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Chapter 2/1 (Physical Layer). Theoretical Basis for Data Communication Guided Transmission Media Wireless Transmission Communication Satellites PSTN - Public Switched Telephone System. The Theoretical Basis for Data Communication. Fourier Analysis Bandwidth-Limited Signals - PowerPoint PPT Presentation
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09/13/2007 EETS 7304 1
• Theoretical Basis for Data Communication
• Guided Transmission Media• Wireless Transmission• Communication Satellites • PSTN - Public Switched Telephone
System
Chapter 2/1 (Physical Layer)
09/13/2007 EETS 7304 2
The Theoretical Basis for Data Communication
• Fourier Analysis• Bandwidth-Limited Signals• Maximum Data Rate of a Channel:
Nyquist TheoremShannon Capacity Theorem
09/13/2007 EETS 7304 3
Fourier Transform: periodic signals g(t)
dtnfttgT
bT
n )2cos(2
0
dttgT
cT
0
2
)2cos()2sin(2
1
11
nftbnftactgn
nn
n
nn
where: dtnfttgT
aT
n )2sin(2
0
From: )2cos()2sin()2sin( nftbnftanftc nnnn
22nnn bac
n
nn a
barctgFollows:
)2sin(2
1
1n
n
nn nftcctg
09/13/2007 EETS 7304 4
Successive approximations to the original signal
A binary signal and its root-mean-square Fourier amplitudes.
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6wt
appr
oxim
atio
n
original
1
2
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5 6wt
appr
oxim
atio
n original
4
7
0
0.1
0.2
0.3
0.4
0.5
0.6
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
n
Cn
09/13/2007 EETS 7304 5
Bandwidth-Limited Signals
09/13/2007 EETS 7304 6
Successive approximations to the original signal
09/13/2007 EETS 7304 7
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.
09/13/2007 EETS 7304 8
Fourier Transform: periodic signals
tjnn
nn
tnfjn
nn eCeCtx 002 w
where dtetXT
C tjn
T
Tn
0
0
0
2
20
1 w
Example: Pulse train
t
A
0
0
0
2
20
sin10
0
0Tfn
Tnf
T
ATdteA
TC tjn
T
Tn
w
T0
T
=>>n
A/2
-5 -4 -3 -2 -1 0 1 2 3 4 5 6
;0;3
;0;;2 443322110
CC
ACCCC
ACC
AC
for T0/T=2 =>
T0/T = 2
09/13/2007 EETS 7304 9
non-periodic signals
dfefStS ftj
2
2
1
dtetSfS ftj 2
Example: unit impulse function (t)
f
f
fj
eedtet
fjfjftj
2
)2sin(
222
1 222
t
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
-12.5 -10 -7.5 -5 -2.5 0 2.5 5 7.5 10 12.5
2f
f = 1/(2)
09/13/2007 EETS 7304 10
Delta impulse
12
dtett ftj or dtet ftj
2
2
1
=>> white spectrum.
t
f
1
white spectrum
0
09/13/2007 EETS 7304 11
Nyquist (1924) analog to digitalThe 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.
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0.0
0
0.1
6
0.3
2
0.4
8
0.6
4
0.7
9
0.9
5
1.1
1
1.2
7
1.4
3
1.5
9
1.7
5
1.9
1
2.0
7
2.2
3
2.3
8
2.5
4
2.7
0
2.8
6
3.0
2
3.1
8
t (ms)
09/13/2007 EETS 7304 12
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.
09/13/2007 EETS 7304 13
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).
09/13/2007 EETS 7304 14
Guided Transmission Media
• Twisted Pair
• Coaxial Cable
• Fiber Optics
09/13/2007 EETS 7304 15
Twisted Pair
(a) Category 3 UTP (Unshielded Twisted Pair), 16 Mbps.(b) Category 5 UTP, 100 Mbps.Category 6 and 7, 250 – 600 Mbps.
09/13/2007 EETS 7304 16
Coaxial Cable
50 Ohm and 75 ohm 1 GHz
09/13/2007 EETS 7304 17
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.
09/13/2007 EETS 7304 18
Transmission of Light through Fiber
Attenuation = 10*log10(transmitted power/received power)
per km of light through fiber in the infrared region.
f = c/ -> 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
09/13/2007 EETS 7304 19
Fiber Cables
(a) Side view of a single fiber.(b) End view of a sheath with three
fibers.
09/13/2007 EETS 7304 20
A comparison of semiconductor laser and LEDs as light sources.
