Seybold J.S. Introduction to RF Propagation

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Suburban Areas

(7.17)

Open Areas

(7.18)

The Hata formulation makes the Okumura model much easier to use and is

usually the way the Okumura model is applied.

Example 7.5. Consider the same system used in Example 7.4. Determine the

median path loss using the Hata model.

Then

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

The ﬁnal result is then L

(dB) = 137.1 dB, which is in agreement with Example

7.4. 䊐

7.4.4 COST 231 Model

The COST 231 model, sometimes called the Hata model PCS extension, is an

enhanced version of the Hata model that includes 1800–1900 MHz [22]. While

the Okumura data extends to 1920 MHz, the Hata model is only valid from

150 to 1500 MHz. The COST 231 model is valid between 1500 and 2000 MHz.

The coverage for the COST 231 model is [23]

Frequency: 1500–2000MHz

Transmitter (base station) effective antenna height, h

: 30–200m

Receiver (mobile) effective antenna height, h

: 1–10m

Link distance, d: 1–20 km

a 3 32 1175 3 497 269

()

=◊

()()

-=. log . . .

Lah

r50

69 55 26 16 870 13 82 68

44 9 6 55 68 3 7

()

[]

()

. . log . log

. . log log .

== =

68 870 0 345

337

m MHz m

mkm

,,.

50 50

54dB urban

()

-log .

LL f f

cc50 50

478 1833 4094dB urban

()

()()

()

-. log . log .

152 NEAR-EARTH PROPAGATION MODELS

The COST 231 median path loss is given by

(7.19)

where

is the frequency in MHz

is the base station height in meters

is the mobile station height in meters

a(h

) is the mobile antenna height correction factor deﬁned earlier

d is the link distance in km

C = 0 dB for medium cities or suburban centers with medium tree density

C = 3 dB for metropolitan centers

The COST 231 model is restricted to applications where the base station

antenna is above the adjacent roof tops. Hata and COST 231 are central to

most commercial RF planning tools for mobile telephony.

7.4.5 Lee Model

The Lee model [24–26] was originally developed for use at 900 MHz and has

two modes: area-to-area and point-to-point. Even though the original data are

somewhat restrictive in its frequency range, the straightforward implementa-

tion, ability to be ﬁtted to empirical data, and the results it provides make it

an attractive option. The model includes a frequency adjustment factor that

can be used to increase the frequency range analytically. The Lee model is a

modiﬁed 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 ﬁt

the model to the measured data.

Lee Area-to-Area Mode For area-to-area prediction, Lee uses a reference

median path loss at one mile, called L

, the slope of the path loss curve, g in

dB/decade, and an adjustment factor F

.The median loss at distance, d, is given

(7.20)

Lee’s model was originally formulated as a received signal level prediction

based on a known transmit power level and antenna gains. The formulation

presented here has been converted from an RSL model to a path loss model

to better ﬁt the format of the other models presented. This means that the

LLd F

50 0 0

10dB

()

g log log

Lfhah

hdC

ctr

46 3 33 9 13 82

44 9 6 55

()

[]

()

. . log . log

. . log log

PROPAGATION IN BUILT-UP AREAS 153

power adjustment factor from the original Lee model is not required since the

path loss is independent of the transmit power. In addition, the reference path

loss distance has been modiﬁed from Lee’s original value at one mile to the

corresponding 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). Some

empirical values for the reference median path loss at 1 km and the slope of

the path loss curve are given in Table 7.2. Data for any given application will

deviate 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 L

are computed, ﬁrst consider the free-space case:

or, in dB,

where l and d are in the same units. Substituting the appropriate values from

above and using d = 1000 m yields

Lee’s empirical data suggests that L

=-85 dB, which is likely a result of the

antennas not being ideal or the test not being ideally free space. Using the P

81 2=- .dB

LGG d

bm0

22 20 20=+ -+

()

log logl

log

900

6814

0214

MHz

dBd dBi

154 NEAR-EARTH PROPAGATION MODELS

TABLE 7.2 Reference Median Path Loss for Lee’s

Model

Environment L

(dB) g

Free space 85 20

Open (rural) space 89 43.5

Suburban 101.7 38.5

Urban areas

Philadelphia 110 36.8

Newark 104 43.1

Tokyo 124.0 30.5

Source: Derived from Ref. 26, with L

values adjusted to 1 km.

