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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(19)
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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