mobile radio propagation 2

Cellular MobileCellular Mobile Communications-Communications-VVMobile Radio Propagation Mobile Radio Propagation

Dr. Nasir D. Dr. Nasir D. GoharGohar

Wireless Communications, Principles and Applications Ch.5 [Small Scale Path Loss] by RAPPAPORTPropagation Characteristics Observed in Macro / Micro Cells by H. L. Bertoni

T.S. Rappaport Ch 4-5T.S. Rappaport Ch 4-5 NDG NotesNDG Notes 22

Mobile Radio PropagationMobile Radio Propagation

Modeling a Radio Channel:Modeling a Radio Channel: Most difficult part Most difficult part in Radio System Designin Radio System Design Highly unpredictable as compared to fixed wire-line Highly unpredictable as compared to fixed wire-line

mediamedia Transmission path and its parameters keeps Transmission path and its parameters keeps

changing instantaneouslychanging instantaneouslyChanges in path profileChanges in path profileObstructions Obstructions Environmental changesEnvironmental changes

Typically done statistically based on field Typically done statistically based on field measurements[System Specific]measurements[System Specific]Physical survey *Physical survey *11Computer simulation using certain models and terrain Computer simulation using certain models and terrain

datadata *2 *2

*1*1 Gives some real picture of the environment and data can be incorporated to new system design and predict its Gives some real picture of the environment and data can be incorporated to new system design and predict its performanceperformance

*2*2 Empirical Models and Terrain data may not be quite updated Empirical Models and Terrain data may not be quite updated


The Multi-path EnvironmentThe Multi-path Environment The received signal is made up of a sum of attenuated, phase The received signal is made up of a sum of attenuated, phase

shifted and time delayed versions of the transmitted signal.shifted and time delayed versions of the transmitted signal. Propagation modes include diffraction, transmission and reflection.Propagation modes include diffraction, transmission and reflection.



The Mult-ipath Environment - The Mult-ipath Environment - contdcontd..Assuming receiver is stationary and there is no

direct path, the received signal can be expressed as a sum of delayed components or in terms of phasor notation:

N

iicir fate

1

)2(cos)(

N

iicir fate

1

)2(cos)(A single pulse

,)()(1

N

iiir ttpate ,)()(

1

N

iiir ttpatePulse train

Where: ai is the amplitude of the scattered signal, p(t) is the transmitted signal (pulse) shape, ti is the time taken by the pulse to reach the receiver, N is the number of different paths taken by the signal to reach receiver, and fc is the carrier frequency



AntennaAntennaab y = a + b

a & b are in phase a & b are out of phase by

Complete fading

Diffractedwave Reflected

wave

No direct path

a b

AntennaAntennab y = 0a

Mobile Radio PropagationMobile Radio PropagationThe Multi-path Environment - The Multi-path Environment - contdcontd..


Is due to multi-path propagation.With respect to a stationary base station, multipath propagation creates a stochastic standing wave pattern, through which the mobile station moves.

Caused by shadowing: when the propagation environment is changing

significantly, but this fading is typically much slower than

the multipath fading.

Modem design is affected mainly by the faster

multipath fading, which can be normally assumed to

be locally wide-sense stationary (WSS).

FadingFadingMobile Radio PropagationMobile Radio Propagation


Slow (Long) Term

0 5 10 15 20 25 Distance ()

Sig

nal s

tren

gth

rela

tive

to 1

uV (

db)

0

10

20

30

Slow fading

Fast fading

Exact representation of fading characteristics is not possible, because of infinite number of situation.

Exact representation of fading characteristics is not possible, because of infinite number of situation.

