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Transcript of Chapter Two Small Scale Fading
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Chapter Two
Mobile Radio Channel Modelling & Mitigations
2.1 Wireless Channel Models and Signal Propagations
Small Scale Fading and Multipath
By : Amare Kassaw
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Objective of the Chapter
In cellular system, calls are occasionally disconnected
Possible cause: Rapid fluctuation of radio signals amplitude
over a short time period or travel distance
Reasons for wireless channels to become selective and dispersive
both in frequency and time
Sources of signal fluctuation: multipath propagation and mobility
Techniques to minimize or modify propagation loss.
To understand how physical parameters such as carrier frequency,
mobile speed, bandwidth, delay spread impact how a wireless
channel behaves from the communication system point of view.
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Lecture Outlines
Introduction
Parameters of the Mobile Radio Channel
Impulse Response Model of the Wireless Channel
Categorization of the Fading Channel
Summery
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Introduction to Wireless Channels
Electromagnetic (EM) signal can transmit through:
A guided medium or
An unguided medium.
Guided mediums such as coaxial cables and fiber optic cables are
wireless or the unguided medium.
It presents limited challenges and conditions which are unique for
this kind of transmissions.
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As the signal travels through the wireless channel, it undergoes
many kinds of propagation effects such as reflection, diffraction
and scattering due to the presence of buildings, mountains and
other such obstructions.
Reflection: occurs when the EM waves impinge on objects which
has very large dimension as compared to the wavelength of the
wave.
Diffraction: occurs when the wave interacts with a surface having
sharp irregularities.
Scattering: occurs when the medium through which the wave is
travelling contains objects which are much smaller than the
wavelength of the EM wave.5
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These varied phenomena's lead to large scale and small scale
propagation losses.
Hence unlike wired channels that are stationary and predictable,
radio channels are extremely random and time varying
Even the speed of motion impacts how rapidly the signal level
a es as a mo e erm na moves n space
Due to the inherent randomness associated with such channels
they are best described with the help of statistical models.
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We have two types of wireless channel models:
Large Scale Path Loss Models: predicts the mean signal strength
for arbitrary transmitter-receiver distances.
They predict the average signal strength for large Tx-Rx
separations, typically for hundreds of kilometres.
Time constants associated with variations are very long as themobile moves, many seconds or minutes.
Useful in estimating the coverage area of an antenna
More important for cell site planning.
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Small Scale Fading Models: describes the signal strength variation
in close spatial proximity to a particular location
Characterize the rapid fluctuations of the received signal strength:
Over very short travel distances (a few wavelengths) or
Over very short time durations (in the order of seconds)
The received power may very by 30-40 dB when the receiver is
moved by fraction of a wavelength
This is because the received signal is the sum of many
contributions (the phases are random) coming from different
directions
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Example: Small scale and large scale fading
Signal variations in an indoor radio communication system
Signal fades rapidly as the receiver moves
By more than 20 dBm
However, the average signal
ecays muc more s ow y
with distance (smoothed line)
Depends on terrain and
obstructions
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Small Scale Fading and Multipath
Small scale fading (simply fading) describes rapid fluctuation of
amplitudes, phases, or multipath delays of a radio signal over:
Short period of time or
Small travel distances
It is more severe than the large-scale path loss
a ng s cause y mu pa se n er erence n wo or more
version of the transmit signal which arrives at the receiver at slightly
different times.
Multipath Waves: Two or more versions of a transmitted signal
Multipath signals, if arrive at slightly different times, may combine
at the receiver antenna distractively that causes signal fluctuation
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Representation of multipath wireless propagation
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Thus fading describes the rapid fluctuation of amplitudes, phases
and multipath delays of the radio signal over a short period of time.
The most important effects of this multipath fading are:
Envelope fading: rapid change in signal strength over a small
travel distance or time interval
Time Dispersion: Echo's caused by multipath propagation delays
Frequency Dispersion: Random frequency modulation due to
varying Doppler shifts on different multipath signals
This Doppler shift is caused by the mobility of mobile which
cause an apparent shift in frequency
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Factors that influence small scale fading :
1. Multipath Propagation: due to the presence of reflecting
objects and scaterers
Multiple version of the signal arrives at the receiver with
different amplitude and time delays
2. Speed of Mobile : due to the relative motion of the base station,
mobile station, and the surrounding environment.
Causes Doppler shift (+ or -) at each multipath component
Results in random frequency modulation or apparent shift in
frequency
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A receiver moving at high speed can pass through several fades in
small period of time
Causes time-varying Doppler shift on the multipath components
If the surrounding objects move at a greater rate than the mobile,
then this effect dominates the small-scale fading and vice versa
The term coherence time determines how static the channel isand depends on the Doppler shift,
e.g., room environment ,outdoor, urban,
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3. The bandwidth of the signal: causes frequency selectivity.
