m. junaid mughal 2006 wireless communications principles and practice 2 nd edition t.s. rappaport...
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M. Junaid Mughal 2006
Wireless CommunicationsPrinciples and Practice
2nd EditionT.S. Rappaport
Chapter 4: Mobile Radio Propagation: Large-Scale Path Loss
UMAIR HASHMI Spring 2011
M. Junaid Mughal 2006
Reflection from Conductors
A perfect conductor reflects back all the incident wave back.
Ei = Er
Өi = Өr ( E in plane of incidence)
Ei = - ErӨi = Өr ( E normal to plane of incidence)
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Ground Reflection (Two-Ray) Model
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• Propagation Model that considers both the direct (LOS) path and a ground reflected path between transmitter and the receiver.
• Reasonably accurate model for predicting large scale signal strength over distance of several kilometres.
• The E-field due to Line-Of-Sight is given by ELOS
• The E-field for the ground reflected wave is given by Eg
• The Total E-field is a sum of LOS and Reflected components,
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Ground Reflection (Two-Ray) Model
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M. Junaid Mughal 2006
Ground Reflection (Two-Ray) Model
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M. Junaid Mughal 2006
Ground Reflection (Two-Ray) Model
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M. Junaid Mughal 2006
Ground Reflection (Two-Ray) Model
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• The path difference between the LOS path and the ground reflected path is represented by lambda
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Ground Reflection (Two-Ray) Model
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• The phase difference and the time arrival delay between the two E-components is given by:
• When d becomes large, difference between d’ and d’’ becomes negligible and ELOS and Eg could be considered equal in magnitude
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Ground Reflection (Two-Ray) Model
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M. Junaid Mughal 2006
Ground Reflection (Two-Ray) Model
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• Now sin(Ө) is approximately equal to Ө when Ө < 0.3 radians.
M. Junaid Mughal 2006
Ground Reflection (Two-Ray) Model
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• The received power Pr and Path Loss PL will be given by:
M. Junaid Mughal 2006
Ground Reflection (Two-Ray) Model
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101
102
103
104
-140
-120
-100
-80
-60
-40
-20
0
20
40
Distance (m)
20lo
g(|E
|)
d = 20 ht h
r/
1/d4
1/d2
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Ground Reflection (Two-Ray) Model
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ExampleA mobile is located 5 km away from a BS and uses vertical
lambda/4 monopole antenna with gain of 2.55 dB to receive cellular signals. The E-field at 1 km from the transmitter is measured to be 10-3 V/m. The carrier frequency is 900 MHz.
a) Find length and gain of receiving antenna
b) Find receiver power at the mobile using 2-ray ground reflection model assuming height of transmitting antenna is 50m and receiving antenna is 1.5 m.
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Diffraction
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• Diffraction is a process that allows radio signals to propagate around curved surfaces and objects and to propagate behind obstructions.
Visible Region
Shadow Region
Obstruction
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Diffraction geometry
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Diffraction geometry
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Visible Region
Shadow Region
Obstruction
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Contribution of Huygen’s Secondary Sources at the Receiver
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Obstruction
TxRx
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Fresnel Zone Geometry
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• A transmitter and receiver separated in free space.
• An obstructing screen of height h is placed at a distance d1 from the transmitter and d2 from the receiver.
• The difference between the direct path and the diffracted path is called the excess path length Δ. Assuming h << d1,d2 and h>>λ
M. Junaid Mughal 2006
Fresnel Zone Geometry
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M. Junaid Mughal 2006
Fresnel Zone Geometry
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• Now tan x is approximately equal to x for x < 0.5 radians
• Fresnel – Kirchoff Diffraction Parameter v is given by
M. Junaid Mughal 2006
Fresnel Zone Geometry
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• The phase difference between LOS and diffracted path is a function of
i) Height and Position of the obstructionii) Transmitter and Receiver Location
FRESNEL ZONES
• Fresnel Zones represent successive regions where secondary waves have a path length from the transmitter to the receiver which are nλ/2 greater than the total path length of a LOS path
The successive concentric circles on the plane have path length increment by λ/2. The successive circles are called Fresnel Zones and successive Fresnel Zones have the effect of producing constructive and destructive interference.
