Mobile Radio Propagation

11

Mobile Radio PropagationMobile Radio PropagationMobile Radio PropagationMobile Radio Propagation Mobile radio channel is an important factor in Mobile radio channel is an important factor in

wireless systems.wireless systems.

Wired channels are stationary and Wired channels are stationary and predictable, while radio channels are random predictable, while radio channels are random and have complex models.and have complex models.

Modeling of radio channels is done in Modeling of radio channels is done in statistical fashion based on receiver statistical fashion based on receiver measurements.measurements.

Mobile radio channel is an important factor in Mobile radio channel is an important factor in wireless systems.wireless systems.

Wired channels are stationary and Wired channels are stationary and predictable, while radio channels are random predictable, while radio channels are random and have complex models.and have complex models.

Modeling of radio channels is done in Modeling of radio channels is done in statistical fashion based on receiver statistical fashion based on receiver measurements.measurements.

22

Types of propagation modelsTypes of propagation modelsTypes of propagation modelsTypes of propagation models Large scale propagation models Large scale propagation models

To predict the average signal strength at a To predict the average signal strength at a given distance from the transmittergiven distance from the transmitter

Controlled by signal decay with distance Controlled by signal decay with distance

Small scale or fading models.Small scale or fading models. To predict the signal strength at close To predict the signal strength at close

distance to a particular location distance to a particular location Controlled by multipath and Doppler Controlled by multipath and Doppler

effects.effects.

Large scale propagation models Large scale propagation models To predict the average signal strength at a To predict the average signal strength at a

given distance from the transmittergiven distance from the transmitter Controlled by signal decay with distance Controlled by signal decay with distance

Small scale or fading models.Small scale or fading models. To predict the signal strength at close To predict the signal strength at close

distance to a particular location distance to a particular location Controlled by multipath and Doppler Controlled by multipath and Doppler

effects.effects.

33

Radio signal patternRadio signal patternRadio signal patternRadio signal pattern-30-30-30-30

-40-40-40-40

-50-50-50-50

-60-60-60-60

-70-70-70-7016161616 18181818 20202020 22222222 24242424 26262626 2828282814141414

T-R Separation (meters)T-R Separation (meters)T-R Separation (meters)T-R Separation (meters)

Rec

eive

d Po

wer

(dB

m)

Rec

eive

d Po

wer

(dB

m)

Rec

eive

d Po

wer

(dB

m)

Rec

eive

d Po

wer

(dB

m)

44

Measured signal parametersMeasured signal parametersMeasured signal parametersMeasured signal parameters

Electrical Field (Volts/m)Electrical Field (Volts/m)Magnitude E = IMagnitude E = IEEI I

Vector Vector Direction Direction EE = = xxEExx + + yyEEyy + + zzEEzz

Electrical Field (Volts/m)Electrical Field (Volts/m)Magnitude E = IMagnitude E = IEEI I

Vector Vector Direction Direction EE = = xxEExx + + yyEEyy + + zzEEzz

Power (Watts or dBm)Power (Watts or dBm)

Power is scalar quantity and easier to Power is scalar quantity and easier to measure.measure.

Power (Watts or dBm)Power (Watts or dBm)

Power is scalar quantity and easier to Power is scalar quantity and easier to measure.measure.

55

Relation between Watts and dBm Relation between Watts and dBm Relation between Watts and dBm Relation between Watts and dBm

P (dBm) = 10 logP (dBm) = 10 log1010 [ [ PP (mW)](mW)]

P (dBm) = 10 logP (dBm) = 10 log1010 [ [ PP (mW)](mW)]

P(mW) P(dBm)

10 10

1 0

10-1 -10

10-2 -20

10-6 -60

66

Physical propagation modelsPhysical propagation modelsPhysical propagation modelsPhysical propagation models Free Space PropagationFree Space Propagation

Transmitter/receiver have clear LOS pathTransmitter/receiver have clear LOS path ReflectionReflection

Wave reaches receiver after reflection off Wave reaches receiver after reflection off surfaces larger than wavelengthsurfaces larger than wavelength

DiffractionDiffraction Wave reaches receiver by bending at sharp Wave reaches receiver by bending at sharp

edges (peaks) or curved surfaces (earth).edges (peaks) or curved surfaces (earth). ScatteringScattering

Wave reaches receiver after bouncing off Wave reaches receiver after bouncing off objects smaller than wavelength (snow, rain).objects smaller than wavelength (snow, rain).

Free Space PropagationFree Space Propagation Transmitter/receiver have clear LOS pathTransmitter/receiver have clear LOS path

ReflectionReflection Wave reaches receiver after reflection off Wave reaches receiver after reflection off

surfaces larger than wavelengthsurfaces larger than wavelength DiffractionDiffraction

Wave reaches receiver by bending at sharp Wave reaches receiver by bending at sharp edges (peaks) or curved surfaces (earth).edges (peaks) or curved surfaces (earth).

ScatteringScattering Wave reaches receiver after bouncing off Wave reaches receiver after bouncing off

objects smaller than wavelength (snow, rain).objects smaller than wavelength (snow, rain).

77

Free Space PropagationFree Space PropagationFree Space PropagationFree Space Propagation Transmitter and receiver have clear, Transmitter and receiver have clear,

unobstructed LOS path between them.unobstructed LOS path between them.

(Courtesy: webbroadband.blogspot.com)(Courtesy: webbroadband.blogspot.com)

Transmitter and receiver have clear, Transmitter and receiver have clear, unobstructed LOS path between them.unobstructed LOS path between them.