Fast (Short) Term (Also known as Rayleigh Fading)

Fading - TypesFading - Types



Slower variation in mean signal strength as the receiver

moves behind buildings and the propagation paths are

obscuredVariations of up to 20dB will cause handovers and

change quality-of-serviceCaused by shadowing:

Terrain configuration: Results in local mean (long term fading) attenuation and fluctuation.The built environment (rural and urban areas etc.), between base station and the mobile unit: Results in local mean attenuation

Slower variation in mean signal strength as the receiver

moves behind buildings and the propagation paths are

obscuredVariations of up to 20dB will cause handovers and

change quality-of-serviceCaused by shadowing:

Terrain configuration: Results in local mean (long term fading) attenuation and fluctuation.The built environment (rural and urban areas etc.), between base station and the mobile unit: Results in local mean attenuation

Fading - Slow (Long) TermFading - Slow (Long) Term



Describes the constant amplitude fluctuations in the received

signal as the mobile moves. Caused by multipath reflection of transmitted signal by local

scatters (houses, building etc.)Observed over distances = /2Signal variation up to 30 dB. Is a frequency selective phenomenon.Can be described using Raleigh statistics, (no line of sight).Can be described using Rician statistics, (line of sight).Causes random fluctuations in the received power, and also

Distorts the pulse carrying the information.

Fading- Fast (Short) TermFading- Fast (Short) Term



N

iicir fate

1

)2(cos)(

A received signal amplitude is given as the sum of delayed components. In terms of phasor notation it is given as:

Or

N

iiic

N

iiicr atfatfte

11

22 )sin()sin()(cos)cos()(

N

iiic

N

iiicr atfatfte

11

22 )sin()sin()(cos)cos()(

In-phase Quadrature

Fading- Fast (Short) Term - Fading- Fast (Short) Term - contd.contd.



The phasei can be assumed to be uniformly distributed in the range (0, 2), provided the locations of buildings etc. are completely random.

This for large N, the amplitude of the received signal is:

)sin()cos()( tfYtfXte ccr 22

where

N

iii

N

iii aYaX

11

)sin(),(cos

X and Y are independent, identically distributed Gaussian random variables.




The envelope of the received signal is:

5022 .)( YXA Which will be Raleigh distributed.

Rayleigh

Exponential

A or power P

Probabilitydensityfunction




If the impulse response If the impulse response hh((, , tt) ) of the mobile of the mobile radio station is time invariant (radio station is time invariant (without a without a significant deterministic significant deterministic ) and has zero mean, ) and has zero mean, then the envelope of the impulse response then the envelope of the impulse response has a Rayleigh Distribution given as: has a Rayleigh Distribution given as:

where where is the total power in the multi-path is the total power in the multi-path

signalsignal

2

2

2 2exp

rr

rp

Mobile Radio PropagationMobile Radio PropagationRaleigh Distribution


If however the impulse response has a non zero mean then there is a If however the impulse response has a non zero mean then there is a

significant component of the direct path significant component of the direct path (line of sight, specular (line of sight, specular

component)component) signal and the magnitude of the impulse response has a signal and the magnitude of the impulse response has a

Ricean distributionRicean distribution

Ricean distribution is the combination of Rayleigh signal with the direct Ricean distribution is the combination of Rayleigh signal with the direct

line of sight signal. The distribution is:line of sight signal. The distribution is:

22 is the power of the line of sight signal and I is the power of the line of sight signal and I00 is a is a Bessel function of the first kindBessel function of the first kind

202

22

2 2exp

rs

Isrr

rp

Rice FadingRice Fading



Multi-path create small-scale fading Multi-path create small-scale fading effectseffectsRapid changes in the Rapid changes in the signal strengthsignal strength

due to movement and/or timedue to movement and/or timeRandom frequencyRandom frequency modulation due to modulation due to

Doppler Doppler shift on different multipath shift on different multipath propagation pathspropagation paths

Time dispersionTime dispersion due to multipath due to multipath propagation delaypropagation delay

FadingFading



Fast Fading – Cases 1: Fast Fading – Cases 1: Stationary MobileStationary Mobile

V

Stationary tFie

ld s

tren

gth

V

V

V

V

Mobile is stationery surrounded by moving cars.

