Chapter 2/1 (Physical Layer)
• Theoretical Basis for Data
Communication
• Guided Transmission Media
• Wireless Transmission
• Communication Satellites
• PSTN - Public Switched Telephone
System
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The Theoretical Basis for Data
Communication
• Fourier Analysis
• Bandwidth-Limited Signals
• Maximum Data Rate of a Channel:
Nyquist Theorem
Shannon Capacity Theorem
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Fourier Transform: periodic signals g(t)
n 
n 
1
g t   c   an sin( 2nft )   bn cos( 2nft )
2
n 1
n 1
T
T
2
2
where: an 
g t sin( 2nft )dt bn   g t cos( 2nft)dt

T 0
T0
From:
cn sin( 2nft  n )  an sin( 2nft)  bn cos(2nft)
Follows:
cn 
a b
2
n
2
n
 bn
 n  arctg 
 an
T
2
c   g t dt
T0



n 
1
g t   c   cn sin( 2nft   n )
2
n 1
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1.2
approximation
approximation
Successive approximations to the original
signal
original
1
2
1
0.8
1
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
-0.2
original
4
7
1.2
0
1
2
3
4
5
6
wt
-0.2
0
1
2
3
4
5
6
wt
-0.4
-0.4
0.6
0.5
A binary signal and its root-meansquare Fourier amplitudes.
Cn
0.4
0.3
0.2
0.1
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
n
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Bandwidth-Limited Signals
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Successive approximations to the original signal
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Relation between data rate and harmonics
If b is bit rate (bps) then bit duration is 1/b s Time to send 8 bits T = 8/b s.
Therefore for b = 300 bps T = 8/300 = 0.02667 s = 26.67 ms. Since T is the
period the first harmonic has frequency 1/T = 300/8 = 37.5 Hz. Within the
bandwidth of 3000 Hz you can send 3000/37.5 = 80 harmonics.
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Fourier Transform: periodic signals
xt  
n 
j 2nf 0t
C
e

 n
n  
n 
jnw 0t
C
e
 n
1
Cn 
T0
where
n  
Example: Pulse train
T0
2


X t  e  jnw0t dt
T0
2
A
t
T
T0
A/2
1
Cn 
T0
T0
2
 Ae

T0
2
 jnw0t
 AT  sin Tnf 0 

dt  
 T0  nTf 0 
T0/T = 2
=>>
n
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
A
A
A
; C  C  0;
for T0/T=2 => C  ; C  C  ; C  C  0; C  C  
1  2
2
3
4
0 2 1
3
3 4
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non-periodic signals
S f  

 S t  e
 j 2ft
1
S t  
2
dt


j 2ft


S
f

e
df


Example: unit impulse function d(t)
d
1  j 2ft
e j 2fd  e  j 2fd sin( 2fd )
d t   
e
dt 

2d
2 j  2fd
2fd
d
1.2
1
1/2d
0.8
0.6
f = 1/(2d )
0.4
0.2
d
d
t
-12.5
0
-10
-7.5
-5
-2.5
0
2.5
5
7.5
10
12.5
-0.2
2fd
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Delta impulse

