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Wireless Communication Channels: Large-Scale Pathloss. Diffraction. Diffraction. Diffraction allows radio signals to propagate behind obstacles between a transmitter and a receiver. h t. h r. Huygen’s Principle & Diffraction. - PowerPoint PPT Presentation
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Wireless Communication Channels: Large-Scale Pathloss
Diffraction
© Tallal Elshabrawy 3
Diffraction
Diffraction allows radio signals to propagate behind obstacles between a transmitter and a receiver
ht
hr
© Tallal Elshabrawy 4
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.
© Tallal Elshabrawy 5
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
<<
© Tallal Elshabrawy 6
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
© Tallal Elshabrawy 7
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
© Tallal Elshabrawy 8
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)
© Tallal Elshabrawy 9
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)
© Tallal Elshabrawy 10
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)
© Tallal Elshabrawy 11
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)
© Tallal Elshabrawy 12
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)
© Tallal Elshabrawy 13
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
© Tallal Elshabrawy 14
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)
© Tallal Elshabrawy 15
Knife-Edge Diffraction Scenarios
ht hr
Tx Rx
d1 d2
h (-ve)
h & ν are –ve Relative Low Diffraction Loss
© Tallal Elshabrawy 16
ht hr
Tx Rx
d1 d2
h =0
Knife-Edge Diffraction Scenarios
h =0 Diffraction Loss = 0.5
© Tallal Elshabrawy 17
Knife-Edge Diffraction Scenarios
ht hr
Tx Rx
d1 d2
h (+ve)
h & ν are +ve Relatively High Diffraction Loss
© Tallal Elshabrawy 18
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
© Tallal Elshabrawy 19
Diffraction Gain
© Tallal Elshabrawy 20
Diffraction Gain Approximation
𝐺𝑑ሺ𝑑𝐵ሻ= 0 𝜈≤ −1
𝐺𝑑ሺ𝑑𝐵ሻ= 20logሺ0.5− 0.62𝜈ሻ − 1 ≤ 𝜈≤ 0
𝐺𝑑ሺ𝑑𝐵ሻ= 20log൫0.5𝑒𝑥𝑝ሺ−0.95𝜈ሻ൯ 0 ≤ 𝜈≤ 1
𝐺𝑑ሺ𝑑𝐵ሻ= 20logቀ0.4−ඥ0.1184−ሺ0.38− 0.1𝜈ሻ2ቁ 1 ≤ 𝜈≤ 2.4
𝐺𝑑ሺ𝑑𝐵ሻ= 20log൬0.225𝜈 ൰ 𝜈> 2.4
© Tallal Elshabrawy 21
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.
Scattering
© Tallal Elshabrawy 23
Scattering
The actual received signal in a mobile radio environment is often stronger than what is predicted by reflection and diffraction
Reason:
When a radio wave impinges on a rough surface, the reflected energy is spread in all directions due to scattering
© Tallal Elshabrawy 24
Reflection Vs Scattering
Reflection: Flat surfaces that have much larger dimension than wavelength
Scattering: When the medium consists of objects with dimensions that are small compared to the wavelength
Testing Surface Roughness using Rayleigh Criterion
hc : Critical Height of Surface ProtuberanceΘi : Angle of Incidenceλ : Wavelength
Smooth Surface Minimum to maximum protuberance h is less than hc
Rough Surface Minimum to maximum protuberance h is greater than hc
© Tallal Elshabrawy 25
Γrough: Reflection Coefficient for Rough SurfacesΓ : Reflection Coefficient for Smooth SurfacesρS : Scattering Loss Factorσh : Standard deviation of the surface height h about the mean surface heightI0(.) : Bessel Function of the first kind and zero order
Reflection Coefficient for Rough Surfaces