The number of fading depends on the :Traffic flowDistance between the mobile and moving cars



Fast Fading – Cases 2: Fast Fading – Cases 2: Non-stationary MobileNon-stationary Mobile

The received signal at the mobile is:

)cos2( xfjr

tAes

Amplitude

x = Vt

Wave number =2/

Transmitting frequency


VtF

ield

str

engt

h

Signal level No scattered signals


SMALL SCALE MULTI-PATH PROPAGATIONSMALL SCALE MULTI-PATH PROPAGATION Multi-path reception of several versions of the same transmitted Multi-path reception of several versions of the same transmitted

radio signal arriving at certain location [Rx] causes fading effects. radio signal arriving at certain location [Rx] causes fading effects.

Rapid Fluctuations in Signal Strength [over very short distance or Rapid Fluctuations in Signal Strength [over very short distance or time period]time period]

Random Frequency Modulation due to Varying Doppler Shifts on Random Frequency Modulation due to Varying Doppler Shifts on Different Multi-Path SignalsDifferent Multi-Path Signals

Time Dispersion / Echoes due to Multi-Path Propagation DelayTime Dispersion / Echoes due to Multi-Path Propagation Delay

Multi-path propagation occurs even when there is LOS path Multi-path propagation occurs even when there is LOS path In multi-path channel environment, the received signal at any In multi-path channel environment, the received signal at any

point would be a vector sum of all the versions/components of point would be a vector sum of all the versions/components of the signal, reaching at the point, which may widely differ in the signal, reaching at the point, which may widely differ in magnitude and phase. magnitude and phase.



Multipath Channel: Multipath Channel: Impulse Response ModelImpulse Response Model A A mobile radio channelmobile radio channel can be modeled as can be modeled as a linear filtera linear filter with with

time varying time varying Impulse ResponseImpulse Response [ [IRIR]. ]. IRIR containscontains all the all the necessary informationnecessary information required to required to simulate simulate

or analyzeor analyze any type of radio transmission through the channel. any type of radio transmission through the channel. IR IR is a useful channel characterization which is a useful channel characterization which can be used to can be used to

predict and compare the performancepredict and compare the performance of many mobile of many mobile communication systems/transmission bandwidths for any given communication systems/transmission bandwidths for any given particular channel condition.particular channel condition.

x(t)h(t)

y(t)

Fig-1: Impulse Response Model of a LTI system. The output signal y(t) can be obtained from the convolution of the input signal x(t) with the IR = h(t) of the system. If x(t) is band limited signal, y(t) is also band limited regardless h(t) is band limited or not. So, we can assume LTI system to be band limited if the input is band limited.



Multipath Channel: Multipath Channel: Impulse Response ModelImpulse Response Model Suppose an MS is moving along the ground at a constant velocity Suppose an MS is moving along the ground at a constant velocity

v.v. At a certain fixed location distant d, the system can be assumed At a certain fixed location distant d, the system can be assumed

as LTI system.as LTI system. Due to multi-path reception, various multi-path components will Due to multi-path reception, various multi-path components will

have different delays associated with them because of difference have different delays associated with them because of difference in distance covered.in distance covered.

So, the IR of this LTI system is a function of time as well as of So, the IR of this LTI system is a function of time as well as of distance, distance, i.e.i.e. IR = h(d,t) IR = h(d,t)

Fig-2: The Mobile Radio Channel as a Function of Time and Spaced spatial position

v



Multipath Channel: Multipath Channel: Impulse Response ModelImpulse Response Model

y(d, t) = x(t)y(d, t) = x(t)h(d,t) = h(d,t) = - - x(x() h(d, t- ) h(d, t- ) d) d

y(d, t) = y(d, t) = tt - - x(x() h(d, t- ) h(d, t- ) d) d when h(d,t) = 0 for t>0. when h(d,t) = 0 for t>0.

When MS is moving at a constant speed v, then d = vt, so, When MS is moving at a constant speed v, then d = vt, so,

y(vt, t) = y(vt, t) = tt - - x(x() h(vt, t- ) h(vt, t- ) d) d

Since v is constant, so, y(vt, t) is a function of time, Since v is constant, so, y(vt, t) is a function of time,

y(t) = y(t) = tt - - x(x() h(vt, t- ) h(vt, t- ) d) d = x(t) = x(t)h(vt,t) = x(t)h(vt,t) = x(t)h(d,t) h(d,t)

As the velocity can be assumed constant over a small time interval (short As the velocity can be assumed constant over a small time interval (short distance), so, Mobile Radio Channel can be assumed as a time varying distance), so, Mobile Radio Channel can be assumed as a time varying multi-path channel where t represents time variation due to MS in motion multi-path channel where t represents time variation due to MS in motion and and represents the channel multi-path delay for a fixed value of t. represents the channel multi-path delay for a fixed value of t.



