Mô tả:
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 :
s(t ) = sin(2πft )+
s1(t) = sin(2Πft)
1
sin 2π (3 f )t
3
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
–
5
an and bn are the sine and cosine of the nth harmonics
(terms).
T
2
an =
g (t ) sin( 2π n f t ) dt
The amplitudes of
T ∫
0
an,bn and c for a given
T
2
bn =
g (t ) cos( 2π n f t ) dt
∫
function g(t) are :
T 0
2
c =
T
T
∫ g (t )dt
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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”
an =
1 π n
3π n
6π n
7π n
cos
−
cos
+
cos
−
cos
4
4
4
π n 4
bn =
1 3π n
π n
7π n
6π n
sin
−
sin
+
sin
−
sin
4
4
4
π n 4
c=
3
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
F
0
c
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
–
–
Detection range
–
–
communication possible
low error rate
detection of the signal
possible
no communication
possible
Interference range
–
–
signal may not be
detected
signal adds to the
background noise
sender
transmission
distance
detection
interference
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Signal Propagation
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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
diffraction
diffraction at edges
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reflection
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
distance to sender
obstacles further away
long term
fading
slow changes in the average power
received (long term fading)
short term fading
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t
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
y
z
z
y
x
x
ideal
isotropic
radiator
Real antennas always have directive effects (vertically and/or
horizontally)
Radiation pattern: measurement of radiation around an antenna
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