# Lecture 04 Large Scale Fading (2)

```4/1/2018
Lecture #04:
DR ABUL KHAIR BIN ANUAR
Dept of Communication Engineering
Faculty of Electrical and Electronic Engineering
Universiti Tun Hussein Onn Malaysia, Johor
PATH LOSS





Free Space Propagation Model
Relating Power to Electric Field
Basic Propagation Mechanisms
Reflection

Ground Reflection (Two Ray)
 Diffraction


Fresnel Zone Geometry
Knife Edge Diffraction Model
 Scattering
 Practical Link Budget Design Using Path Loss Models


Log distance
Log normal
 Outdoor Propagation Models


Model Okumura
Model Hata
 Indoor Propagation Models
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Figure 4.1 Small-scale and large-scale fading.
 Propagation in mobile radio follows the basic propagation
theory, with some addition to compensate for moving
target (mobile).
 Wave propagation mechanism often attributed to
reflection, diffraction and scattering.
 Model such as Free Space Loss Model, Plane Earth
Propagation Loss Model, Diffraction Model is valid to some
extend of propagation scenario.
 Most cellular system operate where no direct line of sight
path is available, causing severe diffraction loss and
multipath.
 Other factors that need to be considered in mobile
propagation are fading, Doppler effect, signal delay and
indoor propagation.
 Some corrections is needed for the basic propagation
model to be accurately represent the real propagation that
took place between the transmitter and the receiver.
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Free Space Propagation Model
 The transmitter-receiver (T-R) path is clear from any obstruction (line
of sight propagation).
 Received power decays as a function of T-R distance raised to
some power (power law function).
 Given by Friss free space equation,
or
where
is the system loss factor not related to propagation.
 Path loss,
10 log
10 log
Note : You should be
able to derive the Friss
transmission equation.
4
 Only valid when the mobile is outside the Near Field region (or in
the Far Field region, the Fraunhofer region)
 Franhoufer distance,
and
- largest linear physical
dimension of the
antenna
≫
Power and Electric Field
 Power flux density, or simply power density is given as
4
/
4
 The intrinsic impedance, 
120  (377).
/
377
where | | is the magnitude of the radiating portion of the
electric field in the far field.
377
4
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Example 4.1
 Find the far field distance for an antenna with maximum
dimension of 1m and operating frequency of (a) 900 MHz
and (b) 1800 MHz.
 An array of patch antennas whose dimension is 40cm by
40 cm is used at the base station. Find the far field
distance of the antenna.
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Example 4.2
 Transmitter power is 50W, express the power in dBW and
dBm. The power is then applied to a unity gain antenna
with 900 MHz carrier frequency, find received power at
(a) 100 m and (b) 10km from the antenna. Also assume
unity gain for the received antenna
Ground Reflection (Two-Ray) Model
 FSPL is inaccurate when used alone as usually no single
direct path from base station and mobile unit.
 GRM or plane earth loss model is based on geometric
optics, and considers both the direct path and the
reflected path between transmitter and receiver.
 Assume flat earth with T-R separation of few km.
) is the result of two rays, the
line of sight component (
) and ground reflected
component ( ).
 Solving for received power yields
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Classical 2-ray ground bounce model
Example 4.4
The mobile is located 5 km away from a base station and
uses a vertical quaterwave monopole antenna with a
gain of 2.55dB to receive cellular signals. The E-field at 1
km from the transmitter is measured to be 10-3 V/m.
Carrier frequency is 900 MHz. Find
(a) the length and the effective aperture of the receiving
antenna
(b) received power at the mobile using the two-ray
ground reflection model assuming the height of the
transmitting antenna is 50 m and the receiver is 1.5 meter
above ground.
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Diffraction
 It is redistribution of energy within a wavefront as it passes
the sharp edges of an object or slits
 The phenomenon that allows light or radio waves to
propagate around corners
 We used the Huygen’s Principle to explain this
phenomenon
 Huygen’s Principle states that:
“Every point on a given spherical wavefront can be
considered as a secondary point source of EM waves from
which other secondary waves (wavelets) are radiated
outward”
Single-Knifed Edge
 Figure shows how plane wavefronts impinging on the edge
from the left become curved by the edge so that, deep
inside the geometrical shadow region, rays appear to
emerge from a point close to the edge, filling the shadow
region with diffracted rays
 Huygen’s principle can be applied in mathematical form to
predict the actual field strength which is diffracted by the
knife-edge
 Contributions from an infinite number of secondary sources
in the region is summed, paying due regard to their relative
amplitude and phases
 Final result can be expressed as propagation loss, which
expressed the reduction in the field strength due to the knife
edge diffraction in decibels
20 log
20 log
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Fresnel diffraction geometry
Figure 4.12 Illustration of Fresnel zones for different knife-edge diffraction scenarios.
