Chapter 9 - Propagation Loss Prediction Models

8/20/2019 Chapter 9 - Propagation Loss Prediction Models

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CHAPTER 9

Propagation Loss Prediction Models

M S RU

HATA

9 1 INTRODUCTION

Propagation loss prediction models play a very important role in the design of cellular

mobile radio communication systems by specifying the key system parameters such as

transmission power, frequency reuse, and so on. Several prediction models have been

proposed for cellular mobile radio systems operating in the quasi-microwave frequency

band.

Some of them were derived in a statistical manner from measurement data, and some

were derived analytically based on diffraction effects. Each model uses specific parameters

to achieve reasonable prediction accuracy. For example, one relatively long-range predic

tion model, intended for macrocell systems, uses base and mobile station antenna heights

and frequency. On the other hand, a prediction model for short-range estimation that was

designed for microcell systems uses building heights, street width, and so on. When the

cell size is quite small, for example, for a specific area, deterministic methods such as ray

tracing are necessary for accurate prediction. Therefore, it is important for designing

mobile systems to select the most appropriate prediction model with the goal of efficient

cell coverage.

This chapter summarizes the propagation loss prediction models commonly used in

land mobile communication system design and discusses their applicability in various

mobile propagation environments.

9 2 EMPIRICAL MODELS

Table 9.1 summarizes the propagation loss prediction models used to design current

cellular systems. The Okumura-Hata model [1,2] is the empirical formula based on field

measurements made in a typical mobile propagation environment (see Fig. 9.1). The

Wireless Communications in the Century, Edited by Shaft, Ogose, and Hattori.

ISBN 0-471-155041-X © 2002 by the IEEE.

169


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3/15

9.2 EMPIRICALMODELS

171

hm

f

s 200

MHz

f 2: 400

MHz

__Base station

,

...

.

~ ~ ~

Parameters used in Ok

median path

I . umura

-Hata model

betw 0 L

ts

expre d i .

een the transmitter and

sse

l.n logarithmic seal .

eceiver: e as a linear fu .

ction of d th die istance

h L dB -A

were A and Bare -

+

Slog d)

The formula for ur functions of frequenc

an , quasi-smooth Y. and base and b' (9.1)

terrain

is su . mo lie station

L

(dB)

=

69 55

mmanzed

as follows' antenna heights .

. + 26.1610 .

+

[44 9 g f) - 13.8210g(h )

where k h ) . . - 6.55 log h

b

) ] log d) b

-

k h

m

)

d' m

IS

the cor .

me ium-sized ci rection facto f

city: r

0 , mobile

stu;

(9.2)

ion antenna heights for

k h

m

)

= [1

. l log f)

a small or

And for I - 0.7]h [1

arge city, m

-

.5610g j) - 0.8]

k h

m

) = 8.29[log(l.54h ]2

_ m

II

_ 3.2[log l1.75h 2

For each k h ) .

m ]

- 4.97

m , If h - I 5

- . m, k 1.5) = 0 d

Applicable runge, B.

f, frequency (MHz)

h

b

, base station 150-2200MHz

h antenna hei h (

m

mob ile stati g t m) 30

-20

d, distance fr on antenna height (m) 0 m

om transmi . 1-10 m

tssion point

(km)

1

-20km


4/15

172

PROPAGATION LOSS PREDICTION MODELS

Based on the field measurement results, the applicable upper frequency range was

extended from 1500 to 2200 MHz [13]. In the formula, L is defined as the loss between

isotropic antennas. Therefore, if dipole antennas are used at base and mobile stations, the

first term of the right-hand side

of

Eq. (9.2) should be 65.25 instead of 69.55. The

following prediction formulas described in this chapter also consider the path loss between

isotropic antennas.

In the Okumura-Hata model, urban and quasi-smooth terrain is the base of the

prediction formula. The influence

of

irregular terrain is defined by terrain correction

factors and given by prediction curves [1]. For suburban and open (rural) areas, correction

formulas have also been produced based on measurement data [2]. However, how to select

correction formulas for an actual application remained uncertain; the environmental

definition was not really clear.

Considering that the categorization of urban, suburban, and rural area depends on the

degree of urbanization, a correction method using a ground cover factor was proposed by

Akeyama et al. [14]. The ground cover factor, a, is defined as the percentage

of

the area

covered by buildings within 500 x 800

nr .

