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TOPIC 8:

Terrain ModelsEE 542

Fall 2008

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Outline

• Fixed Terrestrial Links – Terrain as sharp edges

 – Outdoor propagation models• Satellite Links

References:Simon R. Saunders, “Antennas and Propagation for

Wireless Communication Systems,” Wiley.

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Fixed Terrestrial Links

• Involve a pair of stations mounted on

masts and separated by 10-100s of km.• Masts are typically many 10s of meters

high.• Highly directional antennas are used to

allow for a generous fade margin.

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Free Space Path Loss Model

2

2

2

4

4

4

( ) 32.4 20log 20log

 R T T R

 R

T R

T 

T T R

FS 

 R

FS MHz

P P G G R

P G GP R

P G G R L P

 L dB R f 

λ 

π 

λ π 

π 

λ 

⎛ ⎞=   ⎜ ⎟⎝ ⎠

⎛ ⎞=   ⎜ ⎟⎝ ⎠

⎛ ⎞= ⎜ ⎟⎝ ⎠

= + +

From Frii’s equation:

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Single Knife Edge Loss Model

1 0.225( ) 20log 20log

2KE 

 L vvvπ 

− = −For (v>1)

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Single Obstruction Example

 A microwave link operating at 10GHz with a pathlength of 30 km has a maximum acceptable

path loss of 169 dB. The TX antenna ismounted 20 m above the ground, while theheight of the receiver antenna is TBD. The

ground is level except for a 80 m high hilllocated 10 km away from the TX.

a) Calculate the total path loss assuming the RXis mounted 20m above the ground.

b) Calculate the height of the RX antenna for thepath loss to be just equal to the maximumacceptable value.

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Solution

( ) 32.4 20log 20log

32.4 20log30 20log10000

142

F MHz L dB R f 

dB

= + +

= + +

=

Free space loss:a)

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Solution

Single KE Loss:

2

1

3

2 3 31

60 10 20

; 3 10

2 30 102 60 63 10 10 10 20 10

o o

o o

o o

h m km r km

r  R m

r 

v h R

 ρ 

 ρ λ λ 

 ρ 

−

−

= = =

= = ×

+× ×

= =× × × × ×

Since v>1, use

0.225( ) 20log

28.5

KE  L v

vdB

−

=

a)

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Solution

Total path Loss:

( )

142 28.5 170.5 ( )

FS KE   L L L dB

 L dB

= +

= + =

The total loss is in excess of the acceptable limit!

a)

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Solution

b)We can’t do anything about free space loss unless we are allowed to

change the geometry or frequency. Assuming the RX tower height is the

only variable we can change, we need to reduce the obstruction loss.

The acceptable level for the obstruction loss is: 169-142 = 27 dB. Thus, the

RX antenna height can be determined as:

2720

0.225( ) 27 20log

0.225

510

10 50

2( )

KE 

o o

o o

 L dBv

v

r h v v m

r 

λρ 

 ρ 

−

⎛ ⎞= = −   ⎜ ⎟⎝ ⎠

= =

= = × =

+

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Multiple Knife Edge Diffraction

Models

• Bullington (1946)

• Epstein (1953)

• Deygout (1994)

• Giovanelli (modification to

Deygout)

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Bullington Method

Defines a new effective obstacle at the point where the LOS from the two antennas

cross.

TX RX

Equivalent problem:

hm

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Bullington Method - 2

• Very simple method

• Important obstacles can be ignored,therefore losses can be underestimated

• Reasonably accurate when two KEs rerelatively close.

• Not an accurate method in general as thesame equivalent KE can be the solution to

multiple scenarios.

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Bullington Method -3

TX RX

hm

a ab b

Cases a and b are treated identically.

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Epstein-Peterson Method

Draw lines-of-sight between relevant obstacles and add

the diffraction losses at each obstacle.

