Seybold J.S. Introduction to RF Propagation

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REFERENCES

1. ITU-R Recommendations, The radio refractive index: Its formula and refractivity

data, ITU-R P.453-8, Geneva, 2001.

2. ITU-R Recommendations, Propagation data and prediction methods required for

the design of terrestrial line-of-sight system, ITU-R P.530-9, Geneva, 2001.

3. J. D. Parsons, The Mobile Radio Propagation Channel, 2nd ed., Wiley, West Sussex,

2000, p. 29.

4. ITU-R Recommendations, Reference standard atmospheres, ITU-R P.835-3,

Geneva, 1999.

5. J. D. Parsons, The Mobile Radio Propagation Channel, 2nd ed., Wiley, West Sussex,

2000, p. 28.

6. J. D. Parsons, The Mobile Radio Propagation Channel, 2nd ed., Wiley, West Sussex,

2000, p. 31.

7. W. T. Barnett, Multipath propagation at 4, 6, and 11 GHz, The Bell System Techni-

cal Journal, Vol. 51, No. 2, February 1972, pp. 311–361.

8. K. Morita, Prediction of Rayleigh fading occurrence probability of line-of-sight

microwave links, Review of Electrical Communication Laboratories, Vol. 18,

December 1970, pp. 310–321.

9. R. L. Olsen and B. Segal, New techniques for predicting the multipath fading dis-

tribution on VHF/UHF/SHF terrestrial line-of-sight links in Canada, Canadian

Journal of Electrical and Computing Engineering, Vol. 17, No. 1, 1992, pp. 11–23.

10. R. L. Olsen, T. Tjelta, L. Martin, and B. Segal, Worldwide techniques for predicting

the multipath fading distribution on terrestrial L.O.S. links: Comparison with

regional techniques, IEEE Transactions on Antennas and Propagation, Vol. 51, No.

1, January 2003, pp. 23–30.

11. ITU-R Recommendations, Propagation data and prediction methods required for

the design of terrestrial line-of-sight systems, ITU-R P.530-8, Geneva, 1999.

12. ITU-R Recommendations, Attenuation by atmospheric gases, ITU-R P.676-5,

Geneva, 2001.

13. S. A. A. Abdulla, H. M. Al-Rizzo, and M. M. Cyril, Particle size distribution of Iraqi

sand and dust storms and their inﬂuence on microwave communication systems,

IEEE Transactions on Antennas and Propagation, Vol. 36, No. 1, January 1988,

pp. 114–126.

14. ITU-R Recommendations, Attenuation due to clouds and fog, ITU-R P.840-3,

Geneva, 1999.

EXERCISES

1. A point-to-point communication system has one antenna mounted on a

5-m tower and antenna at the other end of the link is mounted on a 10-m

tower.

(a) What is the distance to the horizon for each antenna?

(b) What is the maximum possible link distance if only line-of-sight is

considered?

132 ATMOSPHERIC EFFECTS

expected amount of water vapor and oxygen loss?

(d) How would these results change if the path were located in a semi-

tropical climate and over a large body of water?

2. What is the probability of a 10-dB or greater multipath fade for a point-to-

point communications link that parallels the coast in the Paciﬁc Northwest

region of the United States? The link is operating at 28 GHz over a 10-km

distance, and the antennas are mounted on 30-m towers.

3. Repeat problem 2 if the link is located along the California coast.

4. Consider a 38-GHz, point-to-point communication system operating on

the east coast of Florida. If the antennas are mounted on 10-m towers and

the communication distance is 8 km, how much multipath fade margin is

required if a 98% multipath availability is required?

5. Consider a ground-to-air communication link operating at 18 GHz. If the

nominal elevation angle to the aircraft is 30 degrees, what is the worst-case

cloud attenuation that can be expected?

6. Approximately how much attenuation will be experienced by a 0.8-km,

1.9-GHz PCS link operating near the Florida coast:

(a) Due to atmospheric absorption?

(b) Due to fog?

EXERCISES 133

134

Introduction to RF Propagation, by John S. Seybold

CHAPTER 7

Near-Earth Propagation Models

7.1 INTRODUCTION

Many applications require RF or microwave propagation from point to point

very near the earth’s surface and in the presence of various impairments.

Examples of such applications include cellular telephones, public service radio,

pagers, broadcast television and radio stations, and differential GPS transmit-

ters. Propagation loss over terrain, foliage, and/or buildings may be attributed

to various phenomena, including diffraction, reﬂection, absorption, or scatter-

ing. In this chapter, several different models are considered for determining

the median (50%) path loss as a function of distance and conditions. These

models are all based on measurements (sometimes with theoretical exten-

sions) and represent a statistical mean or median of the expected path loss.