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Fresnel Zone Geometry
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• The radius of the nth Fresnel Zone is given by
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Knife-Edge Diffraction Model
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Knife-Edge Diffraction Model
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• The receiver is at point R which is located in the shadowed region (called Diffraction Zone). The field strength at R is a vector sum of the fields due to all of the secondary Huygen;s sources in the plane.
• The Electric Field of a knife edge diffracted wave is
• The Diffraction Gain due to the presence of a knife edge is given by
M. Junaid Mughal 2006
Knife-Edge Diffraction Model
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Fresnel Zone Geometry
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• The Diffraction Gain for different values of v is:
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Knife-edge diffraction loss(Summing Secondary Sources)
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-3 -2 -1 0 1 2 3 4 5-30
-25
-20
-15
-10
-5
0
Fresnel Diffraction Parameter v
Kni
fe E
dge
Diff
ract
ion
Gai
n (d
B)
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Fresnel Zone Geometry
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EXAMPLECompute the diffraction loss for the three cases in fig. when
λ=1/3m, d1=1km, d2=1km and (a) h=25m, (b) h=0 (c) h= -25m. Compare the answers with the values obtained from the graph.
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Fresnel Zone Geometry
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EXAMPLEDetermine (a) Loss due to knife-edge diffraction and (b) the height
of the obstacle required to induce 6 dB diffraction loss. Assume f = 900MHz
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Scattering
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• When a wave impinges on a rough surface, the reflected wave is spread out (diffused) in all directions due to scattering.
• The dimensions of the objects inducing Scattering are comparable to λ
• To judge if a surface is smooth or rough (if we will have reflection or scattering) when a wave impinges upon that surface, the Critical Height hc is given by
hc = λ / ( 8 sin Өi)
• If maximum protuberance hmax < hc : Smooth Surface hmax > hc : Rough Surface
• The reflected E-Fields for h > hc is given by :
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Radar Cross Section Model (RCS Model)
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• The Radar Cross Section (RCS) of a scattering object is defined as the ratio of the power density of the signal scattered in the direction of the receiver to the power density of the radio wave incident upon the scattering object.
• The bistatic radar equation is used to compute the propagation of a wave travelling in free space that impinges on a distant scattering object and then reradiated in the direction of the receiver. The objects are assumed to be in the Far-Field region (Fraunhofer region)
PR (dBm) = PT (dBm) + GT (dBi) + 20 log λ + RCS [dB m2 ] – 30 log (4 pi) – 20 log dT – 20 log dR
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Radar Cross Section Model (RCS Model)
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SUMMARY
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• What is Large Scale Path Loss?• Free space Propagation Model
• Friis Free space propagation model• Relating power to Electric field
• The three Basic Propagation mechanisms• Reflection
•Reflection coefficients•Polarization rotation•Brewster angle•Reflection from perfect conductors• Ground Reflection (Two Ray Model)
M. Junaid Mughal 2006
SUMMARY
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• Diffraction • Fresnel Zone Geometry• Knife Edge Diffraction• Multiple Knife edge Diffraction
• Scattering• Rough Surface Scattering• Radar Cross section
Now we know all the propagation mechanisms and can use
them to predict path loss in any environment
M. Junaid Mughal 2006
Log-Distance Path Loss Model
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• Radio Propagation Models • Log-distance Path Loss Model
• Received Power decreases logarithmically with distance, whether in outdoor or indoor radio channels
• Reference distance should be in the far field region of the antenna
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Log-Distance Path Loss Model
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Log-Normal Shadowing
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• Surrounding environment clutter not considered in previous model.
• Received power can vary at quite a significant value at 2 points having same T-R separation distances.
• Path Loss (PL) is random and distributed log-normally about the mean distance-dependent value.
