Transcript Slide 1
Chapter 3 – Data Transmission:
Concepts and Terminology
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Transmission Terminology
data transmission occurs between a transmitter
& receiver via some medium
guided medium
eg. twisted pair, coaxial cable, optical fiber
unguided / wireless medium
eg. air, water, vacuum
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Transmission Terminology
direct link
no intermediate devices
point-to-point
direct link
only 2 devices share link
multi-point
more than two devices share the link
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Transmission Terminology
Simplex transmission
one direction
• eg. television
Half-duplex transmission
either direction, but only one way at a time
• eg. police radio (walkie-talkie: push-to-talk and
release-to-listen)
Full-duplex transmission
both directions at the same time
• eg. telephone
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Time domain concepts of signals
time domain concepts
analog signal
• various in a smooth way over time
digital signal
• maintains a constant level then changes to another
constant level
periodic signal
• pattern repeated over time
aperiodic signal
• pattern not repeated over time
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Analog and digital signals
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Periodic signals
The signal period T is the
inverse of signal frequency f :
1
T
f
T in sec onds ( s)
f in Hertz ( Hz)
The signal s(t) is periodic if:
s(t T ) s(t )
t
The signal amplitude is
denoted by A
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Sine wave
Mathematically, the sine wave is given by :
s(t ) A sin(2 ft )
Three parameters :
1. Peak amplitude (A)
maximum strength of signal
usually measured in volts
2. Frequency ( f )
rate of change of signal
measured in Hertz (Hz) or cycles per second
period = time for one repetition ( T )
T = 1/f
3. Phase ( )
relative position in time
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Varying Sine Waves
s(t ) A sin(2 ft )
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Wavelength (λ)
is the distance occupied by one cycle
assuming signal velocity v, then = vT
or equivalently f = v, since T=1/f
for the special case when v=c
c = 3*108 m/s (speed of light in free space)
c=λf
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Frequency Domain Concepts
signal are made up of many frequencies
components are sine waves
Fourier analysis can shown that any signal
is made up of component sine waves
Fourier series of a square wave with
amplitudes A and –A :
sin(2 kft)
s(t ) A
k 1, k odd
k
4
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Fourier Transform
Mathematical tool that relates the frequency-domain
description of the signal to its time-domain description
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Time-domain vs frequency-domain
Figure 3.5a: frequency domain function for the
signal of Figure 3.4c.
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Time-domain vs frequency-domain
Time-domain
Frequency- domain
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Spectrum and bandwidth
Spectrum
range of frequencies contained in signal
Absolute bandwidth
width of spectrum
effective bandwidth
often just bandwidth
narrow band of frequencies containing most energy
DC Component
component of zero frequency
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Acoustic Spectrum
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Analog and digital data transmission
data
– entities that convey meaning
signals & signalling
– electric or electromagnetic representations of
data, physically propagates along medium
transmission
– communication of data by propagation and
processing of signals
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Audio Signals
freq range 20Hz-20kHz (speech 100Hz-7kHz)
easily converted into electromagnetic signals
varying volume converted to varying voltage
can limit frequency range for voice channel to
300-3400Hz
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Digital Data
as generated by computers etc.