In the next chapter, the effects of multipath and shadowing are examined in

detail. Much of the data collection for near-earth propagation impairment has

been done in support of mobile VHF communications and, more recently,

mobile telephony (which operates between 800 MHz and 2 GHz). Thus many

of the models are focused in this frequency range. While for the most part,

models based on this data are only validated up to 2 GHz, in practice they can

sometimes be extended beyond that if required. Some of the recent measure-

ment campaigns and models have speciﬁcally targeted higher-frequency oper-

ation, particularly the updated ITU models. In their tutorial paper, Bertoni

et al. [1] provide an excellent overview of the subject of near-earth propaga-

tion modeling.

7.2 FOLIAGE MODELS

Most terrestrial communications systems require signals to pass over or

through foliage at some point. This section presents a few of the better-known

foliage models. These models provide an estimate of the additional attenua-

tion due to foliage that is within the line-of-sight (LOS) path. There are of

course, a variety of different models and a wide variation in foliage types. For

that reason, it is valuable to verify a particular model’s applicability to a given

region based on historical use or comparison of the model predictions to meas-

ured results.

7.2.1 Weissberger’s Model

Weissberger’s modiﬁed exponential decay model [2, 3] is given by

(7.1)

where

is the depth of foliage along the LOS path in meters

F is the frequency in GHz

The attenuation predicted by Weissberger’s model is in addition to free-space

(and any other nonfoliage) loss. Weissberger’s modiﬁed exponential decay

model applies when the propagation path is blocked by dense, dry, leafed trees.

It is important that the foliage depth be expressed in meters and that the fre-

quency is in GHz. Blaunstein [3] indicates that the model covers the frequency

range from 230 MHz to 95 GHz.

7.2.2 Early ITU Vegetation Model

The early ITU foliage model [4] was adopted by the CCIR (the ITU’s prede-

cessor) in 1986. While the model has been superseded by a more recent ITU

recommendation, it is an easily applied model that provides results that are

fairly consistent with the Weissberger model. The model is given by

(7.2)

where

F is the frequency in MHz

is the depth of the foliage along the LOS path in meters

Figures 7.1 and 7.2 show comparisons of the Weissberger and ITU models, for

foliage depths of 5, 20, 50, and 100 m. Note that the frequency scale is in GHz

for each plot, but the frequency used in the model is MHz for the ITU model

as speciﬁed. The plots indicate a moderate variation between the models, par-

ticularly as frequency increases. The amount of foliage loss is monotonically

increasing with foliage depth and frequency as expected.

LFd

dB dB

()

= 02

03 06

LdB

Fd d

()

<£

1 33 14 400

045 0 14

0 284 0 588

0 284

FOLIAGE MODELS 135

136 NEAR-EARTH PROPAGATION MODELS

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Weissberger 5 m

ITU 5 m

Weissberger 20 m

ITU 20 m

Vegetation Loss

Frequency (GHz)

Loss (dB)

20 m

5 m

Figure 7.1 Vegetation loss versus frequency for 5- and 20-m foliage depth.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Weissberger 50 m

ITU 50 m

Weissberger 100 m

ITU 100 m

Vegetation Loss

Frequency (GHz)

Loss (dB)

100 m

Figure 7.2 Vegetation loss versus frequency for 50- and 100-m foliage depth.

Example 7.1. Consider a system with the following parameters:

with 12 m of trees in the LOS and vegetation (leaves) present. What is the total

predicted median path loss for this system (excluding antenna gains).

First, compute the free-space loss (FSL):

since

For the Weissberger model, d

< 14 m, so

With d

= 12 m, this yields

Thus the total median path loss predicted by the Weissberger model is

For the ITU model, the loss is given by

With d

= 12 m, the loss due to foliage is found to be

So the total median path loss predicted by the ITU model is

䊐

7.2.3 Updated ITU Vegetation Model

The current ITU models are fairly speciﬁc and do not cover all possible sce-

narios. Nonetheless they are valuable and represent a recent consensus. One

of the key elements of the updated model, which should also be considered

in applying other models is that there is a limit to the magnitude of the

dB= 99 5.

dB= 706.

fdB

MHz=

()

0 2 1000

03 06

97 8= .dB

dB= 54.

GHz=

()

0451

0 284

l= =0 3 1000.,mmd

FSL dB=-

=20

92 44log .

df==11km GHz,

FOLIAGE MODELS 137

attenuation due to foliage, since there will always be a diffraction path over

and/or around the vegetation [5].

