near earth propagation models

134

Introduction to RF Propagation, by John S. SeyboldCopyright © 2005 by John Wiley & Sons, Inc.

CHAPTER 7

Near-Earth Propagation Models

7.1 INTRODUCTION

Many applications require RF or microwave propagation from point to pointvery 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 attributedto various phenomena, including diffraction, reflection, absorption, or scatter-ing. In this chapter, several different models are considered for determiningthe median (50%) path loss as a function of distance and conditions. Thesemodels 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 indetail. Much of the data collection for near-earth propagation impairment hasbeen done in support of mobile VHF communications and, more recently,mobile telephony (which operates between 800MHz and 2GHz). Thus manyof the models are focused in this frequency range. While for the most part,models based on this data are only validated up to 2GHz, in practice they cansometimes 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 orthrough foliage at some point. This section presents a few of the better-knownfoliage 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. Forthat reason, it is valuable to verify a particular model’s applicability to a givenregion 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

df is the depth of foliage along the LOS path in metersF 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 decaymodel 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 frequencyrange from 230MHz to 95GHz.

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 ITUrecommendation, it is an easily applied model that provides results that arefairly consistent with the Weissberger model. The model is given by

(7.2)

where

F is the frequency in MHzdf 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, forfoliage depths of 5, 20, 50, and 100m. Note that the frequency scale is in GHzfor each plot, but the frequency used in the model is MHz for the ITU modelas specified. The plots indicate a moderate variation between the models, par-ticularly as frequency increases. The amount of foliage loss is monotonicallyincreasing with foliage depth and frequency as expected.

L F dfdB dB( ) = 0 2 0 3 0 6. . .

L dBF d d

F d d

f f

f f

( ) =< £< £

ÏÌÓ

1 33 14 400

0 45 0 14

0 284 0 588

0 284

. ,

. ,

. .

.

m

m

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 20

2

4

6

8

10

12

Weissberger 5mITU 5mWeissberger 20mITU 20m

Vegetation Loss

Frequency (GHz)

Los

s (d

B)

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 20

5

10

15

20

25

30

35

Weissberger 50 mITU 50mWeissberger 100 mITU 100 m

Vegetation Loss

Frequency (GHz)

Los

s (d

B)

100 m

50 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 12m of trees in the LOS and vegetation (leaves) present.What is the totalpredicted median path loss for this system (excluding antenna gains).

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

since

For the Weissberger model, df < 14m, so

With df = 12m, this yields

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

For the ITU model, the loss is given by

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

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

�

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. Oneof 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

L50 dB= 99 5.

LdB dB= 7 06.

L dfdB MHz= ( )0 2 10000 3 0 6

.. .

L50 97 8= . dB

LdB dB= 5 4.

L dfdB GHz= ( )0 45 10 284

..

l = =0 3 1000. ,m md

FSL dB= - ÊË

ˆ¯ =20

492 44log .

lpd

d f= =1 1km GHz,

FOLIAGE MODELS 137

attenuation due to foliage, since there will always be a diffraction path overand/or around the vegetation [5].

7.2.3.1 Terrestrial Path with One Terminal in Woodland The scenariocovered 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 metersg is the specific attenuation for very short vegetative paths (dB/m)Am 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-spaceloss and the losses from all other phenomena to determine the total predictedpath loss. Some typical values for the specific attenuation are plotted versusfrequency in Figure 7.4.

7.2.3.2 Single Vegetative Obstruction If neither end of the link is withinwoodland, but there is vegetation within the path, the attenuation can bemodeled using the specific attenuation of the vegetation. For this model toapply, the vegetation must be of a single type, such as a tree canopy, as opposedto a variety of vegetation. When the frequency is at or below 3GHz, 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)Aet £ the lowest excess attenuation for any other path (dB)

A det = g

A A eev md Am= -[ ]1 g dB


( )

d

Woodland

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

The restriction on Aet ensures that if the vegetation loss is very large, any alter-nate paths such as a diffraction path will determine the path loss. The ITUindicates that this model is an approximation and will tend to overestimatethe actual foliage attenuation.

