Lecture 5: Large-Scale Path Loss
Chapter 4 – Mobile Radio Propagation:
Large-Scale Path Loss
I. Problems Unique to Wireless (not wired) systems:
 Paths can vary from simple line-of-sight to ones
that are severely obstructed by buildings,
mountains, and foliage.
 Radio channels are extremely random and
difficult to analyze.
 Interference from other service providers
 out-of-band non-linear Tx emissions
2
 Interference from other users (same network)
 CCI due to frequency reuse
 ACI due to Tx/Rx design limitations & large #
users sharing finite BW
 Shadowing
 Obstructions to line-of-sight paths cause areas of
weak received signal strength
3
 Fading
 When no clear line-of-sight path exists, signals are
received that are reflections off obstructions and
diffractions around obstructions
 Multipath signals can be received that interfere with
each other
 Fixed Wireless Channel → random & unpredictable
 must be characterized in a statistical fashion
 field measurements often needed to characterize radio
channel performance
4
Wireless Communication Channels
From “Wireless Communications” Edfors, Molisch, Tufvesson
 Communications over wireless channels suffer from multi-path propagation
 Multi-path channels are usually frequency selective
 OFDM supports high data rate communications over frequency selective
channels
 ** The Mobile Radio Channel (MRC) has
unique problems that limit performance **
 A mobile Rx in motion influences rates of
fading
 the faster a mobile moves, the more quickly
characteristics change
6
Wave Propagation Basics: Frequency Wavelength
7
Wave Propagation Basics: Frequency Wavelength
8
Statistical Propagation Models
 Prediction of Signal Strength as a function of
distance without regard to obstructions or features
of a specific propagation path
9
II. Radio Signal Propagation
10
Radio Propagation
 Mobile radio channel
 fundamental limitation on the performance of wireless
communications.
 severely obstructed by building, mountain and foliage.
 speed of motion
 a statistical fashion
 Radio wave propagation characteristics
 reflection, diffraction and scattering
 no direct line -of-sight path in urban areas
 multipath fading
 Basic propagation types
 Propagation model: predict the average received signal strength
 Large-scale fading: Shadowing fading
 Small-scale fading: Multipath fading
11
Radio Signal Propagation
12
 The smoothed line is the average signal
strength. The actual is the more jagged line.
 Actual received signal strength can vary by
more than 20 dB over a few centimeters.
 The average signal strength decays with
distance from the transmitter, and depends on
terrain and obstructions.
13
 Two basic goals of propagation modeling:
1) Predict magnitude and rate (speed) of received
signal strength fluctuations over short
distances/time durations
 “short” → typically a few wavelengths (λ) or
seconds
 at 1 Ghz, λ = c/f = 3x108 / 1x109 = 0.3 meters
 received signal strength can vary drastically by 30
to 40 dB
14
 small-scale fluctuations → called _____ (Chapter 5)
 caused by received signal coming from a sum of
many signals coming together at a receiver
 multiple signals come from reflections and
scattering
 these signals can destructively add together by being
out-of-phase
15
2) Predict average received signal strength for
given Tx/Rx separation
 characterize received signal strength over distances
from 20 m to 20 km
 Large-scale radio wave propagation model models
 needed to estimate coverage area of base station
 in general, large scale path loss decays gradually
with distance from the transmitter
 will also be affected by geographical features like
hills and buildings
16
 Free-Space Signal Propagation
 clear, unobstructed line-of-sight path → satellite and
fixed microwave
 Friis transmission formula → Rx power (Pr) vs. T-R
separation (d)
17
Free Space Path Loss
 Isotropic transmit antenna:
Radiates signal equally in all
directions.
 Assume a point source
 At a distance d from the transmitter,
the area of the sphere enclosing the
Tx is: A = 4πd2
 The “power density” on this sphere
is: Pt/4πd2
 Isotropic receive antenna: Captures
power equal to the density times the
area of the antenna
 Ideal area of antenna is Aant= λ2/4π.
 The received power is:
Pr = Pt/ 4πd2 X λ2/4π. = Ptλ2/(4πd)2
18
where
 Pt = Tx power (W)
 G = Tx or Rx antenna gain (unitless)
 relative to isotropic source (ideal antenna which
radiates power uniformly in all directions)
 in the __________ of an antenna (beyond a few meters)
 Effective Isotropic Radiated Power (EIRP)
EIRP = PtGt
 Represents the max. radiated power available
from a Tx in the direction of max. antenna gain,
as compare to an isotropic radiator
19
 λ = wavelength = c / f (m). A
term is related to
antenna gain.
 So, as frequency increases, what happens to the propagation
characteristics?
 Effective area (Aperture) Aeff = ηA. Ratio of power
delivered to the antenna terminals to the incident
power density
• : η Antenna efficiency; A : Physical area
 L = system losses (antennas, transmission lines between
equipment and antennas, atmosphere, etc.)
 unitless
 L = 1 for zero loss and L > 1 in general
20
 d = T-R separation distance (m)
 Signal fades in proportion to d2
 We can view signal strength as related to the
density of the signal across a large sphere.
 This is the surface area of a sphere with radius d.
 So, a term in the denominator is related to distance
and density of surface area across a sphere.
21
 ⇒ Path Loss (PL) in dB:
22
 d2 → power law relationship
 Pr decreases at rate of proportional to d2
 Pr decreases at rate of 20 dB/decade (for line-ofsight, even worse for other cases)
 For example, path loses 20 dB from 100 m to 1 km
 Comes from the d2 relationship for surface area.
 Note: Negative “loss” = “gain”
23
 Example:
 Path loss can be computed in terms of a link budget
calculation.
 Compute path loss as a sum of dB terms for the
following:






