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Diffraction.ppt
- 1. Wireless Communication Channels: Large-Scale Pathloss
- 2. Diffraction
- 3. 3 Diffraction Diffraction allows radio signals to propagate behind obstacles between a transmitter and a receiver ht hr
- 4. 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. 5 Knife-Edge Diffraction Geometry ht hr d1 d2 hobs h Tx Rx α β γ Δ: Excess Path Length (Difference between Diffracted Path and Direct Path) h h d h d h d d d d d d d d d d h x h d d where x for x d d 2 2 2 2 2 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 1 , 1 1 1 2 2 < <
- 6. 6 Ф: Phase Difference between Diffracted Path and Direct Path) d d h d d 2 1 2 1 2 2 2 2 Assume h d d h h d d d d 1 2 1 2 1 2 tan tan d d d d h d d d d 1 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
- 7. 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 n n d d r n d d n r d d d d 2 1 2 1 2 1 2 1 2 2 2 rn: Radius of the nth Fresnel Zone
- 8. 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 Rx l1 l2 d First Fresnel Zone Points l1+l2-d =(λ/2)
- 9. 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 Rx l1 l2 d First Fresnel Zone Points l1+l2-d =(λ/2)
- 10. 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 Rx l1 l2 d First Fresnel Zone Points l1+l2-d =(λ/2)
- 11. 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 l1 l2 d First Fresnel Zone Points l1+l2-d =(λ/2)
- 12. 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 l2 d First Fresnel Zone Points l1+l2-d =(λ/2)
- 13. 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 Rx l1 l2 d Second Fresnel Zone Points l1+l2-d = λ
- 14. 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 Rx l1 l2 d Third Fresnel Zone Points l1+l2-d = (3λ/2)
- 15. 15 Knife-Edge Diffraction Scenarios ht hr Tx Rx d1 d2 h (-ve) h & ν are –ve Relative Low Diffraction Loss
- 16. 16 ht hr Tx Rx d1 d2 h =0 Knife-Edge Diffraction Scenarios h =0 Diffraction Loss = 0.5
- 17. 17 Knife-Edge Diffraction Scenarios ht hr Tx Rx d1 d2 h (+ve) h & ν are +ve Relatively High Diffraction Loss
- 18. 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
- 20. 20 Diffraction Gain Approximation 𝐺𝑑 𝑑𝐵 = 0 𝜈 ≤ −1 𝐺𝑑 𝑑𝐵 = 20 log 0.5 − 0.62𝜈 − 1 ≤ 𝜈 ≤ 0 𝐺𝑑 𝑑𝐵 = 20 log 0.5𝑒𝑥𝑝 −0.95𝜈 0 ≤ 𝜈 ≤ 1 𝐺𝑑 𝑑𝐵 = 20 log 0.4 − 0.1184 − 0.38 − 0.1𝜈 2 1 ≤ 𝜈 ≤ 2.4 𝐺𝑑 𝑑𝐵 = 20 log 0.225 𝜈 𝜈 > 2.4 A rule of thumb is that as long as 55% (many materials say 60%) of the first Fresnel zone is kept clear, the diffraction loss will be minimal.
- 21. 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.
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