Pr (dB)
.
.
.
.
.
.
..
. .. . .. .
.
.
. .
.
.
. .
. .
.
.
.
.
.
.
.
.
.
.
s
1
s
2
s
3
.
.
.
.
.
.
.
.
.
.
.
.
log(d/d )
0
0
log(d /d )
0
log(d /d )
0
1
2
Figure 2.8: Piecewise Linear Model for Path Loss.
time power falls off with path loss exponent
2
:
P
r
(dB) =
P
t
+ K
- 10
1
log
10
(d/d
0
)
d
0
d d
c
P
t
+ K
- 10
1
log
10
(d
c
/d
0
)
- 10
2
log
10
(d/d
c
)
d > d
c
.
(2.32)
The path loss exponents, K, and d
c
are typically obtained via a regression fit to empirical data
[32, 30]. The two-path model described in Section 2.3 can be approximated with the dual-slope model,
with one breakpoint at the critical distance d
c
and attenuation slope s
1
= 20 dB/decade and s
2
= 40
dB/decade. The multiple equations in the dual-slope model can be captured with the following dual-slope
approximation [15, 44]:
P
r
=
P
t
K
L(d)
,
(2.33)
where
L(d) =
d
d
0
1
q
1 +
d
d
c
(
1
-
2
)q
.
(2.34)
In this expression q is a parameter that determines the smoothness of the path loss at the transition
region close to the breakpoint distance d
c
. This model can be extended to more than two regions [16]
2.6.6
Indoor Attenuation Model
Indoor propagation environments have a much greater variability than outdoor environments. In par-
ticular, buildings differ widely in the materials used for walls and floors, the layout of offices, hallways,
windows, and open areas, the location and material in obstructing objects, and the size of each room and
the number of floors. All of these factors have a significant impact on path loss in an indoor environment.
Thus, it is difficult to find generic models that can be accurately applied to determine path loss in a
specific indoor setting.
Indoor path loss models must accurately capture the effects of attenuation across floors due to
partitions, as well as between floors. Measurements across a wide range of building characteristics and
signal frequencies indicate that the attenuation per floor is greatest for the first floor that is passed through
and decreases with each subsequent floor passed through. Specifically, measurements in [17, 19, 24, 20]
indicate that at 900 MHz the attenuation when the transmitter and receiver are separated by a single floor
ranges from 10-20 dB, while subsequent floor attenuation is 6-10 dB per floor for the next three floors,
and then a few dB per floor for more than four floors. At higher frequencies the attentuation loss per floor
is typically larger [19, 18]. The attenuation per floor is thought to decrease as the number of attenuating
40