Unity gain transmission antenna.
Unity gain receiving antenna.
No system losses
Carrier frequency of 3 GHz
Distance = 2000 meters
24
 Close in reference point (do) is used in large-scale models
 do : known received power reference point - typically 100 m or
1 km for outdoor systems and 1 m for indoor systems
 df : far-field distance of antenna, we will always work problems
in the far-field
df 
2D2

d f  D
d f  
 D: the largest physical linear dimension of antenna
25
Near and Far fields
 These distances are rough approximations!
 Reactive near field has substantial reactive components which die
out
 Radiated near field angular dependence is a function of distance
from the antenna (i.e., things are still changing rapidly)
 Radiated far field angular dependence is independent of distance
 Moral: Stay in the far field!
26
 Reference Point Example:
 Given the following system characteristics for largescale propagation, find the reference distance do.
 Received power at do = 20 W
 Received power at 5 km = 13 dBm
 Using Watts:
 Using dBm:
27
III. Reflections
 There are three basic propagation mechanisms
in addition to line-of-sight paths
 Reflection - Waves bouncing off of objects of large
dimensions
 Diffraction - Waves bending around sharp edges of
objects
 Scattering - Waves traveling through a medium
with small objects in it (foliage, street signs, lamp
posts, etc.) or reflecting off rough surfaces
28
 Reflection occurs when RF energy is incident upon
a boundary between two materials (e.g air/ground)
with different electrical characteristics
 Permittivity µ
 Permeability ε
 Conductance σ
 Reflecting surface must be large relative to λ of RF
energy
 Reflecting surface must be smooth relative to λ of
RF energy
 “specular” reflection
29
Fresnel reflection coefficient Γ
 The amount of energy reflected to the amount of
energy incidented is represented by Fresnel
reflection coefficient Γ, which depends upon the
wave polarization, angle of incidence and
frequency of the wave.
 For example, as the EM waves can not pass
through conductors, all the energy is reflected
back with angle of incidence equal to the angle
of reflection and reflection coefficient Γ = −1.
30
 What are important reflecting surfaces for
mobile radio?
 Fresnel reflection coefficient → Γ
 describes the magnitude of reflected RF energy
 depends upon material properties, polarization, &
angle of incidence
31
IV. Ground Reflection (2-Ray) Model
 Good for systems that use tall towers (over 50 m
tall)
 Good for line-of-sight microcell systems in urban
environments
32
 ETOT is the electric field that results from a combination of a
direct line-of-sight path and a ground reflected path

is the amplitude of the electric field at distance d
 ωc = 2πfc where fc is the carrier frequency of the signal
 Notice at different distances d the wave is at a different phase
because of the form similar to
33
 For the direct path let d = d’ ; for the reflected path
d = d” then
 for large T−R separation : θi goes to 0 (angle of incidence
to the ground of the reflected wave) and
Γ = −1
 Phase difference can occur depending on the phase
difference between direct and reflected E fields
 The phase difference is θ∆ due to Path difference , ∆
= d”− d’, between
34
 From two triangles with sides d and (ht + hr) or (ht – hr)
35
 ∆ can be expanded using a Taylor series
expansion
36
 which works well for d >> (ht + hr), which means
and
are small
37
 the phase difference between the two arriving
signals is
E0 d 0
  