Multipath Channel: Multipath Channel: Impulse Response ModelImpulse Response Model

y(t) = y(t) = - - x(x() h(t, ) h(t, ) d) d = x(t) = x(t)h(t, h(t, ) and r(t) = c(t) ) and r(t) = c(t) ½(½(hhbb (t, (t, ) )) )

Here c(t) and r(t) are the complex envelop of x(t) and y(t) such Here c(t) and r(t) are the complex envelop of x(t) and y(t) such that x(t) = Re { c(t) exp (j2that x(t) = Re { c(t) exp (j2 fc t)} and y(t) = Re { r(t) exp (j2 fc t)} and y(t) = Re { r(t) exp (j2 fc t)} fc t)}

Average Power of BP signal xAverage Power of BP signal x22 (t) = ½ |c(t) | (t) = ½ |c(t) |22, over bar denotes , over bar denotes ensemble average of stochastic signal.ensemble average of stochastic signal.

x(t)h(t, ) = Re { hb (t, ) exp (jwct)}

y(t)

c(t)h(t, ) = ½ hb (t, )

r(t)

Fig-3: Base band channel response model and its equivalent RI



Multipath Channel: Multipath Channel: Impulse Response ModelImpulse Response Model If If 0 0 represents the represents the excess time delayexcess time delay of the first arriving multi- of the first arriving multi-

path signal and then path signal and then = = 1 1 - - 0 0 but as but as 0 0 = 0, so, = 0, so, = = 1 .1 .

i i = = i x i x . . , , and if there are N multi-path components, then and if there are N multi-path components, then maximum excess delay of the channel is N x maximum excess delay of the channel is N x

This model can be used to analyze the transmitted signals having This model can be used to analyze the transmitted signals having BW which are less than 1/2 BW which are less than 1/2

hhbb (t, (t, ) = ) = a aii (t, (t, ) exp [j() exp [j(c c ii(t)+ (t)+ ii(t, (t, ) )] ) )] (t, (t, ii(t)). Sum over I = 0 to N-1 (t)). Sum over I = 0 to N-1 where awhere aii (t, (t, ) and ) and ii(t)) are real amplitude and excess delay of ith multi-(t)) are real amplitude and excess delay of ith multi-path component at time t.path component at time t.

The power delay profile of the channel is found by taking the spatial The power delay profile of the channel is found by taking the spatial average of | haverage of | hbb (t, (t, ) |) |22 over a local area. over a local area.

The received power delay profile is given P(t, The received power delay profile is given P(t, ) ) k| h k| hbb (t, (t, ) |) |22 , k is the , k is the gain relating the transmitted power in the probing pulse to the total power gain relating the transmitted power in the probing pulse to the total power received.received.



Multipath Channel: Multipath Channel: Impulse Response ModelImpulse Response Model If a CW signal is transmitted into the channel, let the complex If a CW signal is transmitted into the channel, let the complex

envelop be given by c(t) = 2, then, instantaneous complex envelop be given by c(t) = 2, then, instantaneous complex envelop of received signal is given as envelop of received signal is given as

r(t) = r(t) = a aii exp [j exp [jii(t, (t, ) )] , summation over i = 0 to N-1) )] , summation over i = 0 to N-1

and instantaneous received power is and instantaneous received power is

| | r(tr(t)|2=)|2= | | a aii exp [j exp [jii(t, (t, ) )]|) )]|22 , summation over i = 0 to N-1 , summation over i = 0 to N-1

EXERCISE:EXERCISE: Do Example-4.2 and Example-4.3 carefully at home.Do Example-4.2 and Example-4.3 carefully at home.



