### Channel frequency selectivity and fading

```Mobile Communication
Systems 1
Prof. Carlo Regazzoni
Prof. Fabio Lavagetto
1
Attenuation;
Antenna;
 Doppler effect
 Frequency selective and non-selective fading
Conclusion.
2
The free space attenuation
It is the attenuation, only due to the path length and in presence of a free space
propagation conditions (no obstacles between the transmitter and the receiver);
The free space introduce the following attenuation term:
LFS  32.45  20log10 RKm  20log10 f MHz
The following expression is defined as available loss for the radio link :
Ad dB  32.4  20log10 Lkm  20log10 f pMHz  GT dB  GRdB
Where the two last terms represent the antenna’s gain.
3
Antennas
There are two main types of antennas:
1. Isotropic antenna;
2. Directional antenna.
The first one irradiates its energy in all spatial directions in the
same manner.
The second one irradiates the signal in a particular direction.
The antenna gain is defined as the ratio between the power
isotropic antenna.
In general:


G  4 2 Aeff
  c fp
Aeff  A
4
Introduction
Propagation effects:
There are four phenomena (reflection, refraction, diffraction,
scattering) associated with the propagation of wireless signals
which give rise to
• Multipath;
• Doppler shift.
The wireless channel is considered to be gaussian, additive,
and band-limited (AWGN). Whereas in real world the channel
exhibits non gaussian characteristic (not AWGN).
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propagation
Usually studied channels are characterized by a
time-invariant impulse response;
Instead multipath channel is characterised by a
time-variant impulse response;
On the transmission of a single impulse (ideally a
dirac delta), the response would be typically a time
variant impulse train of impulses dispersed in time
(defined as time spread, t) with different
attenuations.
6
Multi-path propagation: the channel
impulse response
Let the transmitted signal be represented by s(t) and received signal as
x(t).
x(t ) 
 n (t ) st   n (t ) 
s(t )  Re sl (t )e j 2fct



n
The received signal can be represented as:

x(t )  Re 

 n (t )e
 j 2f c n ( t )
n
 j 2f ct 
sl t   n (t )  e



rl (t ) 
 j 2f c n (t )

(
t
)
e
sl t   n (t )
n
n
Where l means the equivalent low pass response.
c( ; t ) 
 (t)e
n
n
    n (t )
 j 2f c n (t )
c( ; t )   ( ; t )e j 2fc
c( ; t) represents the channel response by choosing time t as
the reference time where  represents the delay with respect
to the origin of time axis.
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Multi-path effects
• If the propagating channel is slowly time variant, the value of n(t)
oscillates with time and its variability has small effects;
• However, n(t) can vary up to 2 in a time interval if n(t) varies
along a factor 1/fc, which is a very small value. This can be true for
bandpass signals modulated around fc
•  n(t) is a very sensitive parameter that characterizes the timevariant channel even if it has small oscillation;
• Moreover, the propagation delay related to each path can be often
assumed to change in a complete random uncorrelated way (thus it
is considered as a random process )
• This means that the received signal cannot be modelled as
Gaussian random process.
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modelling
 The received signal is dispersed in time with varying attenuation and
phase. The signal is amplified (if constructive interference occurs) and
attenuated (if destructive interference occurs). When the channel
impulse response can be modeled as a Gaussian random process the
envelope of the received signal can be modeled as:
Rician: if the Gaussian process has non-zero mean. Practically, the
channel can be modeled with a Line on Sight (LoS) path and other nonline of sight paths.
Rayleigh: if the Gaussian process has zero mean. Practically, the
channel can be modeled with non-line of sight paths;
Nakagami: it is a general case which can be expressed for both Rician
9
Channel correlation functions
10
The relation between various
considered fourier function
c  ; t 
FT
Time-variant correlation function
of the channel
C f ; t 
Time-variant correlation function
of the channel
FT
SC f ; 
IFT
S  ;  
Scattering function
IFT
Doppler power spectrum
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In general, the delayed paths are longer than the LoS path;
As consequence the delayed paths arrive at the receiving
antenna with different delays and in different time instants;
The delay spread can be computed according the following
relation:
S max  S min
Tm 
c
•Smax = distance covered by the longest path;.
•Smin = distance covered by the shortest path.
•The major effect due to the delay spread is the presence of
Intersymbol Interference (ISI)
12
Narrowband and wideband channel
and coherence bandwidth
A channel is defined as narrowband if
T > Tm
Where T is the symbol time duration;
A channel is defined as wideband if
T < Tm
The coherence bandwidth is defined according to the
following relations:
C f   C  
1
Bc 
Tm
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Channel frequency selectivity and
If
1
1
B   Bc 
T
Tm
T  Tm
the channel is frequency selective otherwise is not
frequency selective.
Channel
frequency
selectivity
14
Channel frequency selectivity and
The temporal fluctuations of the amplitude of the
This combination can be destructive or constructive
15
Channel frequency selectivity and
Channel frequency selectivity and
The frequency selectivity and the temporal fading are
two different types of distortion that are usually
present on the same channel;
On a wideband channel both the effects of frequency
selectivity and temporal fading are present;
On a narrowband channel the temporal fading is
present
16
Time variance of the channel
frequencies due to the time varying nature of the environment;
Phase time varying of replicas provides a spectral increase in a
transmitted carrier;
This phenomena is characterized by doppler spectrum defined
previously;


the relative velocity of the receiver with respect to the transmitter;
the movements of the objects between the transmitter and the
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Time variance of the channel
In both cases the doppler spread can be computed as:
Bd  f c
Bd  f c
v
c
Path 1
Path 2
v v1  v2

fc
c
c
The coherence time is defined as:
tc  1 Bd
18
If
If
t c  T
t c  T
B  Bc
T  tc
The channel is defined as slowly fading channel and in this case:
Tm Bd  1
Tm Bd  1
Tm Bd  1
19
Conclusion: transmission scheme
Transmission technique
Type of channel
Narrowband digital
modulation