The updated ITU model does not provide for coverage between 3 and 5GHz other than the one terminal in woodland model. Above 5GHz, theupdated 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

R0 = af, the initial slopeR• = b/f c, the final slope

A R d k eveg

R Rdk= + -È

ÎÍ˘˚̇

•- +( )•

10

dB

FOLIAGE MODELS 139

Figure 7.4 Specific attenuation due to vegetation versus frequency. (Figure 2 fromRef. 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 k0, A0, and Rf are also given in Table 7.1. Amin 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 Amin is the smallest height bythe smallest width of illuminated clutter. The height and width are determinedby the height and width of the clutter patch and by the height and width ofthe transmit and the receive antenna patterns (3-dB beamwidth) where theyintersect the vegetation. Figure 7.5 shows the geometry of h1, h2, hv, w1, w2, andwv:

(7.7)A h h h w w wv vmin = ( ) ¥ ( )min , , min , ,1 2 1 2

k k A e eA A R ff= - -( ) -( )[ ]- -0 010 1 10log min


TABLE 7.1 Parameters for Updated ITU Model

Parameter In Leaf Out of Leaf

a 0.2 0.16b 1.27 2.59c 0.63 0.85k0 6.57 12.6Rf 0.0002 2.1A0 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 Amin can also be written in terms of the distances to thevegetation and the elevation and azimuth beamwidths of the antennas.

(7.8)

where

r1 and r2 are the distances to the vegetation as shown in Figure 7.5fT and fR are the transmit and receive elevation beamwidthsqT and qR are the transmit and receive azimuth beamwidthshv and wv are the height and width of the vegetation patch

7.3 TERRAIN MODELING

For ground-based communications, the local terrain features significantlyaffect the propagation of electromagnetic waves. Terrain is defined as thenatural geographic features of the land over which the propagation is takingplace. It does not include vegetation or man-made features. When the terrainis very flat, only potential multipath reflections and earth diffraction, if nearthe 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 thentreated separately.

7.3.1 Egli Model

While not a universal model, the Egli model’s ease of implementation andagreement with empirical data make it a popular choice, particularly for a firstanalysis. The Egli model for median path loss over irregular terrain is [4, 6, 7]

(7.9)

where

Gb is the gain of the base antennaGm is the gain of the mobile antennahb is the height of the base antenna

L G Gh hd

b mb m

50 2

2

= ÈÎÍ

˘˚̇b

A r r h r r hT Rv

T Rvmin = Ê

Ëˆ¯

ÊË

ˆ¯

ÊË

ˆ¯ ¥

ÊË

ˆ¯

ÊË

ˆ¯

ÊË

ˆ¯min tan , tan , min tan , tan ,2

22

22

22

21 2 1 2f f q q

TERRAIN MODELING 141

hm is the height of the mobile antennad is the propagation distanceb = (40/f )2, where f is in MHz

Note that the Egli model provides the entire path loss, whereas the foliagemodels discussed earlier provided the loss in addition to free-space loss. Alsonote 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 notbased 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 afamily of curves showing the terrain factor or adjustment to the median pathloss for the desired fade probability [6]. This way the analyst can determinethe mean or median signal level at a given percentage of locations on the circleof radius d. Stated another way, the Egli model provides the median path lossdue to terrain loss. If a terrain loss point other than the median (50%) isdesired, 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 at100MHz if the antenna heights are 20m and 3m, using the Egli model forterrain loss.


+20

+15

+10

+5

–5

–10

–15

–20

–25

–3040 50 60 80 100 150 200 300 500 1000

0

99

95

90

80

70

60

Median–5040

30

20

10Percent of

locations

Ter

rain

fact

or, d

B

99.9

Frequency (MHz)

5

Figure 7.6 Terrain factor versus frequency for different probabilities for the Eglimodel. (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 beexceeded 10% of the time), approximately 10dB would be added to the L50

value according to Figure 7.6, so

�

The Egli model provides a nice, closed-form way to model terrain effects, butsince it is a one-size-fits-all model, it should not be expected to provide preciseresults in all situations. For detailed planning, there are software packagesavailable that use DTED (Digitized Terrain Elevation Data) or similar terraindata and model the expected diffraction loss on a given path. Such models areideal for planning fixed links, but are of limited utility for mobile links. Oneexception is the Longley-Rice model, which provides both point-to-point andarea terrain loss predictions.

7.3.2 Longley–Rice Model

The Longley–Rice model is a very detailed model that was developed in the1960s and has been refined over the years [8–10]. The model is based on datacollected between 40MHz and 100GHz, at ranges from 1 to 2000km, atantenna heights between 0.5 and 3000m, and for both vertical and horizontalpolarization. The model accounts for terrain, climate, and subsoil conditionsand ground curvature. Blaunstein [8] provides a detailed description of themodel, 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 formof a computer program that accepts the required parameters and computesthe expected path loss. At the time of this writing, the U.S. National Telecom-munications and Information Administration (NTIA) provides one suchprogram on its website [11] free of charge. Many commercial simulation prod-ucts include the Longley–Rice model for their terrain modeling. As indicatedin the previous section, the Longley–Rice model has two modes, point-to-pointand 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.