ETOT (t )  2
sin  
d
 2 
  2 hr ht

 0.3 rad
2
d
E0 d 0 2 hr ht
k
ETOT (t )  2
 2 V/m
d
d
d
38
 For d0=100meter, E0=1, fc=1 GHz, ht=50 meters, hr=1.5 meters, at t=0
39
 note that the magnitude is with respect to a
reference of E0=1 at d0=100 meters, so near 100
meters the signal can be stronger than E0=1
 the second ray adds in energy that would have been
lost otherwise
 for large distances
that
it can be shown
40
41
V. Diffraction
 RF energy can propagate:
 around the curved surface of the Earth
 beyond the line-of-sight horizon
 Behind obstructions
 Although EM field strength decays rapidly as
Rx moves deeper into “shadowed” or
obstructed (OBS) region
 The diffraction field often has sufficient
strength to produce a useful signal
42
 Huygen’s principle says points on a wavefront
can be considered sources for additional
wavelets.
43
 The wavefront on top of an obstruction generates
secondary (weaker) waves.
44
45
Simplified diffraction geometry
 For large d1, d2, we can use the previous geometry, which
assumed ht = hr, to simplify the analysis and it will remain
approximately true for ht ≠ hr, provided the separation
distance is large compared to the heights.
 We are interested in finding the received electric field from
the diffracted path shown, relative to
the line of sight path.
 Its characteristics depend strongly on the path difference ∆
between the length of the diffracted path and the length of
the LOS path.
 Using the geometry shown ∆ is easily found follows in
next slide:
46
47
48
 The difference between the direct path and
diffracted path, call excess path length
 Fresnel-Kirchoff diffraction parameter
 The corresponding phase difference
49
 A Fresnel zone is the group of locations where the
difference between the length of the direct path and
the length of a reflected path is a multiple of a half
wavelength (λ/2).
 Rays from odd-numbered Fresnel zones cause
destructive interference (reduction in received signal
level) while even-numbered ones cause constructive
interference (and an increase in received signal level)
 Fresnel zones are ellipsoids consisting of all points
where the path length difference is n λ /2 as shown in
the following diagram from Wikipedia:
50
51
 For d1 ≫ r and d2 ≫ r the radius of the nth Fresnel zone
radius at distances d1 and d2 can be approximated by:
 A practical implication of Fresnel zones is that for pointto-point links a simple line of sight is not sufficient.
 Objects should also be kept out of (at least) the first
Fresnel zone (n = 1) to avoid causing destructive
interference and signal loss.
 A rule of thumb for point-to point microwave links is that
a minimum of 60% of the first Fresnel zone should be
kept clear of obstructions.
52
 The excess total path length traversed by a ray
passing through each circle is nλ/2
53
 The diffraction gain due to the presence of a knife
edge, as compared the the free space E-field
54
 There is a reasonably good approximation for
diffraction gain in dB defined by Lee as
follows.
55
Diffraction gain as a function of v
A steep drop in gdiff is observed as commencing at v = -1, which corresponds to φ = π/2 or a
quarter wavelength of path difference between the tip of the obstruction and the LOS path.
56
 The actual height of the obstruction depends on the
geometry of the problem. However, if the obstruction
is very close to the receiver (d1 >> d2),
 Solving when v = -1 gives
 which is the critical obstacle height. If the height is
below this value, minimal diffraction effects
will occur
57
58
59
60
61
62
63
Multiple Knife-Edge Diffraction
 If the propagation path is obstructed by more than
one obstruction, the total diffraction loss of all
the obstacles must be computed.
 This is obviously a challenging task that is
realistically simplified by using computers to raytrace and compute the diffraction.
 But a very (overly) simple approach can be obtained
by replacing a series of obstacles with a single
equivalent obstacle, as shown in Figure on next slide
64
Multiple Knife-Edge Diffraction
65
66
67
68
VI. Scattering
 Received signal strength is often stronger than that
predicted by reflection/diffraction models alone
 The EM wave incident upon a rough or complex
surface is scattered in many directions and provides
more energy at a receiver
 energy that would have been absorbed is instead reflected to
the Rx.
 Scattering is caused by trees, lamp posts, towers, etc.
 flat surface → EM reflection (one direction)
 rough surface → EM scattering (many directions)
69
70
VII. Path Loss Models
 We wish to predict large scale coverage using
analytical and empirical (field data) methods
 It has been repeatedly measured and found that
Pr @ Rx decreases logarithmically with
distance
∴ PL (d) = (d / do )n
where n : path loss exponent or
PL (dB) = PL (do ) + 10 n log (d / do )
71
 “bar” means the average of many PL values at a
given value of d (T-R sep.)
 n depends on the propagation environment
 “typical” values based on measured data
72
 At any specific d the measured values vary
drastically because of variations in the
surrounding environment (obstructed vs. lineof-sight, scattering, reflections, etc.)
 Some models can be used to describe a
situation generally, but specific circumstances
may need to be considered with detailed
analysis and measurements.
73
 Log-Normal Shadowing
PL (d) = PL (do ) + 10 n log (d / do ) + Xσ
 describes how the path loss at any specific location may vary
from the average value
 has a the large-scale path loss component we have already
seen plus a random amount Xσ.
74
 Xσ : zero mean Gaussian random variable, a “bell curve”
 σ is the standard deviation that provides the second
parameter for the distribution
 takes into account received signal strength variations
due to shadowing
 measurements verify this distribution
 n & σ are computed from measured data for different
area types
 any other path loss models are given in your book.
 That correlate field measurements with models for different
types of environments.
75
76
Log-normal Shadowing, n and σ
 The log-normal shadowing model indicates the
received power at a distance d is normally
distributed with a distance dependent mean and
with a standard deviation of σ.
 In practice the values of n and σ are computed
from measured data using linear regression so that
the difference between the measured data and
estimated path losses are minimized in a mean
square error sense.
77
Example of determining n and σ
 Assume Pr(d0) = 0dBm
and d0 is 100m
 Assume the receiver
power Pr is measured at
distances 100m, 500m,
1000m, and 3000m,
 The table gives the
measured values of
received power
78
 We know the measured values.
 Lets compute the estimates for received power at
different distances using long distance path loss
model.
 Pr(d0) is given as 0dBm and measured value is
also the same.
 mean_Pr(d) = Pr(d0) – mean_PL(from_d0_to_d)
 Then mean_Pr(d) = 0 – 10logn(d/d0)
 Use this equation to computer power levels at
500m, 1000m, and 3000m.
79