(Courtesy: webbroadband.blogspot.com)(Courtesy: webbroadband.blogspot.com)

88

Friis transmission equationFriis transmission equationFriis transmission equationFriis transmission equation

PPrr = P = Ptt G Gtt G Grr 22

(4(4))22 d d22 L L

PPtt = Transmitted Power (W)= Transmitted Power (W)PPrr = Received Power (W) = Received Power (W)GGtt = Transmitter antenna gain = Transmitter antenna gain GGrr = Receiver antenna gain = Receiver antenna gain LL = System loss factor = System loss factor Due to line losses, but not due to propagationDue to line losses, but not due to propagationL L 1 1

PPrr = P = Ptt G Gtt G Grr 22

(4(4))22 d d22 L L

PPtt = Transmitted Power (W)= Transmitted Power (W)PPrr = Received Power (W) = Received Power (W)GGtt = Transmitter antenna gain = Transmitter antenna gain GGrr = Receiver antenna gain = Receiver antenna gain LL = System loss factor = System loss factor Due to line losses, but not due to propagationDue to line losses, but not due to propagationL L 1 1

99

Antenna GainAntenna GainAntenna GainAntenna Gain Power Gain of antenna Power Gain of antenna

GG = 4 = 4AAee / / 22, ,

AAee is effective aperture area of antenna is effective aperture area of antenna

Wavelength Wavelength = c / f (Hz) = c / f (Hz) = 3 • 10= 3 • 1088 / f , meters / f , meters

Power Gain of antenna Power Gain of antenna

GG = 4 = 4AAee / / 22, ,

AAee is effective aperture area of antenna is effective aperture area of antenna

Wavelength Wavelength = c / f (Hz) = c / f (Hz) = 3 • 10= 3 • 1088 / f , meters / f , meters

1010

Relation between Electric field and PowerRelation between Electric field and PowerRelation between Electric field and PowerRelation between Electric field and Power

Received powerReceived power

PPrr = I = IEErrII2 2 22 G Grr

44 Impedance of medium: Impedance of medium: = = / /

For air or vacuum: For air or vacuum: = (4= (4 • 10 • 10-7-7) /(8.85 • 10) /(8.85 • 10-12-12 ) ) = 377 = 377

Received powerReceived power

PPrr = I = IEErrII2 2 22 G Grr

44 Impedance of medium: Impedance of medium: = = / /

For air or vacuum: For air or vacuum: = (4= (4 • 10 • 10-7-7) /(8.85 • 10) /(8.85 • 10-12-12 ) ) = 377 = 377

1111

ExampleExampleExampleExample

If the received power is PIf the received power is Prr = 7 • 10 = 7 • 10 -10-10 W, W, antenna gain Gantenna gain Grr = 2 and transmitting frequency = 2 and transmitting frequency is 900 MHz, determine the electric field strength is 900 MHz, determine the electric field strength at the receiver. at the receiver.

If the received power is PIf the received power is Prr = 7 • 10 = 7 • 10 -10-10 W, W, antenna gain Gantenna gain Grr = 2 and transmitting frequency = 2 and transmitting frequency is 900 MHz, determine the electric field strength is 900 MHz, determine the electric field strength at the receiver. at the receiver.

1212

SolutionSolutionSolutionSolution

f = 900 MHz =f = 900 MHz = > >

= (3 • 10= (3 • 1088) / (900 • 10) / (900 • 1066) = 0.33 m) = 0.33 m

From field-power equation:From field-power equation:IIEErrII = [(P= [(Prr • • • 4 • 4) / () / ( 22 • G • Grr)])]1/21/2

= [(7 • 10= [(7 • 10 -10-10 • 377 • 4 • 377 • 4) / (0.33) / (0.3322 • 2)] • 2)]1/21/2

= 0.0039 V/m= 0.0039 V/m

f = 900 MHz =f = 900 MHz = > >

= (3 • 10= (3 • 1088) / (900 • 10) / (900 • 1066) = 0.33 m) = 0.33 m

From field-power equation:From field-power equation:IIEErrII = [(P= [(Prr • • • 4 • 4) / () / ( 22 • G • Grr)])]1/21/2

= [(7 • 10= [(7 • 10 -10-10 • 377 • 4 • 377 • 4) / (0.33) / (0.3322 • 2)] • 2)]1/21/2

= 0.0039 V/m= 0.0039 V/m

1313

ExampleExampleExampleExampleA transmitter produces 50W of power. A transmitter produces 50W of power. If this power is applied to a unity gain antenna If this power is applied to a unity gain antenna with 900 MHz carrier frequency, find the received with 900 MHz carrier frequency, find the received power at a LOS distance of 100 m from the power at a LOS distance of 100 m from the antenna. What is the received power at 10 km? antenna. What is the received power at 10 km? Assume unity gain for the receiver antenna.Assume unity gain for the receiver antenna.

A transmitter produces 50W of power. A transmitter produces 50W of power. If this power is applied to a unity gain antenna If this power is applied to a unity gain antenna with 900 MHz carrier frequency, find the received with 900 MHz carrier frequency, find the received power at a LOS distance of 100 m from the power at a LOS distance of 100 m from the antenna. What is the received power at 10 km? antenna. What is the received power at 10 km? Assume unity gain for the receiver antenna.Assume unity gain for the receiver antenna.

1414

SolutionSolutionSolutionSolution

PPrr = = PPtt G Gtt G Grr 22

(4(4))22 d d22 L L

PPtt = 50 W, G = 50 W, Gtt = 1, G = 1, Grr = 1, L = 1, d = 100 m = 1, L = 1, d = 100 m = (3 • 10= (3 • 1088) / (900 • 10) / (900 • 1066) = 0.33 m) = 0.33 m

PPrr = = PPtt G Gtt G Grr 22

(4(4))22 d d22 L L

PPtt = 50 W, G = 50 W, Gtt = 1, G = 1, Grr = 1, L = 1, d = 100 m = 1, L = 1, d = 100 m = (3 • 10= (3 • 1088) / (900 • 10) / (900 • 1066) = 0.33 m) = 0.33 m

Solving, Pr = 3.5 • 10-6 W

Pr (10 km) = Pr (100 m) • (100/10000)2

= 3.5 • 10-6 • (1/100)2 = 3.5 • 10-10 W

1515

Electric Properties of Material BodiesElectric Properties of Material BodiesElectric Properties of Material BodiesElectric Properties of Material Bodies Fundamental constantsFundamental constants

Permittivity Permittivity = = 00 rr , , Farads/mFarads/m

Permeability Permeability = = 00 rr , ,Henries/mHenries/m

Conductivity Conductivity , Siemens/m, Siemens/m Types of materialsTypes of materials

Dielectrics – allow EM waves to passDielectrics – allow EM waves to pass Conductors – block EM wavesConductors – block EM waves Metamaterials – bend EM wavesMetamaterials – bend EM waves