L90 dB= 122 2.

L50 dB= 112 4.

L50 = -◊

◊ ( )ÊË

ˆ¯10

20 310

0 46

2log .


7.3.3 ITU Model

The ITU terrain model is based on diffraction theory and provides a relativelyquick means of determining a median path loss [12]. Figure 7.7 shows threeplots of the expected diffraction loss due to terrain roughness versus the normalized terrain clearance. Curve B is the theoretical knife-edge diffractioncurve. Curve D is the theoretical smooth-earth loss at 6.5GHz using a 4/3 earthradius. The curve labeled Ad is the ITU terrain loss model over intermediateterrain. Each of these curves represents the excess terrain loss, beyond free-space loss. The ITU terrain loss model is given by


–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 blockageand the line-of-sight path between the transmitter and the receiver. If theblockage is above the line of sight, then h is negative. F1 is the radius of thefirst Fresnel zone (Fresnel zones are discussed in Chapter 8) and is given by

(7.11)

where

d1 and d2 are the distances from each terminal to the blockage in kilometers

d is the distance between the terminals in kmf is the frequency in GHz

The ratio h/F1 is the normalized terrain clearance (h/F1 < 0 when the terrainblocks the line of sight). This model is generally considered valid for lossesabove 15dB, but it is acceptable to extrapolate it to as little as 6dB of loss asshown in Figure 7.7. The other two curves shown represent extremes of clearterrain and very rough terrain, so they provide insight into the variability thatcan 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 3km over fairly roughterrain (±2m) at 100MHz. The antenna is a 1.5-m whip mounted on thevehicle, approximately 2m above the ground. How much terrain loss shouldbe expected over and above the free-space loss?

The center of radiation for the antenna is 2.75m above the ground. If a flat-earth model is used, then the maximum terrain height of +2m results in a minimum antenna height above the terrain of

In the absence of specific information about the location of any blockagewithin the line of sight, assume that the blockage occurs at the midpoint of thepath, d/2. The expression for F1 reduces to

Next, by substituting d = 3 and f = 0.1 the value of F1 is found to be

F1 47 4= .

Fdf1 17 3

4= . m

h = 0 75. m

Fd d

fd11 217 3= . m

A h Fd = - +20 101 dB


The normalized terrain clearance is h/F1 = 0.0158 and the terrain attenuationis

which is consistent with Figure 7.7. The plot also shows that terrain loss in theregion of 6–15dB might be reasonably expected. �

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. Theactual propagation of RF though an urban environment is dependent uponfrequency, 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 ofthe 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 frequenciesof 150–3700MHz [14, 15].The curve presented in Figure 7.8 displays an inversefourth-power law behavior, similar to the Egli model. The model for Young’sdata 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 asample area in classification [16]. From Young’s measurements, b is approxi-mately 25dB for New York City at 150MHz. The data in Figure 7.8 suggeststhat 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 1920MHz [17–20]. While not representative of modern U.S.cities, the data and model are still widely used as a basis of comparison. The

L G Gh hd

b mb m

50 2

2

= ÊË

ˆ¯ b

Ad = 9 7. dB


model is empirical, being based solely on the measured data. The actual pathloss predictions are made based on graphs of Okumura’s results, with variouscorrection 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, andthe land cleared for 300–400m ahead (i.e., farmland). The suburban areamodel represents a village or a highway scattered with trees and houses, someobstacles 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 twoor 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 typesis also defined. Quasi-smooth terrain is the reference terrain and correctionfactors are applied for other types of terrain. Okumura’s expression for themedian path loss is

(7.13)

where

L L A H HFSL mu tu ru50 dB( ) = + - -

PROPAGATION IN BUILT-UP AREAS 147

60

70

80

90

100

110

120

130

140

150

160

1700.1 0.2 0.3 0.5 0.7 1.0 2 3 4 5 7 10 20 30

d, miles

Loss

, dB

Flat terrain1%10%

50%

90%

99%

Figure 7.8 Results of Young’s measurement of path loss versus distance in miles inManhattan and the Bronx at 150MHz. (Figure 7.1 from Ref. 15, courtesy of ArtechHouse.)

