large scale path loss 1
DESCRIPTION
consists UPTU wireless comm. Unit-1 P-1TRANSCRIPT
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04/08/2023MIT, MEERUT1
UNIT-1
Mobile Radio Propagation Large-Scale Path Loss
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04/08/2023MIT, MEERUT2
•Electromagnetic wave propagation• reflection• diffraction• scattering
•Urban areas• No direct line-of-sight• high-rise buildings causes severe diffraction loss• multipath fading due to different paths of varying
lengths•Large-scale propagation models predict the mean signal strength for an arbitrary T-R separation distance. •Small-scale (fading) models characterize the rapid fluctuations of the received signal strength over very short travel distance or short time duration.
Introduction to Radio Wave Propagation
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transmittedsignal
receivedsignal
Ts
tmax
LOS
LOSReflectionDiffractionScattering
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04/08/2023MIT, MEERUT4
• Small-scale fading: rapidly fluctuation– sum of many contributions from different
directions with different phases– random phases cause the sum varying
widely. (ex: Rayleigh fading distribution)• Local average received power is predicted by
large-scale model (measurement track of 5 to 40 )
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• Free Space Propagation Model• The free space propagation model is used to
predict received signal strength when the transmitter and receiver have a clear line-of-sight path between them.– satellite communication– microwave line-of-sight radio link
• Friis free space equation
: transmitted power : T-R separation distance (m)
: received power : system loss
: transmitter antenna gain : wave length in meters
: receiver antenna gain
Ld
GGPdP rtt
r 22
2
)4()(
tP
)(dPrtG
rG
d
L
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• The gain of the antenna
: effective aperture is related to the physical size of the antenna
• The wave length is related to the carrier frequency by
: carrier frequency in Hertz : carrier frequency in radians : speed of light (meters/s) • The losses are usually due to
transmission line attenuation, filter losses, and antenna losses in the communication system. A value of L=1 indicates no loss in the system hardware.
2
4
eAG
eA
c
c
f
c
2
f
cc
L )1( L
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• Isotropic radiator is an ideal antenna which radiates power with unit gain.
• Effective isotropic radiated power (EIRP) is defined as
and represents the maximum radiated power available from transmitter in the direction of maximum antenna gain as compared to an isotropic radiator.
• Path loss for the free space model with antenna gains
• When antenna gains are excluded
• The Friis free space model is only a valid predictor for for values of d which is in the far-field (Fraunhofer region) of the transmission antenna.
ttGPEIRP
22
2
)4(log10log10)(
d
GG
P
PdBPL rt
r
t
22
2
)4(log10log10)(
dP
PdBPL
r
t
rP
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• The far-field region of a transmitting antenna is defined as the region beyond the far-field distance
where D is the largest physical linear dimension of the antenna.
• To be in the far-filed region the following equations must be satisfied
and• Furthermore the following equation does not hold
for d=0.
• Use close-in distance and a known received power at that point
or
22Dd f
Dd f fd
Ld
GGPdP rtt
r 22
2
)4()(
0d )( 0dPr2
00 )()(
d
ddPdP rr
fddd 0
d
ddPdP r
r00 log20
W 001.0
)(log10dBm )( fddd 0
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The Three Basic Propagation Mechanisms
• Basic propagation mechanisms– reflection– diffraction– scattering
• Reflection occurs when a propagating electromagnetic wave impinges upon an object which has very large dimensions when compared to the wavelength, e.g., buildings, walls.
• Diffraction occurs when the radio path between the transmitter and receiver is obstructed by a surface that has sharp edges.
• Scattering occurs when the medium through which the wave travels consists of objects with dimensions that are small compared to the wavelength.
