macrocell models

REPORT 1 (16)Uppgjord - Prepared Tfn - Telephone Datum - Date Rev Dokumentnr - Document No.

LV/RT Maria Thiessen 40:45228 1995-11-07 A LV/R-95:068Godknd - Approved Kontr - Checked Tillhr/Referens - File/Reference

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A REVIEW OF SOME IMPORTANTMACROCELL MODELS

CONTENTS:

1 INTRODUCTION 2

2 SIMPLE MODELS 2

2.1 PROPAGATION IN FREE SPACE 22.2 PLANE EARTH PROPAGATION MODEL 32.3 EGLI MODEL 4

3 OKUMURA HATA RELATED MODELS 4

3.1 OKUMURA METHOD 43.2 HATA MODEL 53.3 COST-231 HATA MODEL 63.4 ERICSSON COST-231 HATA MODEL 63.5 9999 ALGORITHM 7

3.5.1 Knife edge diffraction 73.5.2 Description of the algorithm 9

4 MODELS FOR URBAN AREAS 10

4.1 IKEGAMIS MODEL 104.2 WALFISCH BERTONI MODEL 114.3 COST-231 WALFISCH IKEGAMI MODEL 124.4 VODAFONES METHOD 134.5 HALF-SCREEN MODEL 14

5 REFERENCES 16



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1 INTRODUCTION

Wave propagation is difficult, no one can argue against that. Nevertheless it isnecessary, for example when planning mobile telephony systems, to definemethods for predicting propagation in an area. Different models for estimatingsignal strength are used for this purpose. They might be simple expressions,suitable for rough assessments or complicated algorithms that demandconsiderable computation time.

This document is intended to be a survey over existing wave propagationmodels for macrocells. Most of the important and often discussed models areincluded. This overview is restricted to deal with models suitable for the casewhen antenna heights exceed average roof tops and cell ranges typically morethan 500 m.

2 SIMPLE MODELS

2.1 PROPAGATION IN FREE SPACE

The simplest model for wave propagation is the free space case. We assumethat the transmitting and receiving antennas are placed at long distance fromeach other. This is applicable for satellite communication but can also be usedas a reference for comparison with other models. The path loss Lbf [ ]dB canbe expressed as

L dbf = 20

4log pl

(1)

where d : distance [ ]ml : wave length [ ]m

If we write l as l = c f , where c is the speed of light (3 108 m/s) and f is thefrequency, Eq. (1) can be written as

L d fbf = + +32 20 20.4 log log (2)

where the distance d is given in [ ]km and the frequency f in [ ]MHz .



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2.2 PLANE EARTH PROPAGATION MODEL

Figure 1. Different propagation paths.

The electromagnetic field is modelled by three different components, the directwave, the reflected wave and the surface wave. The surface wave can beneglected at frequencies used for mobile communication, but the reflected wavecan not be ignored. If we assume perfect reflection and if h h db m



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2.3 EGLI MODEL

According to different measurements, the path loss is a function of thefreqency. Eglis model contains an empirical terrain factor which has thisdependency,

( )L d h h fb b m= - + 40 20 20 40

log log log (4)

where the frequency f should be given in [ ]MHz . This model is valid forfrequencies above 40 MHz and works in irregular terrain. However it is ratherinaccurate and should only be used for rough estimations when no details of theterrain are known. The model is a systematic interpretation of measurementscovering a wide span of frequencies.

3 OKUMURA HATA RELATED MODELS

3.1 OKUMURA METHOD

The Okumura method is completely empirical and based on extensivemeasurements performed in the Tokyo area []1 . The results are shown in aseries of curves, showing field strength as a function of distance for differentfrequencies and antenna heights.

Figure 2. An example of an Okumura set of curves.



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In the model a base station effective antenna height is defined in order to obtaina field strength suitable for different types of terrain. The model includes amongother things correction factors for suburban and open areas, mixed land-seapath, isolated mountain area and sloping terrain. It is valid for frequency rangesof 150 to 2000 MHz, distances of 1 to 100 km, and for base station effectiveantenna heights of 30 to 1000 m.

3.2 HATA MODEL

The Okumura model was intended for manual use. Hata [ ]2 made an attemptto derive empirical formulas from Okumuras curves for computational use.The path loss Lb [ ]dB can be written as

( )L f h a hb b m= + - - +69 55 2616 13 82. . log . log( )+ - 44 9 6 55. . log logh db (5)

Here h b means the base station effective antenna height. The model worksunder the following conditions: 150 1500 f MHz 1 20 d km 30 200 hb m 1 10 hm m

( )a hm [ ]dB is a correction factor for the vehicular antenna height hm ,a = 0 dB for hm = 1.5 m.