LFSL is the free-space loss for the given distance and frequencyAmu is the median attenuation relative to free-space loss in an urban area,

with quasi-smooth terrain, base station effective height hte = 200m, andmobile antenna height hre = 3m; the value of Amu is a function of bothfrequency and distance

Htu is the base station height gain factorHru is the mobile antenna height gain factor

The signs on the gain factors are very important. Some works have reversedthe signs on the H terms, which will of course lead to erroneous results. If indoubt, check the results using known test cases, or engineering judgment. Forinstance, if increasing the antenna height increases the median path loss, thenthe sign of the antenna height correction factor is clearly reversed.

Figure 7.9 shows plots of Amu versus frequency for various distances. Figure7.10 shows the base station height gain factor in urban areas versus effective


10010

20

30

40

Bas

ic m

edia

n at

tent

uatio

n A

mu(

f, d

) (d

B)

50

60

70

h m = 3 m

h b = 200 m

Urban area

200 300 500Frequency f (MHz)

700 1000 2000 3000

100

100

80

80

60

60

50

50

40

40

30

30

20

20

10

10

5

5

2

2

1

1

d (k

m)

Figure 7.9 Plot of Amu versus frequency for use with the Okumura model. (Figure 4.7Ref. 13, courtesy of Wiley.)

height for various distances, while Figure 7.11 shows the vehicle antennaheight gain factor versus effective antenna height for various frequencies andlevels of urbanization. Figure 7.12 shows how the base station antenna heightis measured relative to the mean terrain height between 3 and 15km in thedirection of the receiver.

Example 7.4. Consider a system with the following parameters:

d = 3 7. km

f = =870 0 345MHz m, .l

hr = 3 m

ht = 68 m


30

20

10

–10

–20

–3020 30 50

Base station effective antenna height hte (m)

70 100 200 300 500 700 1000

0d (km)

d (k

m)

100

80

706050

4020

135

10

70~ 1006040

201~10

Hei

ght g

ain

fact

or H

tu(h

te, d

) (d

B)

Urban area

h te = 200 m

Figure 7.10 Plot of Htu, the base station height correction factor, for the Okumuramodel. (Figure 4.8 from Ref. 13, courtesy of Wiley.)


2000

1000

700

400

200

100

100200400~1000

20

15

10

Ant

enna

hei

ght g

ain

fact

or H

ru(h

re, f

) (

dB)

5

0

–51 2 3 5 7 10

Vehicular station antenna height hre (m)

400 MHz

200 MHz

Urban area

Med

ium

city

Larg

e ci

ty

f (M

Hz)

Figure 7.11 Plot of Hru, the mobile station height correction factor for the Okumuramodel. (Figure 4.9 from Ref. 13, courtesy of Wiley.)

3 km 15 km

Average height

h te

h t

h

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 Hru correction factor is not required since the mobile antenna isat 3m, which is the reference height. �

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 theOkumura model [21–23]. There are three different formulas for the Hatamodel: for urban areas, for suburban areas, and for open areas.

Urban Areas

(7.14)

where

150 < fc < 1500, fc in MHz30 < ht < 200, ht in m1 < d < 20, d in km

and a(hr) is the mobile antenna height correction factor. For a small- ormedium-sized city:

(7.15)

and for a large city:

(7.16)a hh f

h fr

r c

r c

( ) = ( )( ) - £

( )( ) - £

ÏÌÔ

ÓÔ8 29 1 54 1 1 200

3 2 11 75 4 97 400

2

2

. log . . ,

. log . . ,

MHz

MHz

a h f h f hr c r c r( ) = ( ) -( ) - ( ) -( ) £ £1 1 0 7 1 56 0 8 1 10. log . . log . , m

L f h a h h dc t r t50 69 55 26 16 13 82 44 9 6 55dB( ) = + ( ) - ( ) - ( ) + - ( )[ ] ( ). . log . log . . log log

L50 102 6 26 8 136 6dB dB( ) = + - -( ) =. .

LFS = 102 6. dB


Suburban Areas

(7.17)

Open Areas

(7.18)

The Hata formulation makes the Okumura model much easier to use and isusually the way the Okumura model is applied.

Example 7.5. Consider the same system used in Example 7.4. Determine themedian path loss using the Hata model.