Fundamental constantsFundamental constants

Permittivity Permittivity = = 00 rr , , Farads/mFarads/m

Permeability Permeability = = 00 rr , ,Henries/mHenries/m

Conductivity Conductivity , Siemens/m, Siemens/m Types of materialsTypes of materials

Dielectrics – allow EM waves to passDielectrics – allow EM waves to pass Conductors – block EM wavesConductors – block EM waves Metamaterials – bend EM wavesMetamaterials – bend EM waves

1616

Reflection at dielectric boundariesReflection at dielectric boundariesReflection at dielectric boundariesReflection at dielectric boundaries

EErr = = : Reflection coefficient : Reflection coefficient

EEtt = T = 1 + = T = 1 + : Transmission coefficient : Transmission coefficient

EErr = = : Reflection coefficient : Reflection coefficient

EEtt = T = 1 + = T = 1 + : Transmission coefficient : Transmission coefficientEEiiEEii

EEiiEEiiEEiiEEii EErrEErr

EEttEEtt

iiii rrrr

ii = = rrii = = rr

1717

Vertical Polarization Vertical Polarization Vertical Polarization Vertical Polarization

EEttEEtt

EEiiEEii EErrEErr

iiii rrrr

HHiiHHii HHrrHHrr11, , 11, , 1111, , 11, , 11

22, , 22, , 2222, , 22, , 22 tt tt

||||= = 22 sinsintt - - 11 sinsinii

22 sin sintt + + 11 sinsinii

||||= = 22 sinsintt - - 11 sinsinii

22 sin sintt + + 11 sinsinii

1818

Horizontal PolarizationHorizontal PolarizationHorizontal PolarizationHorizontal Polarization

EEiiEEii EErrEErr

EEttEEtt

iiii rrrr

HHiiHHii HHrrHHrr11, , 11, , 1111, , 11, , 11

22, , 22, , 2222, , 22, , 22 tt tt

T T = = 22 sinsintt - - 11 sinsinii

22 sin sintt + + 11 sinsinii

T T = = 22 sinsintt - - 11 sinsinii

22 sin sintt + + 11 sinsinii

1919

Reflection from Perfect Conductor (Reflection from Perfect Conductor (EETT =0) =0)Reflection from Perfect Conductor (Reflection from Perfect Conductor (EETT =0) =0)

Vert. polarizationVert. polarization Horiz. polarizationHoriz. polarization

ii == rr ii == rr

EEii = = EErr EEii = = - E- Err

Vert. polarizationVert. polarization Horiz. polarizationHoriz. polarization

ii == rr ii == rr

EEii = = EErr EEii = = - E- Err

EEiiEEii EErrEErr

EEttEEtt

iiii rrrr

2020

Ground Reflection (2-Ray Model)Ground Reflection (2-Ray Model)Ground Reflection (2-Ray Model)Ground Reflection (2-Ray Model)

EEiiEEii

iiii 0000

EELOSLOSEELOSLOS

EErr=E=EggEErr=E=Egg

EETOTTOT = E = ELOS LOS +E+EggEETOTTOT = E = ELOS LOS +E+Egg

R R (receiver)(receiver)R R (receiver)(receiver)

hhrrhhrr

hhtthhtt

T T (transmitter)(transmitter)T T (transmitter)(transmitter)

dddd

2121

Field EquationsField EquationsField EquationsField Equations

d = several kmsd = several kms

hhtt = 50-100m = 50-100m

EETOTTOT= E= ELOS LOS + E+ Egg

EETOTTOT(d) = (d) =

For d > 20hFor d > 20htthhrr / /

Received power PReceived power Prr==

d = several kmsd = several kms

hhtt = 50-100m = 50-100m

EETOTTOT= E= ELOS LOS + E+ Egg

EETOTTOT(d) = (d) =

For d > 20hFor d > 20htthhrr / /

Received power PReceived power Prr==

2004

d

hhdE rt

4

22

d

hhGGP rtrtt

2222

ExampleExampleExampleExampleA mobile is located 5 km away from a A mobile is located 5 km away from a base station, and uses a vertical base station, and uses a vertical /4 /4 monopole antenna with a gain of monopole antenna with a gain of 2.55dB to receive cellular radio signals. 2.55dB to receive cellular radio signals. The electric field at 1 km from the The electric field at 1 km from the transmitter is measured to be 10transmitter is measured to be 10 -3-3 V/m. V/m. The carrier frequency used is 900 MHz.The carrier frequency used is 900 MHz.(a) Find the length and gain of the (a) Find the length and gain of the receiving antenna.receiving antenna.

A mobile is located 5 km away from a A mobile is located 5 km away from a base station, and uses a vertical base station, and uses a vertical /4 /4 monopole antenna with a gain of monopole antenna with a gain of 2.55dB to receive cellular radio signals. 2.55dB to receive cellular radio signals. The electric field at 1 km from the The electric field at 1 km from the transmitter is measured to be 10transmitter is measured to be 10 -3-3 V/m. V/m. The carrier frequency used is 900 MHz.The carrier frequency used is 900 MHz.(a) Find the length and gain of the (a) Find the length and gain of the receiving antenna.receiving antenna.

2323

ExampleExampleExampleExampleA mobile is located 5 km away from a A mobile is located 5 km away from a base station, and uses a vertical base station, and uses a vertical /4 /4 monopole antenna with a gain of 2.55dB monopole antenna with a gain of 2.55dB to receive cellular radio signals. to receive cellular radio signals. The electric field at 1 km from the transmitter The electric field at 1 km from the transmitter is measured to be 10is measured to be 10-3-3 V/m. V/m. The carrier frequency used is 900 MHz.The carrier frequency used is 900 MHz.

(b) Find the received power at the mobile (b) Find the received power at the mobile using the 2-way ground model assuming the using the 2-way ground model assuming the height of the transmitting antenna is 50 m and height of the transmitting antenna is 50 m and receiving antenna is 1.5 m above the ground.receiving antenna is 1.5 m above the ground.

A mobile is located 5 km away from a A mobile is located 5 km away from a base station, and uses a vertical base station, and uses a vertical /4 /4 monopole antenna with a gain of 2.55dB monopole antenna with a gain of 2.55dB to receive cellular radio signals. to receive cellular radio signals. The electric field at 1 km from the transmitter The electric field at 1 km from the transmitter is measured to be 10is measured to be 10-3-3 V/m. V/m. The carrier frequency used is 900 MHz.The carrier frequency used is 900 MHz.

