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Propagation of RF waves can be divided into two main study areas
Large Scale Effects
• due to terrain and the density & dimensions of objects
• includes random destructive interference and diffraction
• characterized statistically by median path loss & log normal shadowing
• behavior is slowly time varying
 important for predicting coverage areas and service availability
Small Scale Effects
• considers fading associated with
(i) superposition of many E-field components caused by local reflections
(ii) changes in interference patterns at mobile receiver
• due to environment local to the receiver and mobility
• behavior varies much faster in time
• often characterized statistically as Rayleigh fading
 important in design of modulation format & general transceiver design
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3. Mobile Radio Propagation – Large Scale Path Loss
3.1 Introduction to Radio Wave Propagation
3.2 Free Space Propagation Model
3.3 Power and Electric Fields
3.4 Three Basic Propagation Mechanisms
3.5 Reflection
3.6 Ground Reflection
3.7 Diffraction
3.8 Scattering
3.9 Link Budgets Using Path Loss Models
3.10 Outdoor Propagation Models
3.11 Indoor Propagation Models
3.12 Signal Penetration
3.13 Ray Tracing and Site Specific Modeling
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3. Mobile Radio Propagation
• RF channels are random – do not offer easy analysis
• difficult to model – typically done statistically for a specific system
3.1 Introduction to Radio Wave Propagation: diverse mechanisms
of electromagnetic (EM) wave propagation generally attributed to
(i) diffraction
(ii) reflection
(iii) scattering
• non-line of sight (NLOS – obstructed) paths rely on reflections
• obstacles cause diffraction
• multi-path: EM waves travel on different paths to a destination –
interaction of paths causes fades at specific locations
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traditional Propagation Models focus on
(i) transmit model - average received signal strength at given distance
(ii) receive model - variability in signal strength near a given location
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(1) Large Scale Propagation Models: predict mean signal strength
for TX-RX pair with arbitrary separation
• useful for estimating coverage area of a transmitter
• characterizes signal strength over large distances (102-103 m)
• predict local average signal strength that decreases with distance
signal power commonly computed by averaging measurements over
a measurement track of 5  - 40 
e.g. at 2.4 GHz,  =12.5cm 
• measurement tracks range from 0.625m - 5m
• if 0.625m used, for nth point  use segment between 0.625n & 0.625(n+1)
• take measurements at intervals of 0.1  to 
• averaged measurements = nth point
0.625m
1.25m 1.875m
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(2) Small Scale or Fading Models: characterize rapid fluctuations of
received signal over
• short distances (few ) or
• short durations (few seconds)
with mobility over short distances
• instantaneous signal strength fluctuates
• received signal = sum of many components from different directions
• phases are random  sum of contributions varies widely
• received signal may fluctuate 30-40 dB by moving a fraction of 
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Small Scale & Large Scale Fading
received power
dBm
-30
-35
-40
-45
-50
-55
-60
-65
1 point = average over 5 = 0.625m
14 15 16 17 18 19 20 21 22 23 24 25 26
d (meters)
fc = 2.4GHz    0.125m
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3.2 Free Space Propagation Model
used to predict signal strength for LOS path
• satellites
• LOS uwave
• power decay  d –n (d = separation)
Subsections
(1) Friis Equation
(2) Radiated Power
(3) Path Loss
(4) Far Field Region
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(1) Friis free space equation: receive power at antenna separated by
distance d from transmitter
 Gt Gr 2  Pt

Pr(d) = 
2  2
 (4 ) L  d
(3.1)
Pr & Pt = received & transmitted power
Gt & Gr = gain of transmit & receive antenna
 = wavelength
d = separation
L = system losses (line attenuation, filters, antenna)
- not from propagation
- practically, L  1, if L = 1  ideal system with no losses
• power decays by d 2  decay rate = 20dB/decade
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Antenna Gain
G=
4

