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128 PROPAGATIONCHARACTERISTICS OFWIRELESSCHANNELS(1980) model, and the Walfish and Bertoni model (Har
et al., 1999; Ikegami, Tekeuchi, & Yoshida, 1991; Oda
et al., 2000; Okumura et al., 1968; Vogel & Hong, 1988)
are also available to calculate the received power. These
models take into account the antenna heights and other
factors. Yet another approach is to use a two exponent
model, where instead of using a single exponent, two val-
ues,n 1 andn 2 , are used. The loss increases slowly (i.e., the
loss occurs as if we have propagation in free space with
n=n 1 =2) until a break point is reached. Beyond that
point, the loss goes up at a higher rate, withntaking value
ofn 2 in the range 3 to 9 (Bertoni et al., 1994; Rappaport
& Sandhu, 1994). Even though this double exponent ap-
proach may appear to lead to better results, some of the
path loss prediction models can be used to get more sat-
isfactory results. I now describe the Hata (1980) model
for the calculation of the loss suffered by the signal as it
travels from the transmitter to the receiver. The lossLpin
decibels (dB) isLp=Pt(dBm)−Pd(dBm), (7)where the transmitted powerPtand the received power
Pdare once again expressed in decibel units.Hata Model
Based on measurements in a number of cities, Hata (1980)
proposed a model to predict the median loss suffered by
the wireless signal. This model is an improvement over
that proposed by Okumura et al. (1968) because it in-
corporates correction factors to account for the anten-
nae height based on the geographical location. When one
moves from large cities to rural areas, the reduction in
power loss can be accommodated with correction factors
for the antenna height. The median loss in urban areas
according to Hata model,Lpis given byLp(dB) = 69. 55 + 26 .16 log 10 (f 0 )
+(44. 9 − 6 .55 log 10 hb) log 10 d (8)
− 13 .82 log 10 hb−a(hmu),wheref 0 is the carrier frequency (MHz), 400≤f 0 ≤1500;
dis the separation between base station and mobile unit
(km),d>1;hbis the height of the base station antenna
(m);hmuis the height of the mobile unit antenna (m); and
a(hmu) is the correction factor for mobile unit antenna
height.
For large cities, the correction factora(hmu) is given asa(hmu)= 3 .2[log 10 (11. 75 hmu)]^2 − 4 .97 (f 0 ≥400 MHz).
(9)For small and medium cities, the correction factor isa(hmu)=[1.1 log 10 (f 0 )− 0 .7]hmu−[1.56 log 10 (f 0 )− 0 .8].
(10)For suburban areas, the median loss,Lsubis given byLsub(dB)=Lp− 2[
log 10(
f 0
28)] 2
− 5 .4, (11)2 4 6 8 10 12 14 16 18 2090100110120130140150160Distance kmPower Loss dBLarge cityRural areaFigure 5: Loss predictions based on Hata model are shown.
The radio frequency signal is at 900 MHz. The base station
antenna height is 150 m, and the mobile unit antenna height
is 1.5 m.whereLpis the median loss in small–medium cities. For
rural areas, the median loss,Lruris given byLrur(dB)=Lp− 4 .78[log 10 (f 0 )]^2 + 18 .33 log 10 f 0 − 40. 94.
(12)The loss observed in large cities and rural areas is shown
in Figure 5. It is easily seen that the losses are higher in
urban areas.
The Hata model is not capable of predicting losses in
the frequency bands used in some of the present-day sys-
tems operating in the 1,500–2,000 MHz band. The Hata
model can be extended to cover this range (Rappaport,
2002; Saunders, 1999; Shankar, 2001) and the median
power loss in urban areas,LP(dB) can be expressed asLP(dB)= 46. 3 + 33 .93 log 10 (f 0 )− 13 .82 log 10 (hb)
−a(hmu)+[44. 9 − 6 .55 log 10 (hb)] log 10 d (13)
+CorrwhereCorris the additional correction factor given byCorr={
0 dB for medium city and suburban areas
3 dB for metropolitan areasThis model is valid for the following parameters only:f 0 : 1,500–2,000 MHz
hb: 30–200 m
hmu: 1–10 m
d: 1–20 kmThis model is applicable only for distances beyond
1 Km and thus is not applicable in microcells and pic-
ocells in which the distances between the transmitter and
receiver may be only a few hundred meters. Other models