Small-Scale Multipath MeasurementsSmall-Scale Multipath Measurements

Channel Sounding TechniquesChannel Sounding Techniques Used to determine Power Delay Profile/Channel Impulse Response of Used to determine Power Delay Profile/Channel Impulse Response of

any channelany channel

Direct RF Pulse SystemDirect RF Pulse System

Fig-01: Direct RF Channel Impulse Response Measurement System



Small-Scale Multipath MeasurementsSmall-Scale Multipath Measurements

Channel Sounding TechniquesChannel Sounding Techniques

Spread Spectrum Channel Impulse Response Measurement Spread Spectrum Channel Impulse Response Measurement SystemSystem

Fig-02: Spread Spectrum Channel Impulse Response Measurement System



Small-Scale Multipath MeasurementsSmall-Scale Multipath MeasurementsChannel Sounding TechniquesChannel Sounding Techniques

Spread Spectrum Channel Impulse Response Measurement Spread Spectrum Channel Impulse Response Measurement SystemSystem AdvantagesAdvantages

Rejects pass-band noiseRejects pass-band noiseImproves the coverage range of a given Tx powerImproves the coverage range of a given Tx powerNo need of Tx and Rx PN synchronization-thanks to sliding correlatorNo need of Tx and Rx PN synchronization-thanks to sliding correlatorDue to inherent processing gain, Tx power required is considerably Due to inherent processing gain, Tx power required is considerably

lessless DisadvantagesDisadvantages

No real time measurementsNo real time measurementsMeasurement time for power delay profile may be relatively Measurement time for power delay profile may be relatively

excessiveexcessiveDue to non-coherent detection, information about the phases of Due to non-coherent detection, information about the phases of

individual multi-path components is lostindividual multi-path components is lost



Important Multi-path Channel ParametersImportant Multi-path Channel Parameters The Mean Excess Delay The Mean Excess Delay : : It is also called first moment of the power delay profile It is also called first moment of the power delay profile

and is defined as and is defined as

………………………………....E-01E-01

The RMS Delay Spread The RMS Delay Spread : : It is the square root of the second central moment of the It is the square root of the second central moment of the power delay profile and is given aspower delay profile and is given as

………………………………....E-02E-02

where where

………………………………....E-03E-03

* * These delays are measured wrt the first detectable multi-path These delays are measured wrt the first detectable multi-path signal signal component arriving at Rx at component arriving at Rx at 0 0 = 0.= 0.

**** Typical values for Typical values for are in usec for outdoor channels and nsec for indoor mobile are in usec for outdoor channels and nsec for indoor mobile channels.channels.



Important Multi-path Channel ParametersImportant Multi-path Channel Parameters The Maximum Excess Delay The Maximum Excess Delay XX : : The max. excess delay at which a The max. excess delay at which a

multi-path component is within X dB from the strongest multi-path multi-path component is within X dB from the strongest multi-path component (may not necessarily arriving at component (may not necessarily arriving at 00 ). ).

Also known as excess delay spread of the power delay profile. Also known as excess delay spread of the power delay profile.

Fig-3: Example of an indoor power delay profile, mean excess delay, rms delay spread and excess delay spread



Important Multi-path Channel ParametersImportant Multi-path Channel Parameters Coherence Bandwidth BCoherence Bandwidth Bcc

It is a defined relation derived from the rms delay spread It is a defined relation derived from the rms delay spread ..

Range of frequencies over which the mobile channel can be considered Range of frequencies over which the mobile channel can be considered

flat (a channel that passes all frequencies with almost equal gain and flat (a channel that passes all frequencies with almost equal gain and linear phase).linear phase).

BBcc 1/ 50 1/ 50 [[for frequency correlation function of above 0.9]for frequency correlation function of above 0.9]

1/5 1/5 [[for frequency correlation function of above 0.5]for frequency correlation function of above 0.5]

EXAMPLE-01: A multi-path power delay profile is given in Fig-04. Calculate mean excess delay, rms delay spread, and max. excess delay(10 dB). Estimate the 50% coherence bandwidth of the channel. Would it be suitable for AMPS or GSM without equalizers?



