Hata - Empirical Formula for Propagation Loss in Land Mobile Radio Services (1)

317

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. VT-29, NO. 3, AUGUST 1980

Empirical Formula for Propagation Loss in Land Mobile Radio Services Abstract-An empirical formula for propagation loss isderived from Okumura’sreport in order to put his propagation prediction method to computationaluse. The propagation loss in an urban area is presented in a simple form: A + B l o g R, where A and B are frequency and antenna beight functions and R is the distance. The a ir t o d d formula is applicable to system designs for UHF and VHF land mobile rpdio ~enices,with a d formulationerror,underthefoUowing conditiom: frequency range 100-1500 MHz, distaace 1-20 km, base station antenna height 30-2@0 m, and vehicular antenna height 1-10 m.

I. INTRODUCTION

I

N SYSTEM PLANNINGforlandmobileradio service or service quality evaluation, it is indispensable to determine thepropagationcharacteristics. By using manyexperimental results and by statistical data processing, many authors have developed nomograms and charts to permit the calculation of expected field strengths from a given transmitter at chosen receiver locations [ 11 -[7] and made it clear that the propagation loss shows logarithmic behavior to the distance. Of all the studies, Okumura’s report [ l ] is very practical, because it carefully arranges field strength and service area. Not only is the report usedas comparisondatawithotherauthors’reports [ 8 ] - [ l o ] ,b u t also thepropagationpredictionmethods in the report have become standard for planning in today’s land mobile systems in Japan [ 1 11 , [ 121 . In Okumura’spredictionmethod,prediction curves for a basic median field strength were given with these parameters: base stationeffectiveantenna height hb frequency f,,and vehicular station antenna height h,. Fig. 1 shows one of these curves. When malung a system plan using this method, therefore, it is necessary to select the curves according to f,,hb, and h,. It is more cumbersome to use these curves, represented by 1 kW effectiveradiatedpower(ERP)perdipole,sinceit is necessary to convert the value to the transmitter’s power. Under these circumstances, even though the method is practical in theactualwork stage such as radio zone estimation, it is awkward to use directly in the system planning stage required to fit the parameters best. In this report, to make computational use ofOkumura’s prediction methods in system planning, an empirical formula forpropagationloss,whichcorresponds to freespace loss often usedin UHF futedradio communication system planning, is derived from the prediction curves. In order to avoid complication,the following points were considered in its formulation. Manuscript received May 7, 1979; revised January 29, 1980. The author is with the Mobile Communication Equipment Section, ElectricalCommunicationLaboratories,NipponTelegraphandTelephone Public Corporation, 1-2356,Take, Yokisuka-shi, Kanagawa-ken, 238-03,Japan. Telephone 0468-59-2794.

1) Propagation loss between isotropic antennasis treated. 2) Quasi-smooth terrain, not irregular,is treated. 3) The urbanarea propagation loss is presented as the standard formula.Forotherareas,acorrectionequation to the standard is prepared. 11. PROPAGATION LOSS AND EMIPRICAL FORMULA

A. Propagation Loss Between Isotropic Antennas When the effective radiated power of an isotropic antenna is Pt (dBW: EIRP) and the received field strength of an isotropic antenna is E (dBpV/m), the propagation loss L , (dB) between these isotropic antennasis obtained as follows. If A H is the absorption cross sectionof an isotropic antenna and P, is the received power density, the received powerP, is given by Pr

(dBm) = P, (dBm/m2)

+ 10 logl ( A e f f )

(1)

where

A,R = A2/4n,

A: wavelength (m).

P, (dBm/m2) = E (dBpV/m) - 10 loglo (120n) - 90. Since the propagation loss is the difference value between the radiated power and the received power, using (1) we obtain Lp

(dB) = P, - Pr = P, (dBW) - E (dBpV/m) - 10 log1 0 (x2/4n)

+ 145.8.