The deviation from reference median path loss

S is shown in Figure 9.2 and expressed by:

S (dB)

-1910g a)

+ 26 (5% :::; a)

-9.75[log(a)]2 - 3.74 log a)+ 20

20 (a :::;

1

%)

1


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9.2 EMPIRICAL MODELS 173

This correction makes the Okumura-Hata model applicable to suburban and rural areas.

With this correction, an adjustment constant is often added to the formula in actual

applications.

Several propagation loss prediction models were proposed after the Okumura-Hata

model. All of them also follow Eq. (9.1). In the Lee model [3], the median path loss is

given by

L (dB) Al + fJlog d)+F,

(9.5)

where

A

I is the path loss at a range of 1km and fJ is the slope of the path loss curve. Term

F, is the adjustment factor for actual base station antenna heights, antenna gain, and

transmission power with respect to a reference. Values A I and fJ were derived from

experiments for urban, suburban, and rural areas. For an actual environment, it is necessary

to select A

I

and fJ by comparing the environment under consideration with the reference

environment that most closely resembles it. The influence of terrain is given as the

adjustment factor

F,

by calculating the effective base station antenna height.

The Ibrahim-Person model [4] uses two parameters, land usage factor La)and degree

of

urbanization U

d

)

to reflect the environmental condition; La is defined as the percentage

of the 500 x 500m

2

,

which are covered by buildings, regardless of their height; U

d

is

defined as the percentage

of

building site area, within the square, occupied by buildings

having four or more floors. The median path-loss formula is given by:

L

(dB) -20 10g 0.7h

b

) -

810g h

m

) +

f 140

+ 26log f

140)

- 86log[ f + 100)/156] + {40+ 14.15log[ f + 100)/156]}log d)

+

0.265L

a

- 0.37H

g

+x,

9.6)

Applicable range:

f, frequency (MHz) 168-900MHz

h

b

, base station antenna height (m)

h

m

, mobile station antenna height (m) < 3m

d,

distance from transmission point

(km)

1-10

km

where H

g

is the correction term for average ground height, and K;

0.087U

d

- 5.5 for

highly urbanized areas, otherwise

K;

O.

In the models described above, the distance d is more than 1kIn and the base station

antenna height h

b

is higher than the rooftop level of surrounding buildings. This means

that the models are suitable for macrocell systems. To reduce the applicable range to less

than 1kIn, a prediction formula has been proposed by Sakagami et al. [5]. As the model

was based on measurement data considering detailed data on the buildings and streets in

the prediction area, the formula uses many parameters indicating the layout of buildings

and roads:

L (dB)

100 - 7.1log(W) + 0.0238 + 1.4log(h

s

) + 6.1log H)

- [24.37 - 3.

7 H1h

bo )2 ]

log h

b )

+

[43.42 -

3.1log h

b ) ]

log

d)

+

20

log f) +

exp] 13[log f) - 3.23]} (9.7)


6/15

174 PROPAGATION LOSS PREDICTION MODELS

Applicable range :

f,

frequency (MHz) 450

-2200

MHz

d, distance from transmission point (km)

0.5-10

km

T¥

street width (m) 5

-50

m

, street angle to the base station (deg .) 0-90°

h

s

building height along the street (m) 5

-80

m

H , average building height (m) 5-50 m

h

b

, base station antenna height above the mobile station ground (m)

hbQ base station antenna height from the base station ground (m)

H, building height near the base station (m) H S hbQ

20

-100 m

The Sakagami model may indicate the ultimate empirical formula for short-range path

loss prediction. For smaller area prediction, it seems necessary to consider the actual

propagation paths between base and mobile station antennas using precise environment

data of the prediction area.

9.3

ANALYTICAL MODELS

To overcome the range limitations of the empirical formulas and try to explain the

propagation mechanism, analytical models have been proposed [6-12]. As seen in the

Sakagami model, the influences

of

buildings and streets are significant factors determining

the path loss in small-area propagation environments.

Figure 9.3 shows the parameters used in the Walfisch-Bertoni model [7]. The median

path loss, L (dB), is expressed as the summation of three independent terms: the free-space

Base station (BS)

hb

t

d

.

Road

r-

in Walfisch-Ikegami model)

Mobile station (MS)

b hm

FIGURE 9.3 Parameters used in Walfisch-Bertoni model.


