Digital class

M. Junaid Mughal 2006
Wireless Communications
Principles and Practice
2nd Edition
T.S. Rappaport
Chapter 4: Mobile Radio
Propagation: Large-Scale Path Loss
UMAIR HASHMI Spring 2011

Reflection from Conductors
A perfect conductor reflects back all the incident wave back.
Ei = Er
Өi = Өr ( E in plane of incidence)
Ei = - Er
Өi = Өr ( E normal to plane of incidence)

Ground Reflection (Two-Ray) Model
• 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,

• The path difference between the LOS path and the ground
reflected path is represented by lambda

• 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

• Now sin(Ө) is approximately equal to Ө when Ө < 0.3 radians.

• The received power Pr and Path Loss PL will be given by:

10
1
10
2
10
3
10
4
-140
-120
-100
-80
-60
-40
-20
0
20
40
Distance (m)
20log(|E|)
d = 20 ht
hr
/
1/d4
1/d2

Example
A 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.

Diffraction
• 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

Diffraction geometry

Diffraction geometry
Visible Region
Shadow Region
Obstruction

Contribution of Huygen’s Secondary
Sources at the Receiver
Obstruction
Tx
Rx

Fresnel Zone Geometry
• 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

• Now tan x is approximately equal to x for x < 0.5 radians
• Fresnel – Kirchoff Diffraction Parameter v is given by

• The phase difference between LOS and diffracted path is a
function of
i) Height and Position of the obstruction
ii) 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.

• The radius of the nth Fresnel Zone is given by

Knife-Edge Diffraction Model

Knife-Edge Diffraction Model
• 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

• The Diffraction Gain for different values of v is:

Knife-edge diffraction loss
(Summing Secondary Sources)
-3 -2 -1 0 1 2 3 4 5
-30
-25
-20
-15
-10
-5
0
Fresnel Diffraction Parameter v
KnifeEdgeDiffractionGain(dB)

EXAMPLE
Compute 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.

EXAMPLE
Determine (a) Loss due to knife-edge diffraction and (b) the height
of the obstacle required to induce 6 dB diffraction loss.
Assume f = 900MHz

Scattering
• 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 :

Radar Cross Section Model
(RCS Model)
• 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

Radar Cross Section Model
(RCS Model)

SUMMARY
• 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)

SUMMARY
• 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

Log-Distance Path Loss
Model
• 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

Log-Distance Path Loss
Model

Log-Normal Shadowing
• 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.

• 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.

Determination of Percentage
of Coverage Area
• 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.

Determination of Percentage
of Coverage Area

Outdoor Propagation Models
Longley Rice Model
• 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?

Longley Rice Model
• Operates in 2 modes
• Point-to-point mode
• Area mode prediction
• Modification
• Clutter near receiver
• Doesn’t determine corrections due to
environmental factors

Durkin’s Model
• 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

2-D Propagation Raster Model

Representing Propagation

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

Algorithm for LOS

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

Non-LOS Cases
• 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

Multiple Diffraction
Computation

Okumura’s and Hata’s Model

Hata’s Model
• 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

PCS Extension to Hata Model
• Hata’s model to 2GHz

ASSIGNMENT
Review the Outdoor Propagation Models
presented in the slides showing their salient
features and how they differentiate from
each other.

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