has two dc components
bandwidth depends on data rate
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Analog Signals
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Digital signals
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Advantages and disadvantages of digital signals
cheaper
less susceptible to noise
but greater attenuation
digital now preferred choice
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Transmission Impairments
signal received may differ from signal
transmitted causing:
analog - degradation of signal quality
digital - bit errors
most significant impairments are
attenuation and attenuation distortion
delay distortion
noise
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Attenuation
where signal strength falls off with distance
depends on medium
received signal strength must be:
strong enough to be detected
sufficiently higher than noise to receive without error
so increase strength using amplifiers/repeaters
is also an increasing function of frequency
so equalize attenuation across band of
frequencies used
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Delay distortion
propagation velocity varies with frequency
hence various frequency components
arrive at different times
particularly critical for digital data
since parts of one bit spill over into others
causing intersymbol interference
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Noise
Additional unwanted signals inserted
between transmitter and receiver
Thermal
due to thermal agitation of electrons
uniformly distributed
white noise
N 0 kT (W / Hz)
N 0 noise power density in watts per 1Hz of bandwidth
k Boltzm ann' s const ant 1.3810 23 J / K
T Tem praturein Kelvins
Interference from other users in a multi-user
environment (e.g., mobile environment)
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Noise
crosstalk
a signal from one line is picked up by another
impulse
irregular pulses or spikes
• eg. external electromagnetic interference
short duration
high amplitude
a minor annoyance for analog signals
but a major source of error in digital data
• a noise spike could corrupt many bits
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Noise: example
0
+5V
1
-5V
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Data-rate
Data rate: is the rate, in bits per second (bps), at
which data can be communicated
1
1
1
data Rate R
50 kbps
bit duration Tb 0.02m sec
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Spectrum, bandwidth and Data-rate
Spectrum of a signal: is the range of frequencies that it
contains
Absolute bandwidth: is the width of the spectrum
Effective bandwidth: is a relatively narrow band that contains
most signal energy
Any transmission system has a limited bandwidth
Square wave have infinite components and hence infinite
bandwidth, but most energy in first few components
Limited bandwidth increases distortion
Limited bandwidth also limit the data rate that can be carried
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Bandwidth
Bandwidth B 3 f 1 f 2 f
Assum e f 1KHz,
then Bandwidth B 2 KHz
Absolute B
Effective B width of m ain lobe
1
X
Assum e X 1 m sec,
then effective B 1KHz
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Data-rate and bandwidth
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Channel Capacity
Channel Capacity: max possible rate at which data
can be transmitted over a given communication
path, under given conditions
Channel capacity is a function of :
data rate - in bits per second [bps]
bandwidth - in Hertz [Hz]
noise - on communication link
error rate - the rate at which errors occur, reception of 1
when 0 is transmitted, and visa versa
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Nyquist Bandwidth
Consider noise free channels
If rate of signal transmission is 2B then we can
carry signal with frequencies no greater than B
i.e., given bandwidth B, highest signal rate is 2B
For binary signals (0,1), 2B bps need bandwidth B Hz
Can increase rate by using M signal levels or M
symbols (e.g. M=4, Quaternary: 00, 01, 10,11)
Nyquist formula is:
C 2B log2 M
[bps]
So increase rate by increasing signal levels
at cost of receiver complexity
limited by noise & other impairments
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Shannon Capacity Formula
Consider relation of data rate, noise & error rate
faster data rate shortens each bit so bursts of noise affects more bits
given noise level, higher rates means higher errors
signal power
Signal-to-Noise Ratio (SNR): SNR
noise power
SNR in decibles (dB):
SNRdB 10log10 SNR
Shannon’s channel capacity (C) in bits/s is related to the
channel bandwidth (B) in Hertz and SNR by:
C B log2 (1 SNR)
theoretical maximum capacity
get lower in practise
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Nyquit bandwidth and Shannon Capacity
Example: Suppose that the spectrum of a channel is
between 3MHz and 4MHz and the SNRdB=24dB. Find:
1. The channel bandwidth (B)
2. The channel capacity (C)
3. Based on Nyquist formula, how many signalling levels are
required to achieve the max capacity
Solution:
1. B = 4MHz - 3MHz = 1MHz
2. SNRdB 24dB 10log10 SNR
SNR 251
C B log2 (1 SNR) 106 log2 (1 251) 8 106 8Mbps
3. C 2B log2 M
8 106 2 106 log2 M
M 16
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Decibels and signal strength
It is customary to express gain or loss (attenuation) in decibels:
Logarithmic unit (compressed scale)
Multiplication and division reduce to addition and subtraction
The decibel power gain (GdB):
Pout
GdB 10log10
Pin
Pin : input power level
Pout : output power level
The decibel power loss (LdB):
Pout
Pin
LdB 10 log10
10log10
Pin
Pout
Pin
Vin2 / R
Vin
L
10
log
10
log
20
log
The decibel voltage loss: dB
10
10
10
Pout
Vout2 / R
Vout
where V is the voltage across resistor R
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Decibels and signal strength
Example 1: if a signal with a power level of 10mW is inserted
onto a transmission line and the measured power some
distance away is 5mW, then the loss can be expressed as:
LdB 10log10
Pin
10m W
10log10
3dB
Pout
5m W
Example 2: Consider a series of transmission elements in
which the input is at a power level of 4mW, the first element is a
transmission line with 12dB loss, the second element is an
amplifier with 35dB gain, and the third element is a
transmission line with 10dB loss.