(b) Find the received power at the mobile (b) Find the received power at the mobile using the 2-way ground model assuming the using the 2-way ground model assuming the height of the transmitting antenna is 50 m and height of the transmitting antenna is 50 m and receiving antenna is 1.5 m above the ground.receiving antenna is 1.5 m above the ground.

2424

Solution:Solution:

d0 = 1 km

E0 = 10 -3 V/m

d0 = 1 km

E0 = 10 -3 V/m

ht = 50 mht = 50 m hr = 1.5 mhr = 1.5 m

d = 5 kmd = 5 km

2525

(a) (a)

f = 900 MHzf = 900 MHz

= (3 • 10= (3 • 108) / (900 • 10) / (900 • 106) = 0.33 m) = 0.33 m

Length of receiving antenna,Length of receiving antenna,

L = L = / 4 = 0.33/4 = 0.0833 m = 8.33 cm / 4 = 0.33/4 = 0.0833 m = 8.33 cm

(a) (a)

f = 900 MHzf = 900 MHz

= (3 • 10= (3 • 108) / (900 • 10) / (900 • 106) = 0.33 m) = 0.33 m

Length of receiving antenna,Length of receiving antenna,

L = L = / 4 = 0.33/4 = 0.0833 m = 8.33 cm / 4 = 0.33/4 = 0.0833 m = 8.33 cm

2626

(b)

Gain of antenna = 2.55 dB = > 1.8

Er (d) =

= 2 • 10-3 • 1 • 103 • 2 • 50 • 1.5(5 • 103)2 • 0.333

= 113.1 • 10-6 V/m

(b)

Gain of antenna = 2.55 dB = > 1.8

Er (d) =

= 2 • 10-3 • 1 • 103 • 2 • 50 • 1.5(5 • 103)2 • 0.333

= 113.1 • 10-6 V/m

2004

d

hhdE rt

2727

Pr (d)

= I Er I2 2 Gr

4= (113.1 • 10-6) 2 • (0.333) 2 • 1.8

377 4= 5.4 • 10-13 W

= -92.68 dBm

Pr (d)

= I Er I2 2 Gr

4= (113.1 • 10-6) 2 • (0.333) 2 • 1.8

377 4= 5.4 • 10-13 W

= -92.68 dBm

2828

DiffractionDiffractionDiffractionDiffraction Diffraction allows radio signals Diffraction allows radio signals

to propagate around the curved to propagate around the curved surface or propagate behind surface or propagate behind obstructions.obstructions.

Based on Huygen’s principle of Based on Huygen’s principle of wave propagation.wave propagation.

Diffraction allows radio signals Diffraction allows radio signals to propagate around the curved to propagate around the curved surface or propagate behind surface or propagate behind obstructions.obstructions.

Based on Huygen’s principle of Based on Huygen’s principle of wave propagation.wave propagation.

2929

Knife-edge Diffraction GeometryKnife-edge Diffraction GeometryKnife-edge Diffraction GeometryKnife-edge Diffraction Geometry(a) T is transmitter and R is receiver, (a) T is transmitter and R is receiver, with an infinite knife-edge obstruction with an infinite knife-edge obstruction blocking the line-of-sight path.blocking the line-of-sight path.

(a) T is transmitter and R is receiver, (a) T is transmitter and R is receiver, with an infinite knife-edge obstruction with an infinite knife-edge obstruction blocking the line-of-sight path.blocking the line-of-sight path.

hhrrhhrrhhobsobshhobsobshhtthhtt

RRRRTTTT hhhh

dd11dd11 dd22dd22

3030

Knife-edge Diffraction GeometryKnife-edge Diffraction GeometryKnife-edge Diffraction GeometryKnife-edge Diffraction Geometry(b) T & R are not the same height...(b) T & R are not the same height...(b) T & R are not the same height...(b) T & R are not the same height...

hhrrhhrr

h’h’h’h’

hhtthhtt

RRRRTTTT hhhh

dd11dd11 dd22dd22

3131

Knife-edge Diffraction GeometryKnife-edge Diffraction GeometryKnife-edge Diffraction GeometryKnife-edge Diffraction Geometry

...If ...If and and are small and are small and h<<dh<<d11 and and dd22, , then then h h & & h’h’ are virtually identical and are virtually identical and the geometry may be redrawn as in (c).the geometry may be redrawn as in (c).

...If ...If and and are small and are small and h<<dh<<d11 and and dd22, , then then h h & & h’h’ are virtually identical and are virtually identical and the geometry may be redrawn as in (c).the geometry may be redrawn as in (c).

hhrrhhrr

h’h’h’h’

hhtthhtt

RRRRTTTT hhhh

dd11dd11 dd22dd22

3232

Knife-edge Diffraction GeometryKnife-edge Diffraction GeometryKnife-edge Diffraction GeometryKnife-edge Diffraction Geometry(c) Equivalent where the smallest height (c) Equivalent where the smallest height (in this case (in this case hhr r )) is subtracted from all is subtracted from all other heights.other heights.

(c) Equivalent where the smallest height (c) Equivalent where the smallest height (in this case (in this case hhr r )) is subtracted from all is subtracted from all other heights.other heights.

hhtt -- hhrrhhtt -- hhrrRRRR

TTTT

dd11dd11 dd22dd22

hhobsobs-h-hrrhhobsobs-h-hrr

3333

AssumptionsAssumptionsAssumptionsAssumptions

h << d1, d2

h >>

Excess path length

h << d1, d2

h >>

Excess path length

21

212

2

)(

dd

ddh

21

21

2

)(

dd

ddh

3434

...Assumptions...Assumptions...Assumptions...Assumptions

h << dh << d11, d, d22

h >> h >>

Phase differencePhase difference == 2 2 / / == 2 2 h h2 2 (d(d11 + d + d22 ) )

2 2 d d1 1 dd2 2

h << dh << d11, d, d22

h >> h >>

Phase differencePhase difference == 2 2 / / == 2 2 h h2 2 (d(d11 + d + d22 ) )