Then

where the mobile antenna height correction factor (assuming a large city) is

The final result is then L50(dB) = 137.1dB, which is in agreement with Example7.4. �

7.4.4 COST 231 Model

The COST 231 model, sometimes called the Hata model PCS extension, is anenhanced version of the Hata model that includes 1800–1900MHz [22]. Whilethe Okumura data extends to 1920MHz, the Hata model is only valid from150 to 1500MHz. The COST 231 model is valid between 1500 and 2000MHz.The coverage for the COST 231 model is [23]

Frequency: 1500–2000MHzTransmitter (base station) effective antenna height, hte: 30–200mReceiver (mobile) effective antenna height, hre: 1–10mLink distance, d: 1–20km

a 3 3 2 11 75 3 4 97 2 692( ) = ◊( )( ) - =. log . . .

L a hr50 69 55 26 16 870 13 82 68

44 9 6 55 68 3 7

dB( ) = + ( ) - ( ) - ( )+ - ( )[ ] ( )

. . log . log

. . log log .

h f

h dt

r

= = == =

68 870 0 345

3 3 7

m MHz m

m km

, , .

, .

l

L Lfc

50 50

2

228

5 4dB urban( ) = ( ) - ÊË

ˆ¯

ÊË

ˆ¯ -log .

L L f fc c50 502

4 78 18 33 40 94dB urban( ) = ( ) - ( )( ) + ( ) -. log . log .


The COST 231 median path loss is given by

(7.19)

where

fc is the frequency in MHzht is the base station height in metershr is the mobile station height in metersa(hr) is the mobile antenna height correction factor defined earlierd is the link distance in kmC = 0dB for medium cities or suburban centers with medium tree densityC = 3dB for metropolitan centers

The COST 231 model is restricted to applications where the base stationantenna is above the adjacent roof tops. Hata and COST 231 are central tomost commercial RF planning tools for mobile telephony.

7.4.5 Lee Model

The Lee model [24–26] was originally developed for use at 900MHz and hastwo modes: area-to-area and point-to-point. Even though the original data aresomewhat restrictive in its frequency range, the straightforward implementa-tion, ability to be fitted to empirical data, and the results it provides make itan attractive option. The model includes a frequency adjustment factor thatcan be used to increase the frequency range analytically. The Lee model is amodified power law model with correction factors for antenna heights and frequency. A typical application involves taking measurements of the path loss in the target region and then adjusting the Lee model parameters to fitthe model to the measured data.

Lee Area-to-Area Mode For area-to-area prediction, Lee uses a referencemedian path loss at one mile, called L0, the slope of the path loss curve, g indB/decade, and an adjustment factor F0.The median loss at distance, d, is givenby

(7.20)

Lee’s model was originally formulated as a received signal level predictionbased on a known transmit power level and antenna gains. The formulationpresented here has been converted from an RSL model to a path loss modelto better fit the format of the other models presented. This means that the

L L d F50 0 010dB( ) = + ( ) - ( )g log log

L f h a h

h d Cc t r

t

50 46 3 33 9 13 82

44 9 6 55

dB( ) = + ( ) - ( ) - ( )+ - ( )[ ] ( ) +

. . log . log

. . log log


power adjustment factor from the original Lee model is not required since thepath loss is independent of the transmit power. In addition, the reference pathloss distance has been modified from Lee’s original value at one mile to thecorresponding value at 1km. The slope of the path loss curve, g, is the expo-nent of the power law portion of the loss (expressed as a dB multiplier). Someempirical values for the reference median path loss at 1km and the slope ofthe path loss curve are given in Table 7.2. Data for any given application willdeviate from these data, but should be of the same order of magnitude.

The basic setup for collecting this information is as follows:

To see how the L0 are computed, first consider the free-space case:

or, in dB,

where l and d are in the same units. Substituting the appropriate values fromabove and using d = 1000m yields

Lee’s empirical data suggests that L0 = -85dB, which is likely a result of theantennas not being ideal or the test not being ideally free space. Using the Pr0

L0 81 2= - . dB

L G G db m0 22 20 20= + - + ( ) - ( )log logl

LG G

db m

0 204

= ÊËÁ

ˆ¯̃log

lp

f

G

Gb

m

.

.

== == =

900

6 8 14

0 2 14

MHz

dBd dBi

dBd dBi


TABLE 7.2 Reference Median Path Loss for Lee’sModel

Environment L0 (dB) g

Free space 85 20Open (rural) space 89 43.5Suburban 101.7 38.5Urban areas

Philadelphia 110 36.8Newark 104 43.1Tokyo 124.0 30.5

Source: Derived from Ref. 26, with L0 values adjusted to 1 km.

values from Ref. 26 to determine the L0 values is also straightforward. Themeasured P0 values given by Lee were measured using the above conditionsand a 10-W transmitter. Thus the computation is

For free space, Lee measured P0 = -45dBm, which gives L0 = -85dB as statedabove. In Newark, Lee measured P0 = -64dBm, so L0 = -104.

