Wl Rapp Chap5

7/30/2019 Wl Rapp Chap5

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Adaphed from RappaportsChapter 5

Mobile Radio Propagation:

Small-Scale Fading and Multipath


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Small-scale fading (or simply fading) is used to describe

the rapid fluctuation of the amplitude of a radio signal overa short period of time or travel distance.

Fading is caused by interference between two or moreversions of the transmitted signal which arrive at thereceiver at slightly different times.

These waves, called multipath waves, combine at thereceiver antenna to give a resultant signal which can vary

widely in amplitude and phase, depending on thedistribution of the intensity and relative propagation timeof the waves and the bandwidth of the transmitted signal.


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5.1 small-scale multipath propagation

Multipath in the radio channel creates small-scale fadingeffects.

Three most important effects are:

* Rapid changes in signal strength over a small travel distance ortime interval.

* Random frequency modulation due to varying Doppler shifts on

different multipath signals.

* Time dispersion (echoes) caused by multipath propagation

delays.


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5.1.1 Factors influencing Small-Scale Fading

Multipath propagation

* Can cause signal smearing due to intersymbol interference.

Speed of the Mobile

* Results in random frequency modulation due to Doppler shifts oneach of the multipath components.

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

* The bandwidth of the multipath channel can be quantified by thecoherence bandwidth.

* The coherence bandwidth is a measure of the maximum frequencydifference for which signals are still strongly correlated inamplitude.

* If the transmitted radio signal bandwidth is greater than thebandwidth of the multipath channel, the receive signal will bedistorted, but the signal strength will not fade much over a localarea. (i.e., small-scale fading will not be significant.)

* If the transmitted signal has a narrow bandwidth as compared tothe channel, the amplitude of the signal will change rapidly, but thesignal will be distorted in time.


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5.1.2 Doppler shift


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The phase change in the received signal

(5.1)

The apparent change in frequency

(5.2)

Doppler spreading -->increasing the signal bandwidth


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5.2 Impulse Response Model of a Multipath Channel

Small-scale variations of a mobile radio signal can be directly related

to the impulse response of the mobile radio channel.

The impulse response is a wideband channel characterization and

contains all information necessary to simulate or analyze any type of

radio transmission through the channel.

This stems from the fact that a mobile radio channel may be modeled

as a linear filter with a time varying impulse response, where the time

variation is due to receiver motion in space.

This filtering nature of the channel is caused by the summation ofamplitudes and delays of the multiple arriving waves at any instant of

time.


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If the channel impulse response is expressed sa h(d,t), then the receivedsignal

(5.3)

or

(5.6)


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Since v is a constant over a short time (or distance), then

(5.8)

* where the impulse response

completely characteristics the channel, and is a function oftand .

* The t represents the time variations due to motion,

* The represents the channel multipath delay for a fixed value of t.


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It is useful to discretize the multuple delay axis of the

impulse response into equal time delay segments called

excess delay bins.

Excess delay, maximum excess delay

The baseband impulse response can be expressed

(5.12)


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Power delay profile

In actual wireless communication systems, the impulseresponse of a multipath channel is measured in the field

using channel sounding techniques.


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5.2.1 Relationship between Bandwidth and Recuived Power


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5.3 Small-Scale Multipath Measurements

Channel Sounding Techniques

* Direct RF pulse system (Fig5.6 p192)

* Spread Spectrum Sliding Correlator* Frequency Domain Channel Sounding


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5.4 Parameters of Mobile Multipath Channels

Many multipath channel parameters are derived from

the power delay profile, which is found by averaging

instantaneous power delay profile measurements over a

local area in order to determine an average small-scalepower delay profile.


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Time dispersion parameters

* mean excess delay

(5.35)

* rms delay spread

(5.36)

where

(5.37)


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* Maximum excess delay, excess delay spread


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5.4.2 Coherence Bandwidth

* Analog to the delay spread parameters in the time domain,

coherence bandwidth is used to characterize the channel in thefrequency domain.

* The rms delay spread and coherence bandwidth are inversely

proportional to each other.

* coherence bandwidth is a statistical measure of the range of

frequencies over which the channel can be considered flat (I.e., a

channel which passes all spectral components with approximately

equal gain and linear phases.)

* In other words, coherence bandwidth is the range of frequencies

over which two freq components have a strong potential for

amplitude correlation.


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* For frequency correlation function 0.9, then

(5.38)

* If the frequency correlation is relaxed to 0.5, then

(5.39)

* Note that (5.38) and (5.39) are ball part estimates.


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Delay spread and coherence bandwidth are parameters

which describe the time dispersive nature of the channel in

a local area. However, they do not offer information about

the time varying nature of the channel by the Dopplereffect.

5.4.3 Doppler Spread and Coherence Time

* are parameters which describe the time varying nature of the

channel in a small-scale region.

* Doppler Spread BD

:

a measure of the spectral broadening caused by 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. (in the range fc-fd to fc+fd)


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* If the baseband signal bandwidth is much greater than BD, the

effects of Doppler Spread are negligible.

* Coherence Time Tc: the time domain dual of BD

(5.40a)

where: fm is the maximum Doppler Shift given by

the time duration over which two received signals have a strongpotential for amplitude correlation.

* The definition of coherence time implies that two signals arriving

with a time separation greater than Tc are affected differently by

the channel.

m

Cf

T1

vfm


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5.5 Types of small-scale Fading


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Flat fading

* Most common type of fading described in the literature

* The spectral characteristics of the transmitted signal are preserved

at the receiver

* Typically, the fact fading channels cause deep fades, and may

require 20 or 30 dB more transmitter power to achieve low bit

error rates.


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* The most common amplitude distribution is the Rayleigh

distribution.

* To summarize, a signal undergoes flat if

(5.41)

and

(5.42)


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Frequency selective fading

* Due to time dispersion of the transmitted symbols within thechannel. Thus it could introduce the intersymbol interference (ISI)

* Viewed in the frequency domain, certain frequency components in

the received signal spectrum have greater gains than others.

* To summarized, a signal undergoes frequency selective fading if

(5.43)

and(5.44)


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Fast fading

* The channel impulse response changes rapidly within the symbolduration. That is,

BsTc

* This causes frequency dispersion (also called time selective fading)

due to Doppler Spreading, which leads to signal distortion.

Slow fading

* The channel impulse response changes at a rate much slower thanthe transmitted baseband signal

TsBD


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5.6 Rayleigh and Ricean Distribution

Rayleigh distribution is commonly used to describe the

statistical time varying nature of the received envelope of a

flat fading signal, or the envelop of an individual multipathcomponent.


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The Rayleigh distribution has a pdf given by

(5.49)

where

is the rms value of the received signalis the time-average power of the received signal.


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When there is a dominant stationary (non-fading) signal component

present, such as a Line-of-sight propagation path, the small-scale fading

envelope distribution is Ricean.


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5.7 Statistical Model for Multipath Fading channels

Like that of the large-scale modeling, several multipath

models have been suggested to explain the observed

statistical nature of a mobile channel.

Clarkes fading model

Level crossing rate (LCR) and average fade duration of

a Raleigh fading signal.


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Two-ray Raleigh Fading Model


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Saleh and Valenzuela Indoor Statistical Model

SIRCIM (Simulation of Indoor Radio Channel Impulse-

Response Models), SMRCIM (Simulation of Mobile Radio

Channel Impulse-Response Models)


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