Important Multi-path Channel ParametersImportant Multi-path Channel Parameters Doppler Spread BDoppler Spread BDD and Coherence Time T and Coherence Time TCC

Describe the time varying nature of the channel in a small-scale Describe the time varying nature of the channel in a small-scale region.region.

BBD D = f= fmm = v/c * f = v/c * fcc, , the maximum doppler shiftthe maximum doppler shift

TTC C 1/ f1/ fmm

TTC C 0.423/ f0.423/ fmm [A popular rule of thumb][A popular rule of thumb]

EXAMPLE-02: Assuming the consecutive samples having high time correlation, calculate the proper spatial interval required for proper small-scale propagation measurements. If the test van runs at v = 120 km/h and fc = 900 MHz, how many samples would be required in 10 m interval. Assuming that measurements can be made in real time, how much time it take to make these measurements. What is Doppler spread for the channel?

SOLUTION : Worst case Tc = 9/16 *Pi* fm = 9C/16*Pi* v fc = ?Samples should be taken at a rate less than 0.5 *Tc = ?x = vTc/2 =? So, number of samples reqd. over 10 m distance = 10/ x .



Types of Small-Scale FadingTypes of Small-Scale Fading Depending on the signal parameters [BW, Symbol Period] and Depending on the signal parameters [BW, Symbol Period] and

channel parameters [ rms delay spread and Doppler spread], channel parameters [ rms delay spread and Doppler spread], in a in a multi-path environment transmitted signals under go multi-path environment transmitted signals under go different kinds of fading:different kinds of fading:

Multi-path delay spread causes:Multi-path delay spread causes:Flat Fading :Flat Fading : BW of signal < BW of channel and delay spread < BW of signal < BW of channel and delay spread <

symbol period, most common fading, amplitude and phase of the symbol period, most common fading, amplitude and phase of the transmitted signal is changed depending upon the multi-path but no transmitted signal is changed depending upon the multi-path but no frequency shift is observed frequency shift is observed [spectral characteristics preserved].[spectral characteristics preserved].

Frequency Selective Fading: Frequency Selective Fading: BW of signal > BW of the channel BW of signal > BW of the channel and delay spread > symbol periodand delay spread > symbol period

Doppler Spread leads toDoppler Spread leads toFast Fading:Fast Fading: Higher B Higher BDD, T, TCC < symbol period, rapid fluctuations of < symbol period, rapid fluctuations of

signal strength due to very high variations in channel Impulse signal strength due to very high variations in channel Impulse Response faster than base-band signal variationsResponse faster than base-band signal variations

Slow Fading:Slow Fading: Just opposite to fast fading Just opposite to fast fading



Fading Effects due to Multi-Path Time Delay SpreadFading Effects due to Multi-Path Time Delay Spread Flat FadingFlat Fading:: In a multi-path radio channel, signal will undergo a flat In a multi-path radio channel, signal will undergo a flat

fading if fading if

Bs << Bc and Ts >> rms delay spread of the channelBs << Bc and Ts >> rms delay spread of the channel

Spectral characteristics of the signal remain unchanged.Spectral characteristics of the signal remain unchanged.

Amplitude and phase of the transmitted signal will Amplitude and phase of the transmitted signal will change in change in Flat Fading ChannelFlat Fading Channel. . [Also known as [Also known as Amplitude Amplitude Varying Varying Channel or Narrowband ChannelChannel or Narrowband Channel]]

Fig-1: Flat Fading Channel Characteristics



Fading Effects due to Multi-Path Time Delay SpreadFading Effects due to Multi-Path Time Delay Spread Frequency Selective FadingFrequency Selective Fading:: In a multi-path radio channel, signal will In a multi-path radio channel, signal will

undergo a frequency selective fading if undergo a frequency selective fading if

Bs > Bc and Ts < rms delay spread of the channelBs > Bc and Ts < rms delay spread of the channel Amplitude and phase of the transmitted signal will change as well as Amplitude and phase of the transmitted signal will change as well as

spectral characteristics in spectral characteristics in Frequency Selective Fading ChannelFrequency Selective Fading Channel. [Also . [Also known as known as wideband Channelwideband Channel]]

ROT: Ts < 10 ROT: Ts < 10 will make a channel FSFC.will make a channel FSFC.