(2)

B. Okumura’s PredictionCurves and Propagation Loss As Okumura’spredictioncurves give the receivedfield strength at 1 kW ERP/dipole, it is necessary to transform the unitfromERP/dipole to EIRP. This transformation is accomplished by adding the difference value for power gain between the isotropic antenna and the dipole antenna. Since the absolute power gain of the dipole antenna is 2.2 dB, then P, (dBW EIRP) = P,‘ (dBW ERP/dipole)

+ 2.2 (dB).(3)

When P,‘ is 1 kW (ElW/dipole), therefore, P, (dBW EIRP) is 32.2 dB. Using (2) and (3), the progapation loss L , (dB) between the isotropicantennas is given bythepredictioncurvesandthe following equation:

L p (dB) = 178 - 10 loglo (x2/4n) - E (dBpV/m).

0018-9545/80/0800-0317$00.75 0 1980 IEEE

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318

TRANSACTIONS IEEE VEHICULAR ON TECHNOLOGY, VOL.

VT-29, NO. 3, AUGUST 1980

110

TABLE I VALUE OF A

100 lc(MHz)

I

h, (m)

1

150

1

900 450 ~

1

5 0 1 2 2 .151 4 .100 3 . 0

70

i

101.0

100

98.5

150 1 0 8 . 0

96.5

200

94.5

112.0 110.0

'

120.5

132.0

i

129.5

I

127.0 125.0

118.0

~

123.0

,

116.5

121 .o

114.5

106.0

TABLE I1 VALUE O F B

20,

1:

1500

I

124.5 117.0 105.5 30

20

fc ( M H ~

10 30

0

50

-10 I

+Log. Scale

P Linear Scale

Distance (km)

-

1 1

35.0

35.0

34.1 33.4

,

32.5 31.3 3150 1.1

1

30.4

~

~

,

15.7 33.8 32.2

1 ~

~

I

200

29.9

34.1 33.4 32.2

32.5

30.4

35.7

29.4

30.9 2 29 9. 9. 9

Fig. 1. Basic median field strength curve in the 900-MHz band.

C.Empirical Formula for Propagation Loss As astandardformula,thepropagation lossinan urban area over quasi-smooth terrain is introduced by using the basic median field strength curves. By theexaminationofthese curves, forexamplefrom Fig. 1, thecharacteristic is found wherein the field strength E (dB pV/M) can be prescribed as a function of distance R(km) as

where 7 and P are constantsdeterminedby hb (m) and f, (MHz). Therefore, the standard of propagationloss can also be prescribed by substituting (5) into (4),

A

A = a - 13.82 loglo h ,

- a(h,)

a = 69.55 + 26.16 loglo fc.

E (dBpV/m) = 7 + P log10 R

L, (dB)

two regulations: 1) at each frequency f, (MHz), A decreases two by two against logarithmically increasing hb (m), and 2) when f,becomes n times as large for fixed hb, A increases in proportion to log n. Considering these points, A can be shown as in Fig. 2. From this figure, A can be presented by

+ B log10 R

Table I1 alsoshows two regulations: 1) B is almostindependent off,, and 2) decreases constantly against logarithmically increasing h b . B can also be shown as in Fig. 3. Connecting the mean value at each h b , it becomes an almost straight line, as shown in the figure.When this line is represented by

A = 178 - 10 log1 0 (A2/4n)- 7 + a(h,)

B=--p

(8)

the maximum fluctuation width is about *OS, and it becomes the linear approximation error about B. Substituting (9) and (10) into (6), the standardformulaforpropagation loss is obtained by

where a(h,) is the correction factor for the vehicular station antenna height h , (m). In the basic curves, h, is 1.5 m, and correction curves for the other heightsare provided. Therefore, it is convenient to take a = 0 dB for h , = 1.5 m and to introduce the correction equation for the other heights. 1 ) Introduction of the Empirical Formula: Using (5) and (6), A is given by the value of the field strength E (dB pV/m) at R = 1 (km), and B is determinedbytheslope of the field where strength curve. Tables I and I1 show values for A and B taken f,: from the basic median field strength curves. Table I contains

150-1500 MHz,

319

HATA: PROPAGATION LOSS IN LAND MOBILE RADIO

Base Statlon elfectlve antenna helght hb im)

Fig. 2.

Introduction of factor A .