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Knife edge diffraction attenuation : (-) exact (--) large approximation
 Another significant value is
0
6
 Received power reduced by 4 when the knife edge is situated
exactly on the direct path between the transmitter and
 The parameter can be expressed in terms of the
geometrical parameters defined in Figure as
2
2
where ’ is the excess height of the edge above the straight
line from source to the field points
 For most practical case, , ≫ , so diffraction parameter
can be approximated in terms of the distances measured
along the ground
2
2
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 Approximate solution using parameter
Lee (2006);
is provided by
0
1
20 log
0.5
0.62
20 log
0.5 exp
20 log
0.4
20 log
.
1
0.95
0
0
0.1184
0.38
0.1
1
1
2.4
2.4
 Another useful way to consider knife edge diffraction is in
terms of the obstruction of Fresnel zones around the direct
ray.
 The th Fresnel zone is the region inside an ellipsoid defined
by the locus of points where the distance (
) is larger
than the direct path between the transmitter and the
) by half-wavelengths
 Hence the radius of the nth zone
condition
 If we assume that
approximation
≪
and
≪
is given by applying the
2
, then to a good
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Fresnel zones
0.6 x first Fresnel zone clearance defines significant obstruction
 Fresnel zones can be thought of as containing the propagated
energy in the wave
 Contribution within the first zone are all in phase, so any absorbing
obstruction which do not enter this zone will have little effect on the
 Fresnel zone clearance ( / ) can be expressed in terms of the
diffraction parameter as follows
2
2
 When the obstruction occupies 0.6 x the first Fresnel zone, the
parameter is then approximately -0.8. Obstruction loss is the 0 dB.
 This clearance is often used as a criterion to decide whether an
object is to be treated as a significant obstruction
 If this region is kept clear then the total path attenuation will be
practically the same as in the unobstructed case
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Multiple knife-edge diffraction
Example 4.5
Compute the diffraction loss where wavelength is 1/3 m,
1
, 2
1
and (a) 25 m (b) 0 m (c) – 25 m.
1
Compare value with approximated value given by Lee.
Identify in which Fresnel zone is the tip of obstruction lies
for each cases.
(Hint: , excess path length can be find by
∆
and we need to find

which satisfy the relation
/2.)
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Example 4.6
Given the following scenario:
Tx height = 50m, Rx height = 25 m, Tx – Rx distance = 12 km
Knife edge height = 100 m
Distance from Tx to knife-edge = 10 km
f = 900 MHz
Find
(a)Knife edge loss
(b)Height of obstacle for 6 dB loss
Scattering
 When radio wave impinges on a rough surface (lamp
posts, trees), reflected energy is spread out (diffuse) in all
directions due to scattering which may provide
 Surface roughness is tested with Rayleigh criterion which
defines a critical height,
of surface protuberances for
a given angle of incidence  , given by
8 sin
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Path Loss Model
 Detail path loss model hard to factor in overall system
design
 Most important characteristic is power fall-off with
distance
 Analytical models
 Empirical models
 Composite
 Applications:
 Predict large scale coverage for mobile systems
 Estimate and predict SNR
Log Distance Path Loss Model
 Average path loss for an arbitrary T-R separation is expressed as a
function of distance using a path loss exponent,
∝
or
10 log

indicates the rate at which the path loss increases with
distance, 0 is the close-in reference which is determine from
measurements close to the transmitter, and d is the T-R separation
distance. The bars indicate the ensemble average of all possible
path loss values for a given value of .
 Free space reference value chosen according to the
propagation environment, i.e. 1 km for large cell, or 1 or 100 m for
smaller cells.
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Typical large-scale path loss
 Log distance model fails to address the fact that
environmental clutter may be vastly different at two
location having the same T-R separation.
 Measured signals vastly different from the average value.