7/15

9.3 ANALYTICAL MODELS 175

loss

L

f s

) ,

the diffraction loss from rooftop to street

L

rt s

)

and the reduction due to plane

wave multiple diffraction past rows of buildings L

md

) :

(9.8)

where

L

f s

is a function

of

wavelength and distance;

L

rt s

can be calculated by the

geometrical theory of diffraction (GTD) [15], and is a function of average rooftop level,

mobile station antenna height, street width, and wavelength;

L

md

has been evaluated in

closed forms by Xia and Bertoni [9] and is a function of average rooftop level, average

separation distance between the rows of buildings, base station antenna height, street

width, wavelength, and distance.

Recently, simplified formulas have been proposed by Xia [12]. For base station

antennas above the average rooftop level, the prediction formula is given by:

LdB)

== _ 1 0 l 0 g ~ 2 -10

log[_A __1_ )2 ]

4nd 2n

2r

e

2n

+

e

_ 1010g[(2.35

i

( A

1.8] (9.9)

When the base station antenna is near the average rooftop level, the path loss is given by:

L

dB) ==

-10

log

_A_

2

-10 log[_A __1_ )2 ]

2V1nd

2n

2r

e

2n +

e

- 1010gGY (9.10)

For base station antennas below the average rooftop level, the path loss is given by:

L

(dB)

==

-10 log _A_

2

-10

log [_A __1_ )2 ]

2V1nd

2n

2r

2n

+ )

I

[

b ]2 A (

1

1

21

1010

g

2n d - b) J

+

b

2

4>

2n

+ 4>

(9.11)

where A is the wavelength and d is the distance between base and mobile station. The other

parameters, I1h

b

, I1h

m

, b,

and w, are defined in Figure 9.3, and r, e and ¢ are defined by:

r =J h ~

+

w/2)2

e==

tan-

l

[l1h

m/ w /2 ]

In the COST-231-Walfisch-Ikegami model [8], the angle of incident wave l/J shown in

Figure 9.3 is also used as an additional parameter. The diffraction loss from rooftop to

street,

L

rt s

,

and the multiscreen diffraction loss,

L

md

,

in Eq. (9.8) are given by:

L

rt s

(dB) == -16.9 - 10log(w) + 10

log f)

+ 20 10g l1h

m

)

+

Lori

o for L

rt s

< 0

(9.12)


8/15

176


where

Lori == -10 + 354tj1 for 0 ~ tjI < 35°

2.5 +

0.075 tjI -

35) for 35

tjI

< 55°

4.0 - 0.114 tjI - 55) for 55 tjI 90°

where

L

md

(dB)

==

L

bsh

+

k

a

+

k

d

log d)

+

k

f

log f)

- 9 log b)

o for L

md

< 0

(9.13)

L

bsh

==

-1810g 1+

~ h b

for

h

b

>

h

roof

o

for h

b

< h

roof

k

a

== 54 for

h

b

>

h

roof

54 - 0 . 8 ~ h b for d ~ 0.5k

m

and h

b

~ h

roof

54 - 0.8 ~ h b d / 0 . 5 for

d

<

0.5k

m

and

h

b

==

h

roof

k

d

==

18 for h

b

> h

roof

18 - 15 ~ h h

ro

of

for h

b

< h

roof

k

f

==

-4

+ 0.7 //925

-

1) for medium-sized cities and suburban centers with

moderate tree density

- 4

+

1.5 //925

-

1) for metropolitan centers

The applicable range in the COST-231-Walfisch-Ikegami model is

f, frequency (MHz) 800-2000 MHz

h

b

,

base station antenna height (m) 4-50 m

h

m

, mobile station antenna height (m) 1-3 m

d, distance from transmission point

(km)

0.02-5

km

The Walfisch-Bertoni model supports distances less than 1km and base station antenna

heights lower than rooftop level. This means the model is suitable for microcell systems.

However, if the model is applied to a street microcell system whose base station antenna

heights are below the average rooftop level, the prediction error may be large. This is

because it is necessary to consider not only free line-of-sight propagation but also wave

guiding and diffraction at comers. The model does not correspond to this situation.

Figure 9.4 shows the two-path model with street canyon propagation. A calculation of

the theoretical signal level for the two-path process showed that it roughly followed a free

space power law close to the base station before making a transition to the faster

attenuation rate

of

the inverse fourth-power law. As shown in Figure 9.5, measurement

results also showed that close to the base station the propagation followed the free space

power law, and beyond this distance the propagation followed the inverse fourth-power law


9/15

9.3 ANALYTICALMODELS

177

- - - - -

<

Base station

.

Ground

.••..

. . •• Mobile station

............

.