The channel bandwidth can be quantified by the term coherence
bandwidth, Bc
Coherence bandwidth measures the maximum frequency
difference for which signals are still strongly correlated in
amplitude
If BW of the signal is greater than the coherence bandwidth, thereceived signal will be distorted (filtered) in frequency
However, the signal strength will not fade much over a local area
(i.e., small-scale fading will not be significant)
If the transmitted signal has a narrow bandwidth as compared to the
channel, signal will not be distorted in frequency
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Parameters of the Mobile Radio Channel
Wireless propagation are mostly governed by a number of
unpredictable factors .
So, it is preferred to characterise the wireless channel from astatistical point of view using some fundamental parameters.
,
on wireless communication
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1. Doppler Shift: is the change in frequency of a wave for an
observer moving relative to the source of the wave.
Caused by movement of Tx, Rx, and environment
Results multiplicative in time rendering the channel impulse
response linear time variant (LTV).
For the mobile in the next figure, phase change in the received
signal due to path difference is
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The apparent change in frequency
This is Doppler spreading
Remote Source
W c ncrease or ecreasethe signal frequency at Rx
Note that if:
= 0 then fD
is positive
Apparent received frequency:fa= fs+ fD
= then fD is negative
Apparent received frequency:fa= f
s- f
D
= Spatial angle b/n the
direction of motion of
the mobile anddirection of arrival
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2. Time Dispersive Parameters
The wireless channel is fully described by its impulse responsemodel as
= the time-varying attenuation or power delay profile
= phase shift of the channel
= propagation delay of the lthpath
Np = number of multipath of the wireless propagation
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2.1 Power Delay Profile(PDP):
It is a statistical parameter indicating how the power of a Dirac
delta function is dispersed in the time-domain as a consequence
of multipath propagation.
It is usually given in a table where the average power associated
with each multi ath com onent is rovided alon with the
corresponding delay
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In particular the average power of the lthpath is given by
Summing all quantities provides the total average received
power PR.
In practice the PDP is normalized so that the sum of is unity
as
Based on the , we define multipath channel parameters that are
used to characterise the time dispersive channel such as : mean
excess delay, RMS delay spread, maximum excess delay andcoherence BW.
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The Mean Excess Delay( ): is the first moment of the power
delay profile and is defined as
Where is the average power of the delay profiles in linear
.
The RMS Delay Spread( ): is the square root of the second
central moment of the power delay profile and is given by
Where :
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These delays are measured relative to the first detectable signal
arriving at the receiver at 0 =0
Typical values of RMS delay spread are on the order of
microseconds in outdoor mobile radio channels and on the orderofnanoseconds in indoor mobile radio channels.
o e a : e e ay sprea an mean excess e ay are
defined from a single power delay profile which is the temporal or
spatial average of consecutive impulse response measurements
collected and averaged over a local area.
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The maximum excess delay (XdB): the time delay during which
multipath energy falls to XdB below the maximum
x-0 where 0 is the first arrival signal and x is the maximum
signal point at which the multipath component is XdB of thestrongest arrival signal.
e va ue o X s some mes ca e e excess e ay sprea o a
power delay profile, but in all cases it must be specified with a
threshold that relates the multipath noise floor to the maximum
received multipath component.
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Coherence Bandwidth(Bc): is a statistical measure of the range of
frequencies over which the channel can be considered flat.
Flat channel is a channel which passes all spectral components
with approximately equal gain and linear phase.
While the delay spread is a natural phenomenon caused by
re ec e an sca ere propaga on pa s n e ra o c anne ,
the coherence bandwidth is defined based on the relation derived
from the RMS delay spread.
The range of frequencies over which two frequency components
have a strong potential for amplitude correlation.
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Two sinusoids with frequency separation greater than BC are
affected differently
If the coherence bandwidth is defined as the bandwidth over
which the frequency correlation function is 0.9
If the coherence bandwidth is defined as the bandwidth over
which the frequency correlation function is 0.5
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The Coherence Time( Tc):
Delay spread and coherence bandwidth are parameters which describethe time dispersive nature of the wireless channel.