M. Junaid Mughal 2006
Log-Normal Shadowing
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• Log-Normal distribution describes the random shadowing effects which occur over a large number of measurement locations which have the same T-R separation distance.
• This phenomenon is called the log-normal shadowing. Implies that measured signal levels at specific T-R separation have a Gaussian (normal) distribution about the distance-dependent mean.
M. Junaid Mughal 2006
Log-Normal Shadowing
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Log-Normal Shadowing
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Determination of Percentage of Coverage Area
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• The percentage of useful service area i.e. the percentage of area with a received signal level that is greater or equal to a threshold value.
M. Junaid Mughal 2006
Determination of Percentage of Coverage Area
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M. Junaid Mughal 2006
Determination of Percentage of Coverage Area
UMAIR HASHMI Spring 2011
M. Junaid Mughal 2006
Determination of Percentage of Coverage Area
UMAIR HASHMI Spring 2011
M. Junaid Mughal 2006
Determination of Percentage of Coverage Area
UMAIR HASHMI Spring 2011
M. Junaid Mughal 2006
Determination of Percentage of Coverage Area
UMAIR HASHMI Spring 2011
M. Junaid Mughal 2006
Determination of Percentage of Coverage Area
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M. Junaid Mughal 2006
Outdoor Propagation ModelsLongley Rice Model
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• Point to point communication
• 40 MHz to100 GHz
• Different kinds of terrain
• Median Tx loss predicted by path geometry of terrain profile & Refractivity of troposphere
• Diffraction losses predicted by?
• Geometric losses by?
M. Junaid Mughal 2006
Outdoor Propagation ModelsLongley Rice Model
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• Operates in 2 modes
• Point-to-point mode
• Area mode prediction
• Modification
• Clutter near receiver
• Doesn’t determine corrections due to environmental factors
M. Junaid Mughal 2006
Outdoor Propagation ModelsDurkin’s Model
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• Computer simulator described for field strength contours of irregular terrain
• Split into 2 parts, first reconstructs radial path profile & second calculates path loss
• Rx can move iteratively to establish contour• Topographical database can be thought of as 2-
dimensional array• Each array element corresponds to a point on map &
elevation• Radial path may not correspond to discrete data points
thus interpolation
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2-D Propagation Raster Model
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Representing Propagation
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M. Junaid Mughal 2006UMAIR HASHMI Spring 2011
• Height reconstructed by diagonal, vertical & horizontal interpolation methods
• Reduced to 1 D
• Now determine whether LOS – difference btw heights and line joining Tx & Rx
• Positive height difference
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Algorithm for LOS
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M. Junaid Mughal 2006UMAIR HASHMI Spring 2011
• Then checks first Fresnel Zone clearance
• If terrain profile fails first Fresnel Zone Clearance
• a) non LOS
• b) LOS but inadequate Fresnel Zone Clearance
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Non-LOS Cases
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• a) Single Diffraction Edge
• b) Two Diffraction Edges
• a) Three Diffraction Edges
• a) More than three Diffraction Edges
• Method sequentially tests for each
• Angles btw pine joining Tx & Rx and each point on reconstructed profile. Max angle (di,hi)
• Angles between line joining Tx & Rx and Tx Antenna to every point on reconstructed profile
• For single diffraction di=dj
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Multiple Diffraction Computation
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Okumura’s and Hata’s Model
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Hata’s Model
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• Empirical formulation of graphical path loss data• Valid from 150 MHz to 1500 MHz.• Urban Area Propagation loss as a standard and supplied
correction equations for application to other situations• hte=30 m to 200m, hre=1m to 10m
•Compares very closely with Okumura model as long as d doesn’t exceed 1km•Well suited for large cell communications but not PCS
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PCS Extension to Hata Model
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• Hata’s model to 2GHz
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ASSIGNMENT
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Review the Outdoor Propagation Models presented in the slides showing their salient features and how they differentiate from each other.