values from Ref. 26 to determine the L

values is also straightforward. The

measured P

values given by Lee were measured using the above conditions

and a 10-W transmitter. Thus the computation is

For free space, Lee measured P

=-45 dBm, which gives L

=-85 dB as stated

above. In Newark, Lee measured P

=-64 dBm, so L

=-104.

The adjustment factor, F

, is comprised of several factors, F

= F

which allow the user to adjust the model for the desired conﬁguration. Note

that 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 G

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 G

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. The

best 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 includes

an adjustment for terrain slope. The median path loss is given by

(7.21a)

()

eff

50 50

dB dB log

Ff n f

900=

()

, where 2 3 and is in MHz

Fh h

()() ()

mifm

()

Fh h

bb1

30 48 100=

()()

mft.

40dB dBm dBm

()

PROPAGATION IN BUILT-UP AREAS 155

(7.21b)

where h

eff

is in meters. h

eff

is determined by extrapolating the terrain slope at

the mobile back to the base station antenna and then computing the antenna

height (vertically) above the extrapolated line see Figure 7.13. The sign of the

eff

term is another place where typographical errors can sometimes be found.

Lee indicates that the standard deviation of the error in the area-to-area

mode is 8 dB [28] and that for the point-to-point mode is 3 dB [29]. The fre-

quency adjustment coefﬁcient for F

is n = 2 for suburban or open areas with

f < 450 MHz and n = 3 for urban areas and f > 450MHz [26]. Other cases must

be determined empirically.

Example 7.6. What is the expected path loss for a mobile communication

system operating at 600 MHz over suburban terrain, for path lengths between

1 and 5 km? The base station antenna is a 5-dBi colinear antenna at 20-m

height, and the mobile antenna is a quarter-wave vertical with 0-dBi gain at

1-m height.

LLd F

eff

50 0 0

10 20

()

g log log log

156 NEAR-EARTH PROPAGATION MODELS

h¢

TYPE A

TYPE B

(A) Effective antenna height is greater

than actual height.

(B) Effective antenna height is less

than actual height.

Figure 7.13 Determination of the effective base station antenna height for the Lee

model 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. From

Table 7.2 an appropriate value of L

and

The adjustment factors are

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

So the median path loss for this system is given by

where d is expressed in kilometers. Figure 7.14 shows the resulting median

path loss along with the corresponding free-space loss for the same distance

at 600 MHz. 䊐

It is important to remember the conditions that were used to collect the

data. For instance, if a different gain base station antenna is used for the data

collection, then the equation for the F

correction factor will need to be mod-

iﬁed accordingly before using the model. If a simple dipole were used, then

the 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 is

a list of the models covered in this chapter and represents several of the more

popular models in use today. From this table, it is clear that for applications

= relative to a dipole

106 7 38 5=+

()

. . log dB

50=- .dB

600 900 2 76=

()

Fh h

mm3

313 3=

()()

()

<mcemsin

4 3 2 4 0 791=

()

==..

30 48 20 30 48 0 431=

()()

()

=m. . .

g=38 5.

101 7=- .dB

PROPAGATION IN BUILT-UP AREAS 157

158 NEAR-EARTH PROPAGATION MODELS

12345

100

110

120

130

140

Lee Model

FSL

Path Loss (including antenna gains)

Distance (km)

Path Lodd (dB)

Figure 7.14 Path loss from Lee model for Example 7.6, with free-space loss shown

for reference.

TABLE 7.3 Comparison of Propagation Models for Built-Up Areas

Frequency

Model Application (MHz) Advantages Disadvantages

Young Power law with 150–3700 Easily applied Limited data,

beta factor NYC 1952

only

Okumura 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

band

COST 231 Equation 1500–2000 Same as Hata but

also covers PCS

frequencies

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 be

the most popular choice. The fact that the Lee model can be ﬁtted to such a

wide variety of scenarios makes it a sound choice as well.

