Mobile Communication
Large Scale Propagation Models
Propagation Models
 Mobile communication channel propagation models are usually studied
in terms of large scale or small scale.
 Propagation models characterizing signal strength at large transmit
receive distances are culled large scale propagation model.
 Small scale propagation models are the ones that describe rapid
fluctuations received at short distances.
1. Theoretical Models (Deterministic): These models relay on theoretical
background and does not take into consideration all the factors affecting
propagation and it requires the use of a complex topographic data base.
2. Empirical Models (Statistical): These models are based on mean value
and establishes simple relations between attenuation and the distance
between Tx and Rx. The main advantages is that they include all factors
that affect propagation. The main drawback is that they must be
calibrated and validated for each environment.
3. Semi Empirical Models (Mixed): The models are mixed types of both
deterministic and empirical models.
Practical Link Budget Design Using Path Loss Models:
1. Log-distance Path Loss Model:
Both theoretical and measured based propagation models indicate
that the average received signal power decreases logarithmically with distance
(i.e, indoor and outdoor radio channels). The average large scale path loss for
an arbitrary Tx - Rx separation is expressed as a function of distance by using
path loss exponent n.
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Mobile Communication
̅( )
(
( )
)
(
)
Or
̅(
)
̅(
)(
)
(
)
( )
Where: n is the path loss exponent (which indicates the rate at which path loss
increase with distance).
do = close-in reference distance determine from measurements close to the Tx.
d = Tx - Rx separation distance.
do is taken as:
do = l km for macrocells
do = l00 m for microcclls
do = 1 m for indoor

The bars in equation (l) and (2) denote the ensemble average of all
possible path loss values for a given value of d.

The value of n depends on the specific propagation environment as
shown in table (1).

The reference distance should be in the far field of the antenna.

The reference path loss is calculated using the free space loss
equation (2a).
(
)
(
)(
(
)
)
[
(
) ]
2
(
)
Mobile Communication
Table 1: Path Loss Exonent For Digital Environments
Environment
Path Loss Exponent (n)
Free space
2
2.7 – 3.5
Urban area cellular radio
Shadow Urban area cellular radio
3-5
In building line of sight
1.6 – 1.8
Obstructed in building
4-6
Obstructed in factories
2-3
Outdoor Propagation Models:
1- Okumura Model:
This model is most widely used for signal predication in urban area. It
is applicable for[5 ch3p.p116]:
(
)
Frequency range
150 MHz – 3000 MHz
Range
1 km – 100 km
Base station antenna height
30 m – 1000 m
(
)
(
)
(
)
( )
Where:
L = median path loss (dB).
LF = free space loss (dB).
Amu = the median attenuation relative to free space as a function of
frequency (f and distance d).
G(hte) = the base station antenna height gain factor.
G(hre) = the mobile station antenna height gain factor.
GAREA = gain depends on the type of environment (correction factor).
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Mobile Communication
Plots of Amu(f,d) and GAREA for wide range of frequencies are shown
in Fig.(1) and Fig.(2).
(
)
(
)
(
)
(
)
(
)
(
)
1000 m >
> 30 m
≤ 3m
10 m >
......(4a)
......(4b)
>3m
.......(4c)
Okumura's model is wholly based on measured data and does not provide any
analytical explanation.
Fig.(1): Median attenuation relative to free space (Amu(f,d)), over a quasi-smooth terrain.
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Mobile Communication
Fig.(2):Correction factor, GAREA, for different types of terrain.
Example 3.10[5p.p118]
Advantages of the Model:
1. Simplest and best in path loss prediction for cellular and land mobile
systems in cluttered environment.
2. If is very practical and has become a standard for system planning in
modern land mobile system.
Disadvantages:
1. The major disadvantage is its slow response to rapid changes in terrain.
2. The model is fairly good in urban and suburban areas but not as good in
rural areas.
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Mobile Communication
2- Hata Model:
Hata Model is an empirical formulation of the graphical path loss
data provided by Okumura, it is valid for:
 Frequencies: l50 MHz - 1500 MHz.
 The standard formula for median path loss in Urban area is given by:
LUrban(dB)=69.55 + 26.16Log(fc) – 13.82Log(hte) – a(hre) + (44.9- 6.55Log(hte))Log(d)
.....(5)
Where:
fc = frequency 150 MHz - 1500 MHz.
hte = the effective Tx (base station) antenna height in meter= 30 m to 200 m.
hre = is the effective Rx (mobile) antenna height in meter = 1 m to 10 m.
d = distance between BS and MS in km.
a(hre) = correction factor for effective mobile antenna height which is a
function of the size of the coverage area.