In a medium small city, ( )a hm becomes

( ) ( )a h f h fm m= - - +11 0 7 156 0 8. log . . log . (6)

In a large city, ( )a hm instead becomes

( ) ( )( )( )( )a hh f MHz

h f MHzm

m

m

= -

-

8 29 1 54 110 200

3 2 11 75 4 97 400

2

2

. log . .

. log . .(7)

These formulas above are valid for urban area. For suburban and open areas,we have the following correction factors:



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Suburban area: Kf

r =

+2 28

52

log .4

( ) ( )L L Kb b rsuburban urban= -

Open area: ( )Q f fr = - +4 78 18 33 40 942. log . log .( ) ( )L L Qb b ropen urban= -

In both cases, ( )Lb urban is given by Eq. (5).

3.3 COST-231 HATA MODEL

The Hata model is restricted to frequencies below 1500 MHz and thus does notwork in the 1800 MHz band. Okumuras propagation curves have beenanalysed in the upper frequency band for finding a suitable formula []3 :

( )L f h a hb b m= + - - +46 3 33 9 13 82. . log . log( )+ - +44 9 6 55. . log logh d Cb m (8)

( )a hm is defined in Eq. (6) and Cm is given by

CdB for medium sized city and suburban

dBcentres with erate tree density

for metropoli centresm =

0

3mod

tan(9)

The model works under the same conditions as the original Hata model, exceptfor that the frequency range is now from 1500 to 2000 MHz.

3.4 ERICSSON COST 231 HATA MODEL

The Cost 231 Hata model above has been modified within ERA [ ]4 . Thismodel is also valid for frequencies from 1500 to 2000 MHz. The path lossformula is the same as Eq. (8), and in this case the mobile antenna height isassumed to be 1.5 m. However the constant Cm in this case has differentvalues for various types of areas. In the table at next page we have an exampleof how the correction factors can look like in a special case:



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Table 1. Correction factors for different environments.

Area Cm (dB)Dense Urban1 -2.9Urban -2.9Suburban -10.5Rural -21.4Highway -26.7Flat Open -32.4

3.5 THE 9999 ALGORITHM

3.5.1 Knife edge diffraction

So far, we have only discussed models that operate on flat terrain. A model thatconsiders different kinds of obstructing elements such as hills, trees orbuildings, etc. has to be derived. The shadowing caused by a single object canbe estimated by treating the obstruction like a diffracting knife edge. Weintroduce the dimensionless Fresnel parameter, n , as:

nl

= +

hd d

2 1 1

1 2(10)

where h : height of knife edge above line of sight [ ]md1 : distance from base station to knife edge [ ]md2 : distance from mobile station to knife edge [ ]m

Figure 3. Geometry for propagation over a knife edge. 1 In some contiguous Dense Urban areas, Cm = 0.1 dB should be used.



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A negative value of n means that the height of the knife edge does not reachthe line that connects the base antenna and mobile.

Let the electric field at the knife edge be equal to E0 , and E is the field afterthe knife edge. Then the absolute value of the ratio of these fields is:

( ) ( )EE i

iC i S

0

11

12 2

=+

+ - -n n (11)

where ( )C n and ( )S n are the Fresnel integrals,

( )C dn p w wn

= cos 2 2

0

, ( ) ( )C C- = -n n (12)

and

( )S dn p w wn

= sin 2 2

0

, ( ) ( )S S- = -n n (13)

-4 -3 -2 -1 0 1 2 3 40

0.2

0.4

0.6

0.8

1

1.2

v

|E/E

o|

Figure 4. The ratio E E0 as a function of the Fresnel parameter n . Note thata positive value of n means non-line-of-sight (NLOS).



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The path loss Lb [ ]dB is then calculated from

LEEb

= - 200

log (14)

The integrals ( )C n and ( )S n can be found in tables for different values of n ,but that might be an inconvenient way to determine Lb .The path loss can alsobe obtained from diagrams. However, there are some good approximations forEq. (14). If n > -1, Lb can be expressed with good accuracy as

( )Lb = + + +6 20 12.4 log n n (15)When n > 1 it is possible to find a yet simpler approximation:

Lb = +13 20 log n (16)

which is equivalent to E E0 0 225= . n .