36

35

34

31

30

29

50

1c 30

20

70

100

Base statlon effective antenna height

Fig. 3.

hb : 30-200 m, R : 1-20 km,

200 hh ( m )

Introduction of factor B .

translatedinto linearscale,it can beexpectedthat these curves will be shown by straight lines. From this viewpoint correctioncurves arerewritten as shown bytheplottedpoints in Fig. 5 . Since the empirical formula should be as simple and accurate as possible for usability, the approximate lines in this figureare used.

and a@,) is the correction factor for h,, and a = 0 dB for h , = 1.5 m. 2) Determination of Correction Factor a(h,): In the prediction method, correciton curves for h , are given by Fig. 4. As the propagation loss L , of (1 1) has taken h, = 1.5 m Namely, the correction is presented as relative height gain to into standard, the correction factor a(h,) satisfies the condia standard Of hWI = in an urbanarea Over quasi-smoothtionthat = 0 dB for h , = 1.5 m, Ifit is assumed thatthecorterrain. rection curves which satisfy this condition can be presented by 1 ) Correction factors in a medium-small city: In the correctioncurvesforamedium-smallcity, if the horizontal axis is a , .s = tuc) 11, - q ( f c ) , (1 2 )

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320

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. VT-29, NO. 3, AUGUST 1980 20 2000'

Urban area

1-

15

5

400'

4b

200

-!j

.3

-3

9

100'

10

C

100

J

'

,x

5

a

200

400

fe

b

700

5

loo0

-"

'ti

'

:

0

$ 0

-5

1

2

5

3

VehicularStation AntennaHeighth

7

10

(m)

Fig. 4. Prediction curves for vehicular antenna height gain in an urban area.

1500 900

150

c

Vehicular Station

Antenna Height

h,

(m)

Fig. 5. Correction factors in a medium-small city (1).

the coefficients [ ( f , ) and d f , ) are given asfollowsby Fig. 6 :

using

where h,: f,:

l-lOm, 150-1500MHz.

The error to the linear approximation inFig. 5 is in proporto the frequency, and is about1 .O dB when f , = 1500 MHz. As the correction curves in Fig. 4 have irregular characSubstituting (13) into (12), the correction factor a@,) is ob- teristics in h , = 4-5 m, the approximation error of this part tained for vehicular antenna heights in a medium-small city: in Fig. 5 becomes larger than the other part. Therefore, it can be estimated that the maximum error will arise in f c = 1500 a@,) = (1.1 loglo f , - 0.7) h , - (1 -56 loglo f, - 0.8) MHz and h , = 4-5 m. 2) Correction factors in a lave city: Thecorrection (14) curves are given by dashed lines in Fig. 4. These curves can be (13)tion

-

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321

HATA: PROPAGATION LOSS IN LAND MOBILE RADIO 4.5

4.0

2 .o

Frequency IC (MHz)

Fig. 6.

Determination of coefficients Hf,) and ~(f,).

Urban area s o l i d l i n e s : Eq. ( 1 6 )

200

IC

1

1.5

2

3

4

5

Vehicular Station Antenna Height h,

Fig. 7.

6

7

8

MHz

400 MHz

9 1 0

(m)

Correction factors in a large city (1).

considered as parabolas. The following equations are approxi- transform (1 5 ) to an equation whichsatisfies the condition that a = 0 dB for h, = 1.5 m, then the correction factor a(h,) for mate expressions of these curves: vehicular antenna heights becomes ~ 3 =’ 8.29 * (loglo 1.54 A,)’ - 3.69 (dB), a(h,) = 8.29 (loglo 1.54 h,)’ - 1.10 (dB), f,< 200 MHz

.

f,2 400 MHz. Although the curves for f,= 200 MHz and 100 MHz are presented by one equation in (16), the error of this expression is only about 0.5 dB, as shown in Fig. 7. It is also necessary to

(1 6)

As shown in Fig. 8, values given by (16) and values given by Fig. 4 agree well in f,2 400 MHz. Their maximum difference

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322

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. VT-29, NO. 3, AUGUST 1980

plots : Fig. 5

f 5 2 0 0 MHz

fc? 400 MHz

,

t

1.5

I

3

2

~

5

4

7

6

8

9 1 0

V e h i c u l a r S t a t i o n A n t e n n a H e l g h t h m (m)

Fig. 8. Correction factors in a large city (2).

220

220

210

210

200

200

a L?

?

170

--%

160

4

180

i d

$

130

m

=

a.