The mobile antenna correction factor for small to medium sized city is given
by:
a(hre) = (1.1 Log(fc) – 0.7)hre – (1.56 Log(fc) – 0.8)dB
..... (6)
For a large city:
(
)
(
)
(
(
(
(
))
... (6a)
))
(
In suburban area:
The path loss in equation (5) is modified as:
(
)
(
)
*
( )+
6
...... (7)
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Mobile Communication
In open rural area:
For path loss in open rural areas, the formula is modified as:
(
)
(
)
(
( ))
( )
( )
Nodes:
1. The prediction of Hata model compares very closely to Okumura model
as long as d exceed 1 km.
2. This model is well suited for large cell mobile systems, but not personal
communications system (PCS) which has cells of the order of 1 km
radius.
3- Walfisch-Bestoni Model:
The model considers the impact on roof tops and building height by
using diffraction to predict average signal strength at street level. The model
consider the path loss (S) to be a product of three factors[5].
S = PoQ2P1
.......(9)
Po = Free space path loss between isotropic antennas given by:
(
)
(
)
Q2 = The reduction in the rooftop signal due to the row of buildings which
immediately shadow the receiver at street level.
P1 = Term based upon diffraction and determine the signal loss from rooftop
to the street in dB, the path loss is given by:
S(dB) = Lo + Lrts +Lms
Where:
....... (11)
Lo = Free space loss.
Lrts = Roottop-to-street diffraction and scatter loss.
Lms = Multiscreen diffraction loss due to the rows of buildings.
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Mobile Communication
Fig.(3) illustrate the geometry used in the Walfisch-bestoni model.
Fig.(3): Propagation geometry for model proposed by Walfisch-bestoni.
From Fig.(3), we notice that the signals arrive at the receiver from different
ways (reflection, diffraction from the 1st, 2nd and 3rd as the model show that
the signals travels from rooftops)[5 ch3].
This model depends on:
1. The height of the buildings.
2. The width of the streets and the width of the buildings.
3. The distance between buildings.
4. The orientation of the streets relative to the line of sight (LOS) and nonline of sight (NLOS).
5. The distance between the Tx and receivers the height of Tx and Rx
antennas and the frequency.
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Mobile Communication
Indoor Propagation:
Indoor propagation is dominated by the same mechanisms as
outdoor: (reflection, diffraction and scattering).
The indoor radio channel differs from the traditional mobile radio in
some aspects[5 p.p123]:
1. The distance covered is much smaller.
2. The variability of the environment is much greater for a much smaller
range of Tx-Rx separation.
3. Propagation within buildings is strongly influenced by specific features
such as:
 The layout of the building.
 The construction materials.
 The building type.
4. Within buildings, it is difficult to work in the far. field region for all
types of antennas used.
In general indoor channels may be classified either as:
Line of Sight (LOS) or Obstructed (OBS).
Attenuation Factor Model:
An in-building site-specific propagation model that includes the
effect of building type as well as the variations caused by obstacles.
The attenuation factor model is given by[5p.p129]:
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Mobile Communication
̅ ( )[
]
̅(
)[
]
[
( )
]
∑
[
]
(
)
Where:
NSF = The exponent value for the same floor measurement.
FAF = The floor attenuation factor for a specific number of buildings floor.
PAF = The partition attenuation factor for a specific obstruction encountered
by a ray drawn between the Tx and Rx in three dimension.
In equation (12), FAF may be replaced by an exponent which
already considers the effect of multi floor separation.
̅ ( )[
]
̅(
)[
]
( )
∑
[
]
(
)
Where:
nMF = Path loss exponent based on measurements through multi floors.
In buildings, it was found that path loss obeys free space plus an
additional loss factor which increases exponentially with distance. Therefore
equation (12) can be modified as:
̅ ( )[
]
̅(
)[
]
[
( )
]
∑
[
Where:
α = The attenuation constant for the channel with units (dB/m).
10
]
(
)
Mobile Communication
Small-Scale Fading (or short term fading model)
It is used to describe rapid fluctuations of the amplitude, phase, or
multiple delay of radio signal over a short period of time or travel distance.
Small-Scale Multipath Fading Effects:
The three most important effects are[5ch4]:
1. Rapid changes in signal strength over a small travel distance or time
interval.
2. Random frequency modulation due to varying Doppler shift on different
multipath signals.
3. Time dispersion (echoes) caused by multipath propagation delays.
Properties of Small-Scale Multipath Propagation:
 Small Tx-Rx separation distances (a few wavelengths).
 In build-up urban areas, fading occurs due to the height of the mobile
antennas are well below the height of the surrounding structures, so
there is no signal line of sight path to the base station.
 Even when a LOS exists, multipath still occurs due to reflection from
the ground and surrounding structures. The incoming radio waves arrive
from different directions with different propagation delays.
 Multiple copies of tmnsmiued signal arriving at the receiver by different
paths and at different time delays.