Average_Pr(500m) = 0 – 10logn(500/100) = -6.99n
Average_Pr(1000m) = 0 – 10logn(1000/100) = -10n
Average_Pr(3000m) = 0 – 10logn(3000/100) = -14.77n
Now we know the estimates and also measured actual
values of the received power at different distances
 In order approximate n, we have to choose a value for
n such that the mean square error over the collected
statistics is minimized
80
81
82
83
84
Path Loss Models
Path-Loss Models



The most general case of signal reception might consist of a direct path,
reflected paths, diffracted paths, and scattered paths (which makes
mathematical analysis cumbersome)
Path-Loss models are empirical models that are based on fitting curves or
analytical expressions that recreate a set of measured data
Note:

86
A given empirical model might only be valid within the environment where the
measurements used to estimate such model have been taken
Log-Distance Path-Loss Model
Theoretical and Measurement-based Propagation suggest that the
average received signal power decreases logarithmically with
distance
PL (d): Average path-loss for an arbitrary separation
n
: Path-loss exponent
87
Path-Loss Exponent for Different Environments
Environment
Free-Space
Urban area cellular radio
Shadowed urban cellular radio
Path-Loss Exponent n
2
2.7 to 3.5
3 to 5
In building line-of-sight
1.6 to 1.8
Obstructed in building
4 to 6
Obstructed in factories
2 to 3
88
Log-normal distribution
 A log-normal distribution is a probability distribution
of a random variable whose logarithm is normally
distributed:
 Thus, if the random variable X is log-normally
distributed, then Y = ln(X) has a normal distribution.
89
Log-normal Shadowing
 Distance between two nodes alone cannot fully explain the signal
strength level at the receiver
 Shadowing has been introduced as a means to model the variation
of signal propagation behavior between two different signal paths
assuming the same propagation distance
P L d   P L d   X 
 d 
P L  d   P L  d 0   1 0 n lo g 
  X
 d0 
PL (d): Path-loss model for an arbitrary separation d
Xσ
: Shadowing parameter (zero mean Gaussian distributed random
variable in dB with standard deviation σ also in dB)
90
Received Power in Path-Loss Models
PR  d   PT  PL  d   PT  PL  d   X σ
d
dB
d
4
3
PT - PL  d 
d
d
1
91
2
1
2
3
4
Positio
n
Index
Received Power in Path-Loss Models
PR  d   PT  PL  d   PT  PL  d   X σ
dB
PR  d 
d
d
X1
4
3
PT - PL  d 
X 2
X 4
X3
d
d
1
92
2
1
2
3
4
Positio
n
Index
Reception Quality
PR  d   PT  PL  d   PT  PL  d   X σ
dB
PR  d 
d
d
X1
4
3
PT - PL  d 
X 2