The adjustment factor, F0, is comprised of several factors, F0 = F1F2F3F4F5,which allow the user to adjust the model for the desired configuration. Notethat the numbering of these factors is not universal.

The base station antenna height correction factor is

The base station antenna gain correction factor is

where Gb is the actual base station antenna gain relative to a half-wave dipole.The mobile antenna height correction factor is

The frequency adjustment factor is

The mobile antenna gain correction factor is

where Gm is the gain of the mobile antenna relative to a half-wave dipole.For these correction factors, it is important to recognize that misprints in

the signs of the correction factors can sometimes be found in the literature.Such errors can result in confusion and invalid results if not recognized. Thebest advice is to apply a simple test case if in doubt.

Lee Point-to-Point Mode The point-to-point mode of the Lee model includesan adjustment for terrain slope. The median path loss is given by

(7.21a)¢ ( ) = ( ) - ÊËÁ

ˆ¯̃L L

heff50 50 20

30dB dB log

F Gm5 1=

F f n fn

4 900= ( ) < <-, where 2 3 and is in MHz

F h h

F h hm m

m m

32

3

3 3

3 3

= ( )( ) ( ) >= ( )( ) ( ) <

m if m

m if m

F Gb2 4= ( )

F h hb b12 2

30 48 100= ( )( ) = ( )( )m ft.

L P0 0 40dB dBm dBm( ) = ( ) -


or

(7.21b)

where heff is in meters. heff is determined by extrapolating the terrain slope atthe mobile back to the base station antenna and then computing the antennaheight (vertically) above the extrapolated line see Figure 7.13. The sign of theheff term is another place where typographical errors can sometimes be found.

Lee indicates that the standard deviation of the error in the area-to-areamode is 8dB [28] and that for the point-to-point mode is 3dB [29]. The fre-quency adjustment coefficient for F4 is n = 2 for suburban or open areas withf < 450MHz and n = 3 for urban areas and f > 450MHz [26]. Other cases mustbe determined empirically.

Example 7.6. What is the expected path loss for a mobile communicationsystem operating at 600MHz over suburban terrain, for path lengths between1 and 5km? The base station antenna is a 5-dBi colinear antenna at 20-mheight, and the mobile antenna is a quarter-wave vertical with 0-dBi gain at 1-m height.

L L d Fheff

50 0 010 2030

dB( ) = + ( ) - ( ) - ÊËÁ

ˆ¯̃g log log log


h¢1

h¢1

h1h1

TYPE A TYPE B

(A) Effective antenna height is greaterthan actual height.

(B) Effective antenna height is lessthan actual height.

Figure 7.13 Determination of the effective base station antenna height for the Leemodel point-to-point mode. (Figure 2.15 from Ref. 27, courtesy of Wiley.)

Since this is a mobile system, the area mode of the Lee model is used. FromTable 7.2 an appropriate value of L0 is

and

The adjustment factors are

where a value of 2.5 was assumed for n. The compilation of these terms resultsin

So the median path loss for this system is given by

where d is expressed in kilometers. Figure 7.14 shows the resulting medianpath loss along with the corresponding free-space loss for the same distanceat 600MHz. �

It is important to remember the conditions that were used to collect thedata. For instance, if a different gain base station antenna is used for the datacollection, then the equation for the F2 correction factor will need to be mod-ified accordingly before using the model. If a simple dipole were used, thenthe correction factor would simply be

7.4.6 Comparison of Propagation Models for Built-Up Areas

Table 7.3 provides a high-level comparison of the propagation models dis-cussed in this section. This is, of course, not a complete list of models, but it isa list of the models covered in this chapter and represents several of the morepopular models in use today. From this table, it is clear that for applications

F Gb2 = relative to a dipole

L d50 106 7 38 5= + ( ). . log dB

F0 5 0= - . dB

F5 1=F

n4 600 900 2 76= ( ) =-

.

F h hm m3 3 1 3 3= ( )( ) = ( ) <m ce msin

F Gb2 4 3 2 4 0 791= ( ) = =. .

F hb12 2

30 48 20 30 48 0 431= ( )( ) = ( ) =m . . .

g = 38 5.

