1. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni1 XI. Influence of Terrain and Vegetation Terrain Diffraction over bare, wedge shaped hills Diffraction of wedge shaped hills with houses Diffraction over rounded hills with houses Vegetation Effective propagation constant in trees Forest with a uniform canopy of trees Rows of trees next to rows of houses

2. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni2 Influence of Terrain on Path Loss Adapting theoretical results to various terrain conditions.

3. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni3 Diffraction Loss Over Bare, Wedge Shaped Hill

4. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni4 Heuristic Wedge Diffraction Coefficient for Impedance Boundary Conditions UTD diffraction coefficient For TE or TM polarization, plane wave reflection coefficients Partial Coefficients  ’ (2-n)   /2-  ’  -(n-1/2) 

5. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni5 Transition Function for Wedge Diffraction

6. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni6 Example of Wedge Diffraction at 900 MHz 500 500 10 50 90 12.9 5.71 o 188 o 2.29 o 168.6 o 5.71 o 3.42 o

7. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni7 Example – Arguments of Transition Functions

8. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni8 Example – Reflection and Partial Diffraction Coefficients

9. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni9 Example – Diffraction Coefficient

10. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni10 Example – Path Gain and Path Loss

11. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni11 Wedge Shaped Hills Covered With Houses Path gain is the sum of the free space path gain, the total excess gain due to the buildings, and the gain for diffraction to mobile. Compute the total excess gain by replacing the buildings by absorbing half-screens and use numerical integration to go from one screen to the next. Use line source at the transmitter location for the initial field.

12. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni12 Example – Numerical Evaluation of Roof Top Fields for Houses on Wedge Shaped Hill -250

13. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni13 Example – Path Gain for Point Source Excitation from Line Source Results

14. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni14 Diffraction Over an Idealized Wedge Shaped Hill with Houses – Analytic Approach

15. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni15 Comparison of Analytic and Numerical Approaches for House at R B =4000m

16. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni16 Comparison of Analytic Approaches for House at R C = 1000m

17. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni17 See EL675-405.ppt Rows of Houses on a Hill in San Francisco

18. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni18 Diffraction Past Houses on a Cylindrical Hill

19. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni19 Geometry for Finding Path Gain in the Presence of Cylindrical Hill At houses beyond the hill At houses on the backside of hill Tangent Points Tangent Point

20. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni20 Diffraction Coefficient for Cylindrical Hills

21. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni21 Path Gain at Rooftops of Houses on Cylindrical Hills

22. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni22 Influence of Trees Canopy versus trunk For elevated base station, canopy is important For mobile to mobile links, trunk give dominant effect over short links Leaves and branches Scatter and absorb wave energy Mean field dominates over short distances For short distances, attenuation ≤ 20 dB Waves propagate as exp[-j(k+  )L]  =  ’ - j  ” is the change in phase constant and attenuation constant  depends on polarization and direction of propagation At longer distances incoherent field dominates Isolated trees vs. small group of trees vs. forests

23. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni23 and for Horizontal Propagation Through Canopy

24. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni24 Propagation to Mobile Inside the Forest Forest

25. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni25 Approximations for Mobile Inside Forest

26. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni26 Propagation to a Mobile in a Clearing Forest

27. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni27 Rows of Trees Next to Buildings Modify numerical integration to account for Partial transmission through trees

28. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni28 Effect of Trees on Rooftop Fields for a 900MHz Plane Wave Incident at  = 0, 0.5 o