Seybold J.S. Introduction to RF Propagation

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is the height of the mobile antenna

d is the propagation distance

b=(40/f )

, where f is in MHz

Note that the Egli model provides the entire path loss, whereas the foliage

models discussed earlier provided the loss in addition to free-space loss. Also

note that the Egli model is for irregular terrain and does not address vegeta-

tion. While similar to the ground-bounce loss formula, the Egli model is not

based on the same physics, but rather is an empirical match to measured data

[4]. By assuming a log-normal distribution of terrain height, Egli generated a

family of curves showing the terrain factor or adjustment to the median path

loss for the desired fade probability [6]. This way the analyst can determine

the mean or median signal level at a given percentage of locations on the circle

of radius d. Stated another way, the Egli model provides the median path loss

due to terrain loss. If a terrain loss point other than the median (50%) is

desired, the adjustment factor in dB can be inferred from Figure 7.6.

Example 7.2. Determine the median terrain loss for a 1-km link operating at

100 MHz if the antenna heights are 20 m and 3 m, using the Egli model for

terrain loss.

142 NEAR-EARTH PROPAGATION MODELS

+20

+15

+10

–5

–10

–15

–20

–25

–30

40 50 60 80 100 150 200 300 500

1000

Median–50

Percent of

locations

Terrain factor, dB

99.9

Frequency (MHz)

Figure 7.6 Terrain factor versus frequency for different probabilities for the Egli

model. (Figure 3.20 from Ref. 4, courtesy of Wiley.)

Applying equation (7.9),

and thus

If the 90th percentile is desired (i.e., the level of terrain loss that will be

exceeded 10% of the time), approximately 10 dB would be added to the L

value according to Figure 7.6, so

䊐

The Egli model provides a nice, closed-form way to model terrain effects, but

since it is a one-size-ﬁts-all model, it should not be expected to provide precise

results in all situations. For detailed planning, there are software packages

available that use DTED (Digitized Terrain Elevation Data) or similar terrain

data and model the expected diffraction loss on a given path. Such models are

ideal for planning ﬁxed links, but are of limited utility for mobile links. One

exception is the Longley-Rice model, which provides both point-to-point and

area terrain loss predictions.

7.3.2 Longley–Rice Model

The Longley–Rice model is a very detailed model that was developed in the

1960s and has been reﬁned over the years [8–10]. The model is based on data

collected between 40 MHz and 100 GHz, at ranges from 1 to 2000 km, at

antenna heights between 0.5 and 3000 m, and for both vertical and horizontal

polarization. The model accounts for terrain, climate, and subsoil conditions

and ground curvature. Blaunstein [8] provides a detailed description of the

model, while Parsons [9] provides details determining the inputs to the model.

Because of the level of detail in the model, it is generally applied in the form

of a computer program that accepts the required parameters and computes

the expected path loss. At the time of this writing, the U.S. National Telecom-

munications and Information Administration (NTIA) provides one such

program on its website [11] free of charge. Many commercial simulation prod-

ucts include the Longley–Rice model for their terrain modeling. As indicated

in the previous section, the Longley–Rice model has two modes, point-to-point

and area. The point-to-point mode makes use of detailed terrain data or char-

acteristics to predict the path loss, whereas the area mode uses general infor-

mation about the terrain characteristics to predict the path loss.

dB= 122 2.

dB= 112 4.

◊

()

20 3

log .

TERRAIN MODELING 143

7.3.3 ITU Model

The ITU terrain model is based on diffraction theory and provides a relatively

quick means of determining a median path loss [12]. Figure 7.7 shows three

plots of the expected diffraction loss due to terrain roughness versus the

normalized terrain clearance. Curve B is the theoretical knife-edge diffraction

curve. Curve D is the theoretical smooth-earth loss at 6.5 GHz using a 4/3 earth

radius. The curve labeled A

is the ITU terrain loss model over intermediate

terrain. Each of these curves represents the excess terrain loss, beyond free-

space loss. The ITU terrain loss model is given by

144 NEAR-EARTH PROPAGATION MODELS

–1.5 –1 –0.5 0 0.5 1

Figure 7.7 Additional loss due to terrain diffraction versus the normalized clearance.

(Figure 1 from Ref. 12, courtesy of the ITU.)