- ,

........

.

Street

.....

-:

.....

- -.

Canyon of

buildings

FIGURE 9.4 Geometry

of

the two-path model for street microcelIs.

[16, 17]. The distance at which the path-loss law changes is called the breakpoint distance

and given by:

(9.14)

where ), is the wavelength, and h

m

and h

b

are the mobile and base station antenna heights,

respectively. The factor

k

takes values from 11 to 411, and depends on the actual

1000

I I I I I I II I I I I I I

Median signal level for

5.3m base site antenna

height

15 -2010gd

d

145.5 m

100

Distance from the base site (m)

20

E

co

0

0

Qj

>

ro

-20

c

. 2'

C/)

0

Q)

-40

.


10/15

178


environment such as vehicular traffic, trees, and traffic signals. For the example shown in

Figure

9.5,

it has been reported that k == 2n.

Based on this fact and measurement results, a path-loss prediction formula for street

microcells was proposed by Ichitsubo et al.

[18].

For a line-of-site street, the path loss is

given by:

L (dB)

==

P L

I

) -

15.510g(WI) +

Floss

+ 59.9

(9.15)

For a street with intersections, the path loss is given by:

L (dB) P L

I

, L

2

) - 20.210g(wI) - 7.810g(w2) + Floss + 59.8 (9.16)

For parallel streets, the path loss is given by:

L (dB) P L

I

) +

40.410g L

2

) +

18.610g[ L

2

+L

3 L

2

] - 15.410g(WI)

- 19.91og(wz) - 8.510g(w3) + Floss + 40.6 (9.17)


11/15

. b .

: e:::..

. .

9.4 DETERMINISTICMETHODS 179

Cross street

FIGURE

9.6 Parameters used in street microcell path-loss prediction.

The parameters used in the formula are defined in Figure 9.6; Fl oss represents frequency

dependency.

9 4 DETERMINISTIC METHODS

The history of path-loss prediction models shows that information about buildings and

streets is necessary and geometrical paths between transmitter and receiver should be

considered for accurate prediction. The ray-tracing method is a relatively precise approach

for small areas such as indoor picocells and street microcells [19-21].

In the ray-tracing method, rays are launched from the transmitter, and geometrical

reflection, transmission, and diffraction are repeated for walls and edges of buildings, as

shown in Figure 9.7. The rays arriving at the receiver are tracked as traces, and the field

strength at the receiving point is calculated by summing the electric fields of all arrival

rays. The field strength of each ray is determined by calculating all reflection, transmission,

and diffraction losses in the propagation path. The reflection and transmission losses are

usually calculated using Fresnel reflection and transmission coefficients, and diffraction

loss is calculated by using the geometrical theory of

diffraction (GTD). This means that the

prediction accuracy depends on how to find exact ray paths between the transmitter and

receiver.

As shown in Figure 9.8, there are two approaches to ray tracing: the imaging method

and the launching method. In the imaging method, the reflection and transmission points

are determined geometrically by considering the transmitter 's equivalent image. The rays

reaching the receiving point are located by examining all combinations of reflection,

transmission, and all diffraction points between the transmitter and receiver. This method

offers good prediction accuracy but needs long computation time when a lot of images


12/15

18

PROPAGATION LOSSPREDICTION MODELS

FIGURE 9.7 Reflection, transmission, and diffraction between

T,

and

R,.

must be considered. In the launching method, a ray is launched at every angle 110 from the

transmitter, and its path is traced through reflection, transmission, and diffraction. The rays

that reach reception area

I1S

are considered to have arrived at the reception point. Since ray

tracing is performed for each discrete angle

110,

the computation time is shorter than that

of

the imaging method. The prediction accuracy

of

this method depends on the chosen

values of

110

and I1S

.

A combination of these two methods has been reported to simplify

three-dimensional ray tracing [22].

With both methods, there is a trade-off between the prediction accuracy and the

computation time. How to reduce the reflection, transmission, and diffraction points, or

how to find the paths that most strongly contribute to the receiving level is the key to

optimizing this trade-off. The other way to reduce the computation time is to model the

buildings and roads in the prediction area. Regarding roads, for example, each intersection

and the street between intersections can be transferred to a node and an element

component, and the data of street width and building height are stored as the component

Reception Point

Rx

Tx

Rx

Reflecting Object

,

,

,

,

.. .. . . ....

