ECE 5221 Personal Communication Systems
Prepared by:
Dr. Ivica Kostanic
Lecture 3: Planning for Coverage in Cellular
Systems
(Chapter 2.3 )
Spring 2011
Florida Institute of technologies
Outline
Mobile propagation environment
Free space path loss model (review)
Two ray propagation model (review)
Log distance path loss model (review)
Examples
Important note: Slides present summary of the results. Detailed
derivations are given in notes.
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Free space path loss model
 Assumes free space between TX and RX
Definition of quantities:
 Realistic in microwave links to cellular towers
PT = power delivered to antenna terminals
 Not realistic in terrestrial propagation
GT = gain of transmit antenna
ERP = effective radiated power
FSPL = free space path loss
GR = gain of the receive antenna
PR = received power delivered to receiver
If the quantities are expressed in log-units:
PR  PT  GT  FSPL  GR
Free space propagation scenario
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Free Space Path Loss (FSPL)
Free space path loss - log
140
Equation for FSPL (linear)
135
FSPL  4d /  
2
130
125
 = wavelength of the RF wave
120
Equation for FSPL (logarithmic) – Frii’s equations
FSPL [dB]
d = distance between TX and RX
FSPL  36.5  20 log d miles   20 log  f MHz 
FSPL  32.44  20 log d km  20 log  f MHz 
115
110
f = 1GHz
f = 2GHz
f = 3GHz
105
100
95
90
0
10
Notes:
1
2
10
distance [km]
10
FSPL curves 1-3GHz range
FSPL grow 20dB/dec as a function of distance
FSPL grows 20dB/dec as a function of frequency
FSPL curves are straight lines in log-log coordinate system
Detailed derivation of Frii’s equations given in notes
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FSPL example:
Consider microwave communication link. Assume: power delivered to the antenna is 2W,
transmit antenna gain is 20dB, the receive antenna gain is 5dB and minimum required
signal level is -80dB. Estimate the maximum TX-RX separation for three frequencies:
1900MHz, 2.5GHz and 6GHz.
Answers:
1.
For 1900MHz, distance 61.8 miles
2.
For 2.5GHz, distance 48.95 miles
3.
For 6.6GHz, distance 1.58 miles
Notes:
- Answers do not have any margin
- RSL is received power expressed in dBm
- Note decrease of distance with increase of frequency
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Propagation in terrestrial environment
 Three components of path loss
Flat Terrain Median Signal
Slow Fading (Lognormal Shadowing)
Fast Fading
o Log normal shadowing
o Small scale fading
 Separation between TX and RX
o Exponential decay of signal level
o Decay is expressed in X dB/dec
o X is between 20 and 60
 Log normal shadowing
-20
-30
o Additional path loss due to mobile
being in a shadow of terrestrial
objects
o Modeled as a random variable
normally distributed in log domain
 Small scale fading
o Large variations of signal level over
distances comparable to wavelength
0
-10
Received Signal Level (RSL)
o Separation between TX and RX
10
40 Wavelengths
Range from Transmitter Antenna
Notes:
- First two components of the path loss predicted
through macroscopic propagation models
- Third component is virtually unpredictable
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Losses due to TX-RX separation
 Simplified example: two-ray path loss model
 Model derived for:
o Flat Earth
o Perfectly reflecting Earth
o Assuming two ray addition at the RX
point
 Model predicts:
o 40 dB/dec loss as a function of distance
o 20 dB/dec dependence of losses on TX
and RX heights
 In practical situations:
o Separation loss 20-60dB/dec (typical is
still around 40dB/dec)
o Dependence on antenna height still
holds but is somewhat smaller (10-15
dB/dec)
PLdB  40 logR   20 loght   20 loghr 
Notes:
Detailed derivations are presented in notes
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Example
Brevard County, FL has an area of 1,557 sq mi. Assume that
the county is to be covered with a cellular system. The
parameters of the cell sites are: Height of the tower: 50m,
height of the mobile: 1.5m, maximum path loss 120dB.
Use two-ray path loss model to determine:
1.
Size of a cell
2.
The number of circular cells required (neglect the
overlap between the calls)
3.
Cell count assuming that there is about 20% overlap
between cells
Answers:
1.
Radius of a cell is about 5.4 miles
2.
The number of required cells is about 17
3.
Taking the overlap into account, the number of required
cells is 22
Area of circle
R 2
Overlap 

 1.2092
Area of hexagon 3 3 2
R
2
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Log normal fading
Typical RSL
measurements
 Log normal shadowing introduces random
variations of path loss
 Random variations are modeled as a normal
variable in log domain
 Due to these variations the shape of cell is not
regular
 Practical problem:
o Cover the area with irregularly shaped cells
o Prevent excessive overlap between cells
 Practical approach: Assume log distance path loss
model
-60
RSL distance
plot
-65
 The form of the log distance model
-70
y = -41.937x - 75.895
d 
RSL  RSL 0  m log    X 
 d0 
RSL [dBm]
-75
-80
-85
-90
Notes:
-95
The model is straight line approximation
-100
-105
-0.2
Variability captured by random variable
-0.1
0
0.1
0.2
0.3
log(distance) [miles]
0.4
0.5
0.6
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Log distance path loss model - details
Equation of the model
d 
PL  PL0  m log    X 
 d0 
d0 – reference distance
PL – path loss in dB
PL0 – path in dB loss to reference distance
d – distance
m – slope
X – log normal fading in dB
Environment
Slope (dB/dec)
Free space
20
Terrestrial
20-50
Forested areas
Up to 60
In building
16-20
Microcell
16-25
Slope recorded in different us
cities (after W.C.Y. Lee)
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Properties of fading
Probability density function
Standard deviation fading as a function of environment
 x2 
1
X  ~  0,   
exp  2 
2 
 2 
Environment
Standard deviation (dB)
Rural
5-7
Suburban
6-8
Urban
8-10
Dense urban
10-12
Note: for nominal calculations standard deviation
of 8dB is commonly assumed
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Log distance path los model: example
Consider a cell site with ERP = 50dBm. Assume that the path loss follows log-distance path loss
model. The following data are known: reference distance is 1 mile, reference path loss is 109dB,
slope 38.4dB/dec. Calculate:
1.
Median RSL at the distance of 3 miles
2.
Probability that the signal is above level given in 1.
The RSL predicted by log-distance path loss model is -80dBm. Assume log normal shadowing with
standard deviation of 7dB. Calculate probabilities:
1.
RSL > -80dBm
2.
RSL < -80dBm
3.
RSL > -85dBm
4.
RSL < -75dBm
Homework 1 - assigned
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Appendix – Normal distribution table
Q z  
z


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 x2 
1
exp   dx
2
 2
Page 13