But, they do not offer information about the time varying nature of the
channel caused by either relative motion between the mobile and base
station, or by movement of objects in the channel
describe the time varying nature of the channel in a small-scale
region
Doppler spread BD is a measure of the spectral broadening
caused by the time rate of change of the mobile radio channel and
it is the range of frequencies over which the received Doppler
spectrum is essentially nonzero
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Coherence time is the time domain dual of Doppler spread and is
used to characterize the time varying nature of the frequency
dispersiveness of the channel in the time domain
The Doppler spread and coherence time are inversely proportionalto one another as Tc=1/fm.
o erence me s e me ura on over w c wo rece ve
signals have a strong potential for amplitude correlation
If the reciprocal bandwidth of the baseband signal is greater than
the coherence time of the channel, then the channel will change
during the transmission of the baseband message, thus causing
distortion at the receiver
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If the coherence time is defined as the time over which the time
correlation function is above 0.5, then the coherence time is
approximately
A popular rule of thumb for modem digital communications is to
e ne e co erence me as e geome r c mean o e a ove wo
equations as
Generally coherence time implies that two signals arriving with a
time separation greater than Tc are affected differently by the
channel
Example : See Handout
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Impulse Response Model of the Wireless Channel
Small-scale variations of a signal is related to the impulse response
of the mobile radio channel
The impulse response is
A wideband channel characterization
type of channel
A wireless channel can be modelled as a linear time varying
(LTV) filter
The time variation is due to the receiver motion in space
We use discrete-time impulse response model
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Filtering is caused by the summation of amplitudes and delays of
multipath signals at any instant of time.
In multipath channel, the received signal is the sum of
Line-of-sight path component &
All resolvable multipath components
Hence the received low pass signal can be described by
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Thus the low pass equivalent impulse response of the wireless
channel is given by the LTV equation
In this LTV model h(,t):
t represents the time variations due to motion
represents the channel multipath delay for a fixed value of t
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Impulse response of a LTV filter h(,t) is the channel output at t
when the channel input is an impulse applied at t- .
h(,t) is a function of two time variables:
1. The instant when the impulse is applied to its input (initial time)
2. The instant of observing the output (final time)
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Example :
M l i h h i i
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Multipath component characteristics
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C t i ti f S ll S l F di Ch l
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Categorization of Small Scale Fading Channels
Based on the parameters that we have seen before small scale
fading channels can be classified as
Now the above diagram can described as
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Now the above diagram can described as
Flat and Time Invariant Channels
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Flat and Time Invariant Channels
Here the channel could be regarded as invariant over many
signalling intervals.
So the channel impulse response
becomes independent of time as
The corresponding channel frequency response is
With very small path delays
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With very small path delays,
This shows that H(f) is practically constant over the whole signal
bandwidth and therefore the channel is flat.
Thus the complex envelope of the received signal takes the form
which is attenuated and phase rotated version of s(t).
With no LOS component, the phase term, is uniformly distributed
over [-,] and follows a Rayleigh distribution with PDF
Frequency Selective (Time Dispersive ) Channel
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Frequency Selective (Time Dispersive ) Channel
Here the arrival time of scattered multipath signals are inevitablydistinct.
Whether these delays smear the transmitted signal depends on the
product of the signal bandwidth and the maximum differential
dela s read.
A time dispersive (frequency-selective) channel and
its effect on narrow and broad band signals
B f th diff t ti d l th h l i l
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Because of the different propagation delays, the channel impulse
response is superposition of delayed delta functions:
Since the multipath delays, {m} are distinct, the frequency responseof H(f) = {h(t)} will exhibit amplitude fluctuation.
Such fluctuation in the frequency domain will distort the waveform
of a broadband signal.
More specifically in digital communication, a channel is considered
frequency-selective if the multipath delays are distinguishable
relative to the symbol period Tsymbol:
On the other hand if the signal band idth is s fficientl narro
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On the other hand, if the signal bandwidth is sufficiently narrow,
the channel frequency response within the signal bandwidth can be
approximated as constant.
A wireless channel is considered flat if the multipath delays are
indistinguishable relative to the symbol period:
The most important problem of frequency selective fading is ISI
and can be mitigated by channel equalizer and adaptive
modulation.
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Here the system results a SNR degradation : (t) may be drop to
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Here the system results a SNR degradation : (t) may be drop to
very low values(deep fades) which leads to poor SNR that
vulnerable to AWGN
Which can be mitigated by
Channel Coding
Interleaving
Diversity techniques
A frequency dispersive (time-selective) channel and its
effect on short and long symbols
Summery
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y
Small-scale fading composed of multipath & Doppler spread
Multipath delay spread leads to time dispersion and frequency
selective fading
Doppler spread leads to frequency dispersion and time selective
Envelope Fading: affects the signal strength and therefore fading
margin in link budget calculation of the wireless system.
Power control and spatial diversity techniques are among the
most effective means to cope with envelope fading.
Frequency Selective Fading : alters the signal waveform and
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Frequency Selective Fading : alters the signal waveform and
therefore the detection performance.
Channel equalization is utilized to compensate the effect.
By transferring a broadband signal into parallel narrowbandstreams (Multicarrier systems)
Time Selective Fading: smears the signal spectrum and
introduces variation too fast for power control.
Time interleaving and diversity techniques are most effective
means of coping with time-selective fading.