X 4
X3
d
d
1
2
1
2
3
4
Positio
n
Index
γ: Desired received power threshold
93


Pr  PR  d   γ   Pr  X σ  PT  PL  d   γ 


Probability of Bad Reception Quality


Pr  PR  d      Pr  X   PT  PL  d    


Pr  X σ  xth  

1
2πσ
2
e
 x2
 2
 2σ




Xσ follows a normal distribution
with zero mean and standard
deviation σ
dx
xth
x
Let z =  
σ 
Pr  X σ  xth  
fX  x 

1
2π

e
 z2

 2




dz
σ2
 xth 


 σ 
x
Pr  X σ  xth   Q  th
 σ

 xth 
 1

erfc


 2

 2σ 

 PT  PL  d   γ 

Pr  PR  d   γ   Q 


σ


94
x
xth
Note: Q(x)= 1
2π

e
x
 z2 
- 
 2 
 

2
-u 2
dz erfc(x )=
e
du
π x
Percentage of Coverage Area
 Due to the random effects
of shadowing some
locations within the
coverage area will be
below a particular desired
received signal level
 So, its better to compute
how the boundary coverage
area relates to the percent
of area covered within the
boundary
h
R’
R
PR  d   
0  d  R'
PR  d   
0  d  R'
R: Radius of Coverage Area
required for Transmitter
95
Calculation of Percentage of Coverage Area
Assume h (height of antenna) is Negligible, then,
U(γ) depicting the percentage of area with
received signal strength equal to or exceeding γ
may be calculated as follows
1
U γ  
πR 2
1
U γ  
πR 2
 P r  P  r  
dA
r
dθ
γ  d A
R
R
2π R
  P r  P  r  
R
0
r
γ  r d r d θ
0


   PT  PL  r  

Pr  PR  r      Q 





   PT  PL  r 
1
Pr  PR  r      erfc 

2
2



R: Radius of Coverage Area
required for Transmitter
 



    P  PL  d   10nlog  r d   
T
0
0
1



Pr  PR  r      erfc


2
2


96
Calculation of Percentage of Coverage Area


    P  PL  d   10nlog  r d   
0
0
1
 T

Pr  PR  r      erfc 


2
2




    P  PL  d   10nlog  R d   10nlog  r R   
0
0
1
 T

Pr  PR  r      erfc 


2
2


1
U γ  
πR 2
2π R
1
U γ  
πR 2
R
2
U γ   2
R
  Pr  P  r   γ  rdrdθ
R
0 0
2π
2
Pr

P
r

γ

r
d
r
d
θ




0  R
0
R2
R
r
0

 Pr  P  r   γ  rdr
R
0
1
r 

erfc  a  b ln  d r
2
R


γ   PT  PL  d 0   10 n log  R d 0  


a
2σ
97
R
b
10 nloge 
2σ
Calculation of Percentage of Coverage Area
It can be shown that
1
U γ  
2

 1  2ab  
 1  ab
 1  e rf  a   e x p 
 1  e rf 
2
 b

 b

By choosing the signal level such that
P R R   γ
 i .e ., a
 0
Therefore for the case when
Boundary Coverage = 50 %
U
98
γ 
1 
 1 
 1  

 1  e x p  2  1  e r f    
2 
 b 
 b  
 
 
 
Calculation of Percentage of Coverage Area
“Wireless Communications:
Principles and Practice 2nd
Edition”, T. S. Rappaport,
Prentice Hall, 2001
99
Outdoor Propagation Models
 Longley-Rice Model
(Read)
 Durkin’s Model
(Read)
 Okumura’s Model
 Hata Model
 PCS extension to Hata Model
 Walfisch and Bertoni
100
(Read)
Okumura’s Model
 Okumura’s model is one of the most widely used models
for signal predictions in urban and sub-urban mobile
communication areas
 This model is applicable for frequencies ranging from 150
MHz to 1920 MHz
 It can cover distances from 1 km to 100 km and it can be
used for base station heights starting from 30m to 1000m
 The model is based on empirical data collected in detailed
propagation tests over various situations of an irregular
terrain and environmental clutter
101
Okumura’s Model
L50  dB   L F  A mu  f , d   G  h te   G  h re   G AREA