 Path loss at any value d is random and distributed lognormally (normal) about the mean distance dependent
value that is
10
 thus
 is a zero mean Gaussian distributed random variable
(in dB) with standard deviation  (also in dB).
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 Log normal distribution describe the random shadowing
effect over large number of measurement locations
which have the ame T-R separation, but have different
levels of clutter on the propagation path, refers to log
 Close in reference d0, path loss exponent n, and the
standard deviation  statistically describe the path loss
model for an arbitrary location having specific T-R
separation.
 Values of n and  are computed from measured data,
the difference between measures and estimated path
loss is minimized in a mean square error sense over wide
range of measurement locations and T-R separations.
Rayleigh and Log-normal
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Example 5.7
measurement were taken
at distance 100m, 200m,
1km and 3km and given in
the table where it is assume
where d0 = 100m.
100 m
0 dBm
200 m
– 20 dBm
1000 m
– 35 dBm
3000 m
- 70 dBm
 Find the minimum mean
square error (MMSE)
estimate for the path loss
exponent, n
 Calculate the standard
value
power at d = 2km using the
resulting model
 Predict the likelihood that
the signal level at 2 km will
be greater than -60dBm
 Predict the percentage of
area within a 2 km radius
greater than – 60 dBm,
given the result in (d)
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 MMSE estimate may be found using the following
method. Let pi be the received power at a distance
and let ̂ be the estimate for using the / 0 path loss
model. The sum of square errors between the measure
and estimated values is given by
̂
The value of n which minimizes the mean square error
can be obtained by equating the derivative of
to
zero, and then solving for .
Outdoor Propagation Model
 Radio transmission often takes place over irregular terrain
 Terrain profile may vary from simple curved to a
mountainous profile.
 Trees, buildings and other obstacles cannot be
neglected and must be taken in the estimation.
 The purpose of the outdoor model is to predict the
average received signal strength at a given distance
from the TX, as well as the variability of the signal strength
in close spatial proximity to a particular location.
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 Classifications:
 Computer based models:
 Longley-Rice model
 Durkin’s model
 Measurement model
 Okumura model
 Empirical model
 Hata model
 PCS extension and wideband PCS microcell models
 Walfish and Bertoni Model
Longley-Rice Model (LR, ITM)
 In 1965 & 1968, Rice and Longley propose the model to be
applicable to point-to-point communication systems in the
frequency range from 40MHz to100GHz.
 In 1978, Longley-Rice model is also available as a computer
program to calculate large-scale median transmission loss
relative to free space loss over irregular terrain for
frequencies between 20MHz and 10GHz
 Longley Rice has been adopted as a standard by the FCC
 Many software implementations are available commercially
 Includes most of the relevant propagation modes [multiple
knife & rounded edge diffraction, atmospheric attenuation,
tropospheric propagation modes (forward scatter etc.),
precipitation, diffraction over irregular terrain, polarization,
specific terrain data, atmospheric stratification, different
climatic regions, etc. etc. …]
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 Operate in two mode:
 Point-to-Point mode prediction: A detail terrain path profile
is available, the path specific parameters can be easily
determined.
 Area mode prediction: Once the terrain path profile is not
available, the Longley-Rice method provides techniques to
estimate the path-specific parameters.
 Shortcoming:
 Does not providing a way of determining corrections due to
environmental factors in the immediate vicinity of the
 No consideration of correlation factors to account for the
effects of buildings and foliage
 No consideration of multipath
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Durkin’s Model
 In 1969 & 1975, Durkin propose a computer simulator for
predicting field strength contours over irregular terrain.
 Durkin path loss simulator consists of two parts:
 Access a topographic database of a proposed service area
 Reconstruct the ground profile information along the radial
joining the TX to RX.
 Assumption:
 the receiving antenna receives all of its energy along that
 No multipath propagation is considered
 Simply LOS and diffraction from obstacles along the radial, and
excludes reflections from other surrounding objects and local
scatterers
 Refer to Rappaport, pp 146.
Okumura Model
 Most widely used model in urban areas, obtained by
extensive measurements, no analytical explanation – based
on measurement in the city of Tokyo, Japan.