(7.10)

where h is the height difference between the most signiﬁcant path blockage

and the line-of-sight path between the transmitter and the receiver. If the

blockage is above the line of sight, then h is negative. F

is the radius of the

ﬁrst Fresnel zone (Fresnel zones are discussed in Chapter 8) and is given by

(7.11)

where

and d

are the distances from each terminal to the blockage in

kilometers

d is the distance between the terminals in km

f is the frequency in GHz

The ratio h/F

is the normalized terrain clearance (h/F

< 0 when the terrain

blocks the line of sight). This model is generally considered valid for losses

above 15 dB, but it is acceptable to extrapolate it to as little as 6 dB of loss as

shown in Figure 7.7. The other two curves shown represent extremes of clear

terrain and very rough terrain, so they provide insight into the variability that

can be expected for any given value of normalized clearance.

Example 7.3. A VHF military vehicle communication system needs to com-

municate with other military vehicles over a distance of 3 km over fairly rough

terrain (±2 m) at 100 MHz. The antenna is a 1.5-m whip mounted on the

vehicle, approximately 2 m above the ground. How much terrain loss should

be expected over and above the free-space loss?

The center of radiation for the antenna is 2.75 m above the ground. If a

ﬂat-earth model is used, then the maximum terrain height of +2 m results in

a minimum antenna height above the terrain of

In the absence of speciﬁc information about the location of any blockage

within the line of sight, assume that the blockage occurs at the midpoint of the

path, d/2. The expression for F

reduces to

Next, by substituting d = 3 and f = 0.1 the value of F

is found to be

47 4= .

17 3

= .m

h = 075.m

17 3= .m

AhF

=- +20 10

TERRAIN MODELING 145

The normalized terrain clearance is h/F

= 0.0158 and the terrain attenuation

which is consistent with Figure 7.7. The plot also shows that terrain loss in the

region of 6–15 dB might be reasonably expected. 䊐

7.4 PROPAGATION IN BUILT-UP AREAS

Propagation of electromagnetic waves through developed areas from sub-

urban to dense urban is of considerable interest, particularly for mobile tele-

phony. This is a vast subject with numerous papers and models available. The

actual propagation of RF though an urban environment is dependent upon

frequency, polarization, building geometry, material structure, orientation,

height, and density. This section treats propagation between elevated base sta-

tions and mobiles that are at street level in urban and suburban areas [13].

The goal is to determine the median path loss or RSL as a function of the dis-

tance, d, so that the required multipath fading models can then be applied

(Chapter 8). The median value depends heavily upon the size and density of

the buildings, so classiﬁcation of urban terrain is important. The models dis-

cussed are the Young, Okumura, Hata, and Lee models.

7.4.1 Young Model

The Young data were taken in New York City in 1952 and covers frequencies

of 150–3700 MHz [14, 15].The curve presented in Figure 7.8 displays an inverse

fourth-power law behavior, similar to the Egli model. The model for Young’s

data is

(7.12)

where b is called the clutter factor and is not the same b used in the Egli model!

This b is also distinct from the b sometimes used for building volume over a

sample area in classiﬁcation [16]. From Young’s measurements, b is approxi-

mately 25 dB for New York City at 150 MHz. The data in Figure 7.8 suggests

that a log-normal ﬁt to the variation in mean signal level is reasonable.

7.4.2 Okumura Model

The Okumura model is based on measurements made in Tokyo in 1960,

between 200 and 1920 MHz [17–20]. While not representative of modern U.S.

cities, the data and model are still widely used as a basis of comparison. The

LGG

= 97.dB

146 NEAR-EARTH PROPAGATION MODELS

model is empirical, being based solely on the measured data. The actual path

loss predictions are made based on graphs of Okumura’s results, with various

correction factors applied for some parameters.

For the Okumura model, the prediction area is divided into terrain cate-

gories: open area, suburban area, and urban area. The open-area model rep-

resents locations with open space, no tall trees or buildings in the path, and

the land cleared for 300–400 m ahead (i.e., farmland). The suburban area

model represents a village or a highway scattered with trees and houses, some

obstacles near the mobile, but not very congested. The urban area model rep-

resents a built-up city or large town with large buildings and houses with two

or more stories, or larger villages with close houses and tall thickly grown trees.

