Wireless Communication Channels: Large-Scale Pathloss

Diffraction

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Diffraction

Diffraction allows radio signals to propagate behind obstacles between a transmitter and a receiver

ht

hr

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Huygen’s Principle & Diffraction

All points on a wavefront can be considered as point sources for the production of secondary wavelets. These wavelets combine to produce a new wavefront in the direction of propagation.

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Knife-Edge Diffraction Geometry

ht hr

d1 d2

hobs

hTx Rx

α

β γ

Δ: Excess Path Length (Difference between Diffracted Path and Direct Path)

h hd h d h d d d d d d

d d

d dh xh d d where x for x

d d

2 2

2 2 2 21 2 1 2 1 2 1 2

1 2

21 2

1 21 2

1 1

, 1 1 12 2

<<

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Ф: Phase Difference between Diffracted Path and Direct Path)

d dh

d d

21 2

1 2

2 2

2

Assume

h d dh h

d d d d1 2

1 2 1 2

tan tan

d d d dh

d d d d1 2 1 2

1 2 1 2

2 2

Fresnel Zone Diffraction

Parameter (ν)

Fresnel Zone Diffraction Parameter (ν)

2

2

ν2=2, 6, 10 … corresponds to destructive

interference between direct and diffracted paths

ν2=4, 8, 12 … corresponds to constructive interference between direct and diffracted paths

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Fresnel Zones

From “Wireless Communications: Principles and Practice” T.S. Rappaport

Fresnel Zones:

Successive regions where secondary waves have a path length from the transmitter to receiver which is nλ/2 greater than the total path length of a line-of-sight path

nn

d dr n d dnr

d d d d

21 2 1 2

1 2 1 22 2

rn: Radius of the nth Fresnel Zone

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Diffraction Loss

Diffraction Loss occurs from the blockage of secondary waves such that only a portion of the energy is diffracted around the obstacle

ht hr

Tx Rxl1 l2

d

First Fresnel Zone Points l1+l2-d =(λ/2)

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Diffraction Loss

Diffraction Loss occurs from the blockage of secondary waves such that only a portion of the energy is diffracted around the obstacle

ht hr

Tx Rxl1l2

d

First Fresnel Zone Points l1+l2-d =(λ/2)

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Diffraction Loss

Diffraction Loss occurs from the blockage of secondary waves such that only a portion of the energy is diffracted around the obstacle

ht hr

Tx Rxl1

l2

d

First Fresnel Zone Points l1+l2-d =(λ/2)

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Diffraction Loss

Diffraction Loss occurs from the blockage of secondary waves such that only a portion of the energy is diffracted around the obstacle

ht hr

Tx Rx

l1l2

d

First Fresnel Zone Points l1+l2-d =(λ/2)

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Diffraction Loss

Diffraction Loss occurs from the blockage of secondary waves such that only a portion of the energy is diffracted around the obstacle

ht hr

Tx Rx

l1 l2d

First Fresnel Zone Points l1+l2-d =(λ/2)

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Diffraction Loss

Diffraction Loss occurs from the blockage of secondary waves such that only a portion of the energy is diffracted around the obstacle

ht hr

Tx Rxl1 l2

d

Second Fresnel Zone Points l1+l2-d = λ

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Diffraction Loss

Diffraction Loss occurs from the blockage of secondary waves such that only a portion of the energy is diffracted around the obstacle

ht hr

Tx Rxl1l2

d

Third Fresnel Zone Points l1+l2-d = (3λ/2)

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Knife-Edge Diffraction Scenarios

ht hr

Tx Rx

d1 d2

h (-ve)

h & ν are –ve Relative Low Diffraction Loss

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ht hr

Tx Rx

d1 d2

h =0

Knife-Edge Diffraction Scenarios

h =0 Diffraction Loss = 0.5

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Knife-Edge Diffraction Scenarios

ht hr

Tx Rx

d1 d2

h (+ve)

h & ν are +ve Relatively High Diffraction Loss

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Knife-Edge Diffraction Model

The field strength at point Rx located in the shadowed region is a vector sum of the fields due to all of the secondary Huygen’s sources in the plane above the knife-edge

Electric Field Strength, Ed, of a Knife-Edge Diffracted Wave is given By:

E0: Free-Space Field Strength in absence of Ground Reflection and Knife-Edge DiffractionF(ν) is called the complex Fresnel Integral

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Diffraction Gain

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Diffraction Gain Approximation

d

d

d

d

G dB

G dB

G dB

G dB

0 1

20 log 0.5 0.62 1 0

20 log 0.5exp 0.95 0 1

20

d

G dB

2log 0.4 0.1184 0.38 0.1 1 2.4

0.22520 log 2.4

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Multiple Knife-Edge Diffraction

ht hr

Tx Rx

d

In the practical situations, especially in hilly terrain, the propagation path may consist of more than one obstruction.

Optimistic solution (by Bullington): The series of obstacles are replaced by a single equivalent obstacle so that the path loss can be obtained using single knife-edge diffraction models.