3.5.2 Description of the algorithm

This algorithm is developed within ERA [ ]5 and is originally based on theOkumura-Hata model. The model has been improved through analysis of alarge number of wave propagation measurements all over the world. The majorpath loss contribution arises from the modified Okumura-Hata equation, othersources are: Attenuation due to disturbing obstacles, e.g. mountain peeks. These objects

are treated like knife edges, and the algorithm finds the peak along theterrain profile that disturbs the wave propagation to the greatest extent.

Contribution due to earths curvature. When the distance between baseantenna and mobile becomes large enough, the curvature of the earth willattenuate the signals.

Land usage code loss. Different types of ground appearance, e.g. water,forest, rice fields or industrial estate will cause varying diffraction losses.

The output from the algorithm is the path loss Lb [ ]dB , which is described as:

[ ] ( ) ( )L HOA mk mobile KDFR JDFRb = + + +a 2 2 (17)



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where [ ]mk mobile : the land usage code at mobile [ ]dBa : a parameter connected to knife edge diffractionKDFR : contribution from knife edge diffraction [ ]dBJDFR : diffraction loss due to spherical earth [ ]dB

The term HOA [ ]dB is a variant of Okumura-Hatas eqations:

HOA A A A h A d hb b= + + + -0 11 2 3log log log

( )[ ] ( )- +3 2 11 75 2. log . h g Fm (18)

where ( )( ) ( )

AA d if KDFR dBA d A A d if KDFR dB

g F F F

111 64 1 4 6

44 4 781

2

= + - >

= -

loglog log

.49 log . log

Here hb denotes the effective antenna height [ ]m as defined in 9999 and d1is the distance from base antenna to knife edge [ ]km . A0, A1, A2, A3 and A4are tuning parameters.

The algorithm is valid for the following ranges: 150 2000 f MHz 1 100 d km 20 200 hb m 1 5 hm m

4 MODELS FOR URBAN AREA

4.1 IKEGAMIS MODEL

Ikegami et al. [ ]6 have investigated propagation mechanisms in urbanenvironment. In particular they have studied the path loss due to diffractionover roof tops. Two diffracted waves reach the mobile antenna, one of them isreflected against the wall of an adjacent building, but the other one is direct.The contributions of these two waves are added and the resulting path loss dueto roof-top-to-street diffraction, L rts , [ ]dB can be described as:

( ) ( )L w H h frts m= - - + - + + 16 9 10 20 10 10. log log log log sin j (19)



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where w : width of streetH : height of buildingsj : street orientation versus incident wave [ ]deg

Figure 5. Definition of street orientation.

The model is based on theoretical calculations, but it has also been comparedwith field experiments. The result of the comparison was found to be good.

4.2 THE WALFISCH BERTONI MODEL

Walfisch and Bertoni [ ]7 have also made a theoretical study of propagation inurban environment. According to them the total path loss consists of threecomponents: contribution from loss in free space reduction of the fields above the roof tops due to forward diffraction past

many rows of buildings diffraction of the roof top fields down to ground level.

The contribution from the last two components is here denoted Lex [ ]dB andwill be given in the following. Walfisch and Bertoni assume an area havingbuildings of relative uniform height and with parallel street grid. The primarypropagation path lies over the top of the buildings according to them. Lex canbe expressed as:

L A fex = + + -571 18. log log a (20)

where a : the angle between the incident wave and ground [ ]rad



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Figure 6. Parameters in the Ikegami and Walfish-Bertoni models.

For level terrain, a is given by,

a = -DHd

dRe2

(21)

where D H : difference between building height and base antenna height [ ]m

a is here assumed to be small. Re is the effective earth radius, 8 5 103. km.

The term A arises from diffraction down the roof tops,

( ) ( )A b H h b H hbm

m= + -

- +

-

52

9 2022 2log log log arctan (22)

where b : separation between blocks [ ]m

The contribution due to free space, Lbf , is given by Eq. (2) and the total pathloss, Lb [ ]dB , will be obtained by adding Lbf and Lex .

4.3 COST-231 WALFISCH IKEGAMI MODEL

A combination between the two models described in Sections 4.1 and 4.2 hasbeen made in []3 . None of these models are valid for the line-of-sight case. Incase of free sight between base and mobile antennas in a street canyon, then thepath loss will be



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L d fbc = + +42 6 26 20. log log (23)

Worth noting, this expression is equal to that of free space loss (Eq. (2)) whend = 0.02 km. d should extend 0.02 km if the expression will be valid.