 The multipath components combine vectorially at the receiver antenna
of the mobile and causes signal received by the mobile to distort or fade.
 Even when the mobile receiver is stationary, the received signal may
fade due to the movement of the surrounding objects in the radio
channel.
 Distribution of the signal attenuation coefficient are: Rayleigh, Rician
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Mobile Communication
Doppler Shift:
Consider a mobile moving at a constant velocity v, along a path
segment having length d between points X and Y, while it receives signals
from a remote source S, as illustrated in Fig.(4).
Fig.(4): Illustration of Doppler effect.
The difference in path lengths traveled by the wave from source S to
the mobile at points X and Y is
, where
required for the mobile to travel from X to Y, and
is the time
assumed to be same at
points X and Y since the source is assumed to be very far away.
The phase change in the received signal due to the difference in path
lengths is therefore.
(
)
The apparent change in frequency, or Doppler Shift, is given by fd where:
(
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Mobile Communication
equation (16) relate the Doppler shift to the mobile velocity and the spatial
angle between the direction of motion of the mobile and the direction of
arrival of the wave. It can be seen from equation (16) that if the mobile is
moving toward the direction of arrival of the wave, the Doppler shift is
positive (i.e., the apparent received frequency is increased), and if the mobile
is moving away from the direction of arrival of the wave, the Doppler shift is
negative (i.e., the apparent received frequency is decreased).
Example:
Consider a transmitter which radiates a sinusoidal carrier frequency of
1850 MHz. For a vehicle moving 60 mph, compute the received carrier
frequency if the mobile is moving (a) directly toward the transmitter (b)
directly away from the transmiuer, and (c) in a direction which is
perpendicular lo the direction of arrival of the transmitted signal.
Solution:
Carrier frequency fc = 1850 MHz.
Therefore, wavelength
Vehicle speed v = 60 mph= (60*1609)/3600 = 26.82 m/s
(a) The vehicle is moving directly toward the transminer.
The Doppler shift in this case is positive and the received frequency is given
by:
(b)Thc vehicle is moving directly away from the transmitter.
The Doppler shift in this case is negative and hence the received frequency is
given by:
(c)The vehicle is moving perpendicular to the angle of arrival of the
transmitted signal.
In this case, = 90°, cos = 0, and there is no Doppler shift.
The received signal frequency is the same as the transmitted frequency of
1850MHz.
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Mobile Communication
Shadowing:
In the case when large obstacles are represent, this causes a large fading
of the radio signal this is called shadowing or blocking. This type of fade
depends on the frequency of the radio signal and the penetration of the signal
through the obstacles.
When the signal frequency increases, the penetration strength decreases.
The high frequency signals are affected to a larger extend by the obstructing
objects even when objects arc small.
In the presence of a building or a wall or a tree may cause the signal to be
blocked and the signal is not received completely (e.g., the signals of higher
frequencies transmitted by satellites).
Multipath Propagation:
Even when there are no obstructing objects in the direct path between the
Tx and the Rx, but the obstructing objects are in the surrounding area may
cause most of a difficult problem of transmission due to multipath propagation.
The signal arrive at the receiver follow different path because of reflections
from the obstructing objects (i.e., the line of sight signal if present will be first
then followed by the reflected signals depending on the different distances
each signal travels before reaching the receiver). This delay (1 st shortest
distance signal to last longest distance) is called delay spread. This causes the
arrival of many copies of the signal and they are of different amplitude, phase
and angle of arrival causing distortion due to interference of these signals at
the receiver which arrive at the receiver at different times.
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Mobile Communication
Fig.(5): Illustration of Doppler effect.
Parameters of Mobile Multipath channels:
1- Time Dispersive Parameters.
2- Coherence Bandwidth and Delay Spread.
3- Doppler Spread and Coherence Time.
1- Time Dispersive Parameters:
The parameters which quantify (to compare different multipath channels)
the multipath channel are:
 The mean excess delay( ̅ )
 RMS delay spread (
).
 Excess delay spread (XdB).
 The mean excess delay is the 1st moment of the power delay profile and is
defined by:
̅
∑
∑ ( )
∑ ( )
∑
(
)
 The rms delay spread is the square root of the 2nd central moment of the
power delay profile:
√̅
(̅)
(
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)
Mobile Communication
̅
∑
∑
∑ ( )
∑ ( )
(
)
Where P( ) is the absolute power level.
These delays arc measured relative to the first detectable signal arriving at the
receiver at
2- Coherence Bandwidth and Delay Spread:
Delay spread (
) is a natural phenomenon caused by reflected and
scattered propagation path in a radio channel, typical values for rms delay
spread (
):
In outdoor mobile radio channel ≈ microseconds
In indoor mobile radio channel ≈ nanoseconds
 Coherence bandwidth (Bc) is a statistical measure of the range of
frequencies ever which the channel can be considered flat (i.e., a channel
which passes all spectral components with approximately equal gain and
linear phase ). Or
 Coherence bandwidth (Bc) is the range of frequencies over which two
frequency components have a strong potential for amplitude correlation.