120

s

110

0

170

160

1

140

i

m

180

150

150

&

= 900 XIHz

190

190

-

f

143

l

o

130 120

110

1 00

90

90 80

80

io

70

o ,

~

8

1 0

1 ,

I

60

60 1

2

3

5

7

10

20

30

40 50

Distance R (krn)

Fig. 9.

Propagation loss in an urban area (1).

occurs in f, < 200 MHz and h , 2 5 m, and is about 1 dB. Therefore, (16) is used as the correction factor a(h,) for vehicularantennaheightsina large city, where the building height average is more than 15 m. 111. ESTIMATION OF THEAPPROXIMATION ERR-OR

In this section we investigate how accurately the empirical formulasexpresstheprediction curves. Figs. 9 and 10 show the propagation loss in an urban area with parameters f, and h b , respectively.The solidlinesare the values given bythe

1

2

3

5

207

10

30

40 50

Distance R (km)

Fig. 10. Propagation loss in an urban area (2).

formula and the dashedlines are the values given by the prediction curves. Fig. 9 shows that the error at both ends of the frequency range is very small, and the maximum error, which occurs in the middle frequency range, is only about 1 dB. Furthermore, it shows that the error is independent of the distance (1-20 km) and is constant for each frequency. This is the reason that only term A in (7) depends on frequency. Therefore, the error in Fig. 9 mainly indicates the approximation error in (19) which gives termA. Fig. 10 shows that the error fluctuates about h b , and its maximumvalue is about 1 dB. Thisis due to the

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323

HATA: PROPAGATION LOSS INLANDMOBILERADIO 1500 '

900

-5 u

450

i:

L

150

V e h i c u l a r S t a t i o n A n t e n n a H e i g h t h rn (m)

Fig. 11. Correction factors in a medium-small city (2).

linear approximation in Fig. 3. From Fig. 10, it can besaid that (lo), which gives term B , is a fairly accurate equation. Fig. 1 1 shows the correction factor a(h,) for vehicularheights in a medium-smallcity.The solidlines are values calculated by using (14)andtheplottedpointsarethecorrection values given by Fig. 4. As mentioned in Section 11-C, the linear approximation error is porportional to the frequency and the antenna height. The maximum error arises in f, = 1500 MHz and h , = 4-5 m, and its value is about 1.5 dB. Below f, = 900 MHz, the error is only 0.5 dB (except when h , = 4-5 m), or 1 dB (in h , = 4-5 m). Consideringequation simplicity, therefore, it can be said that (14) is a simple and wellapproximated equation. The correction factor a(h,) in a large city is mentioned in the previous section.When using (16), there is little error in f, 2 400 MHz, and the maximum error is about 1 dB in f, < 200 MHz and h , 2 5 m . In practice, there are few cases in whch the vehicular antenna height is above 5 m. Therefore, it can be considered that (16) is very practicable.

3 z L

d a s h e d line :

2 i <

report

;

Okurnurals s o l i d line : Eq. (18)

10

2

1. 4 0 L

c

0 i

U i

0

6

5

0

Fi

"

0 100

IV. CORRECTIONS FOR SUBURBAN AND OPEN AREAS

200

300

500 700

1000

2000

F r e q u e n c r f c (MHz)

According t o Okumura's prediction method, the suburban correction factor K r (dB), which is the difference between the median field strength in the urban area and that in the suburban area,is given by thedashed line in Fig. 12. In this figure the solid line is the approximated curve given by Kr (dB) = 2 {log,o (fc128)12

+ (17) 5.4,

f, : MHz.

Fig. 12. Correctionfactorforsuburban

area.

culated by

On the other hand, the open area correction factorQ, (dB) is given by the dashed line in Fig. 13. In this figure the solid line is the approximated curve given by Qr

(dB) = 4.78 (loglo f,)* - 18.33 loglo f,

+ 40.94,

As Fig. 12 shows that (17) gives a good approximated value, thepropagation

loss insuburban area L,, (dB) will be cal-

f,: MHz.

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3 24

IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. VT-29, NO. 3, AUGUST 1980 7

Frequency IC ( M H ~ )

Fig. 13. Correction factor for open area.

