Wireless Communication Channels: Large-Scale Pathloss

1. Wireless Communication Channels: Large-Scale Pathloss

2. Diffraction

3. Diffraction Diffraction allows radio signals to propagate behind obstacles between a transmitter and a receiver ht hr

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. Knife-Edge Diffraction Geometry α h Tx Rx γ β d2 d1 hobs ht hr < < Δ: Excess Path Length (Difference between Diffracted Path and Direct Path)

6. Fresnel Zone Diffraction Parameter (ν) Ф: Phase Difference between Diffracted Path and Direct Path) Fresnel Zone Diffraction Parameter (ν) • 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

7. Fresnel Zones 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 From “Wireless Communications: Principles and Practice” T.S. Rappaport rn: Radius of the nth Fresnel Zone

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 l2 l1 Tx Rx d ht hr FirstFresnel Zone Points  l1+l2-d =(λ/2)

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 l2 l1 Tx Rx d ht hr FirstFresnel Zone Points  l1+l2-d =(λ/2)

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 l1 Tx Rx l2 d ht hr FirstFresnel Zone Points  l1+l2-d =(λ/2)

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 Tx Rx d l2 l1 ht hr FirstFresnel Zone Points  l1+l2-d =(λ/2)

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 Tx Rx d l1 l2 ht hr FirstFresnel Zone Points  l1+l2-d =(λ/2)

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 l2 l1 Tx Rx d ht hr SecondFresnel Zone Points  l1+l2-d = λ

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 l2 l1 Tx Rx d ht hr ThirdFresnel Zone Points  l1+l2-d = (3λ/2)

15. Knife-Edge Diffraction Scenarios Tx Rx h (-ve) d2 d1 ht hr • h & ν are –ve • Relative Low Diffraction Loss

16. Knife-Edge Diffraction Scenarios Tx Rx h =0 d2 d1 ht hr • h =0 • Diffraction Loss = 0.5

17. Knife-Edge Diffraction Scenarios Tx Rx h (+ve) d2 d1 ht hr • h & ν are +ve • Relatively High Diffraction Loss

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 Diffraction F(ν) is called the complex Fresnel Integral

19. Diffraction Gain

20. Diffraction Gain Approximation

21. Multiple Knife-Edge Diffraction • 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. Tx Rx d ht hr

22. Scattering

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. 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 Protuberance Θi : Angle of Incidence λ : Wavelength Smooth Surface  Minimum to maximum protuberance h is less than hc Rough Surface  Minimum to maximum protuberance h is greater than hc

25. Reflection Coefficient for Rough Surfaces Γrough: Reflection Coefficient for Rough Surfaces Γ : Reflection Coefficient for Smooth Surfaces ρS: Scattering Loss Factor σh: Standard deviation of the surface height h about the mean surface height I0(.) : Bessel Function of the first kind and zero order