Session 4: Diffraction Prof. Katsuyuki Haneda, Clemens Icheln Dept. - - PowerPoint PPT Presentation

Aalto University School of Electrical Engineering

ELEC-E4750

Radiowave Propagation and Scattering

Session 4: Diffraction

• Prof. Katsuyuki Haneda, Clemens Icheln
• Dept. of Electronics and Nanoengineering

ELEC-E4750 03.10.2018 1

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Course books, current topics and exercises

• Course books
• Main books used in this course:
• S. Saunders, Antennas and Propagation for Wireless Communication Systems, Chapters 3, 5,

6-8, 10, 12 15, Wiley.

• H. L. Bertoni, Radio propagation for modern wireless systems, Chapters 2-6, Prentice Hall.
• A. F. Molisch, Wireless Communications, Chapters 1, 5 and 8, Wiley.
• R. Vaughan and J. B. Andersen, Channels, propagation and antennas for mobile

communications, Chapter 3.2.1, IEE Press.

• Supplemental book (for prerequisites)
• D. M. Pozar, Microwave Engineering, Chapters 1 and 14, Wiley.
• Topic 3: Reflection, transmission and diffraction (Ch. 3, Ch. 5)
• Exercise 1: Frequency dependency of reflection and transmission
• Exercise 2: Diffraction due to an absorbing knife edge
• Topic 4: Diffraction (Ch. 3, Ch. 5)
• Exercise 1: Modeling human-body blockage
• Exercise 2: Diffraction losses due to multiple screens
• Exercise 3 (bonus): Diffraction due to building corner

2

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Schedule

3 Wk Date Location New topics, lectures and deadlines 37

• Mon. 10 Sep.

R032/A116 seminar room Introduction

• Wed. 12 Sep.

R032/A113 simlab Lecture 1: prerequisite 38

• Mon. 17 Sep.

R032/A116 Exercise return session 1

• Wed. 19 Sep.

R032/A113 Lecture 2: reflection and transmission 39

• Mon. 24 Sep.

R032/A116 Exercise return session 2

• Wed. 26 Sep.

R032/A113 Lecture 3: reflection, transmission and diffraction 40

• Mon. 01 Oct.

R032/A116 Exercise return session 3 (a)

• Wed. 03 Oct.

R032/A113 Lecture 4: diffraction (b) 41

• Mon. 08 Oct.

R032/A116 Exercise return session 4

• Wed. 10 Oct.

R032/A113 Lecture 5: scattering a: Pasi and Usman are present. b: Lecturer: Clemens Icheln

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Human Blockage Loss

4

• An absorbing knife-edge diffraction model (with multiple

edges) reproduces the measurement well

Rx antenna Tx antenna Seen from top:

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Q1: Which statement is incorrect?

A. Curve “a” fluctuates the most because of the shortest wavelength. B. Curve “c” is for the lowest frequency as the loss is smallest in LOS. C. Human blockage is more significant as the frequency is higher. D. With increasing frequency, absorption becomes more and more significant than scattering.

Link geometry Additional loss vs. free-space at three different frequencies a b c

✓

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Validation of human blockage loss model

6 TX RX

• Diffraction model

(absorbing rectangle with four knife edges)

• vs. measurements

(with real human) Tx Rx x y f Azimuth orientation of human body blocking the link: f

AKE

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Multi-Screen Link Blockage

• Examples: terrestrial links over several hills

and cellular links over several rooftops.

7

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Divergence Factor

• … describes how much the energy is spread after some

propagation distance

x y z θ R O φ

Divergence factor

2 2 1 R2 R1

           r r A A

Small area ΔAR

      d d sin d d sin

2 2 R2 2 1 R1

        r A r A

Power spectral density

R2 R1 1 2

A A S S

R R R R

   

  2 2 tx tx 2 2 1 2 1 tx tx

4 4 r G P r r r G P             

Spherical wave from a point source (at origin)

R1 = r1: R2 = r2:

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Diffraction of Spherical Waves

9

r0 ΔAρ θ Point source r ρ ΔAr Absorbing screen dφ dθ

~sin(d)·(r+r0)

top view side view

~sin(d)·r

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r0 ΔAρ θ Point source r ρ ΔAr Absorbing screen dφ dθ Q2: Which equations are correct? Choose two!

A. B. answer. C. D.   



d d ) ( 0      r r A   d d ) ( 0      r r Ar   d d ) ( 0      r r r Ar    



d d ) ( 0      r A

✓ ✓

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Diffraction behind a screen

11

Divergence factor:

r r r r A A

r

    



• Diffracted field for ρ << r0

 Diffracted field in general

   

  k kr

e D e r e E

j /4 j j D

) ( ) , (

  

  ) ( ) ( ) , (

) ( j /4 j D

r r r r e D e r E

r r k

 

  

 



r0 ΔAρ θ Point source r ρ ΔAr Absorbing screen dφ dθ

D(q) = - 1 2pk 1+cosq 2sinq

diffraction coefficient for GTD solution of an absorbing screen

(see slides of lecture #3)

where

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Diffraction behind a second screen

12

ΔAρ θ Point source ΔAr Absorbing screen #2 dφ dθ r1 Absorbing screen #1 r ρ r0

top view side view

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Q3: Which is the correct Divergence Factor valid behind the second diffraction from two half-plane absorbing screens?