Two sinusoids with frequency separation greater than Bc are affected quite
differently by the channel.
If the coherence bandwidth is defined as the bandwidth over which the
frequency correlation functíon ís above 0.9 then:
(
)
If the frequency correlation function is above 0.5:
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Mobile Communication
(
)
Inter-Symbol Interference (ISI):
The delay spread caused by the arrival of the signals (following different
paths) at the receiver which causes pulse interference, the energy of a certain
symbol is distributed over the adjacent symbols and causes what is called ISI
as shown in Fig.(6). The effect of ISI increase with increase in the symbol rate.
Fig.(6): ISI caused by multipath signals.
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Mobile Communication
3- Doppler Spread and Coherence Time:
Delay spread and coherence bandwidth are parameters describe the time
dispersion nature of the channel in a local area, they do not offer information
about the time varying nature of the channels caused by either.
 Relative motion between the mobile and the base station.
 Or movement of the objects in the channel.
Doppler spread (BD): When a sinusoidal tone of frequency fc is transmitted,
the received signal spectrum called Doppler spectrum will have component in
the range fc - fd , fc + fd where fd is the Doppler shift.
fd is a function of the relative velocity of lhe mobile and the angle Ө
between the direction of motion of the mobile and direction of arrival of
scatter waves.
 If the baseband signal bandwidlh is much greater than B D, the effects of
Doppler spread are negligiblc at the receiver. This is a slow fading
channels.
Coherence time (TC): is the time domain dual of the Doppler spread.
(
)
The definition of Coherence time (TC) implies that rwo signals arriving
with a time separation greater than TC are affected differently by the channel.
lf the coherence time is defined as the time over which the time
correlation function is above 0.5:
(
)
Where fm is the maximum Doppler shift given by
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Mobile Communication
For modem digital communications, coherence time is defined as the
geometric mean of equations 23 and 24:
√
(
)
If the reciprocal (‫ )مقلوب‬bandwidth of the baseband signal is greater than the
coherence time of the channel, then the channel will change during the
transmission of the baseband message, casing distortion at the receiver.
Types of Small-Scale Fading:
1- Fading effects due to multipath time delay spread.
a- Flat fading: If the mobile channel has a constant gain an a linear phase
response over a bandwidth which is greater than the bandwidth of the
transmitted signal, then the received signal undergo flat fading.
Where: BS : The transmined signal bandwidlh.
BC : The channel bandwidth (Coherence Bandwidlh).
b- Frequency selective fading: If the channel has a constant gain and a linear
phase response over a bandwidth that is smaller than the bandwidth of the
transmined signal then the channel creates frequency selective fading on the
received signal. The received signal will be distorted and the channel induces
intersymbol interference (ISI)
BS > BC
When Bs > Bc an equalizer needed at the receiver.
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Mobile Communication
2- Fading effects due to Doppler spreud.
a- Fast fading: the channel impulse response changes rapidly within
the symbol duration.
TS > TC
BS < BD in frequency domain
Where: TS : symbol period of the transmitted signal.
TC : Coherence time.
b- Slow fading: the channel impulse response changes at a rate much slower
than the transmitted baseband signal. In this case the channel may be assumed
to be static over one or several reciprocal bandwidth intervals.
TS << TC
BS >> BD in frequency domain.
It should be clear that the velocity of the mobile and the baseband signal
determines whether a signal undergoes fast or slow fading.
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Mobile Communication
Rayleigh and Ricean Distributions:
1- Rayleigh Fading Distribution:
Rayleigh distribution for the signal arriving at the receivers when there
is no tine of sight (LOS) and described as non-stationary and it occurs when
the Rx is moving or the transrnitter is moving as shown in Fig.(7).
Transmitter
Obstacle
Receiver
Fig.(7): Rayleigh Fading.
2- Ricean Distribution:
The probability distribution for the signal arriving at the receiver is
Ricean when there is a line of signal (LOS) as shown in Fig.(8).
Fig.(8): Ricean Fading.
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Mobile Communication
Comparison Between Rayleigh fading and Ricean fading:
Rayleigh fading
Ricean fading
1- No LOS (Multipath).
1- LOS component (direct-multipath)
2- The total energy of the signal received is 2- Adding a strong component which is the
from reflections, refraction.
3- The direction of Tx is not important.
LOS component to the reflect signal.
3- The direction of Tx is important due to
its direct component.
4- Multipath causes destructive interference 4- The number of fades is less than in
causing deep fades (20-30 d B).
Rayleigh.
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