7.5 SUMMARY

Many applications in RF and wireless involve propagation of electromagnetic

waves in close proximity of the earth’s surface. Thus it is important to be able

to model the effects of terrain, foliage, and urban structures. The foliage

models presented are Weissberger’s model, the early ITU model, and the

recent ITU model. Weissberger’s model and the early ITU model are both

based on a power of the frequency and of the depth of the foliage.The updated

ITU model for one terminal in woodland is an exponential model, while the

model for other foliage scenarios is a dual-slope model that uses the size of

the 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 the

loss 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 has

gained wide acceptance over many decades of use. The model takes many

factors into account and provides accurate predictions of terrain loss.

Propagation loss in built-up areas has been studied extensively in support

of mobile telephony, and many different models are available, with different

implementations, applicability, and levels of ﬁdelity. The most widely recog-

nized models are the Okumura and Hata’s analytic formulation of the

Okumura model. The Okumura model is based on data collected in Tokyo in

1960 and thus may have limited applicability, but its wide following makes it

valuable for a ﬁrst-cut analysis and for comparisons. A similar model that is

not quite so well known is the Young model. The Young model is based on

measurements taken by Young in New York City and may be more represen-

tative of modern urban conditions. The Lee model is a modiﬁed power law

with several adjustment factors to correct for deviations from the conﬁgura-

tion of the baseline. The model can be readily adjusted to accommodate any

measurements 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 provide

some insight into the nature of available models. In the competitive environ-

ment of wireless telecommunications, many organizations have developed

proprietary models, which they feel best predict the performance of their prod-

ucts. Most of the commercial telecommunication modeling packages will

include several different models. It is important to understand which models

are 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 (although

not necessarily the accuracy) of a model is proportional to how widely

accepted 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.

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

2000, pp. 53–54.

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.

160

NEAR-EARTH PROPAGATION MODELS

20. W. C. Y. Lee, Mobile Communication Design Fundamentals, 2nd ed., Wiley, New

York, 1993, p. 68.

21. N. Blaunstein, Radio Propagation in Cellular Networks, Artech House, Norwood,

MA, 2000, pp. 261–264.

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

2000, pp. 85–86.

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, 2nd

ed., McGraw-Hill, New York, 1998, pp. 124–126.

26. W. C. Y. Lee, Mobile Communication Design Fundamentals, 2nd ed., Wiley, New

York, 1993, pp. 59–67.

27. W. C. Y. Lee, Mobile Communication Design Fundamentals, 2nd ed., Wiley, New

York, 1993, p. 74.

28. W. C. Y. Lee, Mobile Communication Design Fundamentals, 2nd ed., Wiley, New

York, 1993, p. 51.

29. W. C. Y. Lee, Mobile Communication Design Fundamentals, 2nd ed., Wiley, New

York, 1993, p. 88.

EXERCISES

1. What is the expected foliage loss for a 10-GHz communication system that

must penetrate 18 m of foliage?

(a) Using the Wiessberger model

(b) Using the early ITU model

2. How much foliage attenuation is expected for an 800-MHz communication

system that must penetrate up to 40 m of foliage?

3. For a ground-based communication system operating at 1.2GHz, with one

terminal located 100 m inside of a wooded area, what is the predicted

foliage loss from the updated ITU model? Assume the antenna gains are

each 3 dB and the antennas are vertically polarized.

4. Use the Egli model to determine the median path loss for a 400-MHz

system over a 5-km path if both antennas are handheld (h ~ 1.5 m)?

5. Repeat problem 4, but compute the 90% path loss (i.e., what level of path

loss will not be exceeded 90% of the time?)

6. Use the Okumura model to predict the median path loss for a 900 MHz

system at 10 km in an urban environment. Assume that the mobile antenna

height is 7 m and the base station antenna height is 50 m.

EXERCISES 161