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• Reflection from dielectrics
• Reflection from perfect conductors– E-field in the plane of incidence
– E-field normal to the plane of incidence
riri EE and
riri EE and
Reflection
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Considering orthogonal polarization
=
Where,
Now velocity (EMW) =
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04/08/2023MIT, MEERUT12
Now, bondry conditions at the surface of incidence, acc to Snells law,
Using boundary conditions from maxwell eq. (by laws of reflection)
&,
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04/08/2023MIT, MEERUT13
If 1st medium is free space &
The reflection coeefficients for vertical and horizontal polarization can be reduced as:-
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04/08/2023MIT, MEERUT14
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04/08/2023MIT, MEERUT15
Brewster AngleThe angle,at which no reflection occurs in the medium of origin .It is given by , as:-
If 1st medium is free space and relative permittivity of 2nd isThan,
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IV. Ground Reflection (2-Ray) Model
Good for systems that use tall towers (over 50 m tall)
Good for line-of-sight microcell systems in urban environments
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ETOT is the electric field that results from a combination of a direct line-of-sight path and a ground reflected path
is the amplitude of the electric field at distance d
ωc = 2πfc where fc is the carrier frequency of the signal
Notice at different distances d the wave is at a different phase because of the form similar to
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For the direct path let d = d’ ; for the reflected path d = d” then
for large T−R separation : θi goes to 0 (angle of incidence to the ground of the reflected wave) and Γ = −1
Phase difference can occur depending on the phase difference between direct and reflected E fields
The phase difference is θ∆ due to Path difference , ∆ = d”− d’, between
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Using method of images (fig below) , the path difference can be expressed as:-
From two triangles with sides d and (ht + hr) or (ht – hr)
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04/08/2023MIT, MEERUT20
Using taylor series the expression can be simplyfied as:-
Now as P.D is known , Phase difference and time delay can be evaluated as:-
If d is large than path difference become negligible and amplitude ELOS & Eg are virtually identical and differ only in phase,.i.e
&
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04/08/2023MIT, MEERUT21
If than ETOT can be expresed as:-
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04/08/2023MIT, MEERUT22
Referring to the phasor diagram below:-
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04/08/2023MIT, MEERUT23
or
As E-field is function of “sin” it decays in oscillatory fashion with local maxima being 6dB greater than free space and local minima reaching to-∞ dB.
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For d0=100meter, E0=1, fc=1 GHz, ht=50 meters, hr=1.5 meters, at t=0
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note that the magnitude is with respect to a reference of E0=1 at d0=100 meters, so near 100 meters the signal can be stronger than E0=1 the second ray adds in energy that would
have been lost otherwise for large distances it can be
shown that
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04/08/2023MIT, MEERUT27
Q.1
Q.2 calculate the free space path loss for a signal transmitted at afrequencyOf 900MHz for T-R seperation 1Km.
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04/08/2023MIT, MEERUT
Diffraction
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Diffraction occurs when waves hit the edge of an obstacle“Secondary” waves propagated into the shadowed regionWater wave exampleDiffraction is caused by the propagation of secondary
wavelets into a shadowed region. Excess path length results in a phase shiftThe field strength of a diffracted wave in the shadowed
region is the vector sum of the electric field components of all the secondary wavelets in the space around the obstacle.
Huygen’s principle: all points on a wavefront can be considered as point sources for the production of secondary wavelets, and that these wavelets combine to produce a new wavefront in the direction of propagation.
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Illustration of diffraction II
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04/08/2023MIT, MEERUT30
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04/08/2023MIT, MEERUT
Diffraction occurs when waves hit the edge of an obstacle “Secondary” waves propagated into the shadowed regionExcess path length results in a phase shift
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04/08/2023MIT, MEERUT
consider that there's an impenetrable obstruction of height h at a distance of d1 from the transmitter and d2 from the receiver. ,
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αh
d1 d2
T Rβ γ
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The path difference between direct path and the diffracted path is
∆ =
Thus the phase difference,
∆
If,
Then,
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Thus , is It is clear that,
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Fresnel zoneThe excess total path length traversed by a
ray passing through each circle is nλ/2
,
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04/08/2023MIT, MEERUT36
The radius of nth fresnel zone circle is denoted by rn
Where,
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Fresnel diffraction geometry
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Knife-edge diffractionFresnel integral, 4.59
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04/08/2023MIT, MEERUT
Knife edge diffraction loss
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04/08/2023MIT, MEERUT
Multiple knife edge diffraction
For multiple knife edges, replace them by single knife edge, as below
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Log-distance Path Loss Models
We wish to predict large scale coverage using analytical and empirical (field data) methods
It has been repeatedly measured and found that Pr @ Rx decreases logarithmically with distance
∴ PL (d) = (d / do )n where n : path loss
exponent or
PL (dB) = PL (do ) + 10 n log (d / do )
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“bar” means the average of many PL values at a given value of d (T-R sep.)
n depends on the propagation environment“typical” values based on measured data
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At any specific d the measured values vary drastically because of variations in the surrounding environment (obstructed vs. line-of-sight, scattering, reflections, etc.)
Some models can be used to describe a situation generally, but specific circumstances may need to be considered with detailed analysis and measurements.
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Log-Normal Shadowing
PL (d) = PL (do ) + 10 n log (d / do ) + Xσ
describes how the path loss at any specific location may vary from the average value
has a the large-scale path loss component we have already seen plus a random amount Xσ.
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Xσ : zero mean Gaussian random variable, a “bell curve”
σ is the standard deviation that provides the second parameter for the distribution
takes into account received signal strength variations due to shadowing
measurements verify this distributionn & σ are computed from measured data for
different area types
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Assingment – determination of % coverage area.