NAVEEN KUMAR
M.E.(ECE), REGULAR
ROLL NO - 112610

 Small Scale Fading
 Small-scale Multipath Propagation
 Fading
 Doppler Effect
 Parameters of Mobile Multipath Channels
 Time Dispersion Parameters
 Coherence Bandwidth
 Doppler Spread and Coherence Time
 Recent Work : IEEE Paper
 Summary
2  References

• Multipath = several delayed replicas of the signal arriving at
the receiver
• Fading = constructive and destructive adding of the signals
• Rapid fluctuation in amplitude with time
• Results in poor signal quality
• Digital communications
– High bit error rates
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 Fading signals occur due to reflections from ground &
surrounding buildings (clutter) as well as scattered signals
from trees, people, towers, etc.
 often an LOS path is not available so the first multipath signal
arrival is probably the desired signal (the one which traveled the
shortest distance)
 allows service even when Rx is severely obstructed by
surrounding clutter
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 Three most important effects:
 Rapid changes in signal strengths over small travel distances
or short time periods.
 Changes in the frequency of signals. Frequency modulation
occurs due to Doppler shifts.
 Time dispersion(echoes) caused by multipath propagation
delays.
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 Even stationary Tx/Rx wireless links can experience fading
due to the motion of objects (cars, people, trees, etc.) in
surrounding environment which creates the reflections.
 Multipath signals have randomly distributed amplitudes,
phases, & direction of arrival.
 Signals combine vectorially at the receiver antenna and gets
distorted or faded.
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 Multipath propagation
 Multiple versions of the signal arrives at the receiver. Can
cause signal smearing due to inter symbol interference.
 Speed of the Mobile
 Results in random frequency modulation due to Doppler
shifts on each of the multipath components. It can be
positive or negative depending on the movement of mobile
receiver.
 Speed of surrounding objects
 If the surrounding objects move at a greater rate than the
mobile, then this effect dominates the small-scale fading.
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 Transmission bandwidth of the signal
 If the transmitted radio signal bandwidth is greater than the
“bandwidth” of the multipath channel, the received signal will be
distorted, but the signal strength will not fade much over a local
area. (i.e., small-scale fading will not be significant.)
 The bandwidth of the “multipath” channel can be quantified by
the coherence bandwidth.
 The coherence bandwidth is a measure of the maximum
frequency difference for which signals are still strongly
9 correlated in amplitude.

 motion causes frequency modulation due to Doppler shift (fd)
 v : velocity (m/s)
 λ : wavelength (m)
 θ : angle between mobile direction
and arrival direction of RF energy
 +ve shift → mobile moving toward S
 −ve shift → mobile moving away from S
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 Two Doppler shifts to consider above
1. The Doppler shift of the signal when it is received at the
car.
2. The Doppler shift of the signal when it bounces off the car
and is received somewhere else.
 Multipath signals will have different fd’s for constant v
because of random arrival directions!!
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 Power delay profiles are generally represented as plots of relative received
power as a function of excess delay with respect to a fixed time delay
reference.
 Are measured by channel sounding techniques
 They are found by averaging instantenous power delay measurements over
a local area
 Local area: no greater than 6m outdoor
 Local area: no greater than 2m indoor
 Samples taken at l/4 meters approximately
 For 450MHz – 6 GHz frequency range.
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Parameters which grossly quatifies the multipath channel are :
 The mean excess delay,
 rms delay spread, and
 excess delay spread (X dB)
 These can be determined from a power delay profile.
 The mean excess delay is the first moment of the power delay
profile and is defined as
∑ ak τ k
2
∑ P (τ k )τ k
k k
τ = =
∑ ak
2
∑ P (τ k )
k k
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 The rms delay spread is the square root of the second central
moment of the power delay profile, where
∑ ak τ k
2 2
∑ P (τ k )τ k
2
k k
σ τ = τ 2 − (τ ) 2 τ2 = =
∑ ak
2
∑ P (τ k )
k k
 Typical values of rms delay spread are on the order of
microseconds in outdoor mobile radio channel and on the
order of nanoseconds in indoor radio channel
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 Maximum Excess Delay (X dB): Defined as the time delay value after
which the multipath energy falls to X dB below the maximum multipath
energy. It is also called excess delay spread.
 It is defined as (τx - τ0), where τ0 is the first arriving signal and τx is the
maximum delay at which a multipath component is within X dB of the
strongest arriving multipath signal.
 The values of time dispersion parameters also depend on the noise
threshold (the level of power below which the signal is considered as
noise).
 If noise threshold is set too low, then the noise will be processed as
18 multipath and thus causing the parameters to be higher.