2 2 d d1 1 dd2 2

3535

Diffraction ParameterDiffraction ParameterDiffraction ParameterDiffraction Parameter

v =

=

v =

=

2

21

21 )(2

dd

ddh

3636

Three CasesThree CasesThree CasesThree Cases Case I: h > 0Case I: h > 0 Case II: h = 0Case II: h = 0 Case III: h < 0Case III: h < 0

Case I: h > 0Case I: h > 0 Case II: h = 0Case II: h = 0 Case III: h < 0Case III: h < 0

3737

Case I: h > 0Case I: h > 0Case I: h > 0Case I: h > 0 and and are positive since are positive since hh is positive. is positive. and and are positive since are positive since hh is positive. is positive.

hhhhRRRR

TTTT

dd11dd11 dd22dd22

3838

Case II: h = 0Case II: h = 0Case II: h = 0Case II: h = 0 and and equal 0, since equal 0, since hh equals 0. equals 0. and and equal 0, since equal 0, since hh equals 0. equals 0.

RRRRTTTTdd11dd11 dd22dd22

3939

Case III: h < 0Case III: h < 0Case III: h < 0Case III: h < 0 and and are negative, since are negative, since hh is negative. is negative. and and are negative, since are negative, since hh is negative. is negative.

hhhhRRRR

TTTTdd11dd11 dd22dd22

4040

The electric field strength of The electric field strength of the diffracted wave is given by:the diffracted wave is given by:

Ed = F(v) • Eo

where Eo is the free space field strength in the absence of both ground and knife edge.

The electric field strength of The electric field strength of the diffracted wave is given by:the diffracted wave is given by:

Ed = F(v) • Eo

where Eo is the free space field strength in the absence of both ground and knife edge.

4141

Approximate Value of Approximate Value of Fresnel Integral F(v):Fresnel Integral F(v):Approximate Value of Approximate Value of Fresnel Integral F(v):Fresnel Integral F(v):

GGdd (dB) = 20(dB) = 20 log Ilog I F(v)F(v) IIGGdd (dB) = 20(dB) = 20 log Ilog I F(v)F(v) II

4242

v Rangev Range GGdd (dB) (dB)

vv -1 -1 00

-1-1vv 0 0 20 log (0.5 – 0.62 v)20 log (0.5 – 0.62 v)

00vv11 20 log (0.5 e20 log (0.5 e-0.95v-0.95v ))

11 vv 2.4 2.4 20 log (0.4 –20 log (0.4 –

vv2.42.4 20 log (0.225 /20 log (0.225 / v)v)

v Rangev Range GGdd (dB) (dB)

vv -1 -1 00

-1-1vv 0 0 20 log (0.5 – 0.62 v)20 log (0.5 – 0.62 v)

00vv11 20 log (0.5 e20 log (0.5 e-0.95v-0.95v ))

11 vv 2.4 2.4 20 log (0.4 –20 log (0.4 –

vv2.42.4 20 log (0.225 /20 log (0.225 / v)v)

))1.038.0(1184.0 2v

4343

Example Example Example Example Compute the diffraction loss Compute the diffraction loss between the transmitter and between the transmitter and receiver assuming: receiver assuming:

= 1/3= 1/3 m m

dd11 = 1 = 1 km km

dd2 2 = 1= 1 km km

h = 25h = 25 mm

Compute the diffraction loss Compute the diffraction loss between the transmitter and between the transmitter and receiver assuming: receiver assuming:

= 1/3= 1/3 m m

dd11 = 1 = 1 km km

dd2 2 = 1= 1 km km

h = 25h = 25 mm

4444

Solution:Solution:Solution:Solution:Given = 1/3 m

d1 = 1 kmd2 = 1 kmh = 25 m

V =

=

= 2.74

Given = 1/3 m d1 = 1 kmd2 = 1 kmh = 25 m

V =

=

= 2.74

21

21 )(2

dd

ddh

)1000)(1000)(3.0(

)10001000(225

4545

Using the table,

GGdd (dB) (dB) = 20 log (0.225/2.74)= -22 dBLoss = 22 dB

Using the table,

GGdd (dB) (dB) = 20 log (0.225/2.74)= -22 dBLoss = 22 dB

4646

ScatteringScatteringScatteringScattering When a radio wave impinges When a radio wave impinges

on a rough surface, the on a rough surface, the reflected energy is spread out reflected energy is spread out or diffused in all directions. or diffused in all directions. Ex., lampposts and foliage.Ex., lampposts and foliage.

The scattered field increases The scattered field increases the strength of the signal at the strength of the signal at the receiver.the receiver.

When a radio wave impinges When a radio wave impinges on a rough surface, the on a rough surface, the reflected energy is spread out reflected energy is spread out or diffused in all directions. or diffused in all directions. Ex., lampposts and foliage.Ex., lampposts and foliage.

The scattered field increases The scattered field increases the strength of the signal at the strength of the signal at the receiver.the receiver.

4747

Radar Cross Section (RCS) ModelRadar Cross Section (RCS) ModelRadar Cross Section (RCS) ModelRadar Cross Section (RCS) Model

RCS (Radar Cross Section) =RCS (Radar Cross Section) =

Power density of scattered wave Power density of scattered wave in direction of receiverin direction of receiver

Power density of radio wave incident Power density of radio wave incident on the scattering objecton the scattering object

RCS (Radar Cross Section) =RCS (Radar Cross Section) =

Power density of scattered wave Power density of scattered wave in direction of receiverin direction of receiver

Power density of radio wave incident Power density of radio wave incident on the scattering objecton the scattering object

4848

Radar Cross Section (RCS) ModelRadar Cross Section (RCS) ModelRadar Cross Section (RCS) ModelRadar Cross Section (RCS) Model

PPRR = P = PTT • G • GTT • • 22 • RCS • RCS

(4(4))3 3 • d• dTT 2 2 • d • dRR

2 2

Where,Where,

PPTT = Transmitted Power= Transmitted Power

GGTT = Gain of Transmitting antenna= Gain of Transmitting antenna

ddTT = Distance of scattering object = Distance of scattering object from Transmitterfrom Transmitter

ddRR = Distance of scattering object = Distance of scattering object from Receiverfrom Receiver

PPRR = P = PTT • G • GTT • • 22 • RCS • RCS

(4(4))3 3 • d• dTT 2 2 • d • dRR

2 2

Where,Where,

PPTT = Transmitted Power= Transmitted Power

GGTT = Gain of Transmitting antenna= Gain of Transmitting antenna

ddTT = Distance of scattering object = Distance of scattering object from Transmitterfrom Transmitter

ddRR = Distance of scattering object = Distance of scattering object from Receiverfrom Receiver

4949

Practical Link BudgetPractical Link BudgetPractical Link BudgetPractical Link Budget Most radio propagation models Most radio propagation models

are derived using a combination are derived using a combination of analytical and empirical of analytical and empirical models.models.