In case of non-line-of-sight, we instead have:

L L L Lb bf rts msd= + + (24)

where Lbf is the free space loss. L rts is the path loss due to roof-top-to-streetdiffraction according to Ikegami et al. with one modification. The term

( )10 log sin j in Eq. (19) has been replaced with the expression Lori [ ]dB :

( )( )

Lori =- + + - - -

10 0 354 0 352 5 0 075 35 35 554 0 0 114 55 55 90

.. .. .

j jj jj j

o

o

o(25)

The angle j is given in Fig. 5. Lmsd is the loss due to multi-screen diffractionand is based on the Walfisch-Bertoni expression, Lex , (Eq. (20)). There areadded terms for short distances (d < 0.5 km) and for base antennas lower thanroof tops. However it has been shown that the accuracies of prediction are bestfor the case hb >> H.

The COST-231 Walfish Ikegami model is restricted to: 800 2000 f MHz 0 02 5. d km 4 50 hb m 1 3 hm m

4.4 VODAFONES METHOD

The British operator Vodafone has developed a method for predicting fieldstrength in different types of areas []8 . When it comes to propagation in urbanarea they have the same philosophy as Ikegami et al.: the main propagationpath is over buildings, not round them. If there are elements remarkablysticking up, the diffraction round or through them will however be calculated.The used models are frequency dependent, including attenuation due todifferent obstacles. Losses from free space field strength are calculated for reflection and diffraction by the ground (including knife edges) ground cover loss along the path caused by buildings, trees etc. ground cover loss near the mobile (similar to Ikegami et al.).



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4.5 HALF-SCREEN MODEL

4.5.1 General

This model is developed within ERA [ ]9 . It is especially suited for predictingpath loss in an urban area, since it takes into account obstructing objects likebuildings etc. The denotation half-screen model arises from the fact that theterrain profile is replaced by absorbing half-screens with heights that are equalto the average height of the obstacles. There are two different ways to use themodel: one approach is statistical, the other one is more deterministic. In thestatistical approach the chosen location of each screen does not have tocoincide with an existing building. Different kinds of environments can bemodelled with different screen heights and screen separations.

Figure 7. Definition of model parameters, statistical approach.

When using the statistical approach, the parameters defined in Fig. 7 are used.hb is the actual base antenna height and h m is the mobile antenna height.However, the resulting path loss is more correlated to the relative antennaheights D H and h. H should describe the average obstacle height and w is thescreen separation. Finally the distance between screen and mobile, w, is animportant parameter.

In some cases it is necessary to use a more deterministic approach: screenpositions will coincide with obstaclespositions. This is because in shortdistances every single building or tree becomes important. When predictingminicells this is relevant. Notable is that in this model, in contradiction to e.g.the Walfish-Ikegami model, it is possible to define a ground height profile, i.e.the ground does not need to be flat. There are also possiblities to define screenswith different heights and different relative distances.



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The model can also be used for long distances, up to 50 km has been tested.Spherical earth correction is taken into account.

4.5.2 Input data

Spherical earth factor and earth radius Frequency Base antenna position and height above ground Mobile antenna position and height above ground Height profile Screen heights and positions



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5 REFERENCES

[1] Okumura, Y. Ohmori, E. Kawano, T. Fukuda, K., Field strength and itsvariability in VHF and UHF land-mobile radio service, Review of theECL, 16, pp 825-873, 1968.

[2] Hata, M., Empirical formula for propagation loss in land mobile radioservice, IEEE Trans. on Vehicular and Technology VT-29, pp 317-325,1980.

[3] Urban transmission loss models for mobile radio in the 900- and 1800-MHz bands, COST 231 TD (90) 119, rev.2, 1991.

[4] Vidin, L., CMS 40 Link Budget for RFP Nominal Cell Plans, Doc. No.EUS/E950538.TEC.

[5] Melin, L., Functional Specification: EPA-Ericsson PropagationAlgorithm, Doc. No. 155 17-CNL 113 156 Uen, 1994.

[6] Ikegami, F., Yoshida, S., Propagation factors controlling mean fieldstrength on urban streets, IEEE Trans. on Antennas and Propagation,AP-32, pp. 822-829, 1984.

[7] Walfish, J., Bertoni, H.L., A Theoretical Model of UHF Propagation inUrban Environments, IEEE Trans. on Antennas and Propagation, AP-36, pp. 1788-1796, 1988.

[8] Causebrook, J., Vodafones field strength prediction method, COST231 TD (93), 1.

[9] Berg, J.-E., A Macrocell Model Based on the Parabolic DiffusionDifferential Equation, Report, Ericsson Radio Systems AB.

macrocell models

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