L0 101 7= - . dB



1 2 3 4 570

80

90

100

110

120

130

140

Lee ModelFSL

Path Loss (including antenna gains)

Distance (km)

Path

Lod

d (d

B)

Figure 7.14 Path loss from Lee model for Example 7.6, with free-space loss shownfor reference.

TABLE 7.3 Comparison of Propagation Models for Built-Up Areas

FrequencyModel Application (MHz) Advantages Disadvantages

Young Power law with 150–3700 Easily applied Limited data,beta factor NYC 1952

onlyOkumura Equation with 200–1920 Widely used as Limited data,

correction a reference Tokyo 1960,factors from tedious to plots apply

Hata Equation 150–1500 Widely used, Based on limited straightforward data, does not to apply cover PCS

bandCOST 231 Equation 1500–2000 Same as Hata but

also covers PCSfrequencies

Lee Equation with 900, plus Relatively easy to Requires local computed analytic apply, can be data collection correction extension fitted to for good factors measurements, accuracy

two modes

outside of the personal communications bands, the Lee model is going to bethe most popular choice. The fact that the Lee model can be fitted to such awide variety of scenarios makes it a sound choice as well.

7.5 SUMMARY

Many applications in RF and wireless involve propagation of electromagneticwaves in close proximity of the earth’s surface. Thus it is important to be ableto model the effects of terrain, foliage, and urban structures. The foliagemodels presented are Weissberger’s model, the early ITU model, and therecent ITU model. Weissberger’s model and the early ITU model are bothbased on a power of the frequency and of the depth of the foliage.The updatedITU model for one terminal in woodland is an exponential model, while themodel for other foliage scenarios is a dual-slope model that uses the size ofthe illuminated foliage area to predict the amount of loss due to the foliage.The updated ITU model includes provisions for limiting the foliage loss to theloss on the diffraction path (i.e., using the lesser of the two losses).

Terrain loss can be easily modeled using the Egli model, which is a fourth-power law with a clutter factor multiplier to fit the model to empirical data.The Longley–Rice model is a very mature, well-validated model that hasgained wide acceptance over many decades of use. The model takes manyfactors into account and provides accurate predictions of terrain loss.

Propagation loss in built-up areas has been studied extensively in supportof mobile telephony, and many different models are available, with differentimplementations, applicability, and levels of fidelity. The most widely recog-nized models are the Okumura and Hata’s analytic formulation of theOkumura model. The Okumura model is based on data collected in Tokyo in1960 and thus may have limited applicability, but its wide following makes itvaluable for a first-cut analysis and for comparisons. A similar model that isnot quite so well known is the Young model. The Young model is based onmeasurements taken by Young in New York City and may be more represen-tative of modern urban conditions. The Lee model is a modified power lawwith several adjustment factors to correct for deviations from the configura-tion of the baseline. The model can be readily adjusted to accommodate anymeasurements that are available for the region of interest. The Lee model fea-tures both an area mode and a point-to-point mode for fixed link scenarios.

While not exhaustive, the set of models presented in this chapter providesome insight into the nature of available models. In the competitive environ-ment of wireless telecommunications, many organizations have developedproprietary models, which they feel best predict the performance of their prod-ucts. Most of the commercial telecommunication modeling packages willinclude several different models. It is important to understand which modelsare being used and the limitation of those models for the particular applica-tion. Use of proprietary models in commercial propagation prediction soft-

SUMMARY 159

ware is unusual and generally not desirable because the credibility (althoughnot necessarily the accuracy) of a model is proportional to how widelyaccepted it is.

REFERENCES

1. H. L. Bertoni, et al., UHF propagation prediction for wireless personal communi-cations, Proceedings of the IEEE, September 1994, pp. 1333–1359.

2. J. D. Parsons, The Mobile Radio Propagation Channel, 2nd ed., Wiley, West Sussex,2000, pp. 52–53.

3. N. Blaunstein, Radio Propagation in Cellular Networks, Artech House, Norwood,MA, 2000, p. 172.


5. ITU-R Recommendations, Attenuation in vegetation, ITU-R P.833-3, Geneva, 2001.6. J. J. Egli, Radio Propagation above 40MC over irregular terrain, Proceedings of the

IRE, October 1957.7. N. Blaunstein, Radio Propagation in Cellular Networks, Artech House, Norwood,

MA, 2000, pp. 156–157.8. N. Blaunstein, Radio Propagation in Cellular Networks, Artech House, Norwood,

