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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

References2

• 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:

1. Rapid changes in signal strengths over small travel distances

or short time periods.

2. Changes in the frequency of signals. Frequency modulation

occurs due to Doppler shifts.

3. 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

correlated in amplitude.9

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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!!

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

a

a

P

P

k kk

kk

k kk

kk

2

2

( )

( )

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The rms delay spread is the square root of the second central

moment of the power delay profile, where

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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2

2 2

2

2

a

a

P

P

k kk

kk

k kk

kk

( )

( )22 )(

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 (x - 0), where 0 is the first arriving signal and x 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

multipath and thus causing the parameters to be higher.18

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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.

Receiver

f1

f2

Frequency Separation: |f1-f2|

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Multipath Channel

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.

is rms delay spread

If correlation is above 0.9, then

If correlation is above 0.5, then

This is called 50% coherence bandwidth.

50

1CB

5

1CB

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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.23

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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Coherence time is also defined as:

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

approximately, where

mfC f

Tm

423.0216

9

Tfcm

9

16f

vm

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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 .

mfCT 1

Coherence time (TC) is defined as:

TS

TC t=t2 - t1t1 t2

f1

f2

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Valcarce, A.; Lopez-Perez, D.; De La Roche, G.; Jie Zhang “Predicting small-scale fading distribution

with Finite-Difference methodsin Indoor-to-Outdoor scenarios”

Vehicular Technology Conference, 2009. VTC Spring 2009. IEEE 69th 

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

point.30

Power measurements with fading laid over the simulation scenario.31

Power measurements with fading (before spatial filtering) and without fading (after spatial filtering).32

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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