 Represented by charts (curves) giving median attenuation
relative to free space attenuation
 Valid under:
 Frequency band: 150-1920 MHz
 T-R distance: 1-10 km,
= 1m to 3m
 BS antenna height: 30-1000 m
 Quasi-smooth terrain (urban & suburban areas)
 among the simplest & best for in terms of path loss accuracy
in cluttered mobile environment
 disadvantage: slow response to rapid terrain changes
 common std deviations between predicted & measured path
loss  10dB - 14dB
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 Okumura developed a set of curves in urban areas with
quasi-smooth terrain
 effective antenna height:
 base station hte = 200m
 mobile: hre = 3m
 gives median attenuation relative to free space (Amu)
 developed from extensive measurements using vertical
omni-directional antennas at base and mobile
 measurements plotted against frequency
 Estimating path loss using Okumura Model
 1. determine free space loss, Amu(f,d), between points of
interest
terrain

,
and correction factors to account for
,
–
–
–
L50 = 50% value of propagation path loss (median)
LF = free space propagation loss
Amu(f,d) = median attenuation relative to free space
G(hte) = base station antenna height gain factor
G(hre) = mobile antenna height gain factor
GAREA = gain due to environment
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
,
&
frequencies
have been plotted for wide range of
 antenna gain varies at rate of 20dB per decade or 10dB per
20 log
10 log
20 log
200
3
3
,
10
,
,
1000
3
3
10
 model corrected for
  = terrain undulation height
 isolated ridge height
 average terrain slope
 mixed land/sea parameter
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Okumura and Hata’s model
Hata Model
 empirical model of graphical path loss data from
Okumura
 predicts median path loss for different channels
 valid over UHF/VHF band from 150MHz-1.5GHz
 charts used to characterize factors affecting mobile land
propagation
 standard formulas for approximating urban propagation loss
 correction factors for some situations
 compares closely with Okumura model as
mobile systems
1
 large
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Parameter
Comment
L50
50th % value (median) propagation path loss (urban)
fc
frequency from 150MHz-1.5GHz
hte, hre
Base Station and Mobile antenna height
 (hre)
correction factor for hre , affected by coverage area
d
Tx-Rx separation
log
69.55
26.16 log
– 13.82 log
–
 represents fixed loss – approximately 2.6 power law
dependence on
 dependence on antenna heights is proportional to
44.9
6.55 log
.
 represents path loss exponent, worst case ≈ 4.5
69.55
26.16log
44.9 – 6.55log
– 13.82log
log
–
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 Mobile Antenna Height Correction Factor for Hata Model
 (hre)
Comment
(1.1log10 fc - 0.7)hre – (1.56log10 fc - 0.8)dB
Medium City
8.29(log10 1.54hre)2 – 1.1 dB
Large City (fc  300MHz)
3.2(log10 11.75hre)2 –
Large City (fc > 300MHz)
4.97 dB
 Hata Model for Rural and Suburban Regions
 represent reductions in fixed losses for less demanding environments
L50 (dB)
Comment
L50 (urban) - 2[log10 (fc/28)]2 – 5.4
Suburban Area
L50 (urban) - 4.78(log10 fc)2 - 18.33log10 fc - 40.94
Rural Area
 Valid Range for Parameters
 150MHz < fc < 1GHz
 30m < hte < 200m
 1m < hre < 10m
 1km < d < 20km
 Propagation losses increase
 with frequency
 in built up areas
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hte = 30, hre = 2
-- f = 1500MHz
-- f = 900 MHz
-- f = 700MHz
hte = 30, hre = 2, f =
900MHz
-- large city
-- small to medium sized
city
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PCS Extension to Hata Model
 European Co-operative Scientific & Technical (EUROCOST)
formed COST-231, extend Hata’s model to 2GHz
46.3
44.9
 
33.9 log
– 13.82 log
6.55
log
defined in the Hata model
 For medium sized city, CM = 0 dB
 Metropolitan centre, CM = 3 dB
 Limits

1500

30

1

1
2
200
10
20
Indoor Propagation Model
 The indoor environment differs from outdoor
 smaller Tx-Rx separation distances than outdoors
 higher environmental variability for much small Tx-Rx separation
 conditions vary from: doors open/closed, antenna position,
 strongly influenced by building features, layout, materials
 Dominated by same mechanisms as outdoor propagation
(reflection, refraction, scattering)
 Classified as either LOS or OBS, with varying degrees of clutter
 Some key models are
 Partition Losses – Same Floor
 Partition Losses – Different Floor
 Log-distance path loss model
 Ericsson Multiple Breakpoint Model
 Attenuation Factor Model
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Partition losses
 Partition Losses (same floor)
 Variety of obstacles and partitions
 Hard partitions – part of the building structure
 Soft partitions – do not span to the ceiling
 Vary widely in their physical and electrical characteristic
 Database for various type of partitions, here or refer to
Rappaport pp 158-159.