L50 is the median value or 50th percentile value of the propagation path loss
LF is the free space propagation path loss
Amu is the median attenuation relative to free space
GAREA is the gain due to the type of environment
G(hte) is the base station antenna height gain factor
G(hre) is the mobile antenna height gain factor
102
Okumura’s Model: Amu Curves
“Wireless Communications:
Principles and Practice 2nd
Edition”, T. S. Rappaport,
Prentice Hall, 2001
103
Okumura’s Model: GArea Curves
“Wireless Communications:
Principles and Practice 2nd
Edition”, T. S. Rappaport,
Prentice Hall, 2001
104
Okumura’s Model: G(hte), G(hre)
 The empirical model of Okumura assumed hte =
200m, hre = 3m
 h te 
G  h te   2 0 lo g 
3 0 m  h te  1 0 0 0 m

 200 
 h re 
G  h re   1 0 lo g 
h re  3 m

 3 
G  h re
105
 h re 
  2 0 lo g 

 3 
3 m  h re  1 0 m
Hata Model
L50  urban  dB   69.55  26.26log  f c   13.82log  h te   a  h re 
  44.9  6.55log  h te   log  d 






106
L50 is the median value or 50th percentile value of the propagation
path loss
fc (in MHz) is the frequency (15MHz to 1500MHz)
hte is the effective transmitter height in meters (30m to 200 m)
hre is the effective transmitter height in meters (1m to 10 m)
d is the T-R separation in Km
a(hre) is the correction factor for effective mobile (i.e., receiver)
antenna height which is a function of the size of the coverage area
Hata Model: a(hre)
 For a Medium sized city, correction factor is given by:
a  h re   1.1log  f c   0.7  h re  1.56log  f c   0.8 
dB
 For a Large city, correction factor is given by:
2
a  h re   8.29  log 1.54h re    1.1
2
a  h re   3.2  log 11.75h re    4.97
107
dB
for f c  300MHz
dB
for f c  300MHz
Hata Model
 Path loss in suburban area, the equation is modified as
2
L 50  dB   L50  urban   2 log  f c / 28    5.4
 For path loss in open rural areas, the formula is modified as
2
L 50  dB   L50  urban   4.78  log  f c    18.33log  f c   40.94
 Hata Model is well-suited for Large cell mobile systems
108
PCS Extension to Hata Model
 An extended version of the Hata model developed by COST-231
working committee for 2 GHz range
L50  urban  dB   46.3  33.9log  f c   13.82log  h te   a  h re 
  44.9  6.55log  h re   log  d   CM





109
fc is the frequency (1500MHz to 2000 MHz)
hte is the effective transmitter height in meters (30m to 200 m)
hre is the effective transmitter height in meters (1m to 10 m)
d is the T-R separation in Km (1 Km to 20 Km)
CM=0 dB for medium sized city and suburban areas, CM=3 dB for
metropolitan centers
Indoor Propagation Models
 The indoor radio channel differs from the traditional mobile
radio channel in the following aspects
 Much smaller distances
 Much greater variability of the environment for a much smaller
range of T-R separation distances
 Difficult to ensure far-field radiation
 Propagation within buildings is strongly influenced by
specific features such as





110
Building layout
Construction materials
Building type
Open/Closed doors
Locations of antennas
Partition Losses (Same Floor)
“Wireless Communications:
Principles and Practice 2nd
Edition”, T. S. Rappaport,
Prentice Hall, 2001
111
Partition Losses between Floors
“Wireless Communications:
Principles and Practice 2nd
Edition”, T. S. Rappaport,
Prentice Hall, 2001
112
Log-Distance Pathloss Model
 The lognormal shadowing model has been shown to be
applicable in indoor environments
113
Ericsson Multiple Breakpoint Model
Lower bound
on the pathloss
Upper bound
on the pathloss
“Wireless Communications:
Principles and Practice 2nd
Edition”, T. S. Rappaport,
Prentice Hall, 2001
114
Attenuation Factor Model
 This was described by Seidel S.Y. It is an in-building propagation
model that includes



115

Effect of building type

Variations caused by obstacles
nSF represents the path-loss exponent for the same floor
measurements
FAF represents the floor attenuation factor
PAF represents the partition attenuation factor for a specific
obstruction encountered by a ray drawn between the transmitter and
receiver
Attenuation Factor Model
 FAF may be replaced by an exponent that accounts for the
effects of multiple floor separation

116
nMF represents the path-loss exponent based on measurements
through multiple floors