XI Influence of Terrain and Vegetation Terrain

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 Polytechnic University, Brooklyn, NY © 2002 by H. L. Bertoni

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

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

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

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

Example of Wedge Diffraction at 900 MHz 12. 9 188 o 5. 71 o 2. 29 o 3. 42 o 2. 29 o 168. 6 o 5. 71 o 10 50 500 Polytechnic University, Brooklyn, NY 500 © 2002 by H. L. Bertoni 90 500 6

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

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

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

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

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. Polytechnic University, Brooklyn, NY © 2002 by H. L. Bertoni

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

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

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

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

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

Rows of Houses on a Hill in San Francisco See Polytechnic University, Brooklyn, NY EL 675 -405. ppt © 2002 by H. L. Bertoni 17

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

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

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

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

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 d. B Waves propagate as exp[-j(k+k)L] k = k’ - jk” is the change in phase constant and attenuation constant k depends on polarization and direction of propagation At longer distances incoherent field dominates Isolated trees vs. small group of trees vs. forests Polytechnic University, Brooklyn, NY © 2002 by H. L. Bertoni 22

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

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

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

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

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

Effect of Trees on Rooftop Fields for a 900 MHz Plane Wave Incident at a = 0, 0. 5 o Polytechnic University, Brooklyn, NY © 2002 by H. L. Bertoni 28