 Partition Losses between Floors
 Structural dimension, materials, type of construction,
windows
 Floor attenuation factor, FAF for three buildings in San
Fransisco.
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 Log Distance Path Loss Model
 n depends on surroundings and building type
  = normal random variable in dB having std deviation 
 identical to log normal shadowing mode, typical value in Table aa
d
PL(dB)  PL(d0 )  10n log    
 d0 
 Ericsson Multiple Breakpoint Model
 measurements in multi-floor office building
 uses uniform distribution to generate path loss values between
minimum & maximum range, relative to distance
 4 breakpoints consider upper and lower bound on path loss
 assumes 30dB attenutation at d0 = 1m
 accurate for f = 900MHz & unity gain anntenae
 provides deterministic limit on range of path loss at given distance
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Ericsson’s indoor model
 Attenuation Factor Model
 includes effect of building type & variations caused by
obstacles
 reduces std deviation for path loss to   4dB
 std deviation for path loss with log distance model  13dB
d
PL(d ) (dB)  PL(d0 ) (dB) 10nSF log   FAF(dB)   PAF(dB)
 d0 
 nSF = exponent value for same floor measurement – must be
accurate
 FAF = floor attenuation factor for different floor
 PAF = partition attenuation factor for obstruction
encountered by primary ray tracing
PAF(1)
FAF
Tx
PAF(2)
Rx
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 Replace FAF with nMF = exponent for multiple floor loss
d
PL(d ) (dB)  PL(d0 ) (dB)  10nMF log    PAF(dB)
 d0 
  decreases as average region becomes smaller-more
specific
 Building Path Loss obeys free space + loss factor ()
(Dev90b)
 loss factor increases exponentially with d
  (dB/m) = attenuation constant for channel
d
PL(d ) (dB)  PL(d0 ) (dB)  20log   d  FAF (dB)   PAF(dB)
 d0 
Measured indoor path loss
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Measured indoor path loss
Measured indoor path loss
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Devasirvatham’s model
Path Loss Exponent & Standard Deviation for Typical Building
Location
n
σ (dB)
number of points
same floor
2.76
12.9
501
through 1 floor
4.19
5.1
73
through 2 floor
5.04
6.5
30
through 3 floor
5.22
6.7
30
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Signal Penetration into Buildings
 no exact models
 signal strength increases with height
 lower levels are affected by ground clutter (attenuation
& penetration)
 higher floors may have LOS channel  stronger incident
signal on walls
 RF Penetration affected by
 frequency
 height within building
 antenna pattern in elevation plain
 Penetration loss
 decreases with increased frequency
 loss in front of windows is 6dB greater than without windows
 penetration loss decreases 1.9dB with each floor when < 15th
floor
 increased attenuation at >15 floors – shadowing affects from
taller buildings
 metallic tints result in 3dB to 30dB attenuation
 penetration impacted by angle of incidence
Penetration Loss vs Frequency for two different building
Frequency
(MHz)
Attenuation
(dB)
441
896.5
1400
Frequency
(MHz)
Attenuation
(dB)
16.4
900
14.2
11.6
1800
13.4
7.6
2300
12.8
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 Ray Tracing & Site Specific Models
 rapid acceleration of computer & visualization capabilities
 SISP – site specific propagation models
 GIS – graphical information systems
 support ray tracing
 augmented with aerial photos & architectural drawings
Example

A BS of 30m height is operating at 900 MHz and transmits 20W
power. The transmitter and receiver antenna gains are 6dB and
2dB respectively. A MS of 2m height is located at 5km from the BS.
If other losses is 5dB and fading =6dB due to log-normal fading,
compare the minimum power received by the MS in dBm if the
following propagation models are used:

Free space propagation loss, FSPL

Plane earth propagation loss, PEPL

log-distance with do=1km, =4 and PL(do)=FSPL, and

diffraction model if an obstacle of 30m height is located at 2km from
the BS

Comment on the practical minimum power received by the MS if an
obstacle stated in (d) exists.
Write a MATLAB program to plot the path loss for each model from
1km to 5 km.
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