1. Wireless Communication Channels: Large-Scale Pathloss

2. Diffraction

3. © Tallal Elshabrawy 3 Diffraction Diffraction allows radio signals to propagate behind obstacles between a transmitter and a receiver htht hrhr

4. © 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.

5. © Tallal Elshabrawy 5 Knife-Edge Diffraction Geometry htht hrhr d1d1 d2d2 h obs h Tx Rx α β γ Δ: Excess Path Length (Difference between Diffracted Path and Direct Path) <<

6. © Tallal Elshabrawy 6 Ф: Phase Difference between Diffracted Path and Direct Path) Fresnel Zone Diffraction Parameter ( ν )  ν 2 =2, 6, 10 … corresponds to destructive interference between direct and diffracted paths  ν 2 =4, 8, 12 … corresponds to constructive interference between direct and diffracted paths

7. © 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 r n : Radius of the n th Fresnel Zone

8. © 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 htht hrhr Tx Rx l1l1 l2l2 d First Fresnel Zone Points  l 1 +l 2 -d =(λ/2)

9. © 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 htht hrhr Tx Rx l1l1 l2l2 d First Fresnel Zone Points  l 1 +l 2 -d =(λ/2)

10. © 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 htht hrhr Tx Rx l1l1 l2l2 d First Fresnel Zone Points  l 1 +l 2 -d =(λ/2)

11. © 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 htht hrhr Tx Rx l1l1 l2l2 d First Fresnel Zone Points  l 1 +l 2 -d =(λ/2)

12. © 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 htht hrhr Tx Rx l1l1 l2l2 d First Fresnel Zone Points  l 1 +l 2 -d =(λ/2)

13. © 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 htht hrhr Tx Rx l1l1 l2l2 d Second Fresnel Zone Points  l 1 +l 2 -d = λ

14. © 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 htht hrhr Tx Rx l1l1 l2l2 d Third Fresnel Zone Points  l 1 +l 2 -d = (3λ/2)

15. © Tallal Elshabrawy 15 Knife-Edge Diffraction Scenarios htht hrhr Tx Rx d1d1 d2d2 h (-ve)  h & ν are –ve  Relative Low Diffraction Loss

16. © Tallal Elshabrawy 16 htht hrhr Tx Rx d1d1 d2d2 h =0 Knife-Edge Diffraction Scenarios  h =0  Diffraction Loss = 0.5

17. © Tallal Elshabrawy 17 Knife-Edge Diffraction Scenarios htht hrhr Tx Rx d1d1 d2d2 h (+ve)  h & ν are +ve  Relatively High Diffraction Loss

18. © 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, E d, of a Knife-Edge Diffracted Wave is given By: E 0 : Free-Space Field Strength in absence of Ground Reflection and Knife-Edge Diffraction F(ν) is called the complex Fresnel Integral

19. © Tallal Elshabrawy 19 Diffraction Gain

20. © Tallal Elshabrawy 20 Diffraction Gain Approximation

21. © Tallal Elshabrawy 21 Multiple Knife-Edge Diffraction htht hrhr 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.

22. Scattering

23. © 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

24. © 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 h c : Critical Height of Surface Protuberance Θ i : Angle of Incidence λ : Wavelength Smooth Surface  Minimum to maximum protuberance h is less than h c Rough Surface  Minimum to maximum protuberance h is greater than h c

25. © Tallal Elshabrawy 25 Γ rough : Reflection Coefficient for Rough Surfaces Γ : Reflection Coefficient for Smooth Surfaces ρ S : Scattering Loss Factor σ h : Standard deviation of the surface height h about the mean surface height I 0 (.) : Bessel Function of the first kind and zero order Reflection Coefficient for Rough Surfaces