The Okumura model uses the urban area as a baseline and then applies cor-

rection factors for conversion to other classiﬁcations. A series of terrain types

is also deﬁned. Quasi-smooth terrain is the reference terrain and correction

factors are applied for other types of terrain. Okumura’s expression for the

median path loss is

(7.13)

where

LLAHH

FSL mu tu ru50

()

=+--

PROPAGATION IN BUILT-UP AREAS 147

100

110

120

130

140

150

160

170

0.1 0.2 0.3 0.5 0.7 1.0 2 3 4 5 7 10 20 30

d, miles

Loss, dB

Flat terrain

10%

50%

90%

99%

Figure 7.8 Results of Young’s measurement of path loss versus distance in miles in

Manhattan and the Bronx at 150 MHz. (Figure 7.1 from Ref. 15, courtesy of Artech

House.)

FSL

is the free-space loss for the given distance and frequency

is the median attenuation relative to free-space loss in an urban area,

with quasi-smooth terrain, base station effective height h

= 200 m, and

mobile antenna height h

= 3m; the value of A

is a function of both

frequency and distance

is the base station height gain factor

is the mobile antenna height gain factor

The signs on the gain factors are very important. Some works have reversed

the signs on the H terms, which will of course lead to erroneous results. If in

doubt, check the results using known test cases, or engineering judgment. For

instance, if increasing the antenna height increases the median path loss, then

the sign of the antenna height correction factor is clearly reversed.

Figure 7.9 shows plots of A

versus frequency for various distances. Figure

7.10 shows the base station height gain factor in urban areas versus effective

148 NEAR-EARTH PROPAGATION MODELS

100

Basic median attentuation A

(f, d ) (dB)

= 3 m

= 200 m

Urban area

200 300 500

Frequency f (MHz)

700 1000 2000

3000

100

d (km)

Figure 7.9 Plot of A

versus frequency for use with the Okumura model. (Figure 4.7

Ref. 13, courtesy of Wiley.)

height for various distances, while Figure 7.11 shows the vehicle antenna

height gain factor versus effective antenna height for various frequencies and

levels of urbanization. Figure 7.12 shows how the base station antenna height

is measured relative to the mean terrain height between 3 and 15 km in the

direction of the receiver.

Example 7.4. Consider a system with the following parameters:

d = 37.km

f ==870 0 345MHz m, .l

= 3m

= 68 m

PROPAGATION IN BUILT-UP AREAS 149

–10

–20

–30

20 30 50

Base station effective antenna height h

(m)

70 100 200 300 500 700 1000

d (km)

100

70~

100

1~10

Height gain factor H

, d ) (dB)

Urban area

= 200 m

Figure 7.10 Plot of H

, the base station height correction factor, for the Okumura

model. (Figure 4.8 from Ref. 13, courtesy of Wiley.)

150 NEAR-EARTH PROPAGATION MODELS

2000

1000

700

400

200

100

200

400~

1000

Antenna height gain factor H

, f ) (dB)

–5

23 5710

Vehicular station antenna height h

(m)

400 MHz

200 MHz

Urban area

Medium cityLarge city

f (MHz)

Figure 7.11 Plot of H

, the mobile station height correction factor for the Okumura

model. (Figure 4.9 from Ref. 13, courtesy of Wiley.)

3 km

15 km

Average height

Figure 7.12 Measuring effective transmitter height. (Figure 4.10 from Ref. 13, cour-

tesy of Wiley.)

What is the predicted path loss using the Okumura model?

First, it is readily determined that

Then the required correction factors from Figures 7.9 and 7.10 are incorpo-

rated to get the resulting median path loss:

Note that an H

correction factor is not required since the mobile antenna is

at 3 m, which is the reference height. 䊐

7.4.3 Hata Model

The Hata model (sometimes called the Okumura–Hata model) is an empiri-

cal formulation that incorporates the graphical information from the

Okumura model [21–23]. There are three different formulas for the Hata

model: for urban areas, for suburban areas, and for open areas.

Urban Areas

(7.14)

where

150 < f

< 1500, f

in MHz

30 < h

< 200, h

in m

1 < d < 20, d in km

and a(h

) is the mobile antenna height correction factor. For a small- or

medium-sized city:

(7.15)

and for a large city:

(7.16)

()

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8 29 1 54 1 1 200

3 2 11 75 4 97 400

. log . . ,

MHz

ah f h f h

rcr c r

()

££11 07 156 08 1 10. log . . log . , m

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102 6 26 8 136 6dB dB

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= 102 6.dB

PROPAGATION IN BUILT-UP AREAS 151