Chapter Two Small Scale Fading

8/12/2019 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.

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Chapter Two Small Scale Fading

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