MA, 2000, pp. 159–163.9. J. D. Parsons, The Mobile Radio Propagation Channel, 2nd ed., Wiley, West Sussex,

2000, pp. 56–60.10. T. S. Rappaport, Wireless Communications, Principles and Practice, 2nd ed.,

Prentice-Hall, Upper Saddle River, NJ, 2002, p. 145.11. Irregular Terrain Model (ITM), from the NTIA web site, http://ntiacsd.

ntia.doc.gov/msam/12. ITU-R Recommendations, Propagation data and prediction methods required for

the design of terrestrial line-of-sight systems, ITU-R P.530-9, Geneva, 2001.13. J. D. Parsons, The Mobile Radio Propagation Channel, 2nd ed., Wiley, West Sussex,

2000, Chapter 4.14. J. D. Parsons, The Mobile Radio Propagation Channel, 2nd ed., Wiley, West Sussex,

2000, pp. 77–79.15. N. Blaunstein, Radio Propagation in Cellular Networks, Artech House, Norwood,

MA, 2000, pp. 254–255.16. J. D. Parsons, The Mobile Radio Propagation Channel, 2nd ed., Wiley, West Sussex,

2000, p. 74.17. T. S. Rappaport, Wireless Communications, Principles and Practice, 2nd ed.,

Prentice-Hall, Upper Saddle River, NJ, 2002, pp. 150–153.18. N. Blaunstein, Radio Propagation in Cellular Networks, Artech House, Norwood,

MA, 2000, pp. 259–261.19. W. C. Y. Lee, Mobile Communication Engineering, Theory and Applications, 2nd

ed., McGraw-Hill, New York, 1998, pp. 127–129.


20. W. C. Y. Lee, Mobile Communication Design Fundamentals, 2nd ed., Wiley, NewYork, 1993, p. 68.

21. N. Blaunstein, Radio Propagation in Cellular Networks, Artech House, Norwood,MA, 2000, pp. 261–264.


23. T. S. Rappaport, Wireless Communications, Principles and Practice, 2nd ed.,Prentice-Hall, Upper Saddle River, NJ, 2002, pp. 153–154.

24. N. Blaunstein, Radio Propagation in Cellular Networks, Artech House, Norwood,MA, 2000, pp. 275–279.

25. W. C. Y. Lee, Mobile Communication Engineering, Theory and Applications, 2nded., McGraw-Hill, New York, 1998, pp. 124–126.

26. W. C. Y. Lee, Mobile Communication Design Fundamentals, 2nd ed., Wiley, NewYork, 1993, pp. 59–67.




EXERCISES

1. What is the expected foliage loss for a 10-GHz communication system thatmust penetrate 18m of foliage?(a) Using the Wiessberger model(b) Using the early ITU model

2. How much foliage attenuation is expected for an 800-MHz communicationsystem that must penetrate up to 40m of foliage?

3. For a ground-based communication system operating at 1.2GHz, with oneterminal located 100m inside of a wooded area, what is the predictedfoliage loss from the updated ITU model? Assume the antenna gains areeach 3dB and the antennas are vertically polarized.

4. Use the Egli model to determine the median path loss for a 400-MHzsystem over a 5-km path if both antennas are handheld (h ~ 1.5m)?

5. Repeat problem 4, but compute the 90% path loss (i.e., what level of pathloss will not be exceeded 90% of the time?)

6. Use the Okumura model to predict the median path loss for a 900MHzsystem at 10km in an urban environment. Assume that the mobile antennaheight is 7m and the base station antenna height is 50m.

EXERCISES 161

7. Use the Hata–Okumura model to determine the expected path loss for a1-km path in a large city for a 1-GHz system. The receive (mobile) antennais at 7-m height and the transmit antenna is at 35-m height. You may wantto compute the free-space loss for the same geometry to provide a sanitycheck for your answer.

8. Use the extended COST 231–Hata model to determine the maximum cellradius for a 1.8-GHz system in a medium-sized city (C = 0dB) if ht = 75mand hr = 3m. Assume that the allowable path loss is 130dB.

9. Use the Lee model to determine the maximum cell radius for a 900-MHzsystem in a suburban area. Assume that hr = 7m and ht = 50m and that theallowable path loss is 125dB.You may assume that the mobile antenna gainis at the reference value (0dBd) and the transmitter antenna gain is also atthe reference value of 6dBd.


near earth propagation models

Documents

foliage models

propagation models

early itu foliage model

model predictions

weissberger model

updated itu models

propagation path

depth of foliage