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UNIT-1

Mobile Radio Propagation Large-Scale Path Loss

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•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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• 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 )

• 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

• 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

• 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

• 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

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.

• 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

Considering orthogonal polarization

=

Where,

Now velocity (EMW) =

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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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If 1st medium is free space &

The reflection coeefficients for vertical and horizontal polarization can be reduced as:-

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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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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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If than ETOT can be expresed as:-

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Referring to the phasor diagram below:-

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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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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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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.

Illustration of diffraction II

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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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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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The radius of nth fresnel zone circle is denoted by rn

Where,

Fresnel diffraction geometry

Knife-edge diffractionFresnel integral, 4.59

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Knife edge diffraction loss

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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.