2
Ae
(3.2)
• Ae = effective area of absorption– related to antenna size
Antenna Efficiency
η = Ae/A
A = antenna’s physical area (cross sectional)
• for parabolic antenna η  45% - 50%
• for horn antenna η  50% - 80%
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(2) Radiated Power
Isotropic Radiator: ideal antenna (used as a reference antenna)
• radiates power with unit gain uniformly in all directions
• surface area of a sphere = 4πd 2
2
Effective Area of isotropic antennae given by Aiso =
4
 2  1 
2

P 
PT
Isotropic Received Power PR = 
2
2  T
4d 
 4  4d 
• d = transmitter-receiver separation
PT 4d 

PR
2
2
Isotropic free space path loss Lp =
• f 2 relationship with antenna size results from dependence of Aiso on 
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Directional Radiation
practical antennas have gain or directivity that is a function of
• θ = azimuth: look angle of the antenna in the horizontal plane
• = elevation: look angle of the antenna above the horizontal plane
Let Φ = power flux desnity

θ
transmit antenna gain is given by:
GT(θ, ) =
Φ in the direction of (θ, )
Φ of isotropic antenna
receive antenna gain is given by:
GR(θ, ) =
Ae in the direction of (θ, )
Ae of isotropic antenna
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Principal Of Reciprocity:
• signal transmission over a radio path is reciprocal
• the locations of TX & RX can be interchanged without changing
transmission characteristics
signals suffers exact same effects over a path in either direction in a
consistent order  implies that GT(θ, ) = GR(θ, )
thus maximum antenna gain in either direction is given by
Ae
4

Ae
G=
2
Aiso 
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EIRP: effective isotropic radiated power
• represents maximum radiated power available from a transmitter
• measured in the direction of maximum antenna gain as compared to
isotropic radiator
EIRP = PtGiso
(3.4)
ERP: effective radiated power - often used in practice
• denotes maximum radiated power compared to ½ wave dipole
antenna
• dipole antenna gain = 1.64 (2.15dB) > isotropic antenna
• thus EIRP will be 2.15dB smaller than ERP for same system
ERP = PtGdipole
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Eg: Area of a parabolic antenna, looking into center-axis given by
beamwidth = angular width of the antenna beam at 3dB points
main lobe = direction of strongest signal propagation
center axis: direction of peak gain
side & back lobes not considered for communications, must be considered
in interference analysis
Aparabolic =
D
4
2
 thus Ae =
Ae D 2 4
 D 

 

G=
2
Aiso
4 
  
D
4
2

2
peak
gain
3dB Beamwidth
G depends on dimensions of antenna and frequency
assume D = 0.6m, fc = 12GHz, and η = 0.5
  0.6m 
0.36 2
 2842.4  35dB
G = 
 
0.025
 c / 12GHz 
2
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For parabolic antenna: increasing D  increases gain, decreases beamwidth
 D 
Gain on center axis, G = 

  
2
Gain off-center axis varies with angle 
 2 J D /  sin     D 
G() =  1
 

sin




 
2
2
• normalized to unity center axis gain
• J1(x) is Bessel function of 1st kind
normalized
G(dB)
0
-10
-20
-30
-40
-30 -20 -10 0 10 20 30 
3dB beamwidth = 58.4 /D
• proportional to wavelength
• inversely proportional to diameter
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(3) Path Loss (PL)
 (4 ) 2 d 2 
Pt

PL =
= 
2 
Pr
G
G

 t r 
 Gt Gr 2  1

PL (dB) = 10 log 10 (Pt /Pr) =  10 log 10 
2  2
(
4

)

d
(3.5)
if G is assumed unit gain:
 2  1

PL (dB) =  10 log10 
2 2
 (4 )  d
(3.6)
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(4) Far-field region of an antenna
eqn 3.1 only valid for d in the far-field of transmitting antenna
• d  df (far-field distance)
• far-field distance aka Fraunhofer region
df =
2D 2

