation function of signal or noise

• Power spectrum density

))()(()( tXtXE

dew jw)()(

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

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

k

Tkc

ectstx

sk

k

T

kti

ks

)/sin(

)()(2

k

sk TkfScfX )/()(

Ts sampling interval, ∆ sampling pulse width

Niquist Chriterium

s(t)

x(t)

t

t

t

Niquist Chriterium

S(f)

X(f)

f

f1/Ts-2/Ts -1/Ts 2/Ts

W-W

Shannon Theorem

• If the channel 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

Modulation

(a) A binary signal

(b) Amplitude modulation(c) Frequency modulation

(d) Phase modulation

Modulation

• Signal is located around carrier frequency w0, and its amplitude and phase depend on the data symbol in each time slot

)(

0

0

Re

))(cos()(

son nTtiwi

nn

nson

n

eer

nTtwats

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.

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

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.

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.

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

and number of satellites needed for global coverage.


The principal satellite bands.

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).


Multiplexing T1 streams into higher carriers.

TDM

• US and Japan T1 1.544Mbps• 24 channels one sync. bit

• 23 data channels, 7 data bits + 1 signalling bit

• Multiplexing degrees 4,7,6

• Others E1 2.048Mbps• 32 channels

• 30 data channels, 8 data bits, 1 bit signalling in every sixth frame

• Multiplexing degree 4, bit rates: 2.048Mbps, 8.848Mbps,

SONET and SDH

• Bellcore and CCITT: Synchronous Optical Networks (SONET), Synchronous Digital Hierarchy (SDH)

• Define frames for bit-rates 50Mbps and up

SONET

Two back-to-back SONET STS-1 frames comprising 810 bytes


SONET and SDH multiplex rates.

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

CDMA – Code Division Multiple Access(e.g. IS-95)

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

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) V.32 for 9600 bps.

(b) V32 bis for 14,400 bps.

(a) (b)

Higher Bit-rate Modems

• 2400 samples (bauds) per second

• V32 to 14.4Kbps, V34 to 33.6Kbps

• V90 35Kbps upstream, 56Kbps downstream

• V92 48kbps upstream, 56Kbps downstream

Digital Subscriber Lines

Bandwidth versus distanced over category 3 UTP for DSL.


Operation of ADSL using discrete multitone modulation.

Up to 8Mbps downstream, and up to 1Mbps upstream.

Modulation similar to V34, 15 bits per sample, 4000 bauds per sec


A typical ADSL equipment configuration.

Internet over Cable

Cable television

Internet over Cable

The fixed telephone system.

Community Antenna Television (CATV)

antenna

HEADEND

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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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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.


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)


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

Can now offer interactive services


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.


The Mobile Telephone System

• Improved mobile telephone system (IMTS): 23 channels, 150-450MHz; Advanced mobile telephone system (AMTS) is cellular system: 832x30kHz channels, 824-894MHz

• Digital: D-AMPS, 30KHz channels, 1850-1990MHz; Global System for Mobile Communications (GSM) 124x200kHz channels 890-960MHz; Code Division Multiple Access (CDMA)

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.

Control Channels

• Broadcast control channel: Base station broadcasts control signal

• Dedicated control channel: Registration, location and connection status of users

• Common control channel• Paging subchannel: announces calls• Random access channel: connection requests• Access grant channel: connection grants

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 service (GPRS) is overlay

packet network over D-AMPS or GSM• WLAN at 2.5 or 5.7GHz 10-50Mbps; WMAN at 10-

66GHz up to 200Mbps; (As oppose to around 50Mbps total for D-AMPS and GSM, and 8Kbps and 13Kbps per user.

The Physical Layer

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