1
 j 2ft
or
d t  
d t    d t   e
dt  1
2



e j 2ft dt

=>> white spectrum.
1/2d
1
d
d
t
f
0
white spectrum
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Nyquist (1924) analog to digital
The minimum sampling rate to recover any bandlimited signal to H Hz is 2H (samples per
second). Example: assume 2400 bps 10 harmonics bandwidth 3000 Hz. T = 3.33 ms.
Minimum sampling rate is 6000 samples/sec, or every 1/6 = 0.167 ms or 20 samples per period.
1.2
1
0.8
0.6
0.4
0.2
0
3.18
3.02
2.86
2.70
2.54
2.38
2.23
2.07
1.91
1.75
1.59
1.43
1.27
1.11
0.95
0.79
0.64
0.48
0.32
0.16
0.00
-0.2
t (ms)
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Telephone example
• Subscriber loop has a bandwidth over 1 MHz. However,
switching office filters every signal to 4000 Hz. Therefore,
after entering a switch the analog voice is limited to 4000
Hz. Minimum sampling rate is then 8000 samples (pulses)
per sec.
• Pulse per sec = baud.
• Since the value of every sample is represented by 8 bits a
digital voice bit rate is: 8000 bauds * 8 bits/baud = 64000
bps = 64 kbps.
• Inversely Nyquist theorem also says that maximum sample
(pulse) rate going through the filter H that can be
recovered is 2H.
• In addition if max amplitude pulse is divided into V levels
then the bit rate carried with 2H baud is 2H*log2V.
• For example modem with 2400 bauds and V = 64 has bit
rate 14,400 bps.
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Shannon (1948) theorems
• Bit rate in a noisy channel. Shannon Capacity Theorem:
maximum bit rate = H log2(1 + S/N), where
H - channel bandwidth,
S – signal power,
N – noise power.
• For instance: Voice-grade line channel H = 3000 Hz and
S/N = 30 dB -> S/N = 1000, therefore,
maximum bit rate = 3000 log2(1001) = 30000 bps.
• Definition of dB = 10 log10(S/N).
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Guided Transmission Media
• Twisted Pair
• Coaxial Cable
• Fiber Optics
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Twisted Pair
(a) Category 3 UTP (Unshielded Twisted Pair), 16 Mbps.
(b) Category 5 UTP, 100 Mbps.
Category 6 and 7, 250 – 600 Mbps.
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Coaxial Cable
50 Ohm and 75 ohm
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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.
Multimode uses total reflection.
Single mode 50 Gbps over 100 km.
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Transmission of Light through Fiber
Attenuation = 10*log10(transmitted power/received power)
per km of light through fiber in the infrared region.
f = c/l -> f = 300,000,000/1.3*10^-6 = 2.31*10^14 = 231 THz.
Bandwidth = 300,000,000*(1/1.22 – 1/1.37)*10^6 = 0.27*10^14 = 27000
GHz
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Fiber Cables
(a) Side view of a single fiber.
(b) End view of a sheath with three
fibers.
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A comparison of semiconductor laser and
LEDs as light sources.
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A fiber optic ring with active repeaters
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A passive star connection in a fiber optics network
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Fiber vs. copper
• Repeaters: copper every 5 km vs. fiber 50 km.
• 1000 twisted pairs 1 km long weights 8 Tones vs. 2 fibers
with more capacity weight 100 kg.
• Fiber doesn’t leak the light -> excellent security.
• Fiber is much lighter to hang on the poles.
• Fiber is dug about 1 m (3 ft) underground or replaces
copper in ducts.
• Fiber is new technology therefore more expensive parts.
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Wireless Transmission
• The Electromagnetic Spectrum
• Radio Transmission
• Microwave Transmission
Above 100 MHz for relaying 80 km.
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The Electromagnetic Spectrum
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Wireless bit rate
With current technology it is possible to code
about 8 bps/Hz of bandwidth. Examples:
• Coax 750 MHz bandwidth -> 6 Gbps.
• Fiber:
f = c/l > Df = cDl/l2
For l = 1.3 m band Dl= 0.17 m that gives the
bandwidth Df = 40 THz to get about 300 Tbps.
Two modes of transmission:
• narrow band (Df/f << 1) notably frequency hopping
spread spectrum (to avoid fading).
• direct sequence spread spectrum.
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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.
Microwave transmission uses above 100 MHz. MCI
(Microwave Communications Inc.) was a long
distance carrier before merged with WorldCom.
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The ISM bands in the United States
Radio spectrum is owned by governments or FCC in US. FCC
allocates the spectrum while governments sell it to carriers on
auctions. Some spectrum is left unsold for unlicensed use.
Bluetooth and WiFi
WiFi
ISM (Industrial, Scientific, Medical) are not allocated but limited
by distance like garage door openers, cordless phones, radio
controlled toys etc. It is mandated by power < 1 W.
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Communication Satellites
• Geostationary Satellites 1962
• Medium-Earth Orbit Satellites – GPS
24 GPS satellites orbiting at 18,000 km
every 6 hours.
• Low-Earth Orbit Satellites (Communications)