09/13/2007 EETS 7304 21
A fiber optic ring with active repeaters
09/13/2007 EETS 7304 22
A passive star connection in a fiber optics network
09/13/2007 EETS 7304 23
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.
09/13/2007 EETS 7304 24
Wireless Transmission
• The Electromagnetic Spectrum
• Radio Transmission
• Microwave Transmission
Above 100 MHz for relaying 80 km.
09/13/2007 EETS 7304 25
The Electromagnetic Spectrum
09/13/2007 EETS 7304 26
Wireless bit rateWith current technology it is possible to code about 8 bps/Hz of bandwidth. Examples:• Coax 750 MHz bandwidth -> 6 Gbps.• Fiber:
f = c/ f = c
For = 1.3 band = 0.17 that gives the bandwidth f = 40 THz to get about 300 Tbps.
Two modes of transmission: • narrow band (f/f << 1) notably frequency hopping
spread spectrum (to avoid fading).• direct sequence spread spectrum.
09/13/2007 EETS 7304 27
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.
09/13/2007 EETS 7304 28
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.
The ISM bands in the United States
09/13/2007 EETS 7304 29
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)
09/13/2007 EETS 7304 30
Communication Satellites
Orbital period proportional to radius^(3/2). Latency = round-trip delay time
Number of satellites needed for global coverage.
24 h
6 h
1.5 h
P
09/13/2007 EETS 7304 31
ITU allocates the orbits as well as satellite bands
09/13/2007 EETS 7304 32
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.
09/13/2007 EETS 7304 33
Globalstar
(a) Relaying in space (Iridium).(b) Relaying on the ground (Globalstar 48 LEOs).
09/13/2007 EETS 7304 34
Public Switched Telephone System
• Structure of the Telephone System
• The Politics of Telephones
• The Local Loop: Modems, ADSL and Wireless
09/13/2007 EETS 7304 35
Structure of the Telephone System
(a) Fully-interconnected network.
(b) Centralized switch.
(c) Two-level hierarchy.
09/13/2007 EETS 7304 36
Structure of the Telephone System (2)
A typical circuit route for a medium-distance call.
09/13/2007 EETS 7304 37
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.
09/13/2007 EETS 7304 38
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.
09/13/2007 EETS 7304 39
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.
09/13/2007 EETS 7304 40
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.
09/13/2007 EETS 7304 41
Handshaking between two modems in RS-232CDSR
DTR
RI
RTS
CTS
CD
TD
RD
DSR
DTR
RI
RTS
CTS
CD
TD
RD
DTE DCE
TD
RTS
DTR
RD
CTS
DSR
RI
CD
GRND
DTEDCE
TD
RTS
DTR
RD
CTS
DSR
RI
CD
GRND
Data Set Ready
Data Terminal Ready
Ring Indicator
Request To Send
Clear To Send
Transmit Data
Receive Data
Modem PC
Carrier Detect
DB9 bit connector
ModemPC
RI RTS RTS
09/13/2007 EETS 7304 42
RS232 electrical signals
Speed pulse/sec = baud1200/2400/4800/9600/19200 baud
Control charactersRTS – 0011110RI - 0000111
Start( “0”) + 7 data + parity + Stop (at least 1.5 “1”)
ASCII Data (binary) 0 0 1 1 1 1 0
Start “0”
Stop “1”
0 0 1 1 1 1 0
+15 V
-15 V
parityStop “1”
tline signals
Amplitude“0” +5/+15 V “1” -5/-15 V
09/13/2007 EETS 7304 43
Modems use carriers between 1 and 2 kHz
(a) A binary signal
(b) Amplitude modulation(c) Frequency modulation
(d) Phase modulation
09/13/2007 EETS 7304 44
Modems (2)
(a) QPSK.
(b) QAM-16: V.32 for 9600/2400 = 4.
(c) QAM-64: V32 bis for 14,400/2400 = 6.
09/13/2007 EETS 7304 45
Modems (3)
(a) 2400 *5 = 12000 bps (b) 2400 * 7 = 16800 bps
09/13/2007 EETS 7304 46
Digital Subscriber Lines
Maximum bit rate versus distance over category 3 UTP for DSL.
09/13/2007 EETS 7304 47
Digital Subscriber Lines
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
Operation of ADSL using discrete multitone modulation.256 channels * 4312.5 Hz = 1.1040 MHz.
It works as 250 different frequency modems.
09/13/2007 EETS 7304 48
Digital Subscriber Lines
NID – Network Interface Device.DSLAM – Digital Subscriber Line Access Multiplexer.
09/13/2007 EETS 7304 49
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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