7.2.3.1 Terrestrial Path with One Terminal in Woodland The scenario

covered by this model is shown in Figure 7.3. The model for the excess atten-

uation due to vegetation is

(7.3)

where

d is the length of the path that is within the woodland in meters

g is the speciﬁc attenuation for very short vegetative paths (dB/m)

is the maximum attenuation for one terminal within a speciﬁc type and

depth of vegetation (dB)

The excess attenuation due to vegetation is, of course, added to the free-space

loss and the losses from all other phenomena to determine the total predicted

path loss. Some typical values for the speciﬁc attenuation are plotted versus

frequency in Figure 7.4.

7.2.3.2 Single Vegetative Obstruction If neither end of the link is within

woodland, but there is vegetation within the path, the attenuation can be

modeled using the speciﬁc attenuation of the vegetation. For this model to

apply, the vegetation must be of a single type, such as a tree canopy, as opposed

to a variety of vegetation. When the frequency is at or below 3 GHz, the veg-

etation loss model is

(7.4)

where

d is the length of the path that is within the vegetation (in meters)

g is the speciﬁc attenuation for short vegetative paths (dB/m)

£ the lowest excess attenuation for any other path (dB)

AA e

ev m

[]

138 NEAR-EARTH PROPAGATION MODELS

( )

Woodland

Figure 7.3 Propagation path with one terminal in woodland for ITU model.

The restriction on A

ensures that if the vegetation loss is very large, any alter-

nate paths such as a diffraction path will determine the path loss. The ITU

indicates that this model is an approximation and will tend to overestimate

the actual foliage attenuation.

The updated ITU model does not provide for coverage between 3 and

5 GHz other than the one terminal in woodland model. Above 5GHz, the

updated ITU model is based on the type of foliage, the depth of the foliage,

and the illuminated area of the foliage. The excess attenuation due to vegeta-

tion is given by

(7.5)

where

= af, the initial slope

•

= b/f

, the ﬁnal slope

ARdke

veg

=+-

•

()

•

FOLIAGE MODELS 139

Figure 7.4 Speciﬁc attenuation due to vegetation versus frequency. (Figure 2 from

Ref. 5, courtesy of the ITU.)

f is the frequency of operation (in GHz)

a, b, and c are given in Table 7.1

and

(7.6)

where k

, A

, and R

are also given in Table 7.1. A

min

is the illumination area,

which is computed based on the size of the vegetation patch and the illumi-

nation pattern of the antenna. The deﬁnition of A

min

is the smallest height by

the smallest width of illuminated clutter.The height and width are determined

by the height and width of the clutter patch and by the height and width of

the transmit and the receive antenna patterns (3-dB beamwidth) where they

intersect the vegetation. Figure 7.5 shows the geometry of h

, h

, w

, and

(7.7)

Ahhhwww

vvmin

()

min , , min , ,

12 1 2

kk A e e

=- -

()

[]

10 1 1

log

min

140 NEAR-EARTH PROPAGATION MODELS

TABLE 7.1 Parameters for Updated ITU Model

Parameter In Leaf Out of Leaf

a 0.2 0.16

b 1.27 2.59

c 0.63 0.85

6.57 12.6

0.0002 2.1

10 10

Source: Table 1 from Ref. 5, courtesy of the ITU.

Figure 7.5 Geometry of minimum illuminated vegetation area. (Figure 3 from Ref. 5,

courtesy of the ITU.)

The expression for A

min

can also be written in terms of the distances to the

vegetation and the elevation and azimuth beamwidths of the antennas.

(7.8)

where

and r

are the distances to the vegetation as shown in Figure 7.5

and f

are the transmit and receive elevation beamwidths

and q

are the transmit and receive azimuth beamwidths

and w

are the height and width of the vegetation patch

7.3 TERRAIN MODELING

For ground-based communications, the local terrain features signiﬁcantly

affect the propagation of electromagnetic waves. Terrain is deﬁned as the

natural geographic features of the land over which the propagation is taking

place. It does not include vegetation or man-made features. When the terrain

is very ﬂat, only potential multipath reﬂections and earth diffraction, if near

the radio horizon, need to be considered. Varied terrain, on the other hand,

can produce diffraction loss, shadowing, blockage, and diffuse multipath,

even over moderate distances. The purpose of a terrain model is to provide

a measure of the median path loss as a function of distance and terrain

roughness. The variation about the median due to other effects are then

treated separately.

7.3.1 Egli Model

While not a universal model, the Egli model’s ease of implementation and

agreement with empirical data make it a popular choice, particularly for a ﬁrst

analysis. The Egli model for median path loss over irregular terrain is [4, 6, 7]

(7.9)

where

is the gain of the base antenna

is the gain of the mobile antenna

is the height of the base antenna

LGG

Ar rhr rh

vmin

min tan , tan , min tan , tan ,2

12 12

ff qq

TERRAIN MODELING 141