XI. Influence of Terrain and Vegetation

Transcription

1 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 00 by H.L. Bertoni 1

2 Influence of Terrain on Path Loss Adapting theoretical results to various terrain conditions. α A θ α B h eff A C B Location : A - Use local angle α to compute Q B - Account for diffraction loss at top of hill, use local angle α B A to compute Q C - Use wedge diffration or creeping ray description of the fields going over the hill 00 by H.L. Bertoni

3 Diffraction Loss Over Bare, Wedge Shaped Hill R 1 φ φ ( n)π R α B R R1 + R PG PG R + = { } R 0 RR 1 where and PG 0 λ = 4π( R1 + R) = + D T( φφ, ) Q ( gpb) PG Qg 3. 50g 3. 37g 0. 96g with 3 PB PB PB PB g PB = 1 sinα B d λ { }{ } 00 by H.L. Bertoni 3

4 Heuristic Wedge Diffraction Coefficient for Impedance Boundary Conditions UTD diffraction coefficient w w w D φφ, D D Γ D Γ D T = w 1 n For TE or TM polarization, plane wave reflection coefficients 1 Γ0 = Γ π Γ Γ = EH, φ and n EH, φ n π Partial Coefficients D D w 1, w 34, 1 π ± φ φ = cot n πk n 1 π ± φ + φ = cot n πk n ± F kla φ φ [ ] ± F kla φ + φ where F [] is the transition function [ ] π/-φ φ φ-(n-1/)π φ (-n)π 00 by H.L. Bertoni 4

5 Transition Function for Wedge Diffraction RR 1 ± Argument : L = and a = ± β cos n N R + R π β 1 ± where N are the integers closest to β ± π πn For broad wedge 1 < n < 1.5 and shallow diffraction ( π < φ- φ < 15. π) and ( π < φ + φ < π) + N ( φ φ ) = 1; N ( φ φ ) = 0 and N + = ( + ) = φ + φ 1; N φ φ 0 φ φ ( φ φ ) = π + a cos n ; a φ φ = φ φ ( φ + φ ) = π + + a cos n ; a φ + φ = cos cos φ φ φ + φ 00 by H.L. Bertoni 5

6 Example of Wedge Diffraction at 900 MHz 188 o 5.71 o.9 o 3.4 o o o o o o o Wedge angle π n = ( π Wedge angle) π = Half width of transition zone is the same as the Fresnel width W = f = = RR 1 λ R + R = 1. 9m by H.L. Bertoni 6

7 Example Arguments of Transition Functions k = πλ= 6π RR L = = R + R = 500 o o φ = 3.40 ( πrad) ; φ = ( π rad) φ- φ + = π ; φ φ = π + kla ( φ φ ) = 6000πcos ( π π) = 154. π kla ( φ φ ) = 6000πcos ( π) = 8. 74π kla kla + = = = = φ + φ 6000πcos π π 59. 4π φ + φ 6000πcos π 59. 4π Since all arguments >> π, F 1 in all terms []= 00 by H.L. Bertoni 7

8 Example Reflection and Partial Diffraction Coefficients Angle of incidence : π φ = π π φ- n-1 π π π For Vertical Polarization and εr = 15 : 1 o o sinθt = sin and θt = εr cosθ cosθt ΓH = = ε cosθ + cosθ Partial diffraction coefficients : D D w 1, w 34, = = r T o = = = ( φ- φ = π, φ + φ = π) 1 π ± π π π = cot π ± π π π = cot by H.L. Bertoni 8

9 Example Diffraction Coefficient D = D + D + Γ D + D w w w w ( + ) = = Using Felsen coefficient for angle = [ + ] θ = π φ φ π o = π D = πk θ π θ = π 6π π. 055π = by H.L. Bertoni 9

10 Example Path Gain and Path Loss λ R + R 1 PG = D 4π( R1 + R) RR 1 D = λ RR( R + R) = 13 4π 4π = PL = log. 65 = db ( ) For antenna in free space PG PL 0 0 λ = = π( R1 + R) = log = db by H.L. Bertoni 10

11 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. 00 by H.L. Bertoni 11

12 Example Numerical Evaluation of Roof Top Fields for Houses on Wedge Shaped Hill d f = 50m = 900MHz For line source radiation e jkr kr by H.L. Bertoni 1

13 Example Path Gain for Point Source Excitation from Line Source Results For line source Excess Path Gain For point source = ELS 0log 0log ELS 10log 1 kr = + ( kr) λ PG = 10log + Excess Path Gain 4πR λ = 10log + 0log 4 R kr E LS π λ = 10log + 0log ELS 8πR 1/ 3 At RB = 4000m, R = 450mand PG = 10log π 450 =. db At 13 = 1000 = 150 = 10 / R, and log π 150 = C m R m PG. db 00 by H.L. Bertoni 13

14 Diffraction Over an Idealized Wedge Shaped Hill with Houses Analytic Approach θ C θ B α 1 α α B R C R 1 R B At rooftops beyond the hill D B PGB = λ θ 4π RR 1 B R1 + R At rooftops on backside of hill PG C = λ 4π D θc RR R + R 1 C 1 B C { Qg ( P1) Qg ( P) Qg ( PB) } Qg N P1 C 00 by H.L. Bertoni 14

