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Lecture 07
EEE 441Wireless And Mobile Communications
Quiz2 soln
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Propagation of Radio Waves:Large-Scale Path Loss
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Radio Wave Propagation
Large-scale path loss
Observed at receiver distances that are largecompared to the wavelength of the carrier signal
Free-space propagation loss
The 3 basic propagation mechanisms of reflection,diffraction and scattering
Small-scale path loss
Rapid fluctuations that occur over small movements inreceiver position (a few wavelengths)
Also known as fading
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Small-Scale and Large-Scale Fading
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T-R Separation (meters)
-70
-60
-50
-40
-30
Received Power (dBm)
This figure is just an illustrationto show the concept. It is not based on readdata.
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Unit for Power Loss
The decibel, dB
A logarithmic unit that is used to describe a ratio
Given two power values P1 and P2, the difference(as a ratio) is expressed in dB as:
10 log (P1/P2) (dB)
Example
Tx Power P1 = 100W, Rx Power P2 = 1W
The loss = 10 log(100/1) = 20 dB
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Decibel (dB)
versus
Power Ratio
Comparison of
two Sound Systems
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Decibel milli
Used to denote a power level with respect to1mW as the reference power level
Example: Tx power is P1 = 100W
Loss = 10 log(100W/1mW) = 10 log (100,000) = 50 dBm
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Decibel Watt
Used to denote a power level with respect to1W as the reference power level
Example: Tx power is P2 = 100W
Loss = 10 log(100W/1W) = 10 log (100) = 20 dBW
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Radio Wave Propagation
At VLF, LF, and MF bands, radio
waves follow the ground. AM radio
broadcasting uses MF band
At HF bands, the ground
waves tend to be absorbed by the
earth. The waves that reach ionosphere
(100-500km above earth surface),
are reflected and sent back to
earth.
absorption
reflection
Ionosphere
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Radio Wave Propagation (cont’d)
LOS path
Reflected Wave
- When directional antennas are used, waves followmore direct paths
- LOS: Line-of-Sight Communication
- Reflected wave interfere with the original signal
VHF Transmission
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Coverage Environment
Line-of-Sight (LOS) between Tx/Rx
Waves obstructed and absorbed bybuildings, foliage, rain …
Velocity of Rx leads to Doppler effects
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Free-Space PropagationModel
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Free-Space Propagation Model
Used to predict the received signal strengthwhen Transmitter and Receiver have clear,unobstructed LOS path between them
The Rx power decays as a function of the T-Rseparation distance raised to some power
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Friis Free-Space Equation
Free space power received after a distance d isgiven by Friis free-space equation:
Pr(d) = (PtGtGr2) / ((4)2d2L)
Pt is transmitted power
Pr is received power
Gt is transmitter antenna gain (dimensionless quantity)
Gr is receiver antenna gain (dimensionless quantity)
d is T-R separation distance (in meters)
L is system loss factor not related to propagation (L >= 1)
is wavelength (in meters)
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Antenna Gain
The gain of an antenna G is related to its affectiveaperture Ae by:
G = 4Ae / 2
The effective aperture of Ae is related to the physicaldimensions of the antenna
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Isotropic Antennas andEffective Gain
An isotropic radiator is an ideal antenna that radiatespower with unit gain uniformly in all directions
Antenna gains are given in units of dBi
(dB gain with respect to an isotropic antenna)
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Path Loss
Path Loss
signal attenuation, measured in dB:
PL(dB) = 10 log (Pt/Pr) = -10log[(GtGr2)/(4)2d2]
If antennas have unity gains (exclude them):
PL(dB) = 10 log (Pt/Pr) = -10log[2/(4)2d2]
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Long Distance Path-Loss Model
The average large-scale pathloss is expressed as a functionof distance
The value of n depends on thepropagation environment:
n=2 for free space, higherwhen obstructions are present
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Path-Loss Exponent for DifferentEnvironments
Environment
Path Loss Exponent, n
Free space
2
Urban area cellular radio
2.7 to 3.5
Shadowed urban cellular radio
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
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What Scale is “Large-Scale”?
For Friis free-space equation to hold, d should bein the far-field of the Tx antenna
The far-field, or Fraunhofer region, is given by:
df = 2D2/
D is largest physical dimension of the antenna
Additionally, df >> D and df >>
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Reference Distance, d0
Free-space equation does not hold for d = 0
We use a small distance d0 as the reference point
d0 should be > df
d0 should be < any practical distance d where we wishto measure the power of a mobile receiver
Received power Pr(d), at a distance d > d0 from atransmitter, is related to Pr at d0, Pr(d0), by:
Pr(d) = Pr(d0)(d0/d)2 given that d >= d0 >= df
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Reference Distance d0 (cont’d)
Expressing the received power in dBm and dBW:
Pr(d) (dBm) = 10 log [Pr(d0)/0.001W] + 20log(d0/d)where Pr(d0) is in Watts
Pr(d) (dBW) = 10 log [Pr(d0)/1W] + 20log(d0/d) wherePr(d0) is in Watts
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Selection of Reference Distance d0
In large coverage cellular systems
About 1km
In microcellular systems
About 1m ~ 100m
Must be in the far-field of the antenna,so that near-field effects do not result
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Fraunhofer Region
For Friis equation to hold, distance d should be inthe far-field of the Tx antenna
The far-field, or Fraunhofer region, of a transmittingantenna is defined as:
df = 2D2/
D is the largest physical dimension of the antenna.
Additionally, df >> D and df >>
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Notices
Reading
Rappaport, Ch 4.1 – 4.2 (selections)