TX RX

21 3

L1: (TX-1-2)L1 = L(d1,d2,h1)

L2: (2-3-RX)L2 = L(d3,d4,h3)

L = L1 + L2

h1

d1 d2 d4d3

h3

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Epstein-Peterson - 2

• Overcomes the primary limitation of

Bullington – that important obstacles canbe ignored.

• Has large errors for two closely spacedobstructions. In this case Bullington

method is better.

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Deygout Method

• Search the entire path for a main obstacle,

i.e., the point with the highest value of valong the path.

• Diffraction losses over "secondary"

obstacles may be added to the diffractionloss over the main obstacle.

• Diffraction for secondary obstacles iscalculated wrt the main obstacle and thevisible terminal.

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Deygout Method - 2

m1

Main obstacle

vmax

Secondary termMain term

2

Secondary term

L = Lm + L1 + L2

L1: TX-1-m

L1 = L(d1,d2,h1)

d1 d2 d3 d4

h1

L2: m-2-RXL2 = L(d3,d4,h2)

h2

TX RX

Lm: TX-m-RX

Lm = L(d1+d2,hm,d3+d4)

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Deygout Method - 3

• Typically agrees well with rigorous

techniques• Overestimates loss, especially when there

are multiple obstacles close together 

• The accuracy is higher when there is onedominant obstacle

• Superior to Bullington and Epstein-Peterson methods for highly obstructedpaths

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Giovanelli Method

• Modification to Deygout Method

• Identifies a main obstacle as in Deygout.• Find a reference point for diffraction

calculations

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Other Methods

• Many different approaches exist.

• Some are modifications to the methodsmentioned.

• Examples: – Causebrook

 – Vogler (analytic approach)

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Good agreement for large h2

Vogler 

grazing

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Vogler 

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Other Outdoor Propagation Models

• The methods discussed so far all depend onreducing the terrain to sharp edges.

• The terrain profile may vary from a simplecurved earth profile to a highly mountainousprofile with the presence of trees, buildings andother obstacles.

• This results in deterministic + randomcomponents for the path loss.

• Numerous propagation models exist based onmeasurement data and statistical methods.

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Outdoor Propagation Models

• Longley-Rice

• Durkin• Okumura

• Hata• Lee

• ….. So on…

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Okumura Model

• One of the most widely used models for signalprediction in urban areas.

• Fully empirical method, based on extensiveseries of measurements made around Tokyo.

• There is no attempt to base the prediction to a

physical method.• In general applicable to

 – f: [150 MHz – 1920 MHz]

 – D: [1km – 100 km] – H: [30 m – 1000 m]

• Predictions are made via a series of graphs

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Okumura-Hata Model

• Hata approximated Okumura’s

measurements in a set of formulae.• The urban values have been standardized

by ITU for international use.

• The method involves dividing the area into

a series of categories: open, suburban and

urban.

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Okumura-Hata Model

• The median path loss are calculated using

the following expressions:

 – URBAN: L(dB) = A + BlogR – E

 – SUBURBAN L(dB) = A + BlogR – C

 – OPEN L(dB) = A + BlogR - D

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Okumura-Hata Model

( )

( )

( )

2

2

2

2

69.55 26.16log 13.82log

44.9 6.55log

2 log( ) 5.428

4.78 log 18.33log 40.94

3.2 log(11.75 ) 4.97 for large cities, 300

8.29 log(1.54 ) 1.1 for large cities, 300

c b

b

c

c c

m c

m c

 A f h

 B h

 f C 

 D f f 

 E h f MHz

 E h f MHz

 E 

= + −

= −

⎛ ⎞= +⎜ ⎟⎝ ⎠

= + +

= − ≥

= − <= ( ) ( )1.1log 0.7 1.56log 0.8 for medium to small citiesc m c f h f − − −

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Fixed Satellite Links

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Specific Attenuation Through Trees

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Specific Attenuation Through Trees

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Scintillation Event – Scintillation

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Only

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