Empirical approach is based on Empirical approach is based on fitting curves or analytical fitting curves or analytical expressions that recreate a set expressions that recreate a set of measured data.of measured data.

Most radio propagation models Most radio propagation models are derived using a combination are derived using a combination of analytical and empirical of analytical and empirical models.models.

Empirical approach is based on Empirical approach is based on fitting curves or analytical fitting curves or analytical expressions that recreate a set expressions that recreate a set of measured data.of measured data.

5050

...Practical Link Budget...Practical Link Budget...Practical Link Budget...Practical Link Budget Advantages of empirical models;Advantages of empirical models;

Takes into account all propagation Takes into account all propagation factors, both known and unknown.factors, both known and unknown.

Disadvantages:Disadvantages:New models need to be measured for New models need to be measured for different environment or frequency.different environment or frequency.

Advantages of empirical models;Advantages of empirical models;

Takes into account all propagation Takes into account all propagation factors, both known and unknown.factors, both known and unknown.

Disadvantages:Disadvantages:New models need to be measured for New models need to be measured for different environment or frequency.different environment or frequency.

5151

T d0 R

PPTT PPRR(d(d00) ) PPRR(d)(d)

T d0 R

PPTT PPRR(d(d00) ) PPRR(d)(d)

Log-Distance Path ModelLog-Distance Path ModelLog-Distance Path ModelLog-Distance Path Model Over many years, some classical Over many years, some classical

propagation models have been propagation models have been developed, which are used to predict developed, which are used to predict large-scale coverage for mobile large-scale coverage for mobile communication system design.communication system design.

Over many years, some classical Over many years, some classical propagation models have been propagation models have been developed, which are used to predict developed, which are used to predict large-scale coverage for mobile large-scale coverage for mobile communication system design.communication system design.

5252

...Log-Distance Path Model...Log-Distance Path Model...Log-Distance Path Model...Log-Distance Path Model

Path loss at dPath loss at d00 = P = PTT/P(d/P(d00) = K(d) = K(d00))nn = PL(d = PL(d00))

Path loss at d = PPath loss at d = PTT/P(d) = K(d)/P(d) = K(d)nn = PL(d) = PL(d)

PL(d) / PL(dPL(d) / PL(d00) = (d/d) = (d/d00))n n

PL(d) [dB] = PL(dPL(d) [dB] = PL(d00) [dB] + 10n log) [dB] + 10n log1010 (d/d (d/d00))

Path loss at dPath loss at d00 = P = PTT/P(d/P(d00) = K(d) = K(d00))nn = PL(d = PL(d00))

Path loss at d = PPath loss at d = PTT/P(d) = K(d)/P(d) = K(d)nn = PL(d) = PL(d)

PL(d) / PL(dPL(d) / PL(d00) = (d/d) = (d/d00))n n

PL(d) [dB] = PL(dPL(d) [dB] = PL(d00) [dB] + 10n log) [dB] + 10n log1010 (d/d (d/d00))

5353

Received Power in Log-distance modelReceived Power in Log-distance modelReceived Power in Log-distance modelReceived Power in Log-distance model

PPRR(d) [dbm] = P(d) [dbm] = Ptt [dbm] – PL(d) [db] [dbm] – PL(d) [db]n -> path loss exponentn -> path loss exponent

dd00 -> reference distance close to transmitter -> reference distance close to transmitter

EnvironmentEnvironment nn

Free spaceFree space 22Urban area cellular radio Urban area cellular radio 2.7 – 3.52.7 – 3.5LOS in buildingLOS in building 1.6 – 1.81.6 – 1.8

PPRR(d) [dbm] = P(d) [dbm] = Ptt [dbm] – PL(d) [db] [dbm] – PL(d) [db]n -> path loss exponentn -> path loss exponent

dd00 -> reference distance close to transmitter -> reference distance close to transmitter

EnvironmentEnvironment nn

Free spaceFree space 22Urban area cellular radio Urban area cellular radio 2.7 – 3.52.7 – 3.5LOS in buildingLOS in building 1.6 – 1.81.6 – 1.8

5454

Log-Normal ShadowingLog-Normal ShadowingLog-Normal ShadowingLog-Normal Shadowing Log-distance path loss normal gives Log-distance path loss normal gives

only the average value of path loss.only the average value of path loss. Surrounding environment may be Surrounding environment may be

vastly different at two locations vastly different at two locations having the same T – R separation d.having the same T – R separation d.

Log-distance path loss normal gives Log-distance path loss normal gives only the average value of path loss.only the average value of path loss.

Surrounding environment may be Surrounding environment may be vastly different at two locations vastly different at two locations having the same T – R separation d.having the same T – R separation d.

5555

Log-Normal ShadowingLog-Normal ShadowingLog-Normal ShadowingLog-Normal ShadowingMore accurate model includes a random More accurate model includes a random variable to account for change in variable to account for change in environment. environment.

PL(d) [db] PL(d) [db] = PL(d) + X= PL(d) + X

= PL(d= PL(d00) + 10n log (d / d) + 10n log (d / d00) + X) + X

XX -> Zero mean Gaussian -> Zero mean Gaussian random variable (dB)random variable (dB)

-> Standard deviation (dB)-> Standard deviation (dB)

More accurate model includes a random More accurate model includes a random variable to account for change in variable to account for change in environment. environment.