(3.7)
• D = largest physical linear dimension of transmitters antenna aperture
• further df >> D and df >>  must hold
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if d  0  large scale models use d0 (received power reference point)
• for any d > d0  Pr(d) can be related to Pr(d0)
Pr(d0) predicted using 3.1 or average of many measurements at
distance d0
• d0 must be selected to lie in far-field region d0  df
• d0 selected to be smaller than any practical d in mobile system
• practical choices for received power reference point are:
- indoors d0 ≈ 1m
- outdoors d0 ≈ 102m - 103m
 d0
Pr(d) (watts) = Pr(d0) 
d



2
d  d0  df
(3.8)
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Measuring in dB
dbm & dBW relative power measurements
• Pr in mobile systems can change by many dB in a coverage area ≈ 1km2
• dBm or dBW units are used to express power levels
• conversion from watts – take log of both sides & multiply by 10
 Pr (d 0 ) 
 d0 
  20 log 
Pr(d) dBm = 10 log
 0.001W 
d 
d  d0  df
(3.9)
e.g. Pr = 20 mW  Pr (dBm) = 10 log(20 mW/1mW) = 13 dBm
dBi – antenna gain with respect to isotropic source
dBd – antenna gain with respect to dipole antenna
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3.3 Power and Electric Fields
• radiating structures produce electric fields (E) & magnetic fields (H)
• consider small linear radiator of length L, where L <<
• current flows through antenna  resulting electrical & magnetic
fields expressed as
i0 L cos   1
c   jwc (t d / c )

e

Er =
2
3 

20c  d
jwc d 
i0

(3.10)
P
d
L
i0 L sin   jwc
c   jwc (t d / c )

e

E =
(3.11)
2 
3
4 0 c  d
jwc d 
z
i0 L sin   jwc c   jwc ( t  d / c )
 2 e

H =
4c  d
d 
H , E , Hr all = 0
 r

(3.12)
y
x
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term
d-1
d-2
d-3
component represented
radiation field
induction field
electrostatic field
• electrostatic (d-3) & induced (d-2) fields decay much faster than
radiated field
• far from transmitter (d > df)  electrostatic & inductive fields ≈ 0
• if d > df only radiated field components are considered E & H
Er ≈ 0
i0 L sin   jwc   jwc (t d / c )
e
E ≈
2 
4 0 c  d 
H ≈
i0 L sin   jwc  jwc ( t d / c )

e
4c  d 
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(1) Power flux density Pd in free space (W/m2)
• |E | = magnitude of radiating portion of electric field in far-field (V/m)
• Pd disperses in free space from an isotropic point source
1m
• Pd ≈ EIRP  surface area of sphere of radius d
• surface are of a sphere = 4πd2
EIRP Pt Gt
E2 E2



Pd =
2
2
R fs 
4d
4d
d
(W/m2)
1m
PtGt
(3.13)
Rfs = intrinsic impedance of free space given by  = 120Ω
Pd =
E
2
120 

E
2
377
(W/m2)
(3.14)
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(2) Received Power, Pr(d)
Pr(d) = power flux density  receive antenna effective aperture
• received power at distance d from transmitter
• can be related to electric field using (3.1), (3.2), (3.13),(3.14)
Induced electric field (V/m) at receiver vs received power (W)
• assume L = 1 (system loss)
Pr(d) = Pd Ae 
2
E Gr 2
2
Pt Gt Gr 
Ae 

2 2
120
( 4 ) d
480
E
2
(W )
(3.15)
• |E | = magnitude of radiating portion of electric field in far-field
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(3) Receiver Input Voltage And Receive Power Level
• model receive antenna as matched resistive load, Rant
• receiver antenna will induce rms voltage, V, into receiver
• induced voltage = ½ open circuit voltage at antenna: V = ½ Vant
• Rant = antenna resistance
open circuit
Vant
Pr(d) =
V / 2 2 
Rant
V2
4Rant
Rant
V
to matched
receiver
(3.16)
Induced Electric Field, E vs Receiver Input Voltage, V
2
2
V
Pr(d) =
Ae 
120
4 Rant
E
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