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 Coherence bandwidth is used to characterize the channel in the frequency
domain.
 It is a statistical measure of the range of frequencies over which the channel
can be considered flat.
 Two sinusoids with frequency separation greater than Bc are affected quite
differently by the channel.
f1
Multipath Channel Receiver
f2
Frequency Separation: |f1-f2|
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 Frequency correlation between two sinusoids: 0 <=Cr1,
r2 <=1.
 Coherence bandwidth is the range of frequencies over which
two frequency components have a strong potential for
amplitude correlation.
1
BC =
 σ is rms delay spread 50σ
1
BC =
 If correlation is above 0.9, then 5σ
 If correlation is above 0.5, then
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 This is called 50% coherence bandwidth.

 Delay spread and Coherence bandwidth describe the time
dispersive nature of the channel in a local area.
 They don’t offer information about the time varying
nature of the channel caused by relative motion of
transmitter and receiver.
 It is measure of spectral broadening caused by motion, the time
rate of change of the mobile radio channel, and is defined as the
range of frequencies over which the received Doppler spectrum
is essentially non-zero.
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 We know how to compute Doppler shift: fd
 Doppler spectrum have components in the range of fc-fd to fc+fd
 Doppler spread, BD, is defined as the maximum Doppler shift:
fm = v/l
 If the baseband signal bandwidth is much less than BD then
effect of Doppler spread is negligible at the receiver. This is
slow fading channel characteristics.
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0.423
Coherence time is also defined as: C ≈
T =
9
 2
16πf m
fm
 The time domain dual of BD
 Coherence time definition implies that two signals arriving with
a time separation greater than Tc are affected differently by the
channel.
 If the coherence time is defined as the time over which the time
correlation function is above 0.5, then the coherence time is
v
9
Tc ≈ fm =
approximately, 16πf m where λ
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 If the symbol period of the baseband signal (reciprocal of the baseband
signal bandwidth) is greater the coherence time, than the signal will distort,
since channel will change during the transmission of the signal .
Coherence time (TC) is defined as:
TC ≈ 1
fm
f2
TS f1
TC
t1 ∆t=t2 - t1 t2
26

Valcarce, A.; Lopez-Perez, D.; De La Roche, G.; Jie Zhang
“Predicting small-scale fading distribution
with Finite-Difference methods
in Indoor-to-Outdoor scenarios”
Vehicular Technology Conference, 2009. VTC Spring 2009
Publication Year: 2009 , Page(s): 1 - 5

 Finite-Difference electromagnetic methods have been used for the
deterministic prediction of radio coverage in cellular networks.
 This paper introduces an approach that exploits the spatial power
distribution obtained from these techniques to characterize the random
variations of fading due to multipath propagation.
 Furthermore, in order to test the reliability of this approach, the predicted
fading distributions are compared against real measurements in a residential
Indoor-to-Outdoor scenario.
 Finally, the practical usability of this fading prediction approach is tested
throughout implementation in a WiMAX femtocells system-level simulator.
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 The need for radio network planning tools that aid operators to design and
optimize their wireless infrastructure is rising.
 In order to increase the reliability of these tools, accurate radio wave
propagation models are necessary.
 In this paper, the aim is first to use a deterministic propagation model, to
provide a coverage map of the received signal at a very fine resolution.
 Then, in a second step, the distribution of the received signal can be
analyzed to extract fading parameters that can be taken into account by a
system- level simulation tool.
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 The Finite-Difference Time-Domain is a method that approximates
the solution to the Maxwell equations by means of a discretization
in the spatial and time domains.
 The main purpose of this work was to create a reliable fading model,
suitable for its implementation on a system-level simulator (SLS) for
WiMAX femtocells.
 The main advantage of using FDTD for the prediction of fading
distributions is that it allows for the computation of localized fading
distributions, i.e. the fading distribution will vary from point to
30 point.

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Power measurements with fading laid over the simulation scenario.

Power measurements with fading (before spatial filtering) and without fading (after spatial filtering).
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Random snapshot in a WiMAX system-level simulation containing a distant macro cell and 9
femtocells. The pseudocolor background represents the predicted power received from the best server
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 Theodore S. Rappaport, “Wireless Communications”, 2nd
Edition, Chapter 5 (Page 177-203)
 www.cs.bilkent.edu.tr/~korpe/courses/cs515-fall2002/slides6.ppt
 netlab.cse.yzu.edu.tw/~bpmania/ 罐頭 / 修
課 /942/.../WL_CHAP5.ppt
 www.egr.uh.edu/courses/ECE/ECE6331/.../EE6331_class8.ppt
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 We have studied effects of various factors on small scale
multipath channel.
 Doppler effect affects the channel even the mobile unit is
stationary (because of the surrounding objects).
 Parameters are analysed in both time and frequency domain.
 Prediction of these parameters is important for designing the
system.
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