EE 447 Mobile and Wireless Communications Fall 2006 Outdoor Propagation Models

1. EE 447 Mobile and Wireless Communications Fall 2006 Outdoor Propagation Models Richard S. Wolff, Ph. D. rwolff@montana.edu 406 994 7172 509 Cobleigh Hall

2. Small scale and large scale fading

3. Free space propagation • Friis free space equation (fancy way of saying that energy is conserved!)

4. Free Space Path Loss The total received power Antenna effective area

5. Free Space Path Loss Free Space Path Loss General Path Loss formula where Lp(do) is path loss at the reference distance d0 loss exponent γ is the slope of the average increase in path loss with dB-distance, Shadowing S denotes a zero-mean Gaussian random variable with standard deviation σ.

6. Received power reference point A few conditions and useful terms • Applies to received power in far-field (Fraunhofer region): D = largest dimension of transmitting antenna

7. Log notation frequently used

8. Free space path loss: practical application Convenient tool: http://www.terabeam.com/support/calculations/free-space-loss.php

9. Typical large-scale path loss exponents

10. Measured large-scale path loss

11. Basic propagation mechanisms • Reflection • Dimensions of reflector are large compared to l • Applies to surface of earth, buildings, etc. • Diffraction • Obstacle with sharp edges in path between T and R (could be totally blocking the path) • Depends on geometry of object, l, phase, polarization, etc. • Scattering • Objects small compared to l in path between T and R • Caused by rough surfaces, foliage, etc. • Absorption • Attenuation by solid materials (walls, etc.) • Rain

12. Reflection from smooth surface

13. Typical electromagnetic properties of materials

14. Reflected wave will 100% polarized perpendicular to plane of Incidence when qi is equal to the Brewster angle Reflection coefficients for parallel and perpendicular polarized fields

15. Classical 2-ray ground bounce model

16. ht hr r Path loss over reflecting surface Direct path is reflection coefficient indirect path Is phase difference between direct path and indirect path

17. Propagation near the earth’s surface Note fourth power dependence with distance!

18. Received signal power as a function of distance

19. Effect of antenna height on received power

20. Diffraction • Allows radio waves to propagate over the horizon • Radio waves can propagate into shadowed (obstructed) areas • Governed by Huygen’s principle: • all points on a wave front can be considered as point sources to produce secondary wavelets • Secondary wavelets combine (vector sum) to form a new wave in the direction of propagation

21. Wavelets form on knife edge, transmit a new wave into shadowed zone Huygen’s wavelet approach

22. Fresnel zones: locus of points of equal path length (phase) relative to direct path

23. Examples of Fresnel diffraction geometries Figure 4.12 Illustration of Fresnel zones for different knife-edge diffraction scenarios.

24. Fresnel Zone Fresnel zone clearance: practical application • Typically, 20% Fresnel Zone blockage introduces little signal loss to the link. Beyond 40% blockage, signal loss will become significant http://www.terabeam.com/support/calculations/fresnel-zone.php

25. Effect of obstructions: treat with knife-edge diffraction

26. Knife-edge diffraction loss

27. Multiple knife-edge diffraction –used to calculate propagation in rough terrain

28. Propagation modeling for diffraction - RF Propcalc

29. Scattering • Important when the dimensions of obstructions or surface features are small relative to l • Rayleigh criterion: A surface is smooth if the peak to peak protuberances Are less than hc

30. Measured results: scattering from a stone wall

31. Absorption: attenuation caused by rain

32. Log-normal (Gaussian) shadowing • Loss along two different paths with same d can vary greatly • Measured signals with same d can deviate from average given by path loss equation • Measurements show that is random and distributed log-normally (normal in dB) about the mean,

33. Log-normal shadowing

34. Normalized Gaussian distribution, zero mean Gaussian distribution

35. y0 Q, erf and erfc functions

36. Q, erf and erfc functions Note: Q(-z) = 1-Q(z) Q(0)= 1/2 If the distribution has a non-zero mean m, z =(y-m)/s

37. Q, erf and erfc functions Note erfc(z) = 1-erf(z)

38. Q, erf and erfc functions Some useful relationships:

39. Log-normal shadowing Probability that the received signal level (in dB) will exceed a level g: Probability that the received signal level (in dB) will be less than a level g:

40. Log-normal shadowing - example Suppose at a distance d, the mean received power level P r(d) is -70dBm and the standard deviation s is 10 dB. Find the probability that the received signal level (in dB) will exceed a level g= -60dBm: Pr[P r(d)>60]=Q{(-60+70)/10}=Q(1)=1/2erfc(1/1.414) Pr[P r(d)> -60]=1/2{1-erf(.707)} Pr[P r(d)> -60]= .16

41. Multiple received rays due to scattering Ricean: Nirect and scattered rays combine at receiver Rayleigh: No direct ray (only scattered rays reach receiver)

42. Rayleigh distribution

43. Comparison of Rayleigh and Ricean distributions A represents the power in the direct signal