Fig-2: Frequency Selective Fading Channel Characteristics



Fading Effects due to Doppler SpreadFading Effects due to Doppler Spread

Fast Fading: Fast Fading: In a multi-path radio channel, signal will undergoes In a multi-path radio channel, signal will undergoes a fast fading if a fast fading if

Ts > Tc and Bs < BTs > Tc and Bs < BDD

Channel impulse response changes rapidly within the symbol Channel impulse response changes rapidly within the symbol duration.duration.Leads to frequency dispersion which in turn increases signal Leads to frequency dispersion which in turn increases signal distortion.distortion.

Slow Fading: Slow Fading: In a multi-path radio channel, signal will undergoes In a multi-path radio channel, signal will undergoes a slow fading if a slow fading if

Ts << Tc and Bs >> BTs << Tc and Bs >> BDD

Channel impulse response varies at a rate much slower than the Channel impulse response varies at a rate much slower than the transmitted base-band signal. {Static Channel]transmitted base-band signal. {Static Channel]

** ** Fast and Slow Fading should not be confused with Large-Scale Fast and Slow Fading should not be confused with Large-Scale and Small-Scale fading.and Small-Scale fading.



Fading Effects due to Doppler SpreadFading Effects due to Doppler Spread

Fig-3: Fading of signal as function of Symbol Period and Base-band Signal BW



Mobile Radio PropagationMobile Radio PropagationClassification of the ChannelsClassification of the Channels

Time-Flat Channel:Time-Flat Channel: A time-invariant channel which remains flat A time-invariant channel which remains flat (constant) during at least the transmission time of one symbol.(constant) during at least the transmission time of one symbol.

Frequency-Flat Channel:Frequency-Flat Channel: A frequency non-selective channel A frequency non-selective channel in which bandwidth of the transmitted signal Bs is less than in which bandwidth of the transmitted signal Bs is less than coherence bandwidth Bc of the channel.coherence bandwidth Bc of the channel.

Flat-Flat Channel: Flat-Flat Channel: A time-flat and frequency flat channel.A time-flat and frequency flat channel. Non-Flat Channel:Non-Flat Channel: A time-variant and frequency selective A time-variant and frequency selective

channel channel

Fig-4: Classification of the Channels

Time-FlatTime-Flat Non-FlatNon-Flat

Flat-FlatFlat-Flat FrequencFrequency-Flaty-Flat

Symbol Time/Channel Correlation Time

Sig

nal B

an

dw

idth

/

Ch

an

nel C

ore

lati

on

ban

dw

idth


Link Budget CalculationLink Budget Calculation Large-Scale FadingLarge-Scale Fading Shadowing EffectShadowing Effect Small-Scale [Fast] FadingSmall-Scale [Fast] Fading

Fig-6: Link Budget Calculation for Fading Channels [AB-2000]



Statistical Models for Multi-path Fading ChannelsStatistical Models for Multi-path Fading Channels Clark’s Model for Flat FadingClark’s Model for Flat Fading

Basic AssumptionsBasic Assumptions Takes into account only Scattering mechanismTakes into account only Scattering mechanism No direct line-of-sight path consideredNo direct line-of-sight path considered A fixed Tx with vertical polarizationA fixed Tx with vertical polarization N azimuthal plane waves with arbitrary phases and angle of incidence and equal N azimuthal plane waves with arbitrary phases and angle of incidence and equal

average amplitudeaverage amplitude


Fig-01: N Azimuthal plane waves arriving at random anglesFig-01: N Azimuthal plane waves arriving at random angles


Statistical Models for Multi-path Fading Statistical Models for Multi-path Fading ChannelsChannels Clark’s Model for Flat FadingClark’s Model for Flat Fading