PL(d) [db] PL(d) [db] = PL(d) + X= PL(d) + X

= PL(d= PL(d00) + 10n log (d / d) + 10n log (d / d00) + X) + X

XX -> Zero mean Gaussian -> Zero mean Gaussian random variable (dB)random variable (dB)

-> Standard deviation (dB)-> Standard deviation (dB)

5656

Received Power in Received Power in Log-Normal Shadowing Model Log-Normal Shadowing Model Received Power in Received Power in Log-Normal Shadowing Model Log-Normal Shadowing Model PPRR(d) [dbm] = P(d) [dbm] = PTT[dbm] – PL(d) [db][dbm] – PL(d) [db] Values of n and Values of n and are computed from are computed from

measured data.measured data. Linear regression method which Linear regression method which

minimizes the difference between minimizes the difference between measured and estimated path measured and estimated path

Estimated over a wide range of Estimated over a wide range of measurement locations and T – R measurement locations and T – R separations.separations.

PPRR(d) [dbm] = P(d) [dbm] = PTT[dbm] – PL(d) [db][dbm] – PL(d) [db] Values of n and Values of n and are computed from are computed from

measured data.measured data. Linear regression method which Linear regression method which

minimizes the difference between minimizes the difference between measured and estimated path measured and estimated path

Estimated over a wide range of Estimated over a wide range of measurement locations and T – R measurement locations and T – R separations.separations.

5757

...Received Power in ...Received Power in Log-Normal Shadowing ModelLog-Normal Shadowing Model...Received Power in ...Received Power in Log-Normal Shadowing ModelLog-Normal Shadowing Model

Probability [ PProbability [ PRR (d) > (d) > ] = ] =

Probability [ PProbability [ PRR (d) < (d) < ] = ] =

Probability [ PProbability [ PRR (d) > (d) > ] = ] =

Probability [ PProbability [ PRR (d) < (d) < ] = ] =

)(dPQ R

)(dPQ R

5858

ee xx22//22

zzxx

Calculation of Q FunctionCalculation of Q FunctionCalculation of Q FunctionCalculation of Q Function

Q(z) = Q function =

Q(-z) = 1- Q(z)

Q(0) = 1/ 2

Q(z) obtained from Appendix F,

Table F.1, page 647

Q(z) = Q function =

Q(-z) = 1- Q(z)

Q(0) = 1/ 2

Q(z) obtained from Appendix F,

Table F.1, page 647

dxex

z

x

2

2

2

1

5959

Calculation of Q FunctionCalculation of Q FunctionCalculation of Q FunctionCalculation of Q Function

6060

ExampleExampleExampleExample Four received power measurements Four received power measurements

were taken at the distances of were taken at the distances of 100m, 200m, 1 km and 3 km from a 100m, 200m, 1 km and 3 km from a transmitter. These measured values transmitter. These measured values are given in the following table.are given in the following table.

The path loss equation model for The path loss equation model for other measurements follows log other measurements follows log normal shadowing model where normal shadowing model where dd0 = 100 m. = 100 m.

Four received power measurements Four received power measurements were taken at the distances of were taken at the distances of 100m, 200m, 1 km and 3 km from a 100m, 200m, 1 km and 3 km from a transmitter. These measured values transmitter. These measured values are given in the following table.are given in the following table.

The path loss equation model for The path loss equation model for other measurements follows log other measurements follows log normal shadowing model where normal shadowing model where dd0 = 100 m. = 100 m.

6161

ExampleExampleExampleExampleA. Find the minimum mean square error

(MMSE) estimate for the path loss exponent n.

B. Calculate the standard deviation about the mean value.

C. Estimate the received power at d = 2 km using the resulting model.

D. Predict the likelihood that the received signal at 2 km will be greater than –60 dBm.

A. Find the minimum mean square error (MMSE) estimate for the path loss exponent n.

B. Calculate the standard deviation about the mean value.

C. Estimate the received power at d = 2 km using the resulting model.

D. Predict the likelihood that the received signal at 2 km will be greater than –60 dBm.

6262

Let Pi be the average received power at distance di

Pi (d) = Pi (d0) – 10n log (d /100)

d = d0 = 100m = > P0= 0 dBm

Let Pi be the average received power at distance di

Pi (d) = Pi (d0) – 10n log (d /100)

d = d0 = 100m = > P0= 0 dBm

Solution:Solution:Solution:Solution: T-R distanceT-R distance Measured PowerMeasured Power

100 m 100 m 0 dBm 0 dBm200 m200 m - 20 dBm - 20 dBm1 km1 km - 35 dBm - 35 dBm3 km3 km - 70 dBm - 70 dBm

T-R distanceT-R distance Measured PowerMeasured Power100 m 100 m 0 dBm 0 dBm200 m200 m - 20 dBm - 20 dBm1 km1 km - 35 dBm - 35 dBm3 km3 km - 70 dBm - 70 dBm

6363

A.A.A.A.dd11= 200 m, P= 200 m, P11= -3n, = -3n,

dd22= 1 km, P= 1 km, P33= -10n, = -10n,

dd33= 3 km, P= 3 km, P44= -14.77n= -14.77n

Mean square error J = Mean square error J = (P – P (P – Pii))22

= (0 – 0)= (0 – 0)22 + [-20 – (-3n)] + [-20 – (-3n)] 22

+ [-35 – (-10n)]+ [-35 – (-10n)] 22 + [-70 – (-14.77n)] + [-70 – (-14.77n)]

22

= 6525 – 2887.8n + 327.153n= 6525 – 2887.8n + 327.153n22

Minimum value = > dJ(n) / dnMinimum value = > dJ(n) / dn= 654.306n – 2887.8 = 0= 654.306n – 2887.8 = 0 n = 4.4n = 4.4

dd11= 200 m, P= 200 m, P11= -3n, = -3n,

dd22= 1 km, P= 1 km, P33= -10n, = -10n,

dd33= 3 km, P= 3 km, P44= -14.77n= -14.77n

Mean square error J = Mean square error J = (P – P (P – Pii))22

= (0 – 0)= (0 – 0)22 + [-20 – (-3n)] + [-20 – (-3n)] 22

+ [-35 – (-10n)]+ [-35 – (-10n)] 22 + [-70 – (-14.77n)] + [-70 – (-14.77n)]

22

= 6525 – 2887.8n + 327.153n= 6525 – 2887.8n + 327.153n22

Minimum value = > dJ(n) / dnMinimum value = > dJ(n) / dn= 654.306n – 2887.8 = 0= 654.306n – 2887.8 = 0 n = 4.4n = 4.4

6464

B.B.B.B.