:

Image ofTx

Imaging Method

ReceptionArea

L lS

Reflecting Object

Launching Angle

L l8 ,

Tx

Launching Method

FIGURE 9.8 Imaging and launching methods for ray tracing.


13/15

9.5 SUMMARY 181

,.L....1......J : ~ ~

, .

....

:: I,

.: I

................

Delay

profile .

L. .

a

0. .

-0 . :::

~ ~

ay arrival time

....

I

Building

FIGURE 9.9 Example of ray-tracing results for macrocell system.

factors. In a similar manner, the prediction area can be transformed into a plane with

pixels, and each pixel holds data on terrain and buildings. By introducing such modeling to

the database structure, preprocessing becomes possible before the ray-tracing process, and

it also becomes possible to refer to the database quickly during the calculations.

When the ray-tracing method is applied to a wide area, a huge database is required, and

computation time exponentially increases with the number of traces. However, the

enormous increase in the processing performance of computers and the commercialization

of CD-ROM map, including the data of terrain and obstacles, has increased interest in this

method for microcell and macrocell system design tools [23, 24]. Figure 9.9 shows an

example of a ray-tracing result for a macrocell system.

9 5 SUMMARY

Figure 9.10 shows the applicable areas and simplicity of the major prediction models. The

cell size of current cellular systems in urban areas is shrinking to cope with increasing

demand. For designing of microcells and indoor picocells, the ray-tracing method is now

practical. The Walfisch-Bertoni model is also useful for microcells somewhat larger than

street microcells. Macrocells with cell radii larger than 1km are still needed for suburban

and rural areas to realize cost-efficient systems. The Okumura-Hata model with the

Akeyama correction and terrain correction is useful in these application areas due to its

simplicity.

Each prediction model has its own applicable conditions. In particular, the range of

application area is different from each other. Prediction accuracy of each model is assured

under the indicated applicable conditions. Therefore , when we design cellular mobile radio

systems, it is important to select the prediction model appropriate for the intended cell size.

In actual case, it is necessary to use one or several prediction models for determining the

path loss [25].


14/15

182


' :8 burban

.

c

o

§

:: l

o

co

o

a

£

Ci

E

(]j

.. .. .. . . . . .

:

>

. : : : :: 1 ~ e ~ a c e

1 km 10 km

Applicable Cell Size

FIGURE 9.10 Application areas and simplicity

of

prediction models.

The applicable frequency range of propagation loss prediction models proposed so

far is up to around 2 GHz. The third-generation mobile communication system, the inter

national mobile telecommunications 2000 (IMT-2000), will be introduced in the 2-GHz

frequency band. IMT-2000will use the bandwidth of more than 5 MHz to support user bit

rates of up to 2Mbits

js

. The wideband characteristics of the propagation channel, for

example, the characteristics

of

individual paths in multipath propagation are necessary for

such system design. The fourth-generation system will provide multimedia services

beyond IMT-2000 by using microwave and millimeter wave frequency bands and so

will require even wider bandwidth. In such a situation, microcells and picocells will be

introduced to compensate the increased path loss. The space-time equalization technology,

which combines adaptive equalizers and adaptive array antennas, may be the breakthrough

needed to overcome the increase in path loss and delay spread [26]. The path loss,

the direction of

arrival (DOA) and the time

of

arrival (TOA)

of

each path are essential

characteristics in developing these technologies. The ray-tracing method appears

to be most effective in these cases and so will become more important in future system

designs.

R F R N S

1. Y. Okumura, E. Ohmori, T. Kawano, and K. Fukuda, Field Strength and its Variability in VHF

and UHF Land Mobile Service, Rev. Elec. Commun. Lab., Vol. 15, pp. 825-873, 1968.

2. M. Hata, Empirical Formula for Propagation Loss in Land Mobile Radio Services, IEEE Trans.

Veh. Tech., Vol. 29, pp. 317-325, Aug. 1980.

3. W. C. Y. Lee, Mobile Communi cation Engineering, McGraw-Hill, New York, 1982.

4. M. F. Ibrahim and 1. D. Person, Signal Strength Prediction in Build-up Areas. Part I: Median

Signal Strength, lEE Proc., Vol. 130, Part F, pp. 377-384, 1983.

5. S. Sakagami and K. Kuboi, Mobile Propagation Loss Prediction for Arbitrary Urban Environ

ments, Elec. Commun. Japan , Part I , Vol. 74 , No. 10, pp . 87-99, 1991.


15/15

REFERENCES

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Documents

Chapter 9 - Propagation Loss Prediction Models