TABLE 111 EXPERIMENTAL FORMULA FOR PROPAGATION LOSS L p = 69.55 + 26.16

Urban Area

'

fc

log

- 13.82

,

log

hb - a ( h m ) *

+ ( 4 4 . 9 - 6 . 5 5 . log hbj . log R (dB) -- - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

c o r r e c t i o n factor for v e h l c u l a r station a n t e n n ah e i g h t medium-small city a (h,)

= (1.1

. log

fc

- 0 . 7 ) , hm - ( 1 . 5 6

log

IC

- 0.8)

l a r g e city a ih,)

=

8.29

= 3.2

'

(log 1o 1 . 5 4h m j 2

. (log

Suburban L

= {Urban ~p

area)

Area

x

11.75hm)'

-2

- 1 .1

; fc ~ 2 0 0 MHz

- 4.97

;

{loglo ( r c / 2 8 ) }

rcz

- 5.4

400

M H ~

(dB)

here

(MHz) ---------- 150 -1 500 (MHz)

fc

: frequency

hb

: base stallon e f f e c t w e

-_-_-_30-200

(m)

antenna helght (mj

Fig. 13 .shows that (19) gives a good approximated value, and taken down to one decimal place, the error becomes very large. therefore, the propagation loss in open area L,, (dB) will be Therefore, coefficients are futed down to two decimal places. calculated by V. SUMMARY (20) L p o (dB) = L p {eq (1 1)) Qr. In order to put Okumura's prediction methods to computa-

-

In (17) and (19), if the coefficients are taken down to three tional use in system planning, prediction curves are formularin Table places of decimals, the error becomes slightly smaller, but the izedas propagation loss.Theseresultsarearranged 111. Since the propagation loss can be treated as a formula, it equationbecomesmorecomplicated.If the coefficientsare

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325

U T A : PROPAGATION LOSS IN LAND MOBILE RADIO

propagation at 800 MHz in the Philadelphia area,’’ I€E€ Tram. Veh. becomes possible to put the formula into various calculations c h l . , vol. VT-21, May 1972. about system planning. However,since the formula can only be [6] TA.e P. Barsis. “Determination of service area for VHF/UHF land mobile applied in restrictedranges,it is necessary to takenotice of and broadcast operations over irregular tenain,” I€&€ Trans.Veh. Technol.. vol. VT-22. May 1973. its applicable ranges and units.

[7] J . Durkin, “Computer pndiction of service area for VHF and UHF land mobile radio services,” I&€& Trans. Veh. Technol., vol. VT-26, Nov.

ACKNOWLEDGMENT Theauthorthanks Mr. K. Izumi and K. Hirade,Mobile Communication Equipment Section, Yokosuka Electrical Communication Laboratories, for their useful suggestions.

REFERENCES Y. Okumura et ai., “Field strength and i t s variability in UHF and VHF land-mobile radio service,” Rev. Elec. Commun. Lab.. vol. 16, 1968. CCIR, Recommendation 370-1, 11, Oslo, 1 9 6 6 : Report 565, Geneva, 1974. W.R. Young, Jr., “Comparison of mobile radio transmission at 150, 450, 900 and 3700 MHz,” Bell Syst. Tech. J . , vol. 3 I , Nov. 1952. A. P. Barsis. “Radio wavepropagation over irregular tenain in the 769200 MHz frequency range,” I&&€ Trans.Veh.Technol.. vol. VT-20, Aug. 1971. D. M. BlackandD. 0. Reudink, “Some characteristics of radio

1977. [8] G. D. Ott, “Vehicle location in cellular mobileradio systems,’’ IE€E

Tram. Veh.Technol., vol. VT-26, Feb. 1977. [9] K. Allsebrook and J. D. Parsons, “Mobile radio propagation in British cities at frequencies in the VHF and UHF bands,” I€&€ Trans. Veh. Technol., vol. VT-26, Nov. 1977. [IO] W. C. Jakes,Jr.. Microwave Mobile Communications. New Yo&: Wiley, 1974. [ I I] F. Ikegami, “Mobile radio communication in Japan,” /E&€ Trans. C ~ m m ~ rVOI. . . COM-20, 1972. [ 121 N. Yoshikawa and T. Nomura, “On thedesign of a smallzoneland mobile radio system in UHF band,’’ /€E€ Trans.Veh.Technol., VT-25, Aug. 1976.

Masaharu Hsta (“80) for a biography and photograph see page 252 of the May 1980 issue of this TRANSACTIONS.

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