Mobile Rx is in motion at velocity v in x-direction.Mobile Rx is in motion at velocity v in x-direction.The Doppler shift of nth plane wave arriving at angle is given The Doppler shift of nth plane wave arriving at angle is given

as as

ffnn = v cos = v cosn n / /

It can be shown* thatIt can be shown* that random received signal envelop r has random received signal envelop r has a Rayleigh Distribution given by a Rayleigh Distribution given by

p ( r ) = (r/ p ( r ) = (r/ 22 ) exp ( - r ) exp ( - r22 / 2 / 2 22 ) for 0 <= r <= ) for 0 <= r <=

= 0 for r < 0= 0 for r < 0

* Derivation follows, as given in the TB pp-178-179



Statistical Models for Multi-path Fading Statistical Models for Multi-path Fading ChannelsChannels Clark’s Model for Flat FadingClark’s Model for Flat Fading Spectral Shape in Clark’s ModelSpectral Shape in Clark’s Model

Gans developed a spectrum analysis for Clark’s ModelGans developed a spectrum analysis for Clark’s ModelTotal received power at Rx can be expressed asTotal received power at Rx can be expressed as

and instantaneous frequency of the received signal component is and instantaneous frequency of the received signal component is given as given as

And it can be shown* that output spectrum is And it can be shown* that output spectrum is [see Fig-02][see Fig-02]

* Derivation is as given in TB pp-179-180



Statistical Models for Multi-path Fading ChannelsStatistical Models for Multi-path Fading Channels Clark’s Model for Flat FadingClark’s Model for Flat Fading Spectral Shape in Clark’s ModelSpectral Shape in Clark’s Model


Fig-02: Doppler Power Spectrum for an un-modulated CW carrierFig-02: Doppler Power Spectrum for an un-modulated CW carrier


Mobile Radio PropagationMobile Radio Propagation Statistical Models for Multi-path Fading ChannelsStatistical Models for Multi-path Fading Channels

Clark’s Model for Flat FadingClark’s Model for Flat Fading Simulation of Clark’s ModelSimulation of Clark’s Model

Fig-03: Clarke’s Simulator using AM with a [a] Doppler Filter [b] Base-Band Doppler Filter


Statistical Models for Multi-path Fading ChannelsStatistical Models for Multi-path Fading Channels Clark’s Model for Flat FadingClark’s Model for Flat Fading Level Crossing and Fading StatisticsLevel Crossing and Fading Statistics

Important statistical parameters useful for designing Error Control CodesImportant statistical parameters useful for designing Error Control CodesLevel Crossing Rate (LCR) is expected rate at which Rayleigh fading Level Crossing Rate (LCR) is expected rate at which Rayleigh fading

envelop, normalized to the local rms signal level, crosses a specified level envelop, normalized to the local rms signal level, crosses a specified level in positive-going direction. And this number is given by in positive-going direction. And this number is given by

Where r is Where r is d (r(t))/dt, p(R,r)d (r(t))/dt, p(R,r) is the joint density function of r and r at is the joint density function of r and r at r = r = RR, and fm is max. Doppler shift, and , and fm is max. Doppler shift, and ρρ = R/R = R/Rrmsrms

Average Fade Duration is the average period of time for which the Average Fade Duration is the average period of time for which the received signal is below a specified level R. For Rayleigh fading received signal is below a specified level R. For Rayleigh fading signal it is given bysignal it is given by



Statistical Models for Multi-path Fading Statistical Models for Multi-path Fading ChannelsChannels Clark’s Model for Flat FadingClark’s Model for Flat Fading Example-1: Example-1: For a Raleigh fading signal, calculate N For a Raleigh fading signal, calculate N

such that such that ρρ = 1 = 1 andand fm = 20 Hz. fm = 20 Hz. If fcIf fc = 900 = 900 MHz MHz what would be the velocity of the mobile to get this what would be the velocity of the mobile to get this Doppler shift?Doppler shift?

Example-2: Example-2: Calculate the Average fade duration for Calculate the Average fade duration for previous example. Repeat it when threshold level is previous example. Repeat it when threshold level is

reduced toreduced to ρρ = 0.01. = 0.01.


mobile radio propagation 2

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