Mob 2 wireless transmission 2010

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Wireless Transmissions
 frequencies & regulations
 signals
 Signal
 Signal propagation
 Antennas,
 Link budget
 multiplexing, modulation, spread
spectrum, cellular systems
Analog and Digital Message
 Message = data that a user wants to transmit
 Analog message
– Set of continuous values and time
– ex : voice, video, sensor collected data
x(t)
t
 Digital message
– Discrete time, set of discret values
– ex : text, integer
010001100…
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Analog versus Digital Signal
 Signals are the physical representations of the message to
transmit.
– They usually exist as an electrical value (voltage, intensity) that can
then be converted into an electric or electromagnetic form for
transmission
– Analog signal: signal that represents a analog message
– Digital signal: signal resulting from a digital message
 It is represented as a succession of wave forms that can take one value
among a given and finite set of possibilities
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Signal transmission
any signal is composed of several frequential
components.
For a periodic signal these components are all multiple of
the fundamental frequency f..
– Example :
1
s(t ) = sin(2πft )+
3
(
sin 2π (3 f )t )
s1(t) = sin(2Πft) s2(t) = 1/3 sin(2Π(3f)t) s(t) = s1(t) +s2(t)
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Signal transmission
 19th century : Fourier shows that a simple periodic function
g(t) can be decomposed into a sum of sine and cosine with q
fundamental freauency of f= n/T
1 ∞ ∞
g (t ) = c + ∑ an sin (2π n f t )+ ∑ bn cos(2π n f t )
2 n =1 n =1
– an and bn are the sine and cosine of the nth harmonics
(terms). T
2
The amplitudes of an = g (t ) sin( 2π n f t ) dt
T ∫
0
an,bn and c for a given 2
T
function g(t) are : bn = ∫ g (t ) cos( 2π n f t ) dt
T 0
T
2
c = ∫ g (t ) dt
5 T 0
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Signal transmission
 Example :
– Let’s consider the transmission of “b” coded with the following 8 bits :
“01100010”
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Signal transmission
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Signal transmission
– b coded with 8 bits : “01100010”
1   π n  3π n   6π n   7π n  
an = cos  − cos  + cos  − cos 
π n   4   4   4   4  
1   3π n   π n  7π n   6π n  
bn = sin   − sin   + sin   − sin  
π n   4   4   4   4  
3
c=
4
the frequency spectrum associated to a given periodic
function is the comb spectrum. Each ray of the comb
corresponds to the amplitude of each harmonic.
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Signal transmission
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Data signal characterisation
– Spectral support of the signal is the set of frequencies it uses
– Spectral support at n dB
– Bandwidth is the width of the support
^ 2
x( f )
Max
Max/2
Fc
0 f
LB à 3 dB
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Maximum data rate of a channel
 Shannon’s law
– Shows the existence of a fundamental limit of the
transmission rate beyond which it is not possibe to
transmit without error
C = B . log2 (1 + PS/PN)
 C maximum theoritical capacity of the channel (bit/s)
 B bandwidth of the channel (Hz)
 PS/PN signal to noise ratio (Power of the signal over the power of
the noise)
 S/N = 10 . log10 (PS/PN)
S/N in dB
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Maximum data rate of a channel
 Example:
– Bandwidth= 3KHz, Noise= 30 dB
What is the maximum capacity on that channel ?
Solution:
10 log10(S/N) = 30 dB
<=> S/N = 103
Capacity = 3000. log2 (1+S/N) = 30000 bit/s
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Maximum data rate of a channel
 Nyquist’s theorem
– On a noiseless channel the maximum data rate is limited
Maximum data rate = 2 B Log2 V (bit/s)
With V number of discrete values of the signal
– Example : Bandwidth= 3KHz, Noise= 30 dB
What is the maximum capacity on that channel for a
binary signal ?
… when the valence is 8 ?
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Signal propagation ranges
 Transmission range
– communication possible
– low error rate
 Detection range
– detection of the signal sender
possible transmission
– no communication
possible distance
detection
 Interference range
– signal may not be interference
detected
– signal adds to the
background noise
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Signal Propagation
 Propagation in free space always like light
(straight line)
 Receiving power proportional to 1/d²
(d = distance between sender and receiver)
 Receiving power additionally influenced by
 fading (frequency dependent)
 shadowing
 reflection at large obstacles
scattering
 scattering at small obstacles reflection
diffraction
 diffraction at edges
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Example in the real world
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Multi path Propagation
signal transmitted
Signal received
 Signal can take many different paths between sender and receiver
due to reflection, scattering, diffraction
 Time dispersion: signal is dispersed over time
 interference with “neighbor” symbols, Inter Symbol Interference
(ISI)
 The signal reaches a receiver directly and phase shifted
 distorted signal depending on the phases of the different parts
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Effects of mobility
 Channel characteristics change over time and location
– signal paths change
– different delay variations of different signal parts
– different phases of signal parts
  quick changes in the power received (rapid fading)
 Additional changes in puissance long term
– distance to sender fading
– obstacles further away
  slow changes in the average power
received (long term fading)
short term fading t
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Effects of mobility
 Doppler-Fizeau effect
- The Doppler effect, named after Christian Doppler, is
the change in frequency and wavelength of a wave that
is perceived by an observer moving relative to the source
of the waves.
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Antennas: isotropic radiator
 Radiation and reception of electromagnetic waves, coupling of wires to
space for radio transmission
 Isotropic radiator: equal radiation in all directions (three dimensional) -
only a theoretical reference antenna
z
y z
y x ideal
x isotropic
radiator
 Real antennas always have directive effects (vertically and/or
horizontally)
 Radiation pattern: measurement of radiation around an antenna
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