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Communication Satellites
P
24 h
6h
1.5 h
Orbital period proportional to radius^(3/2).
Latency = round-trip delay time
Number of satellites needed for global coverage.
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ITU allocates the orbits as well as satellite bands
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Low-Earth Orbit Satellites
Motorola Iridium launched 1997
• The Iridium: six necklaces by 11 = 66 satellites (750 km).
• Each satellite covers 48 cells = 1628 moving cells.
• Satellite phones didn’t have much success in competition with terrestrial
and 5 b$ was sold for 25 m$ resumed service in 2001.
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Globalstar
(a) Relaying in space (Iridium).
(b) Relaying on the ground (Globalstar 48 LEOs).
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Public Switched Telephone System
• Structure of the Telephone System
• The Politics of Telephones
• The Local Loop: Modems, ADSL
and Wireless
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Structure of the Telephone System
(a) Fully-interconnected network.
(b) Centralized switch.
(c) Two-level hierarchy.
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Structure of the Telephone System (2)
A typical circuit route for a medium-distance call.
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Major Components of the Telephone System
• Local loops: analog twisted pairs going to houses and
businesses: the weakest link.
• Trunks: digital fiber optics connecting the switching
offices.
Three different way of multiplexing: frequency,
time, and wavelength.
• Switching offices: where calls are moved from one
trunk to another.
Types of switching: circuit switching vs. packet
switching.
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The Politics of Telephones
1984 US was divided into 164 LATAs (Local Access and Transport Area equivalent
to an area code). BOC has monopoly by its ILECs (Incumbent Local Exchange
Carrier) within LATA. AT&T (IXC#1) and competitors (IXC#2) use IXCs
(IntereXchange Carrier) for traffic between LATAs. Long Distance carrier also
must build IXC POP switches at each LATA to connect it to IXC. BOCs are
required to connect to each IXC POP. 1996 interference was allowed.
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Present day Internet
POP – Point Of Presence are ISP (e.g. AOL) modems connected to Regional ISP network.
Regional ISP network is connected to the backbone. Backbones are connected by NAP
(Network Access Point) or by their own routers. Finally Server Farm (multiplicity of
identical servers) are connected to the router.
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The Local Loop: Modems, ADSL, and Wireless
ISP1 handles Internet call from the computer. Digital > modem>analog
subscriber line>codec>digital trunk>codec>analog subscriber line>modem
(bank) >ISP1 computer (POP). ISP2 handles it faster.
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Handshaking between two modems in RS-232C
PC
DTE
TD
RTS
DTR
RD
CTS
DSR
RI
CD
GRND
Modem
Data Set Ready
DSR
DTR
Data Terminal Ready
RI
Ring Indicator
RTS
DCE
Request To Send
CTS
CD
Clear To Send
Carrier Detect
TD
Transmit Data
RD
Receive Data
RI
Modem
DCE
TD
RTS
DTR
RD
CTS
DSR
RI
CD
GRND
PC
RTS
RTS
DSR
DTR
RI
DTE
RTS
CTS
CD
TD
RD
DB9 bit
connector
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RS232 electrical signals
ASCII Data (binary)
0
0
1
1
1
1
0
+15 V
line
signals
Start
“0”
0
0
1
1
1
Stop
“1”
1
0
Start( “0”) +
7 data + parity +
Stop (at least 1.5 “1”)
t
parity
Stop
“1”
-15 V
Amplitude
“0” +5/+15 V
“1” -5/-15 V
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Speed
pulse/sec = baud
1200/2400/
4800/9600/
19200 baud
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Control
characters
RTS – 0011110
RI - 0000111
42
Modems use carriers between 1 and 2 kHz
(a) A binary signal
(b) Amplitude modulation
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(c) Frequency modulation
(d) Phase modulation
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Modems (2)
(a) QPSK.
(b) QAM-16: V.32 for 9600/2400 = 4.
(c) QAM-64: V32 bis for 14,400/2400 = 6.
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Modems (3)
(a) 2400 *5 = 12000 bps
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(b) 2400 * 7 = 16800 bps
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Digital Subscriber Lines
Maximum bit rate versus distance over category 3 UTP for DSL.
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Digital Subscriber Lines
Operation of ADSL using discrete multitone modulation.
256 channels * 4312.5 Hz = 1.1040 MHz.
It works as 250 different frequency modems.
Ch – 0 voice; Ch 1-5 not used
32 Chs * 32 kbps = 1 Mbps upstream data + 1 ch for control
216 Chs * 32 kbps = 7 Mbps downstream data + 1 for control
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Digital Subscriber Lines
NID – Network Interface Device.
DSLAM – Digital Subscriber Line Access Multiplexer.
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Wireless Local Loops
Connection to the CLEC (Competitive Local Exchange Carrier): LMDS
(Local Multipoint Distribution System).
FCC allocated bandwidth 198 MHz at 2.5 GHz taken from Instructional TV.
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