A. First choice is not a right answer. B. Second choice is a right answer. C. Third choice is not a right answer. D. None of above. r r r r A A

r

   

1 1





r r r r r r r r r A A

r

        

1 1 1





r r r r r r A A

r

      

1 1

 



ΔAρ θ Point source ΔAr Absorbing screen #2 dφ dθ r1 Absorbing screen #1 r ρ r0

✓

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Diffraction behind a second screen

14

• Diffracted field for ρ << r1
• Divergence factor

 Diffracted field in general

    

   k r r k

e D e r r r r e D e E

j 2 /4 j 1 1 ) ( j 1 /4 j D

) ( ) ( ) ( ) , (

1

    

   ) ( ) ( ) ( ) , (

1 1 ) ( j 2 1 /2 j D

1

r r r r r r e D D e r E

r r r k

  

   

  



r r r r r r A A

r

      

1 1

 



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Deygout Method for multiple knife edges

15

Main edge ) ( 4 ) ( ˆ ) ( ) ( ˆ

4 3 2 1 3 2 1

d d d d D D D E          

෡ 𝐸1 is the diffraction coefficient when Rx ( : Tx) is replaced by

the main edge as a virtual secondary receiver ( : secondary source).

෡ 𝐸3 ෡ 𝐸3

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Q4: Which statement is incorrect when calculating the pathloss for the illustrated hilly terrain using the Deygout method?

A. The main edge is hill #2. B. The diffraction coefficient of hill #3 is calculated with a virtual source located at the tip of hill #2. C. The diffraction coefficient of hill #4 may be inaccurate when using the GTD. D. The diffraction coefficient of hill #4 is calculated using d3, d4 and d5.

✓

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Diffraction from a Right-Angle Wedge

• … is applicable to determine field attenuation due to a

building corner

𝐸 𝜒, 𝜒′ = 𝐸1 + 𝐸2 + Υ𝐹,𝐼(𝐸3 + 𝐸4) 𝐸1,2 = −1 3 2𝜌𝑙 cot 𝜌 ± (𝜒 − 𝜒′) 3 𝐸3,4 = −1 3 2𝜌𝑙 cot 𝜌 ± (𝜒 + 𝜒′) 3 Υ𝐼 = 1 Υ𝐹 = −1 for perpendicular polarization for parallel polarization Right-angle wedge 𝜒 𝑃 𝜒′ Tx Rx

Incident wave shadow boundary Reflected wave shadow boundary

Diffraction coefficient from GTD for a wedge of perfect electric conductor

Disclaimer: The formulas are from Section 5.3c of Bertoni’s book. However, prof. Haneda was not able to track exact derivations of these formulas after reading the books of Bertoni and McNamara. For now we therefore take these formulas as granted for the practical study of building-corner loss in exercise problem 5.3 (bonus exercise).

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Q5: Which statements are correct? (can be more than 1)

A. For a deep shadowed region behind a corner, knife-edge diffraction estimates greater diffraction loss than uniform theory of diffraction. B. When θd < 0o, there is no diffracted field. C. PEC wedges give polarization-dependent diffraction coefficients. D. Diffraction coefficient of infinitesimally-thin PEC screen depends on polarization.

Additional loss vs. free-space Diffraction over a PEC building corner Top view

• 10

10 20 30 40 50

Diffraction angle [ d

°]

• 50
• 40
• 30
• 20
• 10

10

RX signal amplitude [dB]

Uniform Theory of Diffraction Absorbing Knife Edge Diffraction

✓ ✓

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Next Contact Sessions

• Learning outcomes of the exercise problems for topic 5 are to

– Explain the influence of radio propagation mechanisms on images obtained in remote sensing (problem 1) – Understand the effects of surface roughness on the reduction of specular reflection power (problem 2)

• During the contact sessions, you

– solve the exercise problems by referring to relevant parts of the course books.

• a limited number of course books are available in the room.

– are encouraged to discuss with other students and teachers. – should contact teachers once your solutions are ready.

• if you prepare exercise solutions in an electronic format (recommended), upload the

solution to MyCourses first and then contact teachers.

– will propose points for your ready solutions to the teachers. – will not get exercise points without discussing with teachers!

• The discussions MUST happen in the contact sessions.

– Are reminded that four exercise problems must be completed in total before the end of the next Monday session on the 8th of October.