Variance 2 = J / 4 = ( P – Pi)2 / 4

= (0= (0 ++ 0) + (-200) + (-20 +13.2)+13.2)22 + (-35 + (-35 ++ 44)44)22 + (-70 + (-70 ++ 64.988)64.988)22

4= 152.36 / 4 = 38.09

= 6.17 dB

Variance 2 = J / 4 = ( P – Pi)2 / 4

= (0= (0 ++ 0) + (-200) + (-20 +13.2)+13.2)22 + (-35 + (-35 ++ 44)44)22 + (-70 + (-70 ++ 64.988)64.988)22

4= 152.36 / 4 = 38.09

= 6.17 dB

6565

C.C.C.C.

Pi (d = 2 km)

= 0 – 10(4.4) log (2000/100)

= -57.24 dBm

Pi (d = 2 km)

= 0 – 10(4.4) log (2000/100)

= -57.24 dBm

6666

D.D.D.D.Probability that the received signal will be greater than –60 dBm is:

_____PR = [PR(d) > -60 dBm] = Q [(- PR (d)) / ]

= Q [(-60 + 57.24) / 6.17 ]= Q [- 0.4473]= 1 – Q [0.4473]= 1 – 0.326= 0.674 = > 67.4%

Probability that the received signal will be greater than –60 dBm is:

_____PR = [PR(d) > -60 dBm] = Q [(- PR (d)) / ]

= Q [(-60 + 57.24) / 6.17 ]= Q [- 0.4473]= 1 – Q [0.4473]= 1 – 0.326= 0.674 = > 67.4%

6767

Area AArea A

% of Coverage Area% of Coverage Area% of Coverage Area% of Coverage Area Given a circular Given a circular

coverage area coverage area of radius R...of radius R...

In the area A, the received power PR

The area A is defined as U()

Given a circular Given a circular coverage area coverage area of radius R...of radius R...

In the area A, the received power PR

The area A is defined as U()

r R

6868

Calculation of Coverage Area U(Calculation of Coverage Area U())Calculation of Coverage Area U(Calculation of Coverage Area U())

U (U () = (1 / ) = (1 / R R22 )) ƒ Prob [PProb [PRR (R) > (R) > ] dA ] dA

__________

Where Prob [PWhere Prob [PRR ( (RR) > ) > ] = Q [ ] = Q [ - P - PRR ( (RR) / ) / ] ]

U (U () = (1 / ) = (1 / R R22 )) ƒ Prob [PProb [PRR (R) > (R) > ] dA ] dA

__________

Where Prob [PWhere Prob [PRR ( (RR) > ) > ] = Q [ ] = Q [ - P - PRR ( (RR) / ) / ] ]

6969

Final Equation for U(Final Equation for U())Final Equation for U(Final Equation for U())

The error function erf(z) =

The error function erf(z) =

)2(21

2

0

2

zQ

ez

x

2

log102

)log(10)(

:

))]1(1()(1[

2

1)(

00

)21(2

enb

dR

ndPLP

a

whereb

aberfeaerfU

t

b

ab

7070

Alternate method: Use Fig. 4.18 (p 143)Alternate method: Use Fig. 4.18 (p 143)Alternate method: Use Fig. 4.18 (p 143)Alternate method: Use Fig. 4.18 (p 143)

7171

ExampleExampleExampleExampleFor the previous problem, For the previous problem, predict the percentage of area predict the percentage of area with a 2 km radius cell that with a 2 km radius cell that receives signals greater than receives signals greater than –60 dBm.–60 dBm.

For the previous problem, For the previous problem, predict the percentage of area predict the percentage of area with a 2 km radius cell that with a 2 km radius cell that receives signals greater than receives signals greater than –60 dBm.–60 dBm.

7272

SolutionSolutionSolutionSolutionFrom solution to previous example,From solution to previous example,

Prob [PProb [PR (R) > (R) > ] = 0.674 ] = 0.674 =>(=>( / n) = 6.17 / 4.4 / n) = 6.17 / 4.4

= 1.402= 1.402

From Figure 4.18, From Figure 4.18, Fraction of total area = 0.92 => 92%Fraction of total area = 0.92 => 92%

From solution to previous example,From solution to previous example,

Prob [PProb [PR (R) > (R) > ] = 0.674 ] = 0.674 =>(=>( / n) = 6.17 / 4.4 / n) = 6.17 / 4.4

= 1.402= 1.402

From Figure 4.18, From Figure 4.18, Fraction of total area = 0.92 => 92%Fraction of total area = 0.92 => 92%

7373

Other Propagation ModelsOther Propagation ModelsOther Propagation ModelsOther Propagation Models Outdoor propagation modelsOutdoor propagation models

Longley Rice model: Longley Rice model: point-to-point communication systems point-to-point communication systems (40MHz–100MHz)(40MHz–100MHz)

Okumara’s model: Okumara’s model: widely used in urban areas widely used in urban areas (150 MHz – 300 MHz)(150 MHz – 300 MHz)

Hata model: Hata model: graphical path lossgraphical path loss(150 MHz – 1500 MHz)(150 MHz – 1500 MHz)

Outdoor propagation modelsOutdoor propagation models Longley Rice model: Longley Rice model:

point-to-point communication systems point-to-point communication systems (40MHz–100MHz)(40MHz–100MHz)

Okumara’s model: Okumara’s model: widely used in urban areas widely used in urban areas (150 MHz – 300 MHz)(150 MHz – 300 MHz)

Hata model: Hata model: graphical path lossgraphical path loss(150 MHz – 1500 MHz)(150 MHz – 1500 MHz)

7474

Other Propagation ModelsOther Propagation ModelsOther Propagation ModelsOther Propagation Models Indoor propagation modelsIndoor propagation models

Log-distance path loss Log-distance path loss modelmodel

Ericsson multiple Ericsson multiple breakdown modelbreakdown model

Indoor propagation modelsIndoor propagation models Log-distance path loss Log-distance path loss

modelmodel Ericsson multiple Ericsson multiple

breakdown modelbreakdown model