1. The net gain is -12 + 35 – 10= 13dB
Pout
2. The output power (Pout): GdB 13dB 10log10
4m W
Pout 4 101.3 m W 79.8m W
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Decibels and signal strength
The dBW (decibel-Watt):
powerdBW
powerW
10log10
10log10 ( powerW )
1W
Example: a power of 1W is 0dBW,
a power of 1000W is 30dBW,
a power of 1mW is –30dBW
The dBm (decibel-milliWatt):
powerdBm
powermW
10log10
1m W
Example: a power of 1mW is 0dBm,
a power of 30dBm is 0dBW
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Example
Given a receiver with an effective noise temperature of 294K
and a 10 MHz bandwidth. Find the thermal noise level (N0) at
the receiver’s output in units of dBW?
N 0 kT
[W / Hz]
N kTB [W ],
k Boltzm ann' s const. 1.3810 23 J / K
T Tem praturein Kelvins
B Bandwidth
kTB
N dBW 10 log10
10 log10 kTB 10 log10 k 10 log10 T 10 log10 B
1W
10 log10 (1.3810 23 ) 10 log10 (294) 10 log10 (107 )
228.6 24.7 70
133.9dBW
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The expression Eb/N0
The expression Eb/N0 : is the ratio of signal energy per bit (Eb) to
noise power density per Hz (N0)
Eb STb ,
where S : signal power
Tb : bit duration
N 0 kT ,
where k : Boltzm annconst.
T :Tem prature
1
data Rate R
Tb
Eb S / R
S
N0
N0
kTR
in decibel notation,
Eb
S dB 10 log10 R 10 log10 k 10 log10 T
N 0 dB
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Example
For Binary Phase Shift Keying (BPSK) modulation, Eb/N0 = 8.4
dB is required for a bit error rate of 10-4 (one bit error out of
every 10000 bits). If the effective noise temperature is 290 K
(room temperature) and the data rate is 2400 bps, what
received signal power level is required?
Eb
S dB 10 log10 R 10 log10 k 10 log10 T
N 0 dB
8.4 S dB 10 log10 2400 (228.6) 10 log10 290
8.4 S dB (10)(3.38) 228.6 (10)(2.46)
S dB 161.8 dB
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Eb/N0 versus SNR
We can relate Eb/N0 to the Signal-to-Noise Ratio (SNR):
Eb S / R
N0
N0
Noise power N N 0 B, where B is the bandwidth
Eb
S/R S B
S
, where
is the Signalto Noise Ratio( SNR)
N0 N / B N R
N
S
The Shannonchannelcapacity: C B log2 (1 SNR) B log2 (1 )
N
S
2C / B 1
N
E
S B
B
B
b
2C / B 1 2C / B 1
N0 N R
R
C
where C / B is the spectral efficiency
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Example
Suppose we want to find the minimum Eb/N0 required to achieve
a spectral efficiency C/B of 6bps/Hz
Eb
B
1
2C / B 1 26 1 10.5 10.21dB
N0
C
6
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