15 Comparison of Analytic and Numerical Approaches for House at R B =4000m Since Tx is at the same elevation as the highest rooftop α1 = θc = tan = rad and αb = θb = tan = rad α = θ θ = rad C B 3 P P P P P Also g = sin α λ d and Q( g )= 3. 50g 3. 37g g = = = = = gp1 = , Q gp while gp 0. 78, Q gp and gp , Q gp Transition parameter S= k RR B sin ( θb )= > π so that FS 1 R + R Thus PG B D = λ 4π π θ π + θ ( θb ) = k B D θb RR R + R 1 B 1 B 1 B B = { Qg Qg Qg } = P1 P P3 13 ( PG) = 10. 5dB compared to 1. 1 db Good agreement! db 00 by H.L. Bertoni 15

16 Comparison of Analytic Approaches for House at R C = 1000m 1000 NC = = 0 50 D θ PG = C C = λ 4π D θc RR R + R 1 C 1 C Qg N P1 C = = PG 136. db compared to 17. 7dB C db Analytic method is too pesimistic 00 by H.L. Bertoni 16

17 Rows of Houses on a Hill in San Francisco See EL ppt 00 by H.L. Bertoni 17

18 Diffraction Past Houses on a Cylindrical Hill Scree n Heig ht ( m) 60 Tx Screen Placement (m) Field Stre ngt h(db) Screen Position (m) 00 by H.L. Bertoni 18

19 Geometry for Finding Path Gain in the Presence of Cylindrical Hill P 1 Tangent Points At houses beyond the hill R 1 θˆ P α B R R H R Tangent Point P 1 R 1 At houses on the backside of hill θˆ R H R 00 by H.L. Bertoni 19

20 Diffraction Coefficient for Cylindrical Hills MHz 1800 MHz D H D MHz 1800 MHz Hill Radius (m) Hill Radius (m) 00 by H.L. Bertoni 0

21 Path Gain at Rooftops of Houses on Cylindrical Hills At houses beyond the hill PG B = λ 4π ψθ De 1 kr R R Qg { } 1 PB where the attuation constant is 13 πr H d ψ = λ λ ˆ ψ At houses on the backside of hill PG C = λ 4π ψθˆ De H RR d = 50 m d = 100 m James Hill Radius (m) 00 by H.L. Bertoni 1

22 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 0 db Waves propagate as exp[-j(k+κ)l] κ = κ - jκ is the change in phase constant and attenuation constant κ depends on polarization and direction of propagation At longer distances incoherent field dominates Isolated trees vs. small group of trees vs. forests 00 by H.L. Bertoni

23 κ and κ for Horizontal Propagation Through Canopy Real ( κ ' ) rad/m Imag ( κ ' ) nep/m ad=5cm t=0.5mm ρd=350/m3 ac=1.6cm l=50cm ρc=/m3 θ i = 90 degrees vv-polarization hh-polarization Frequency (GHz) 1.0 Frequency (GHz) 1.5 ad= 5cm t =0.5mm ρd=350/m3 ac=1.6cm l=50cm ρc=/m3 θ i=90 degrees vv-polarization hh-polarization κ" = attnuation in nepers/m α = attenuation db/m α = 87. κ" At f = 1 GHz α = = 096. db/m Wavenumber in the trees kt = k+ κ = k so that ( k + κ) εr = k Polarizability 00 by H.L. Bertoni 3 ε κ 1+ k χ = εr 1 κ k At f = 1 GHz χ = 00 (. j011. )( 0π/) 3 = j0.010 r

24 Propagation to Mobile Inside the Forest θ = o 90 α α θ T θ C h BS Forest h m H T Wavenumber in vertical direction k cosθ T = k T ε cosθ = k ε ( 1 sin θ ) = k ε sin r r r T θ T R { [ θ] } [ θ] 3 PG = R T H h k T m r λ exp π Im ε 4 sin Provided ( H h ) kim ε sin T m r o Note that at 00 MHz and θ 90, [ ] = κ kim εr sin θ kim[ εr 1] kim k k = Im[ κ ] = = Im 005. j0094. π / For this case, HT hm = 6. 4m 00 by H.L. Bertoni 4

25 Approximations for Mobile Inside Forest For small angle α cosθ = sin α << ε 1 = κ/ k and sinθ = cosα 1 4 hbs HT PG / PG0 = R r sin θ 1 Since εr sinθt = sinθ, then cosθt = 1 sin θt = 1 1 εr εr For vertical E polarization εr cosθ εr sinα ε sinα h r BS HT T = εr cosθ+ cosθ 1 T ε sinα+ ε εr r r 1 1 R κ / k εr (The same approximate T is found for horizontal E polarization.) hbs HT PG = HT hm k k λ 4 ( ) exp{ ( ) Im [ κ / 4 ]} 4π R κ/ k { } ( HT hm) k [ κ k] exp Im / κ / k If hbs HT = 10m, HT hm = 5m and R= 1000m, then at f = 00MHz, PG / PG db = 0 db 00 by H.L. Bertoni 5

26 Propagation to a Mobile in a Clearing α h BS Forest H T R x h m Total field incident on the edge is E + ΓE = ( 1+ Γ) E = TE in in in in PG R T D hbs HT = D λ 1 λ 1 4π ρ 4πR R κ / k ρ. Therefore Use the transmission coefficient T into forest and Felsen diffraction coefficient Note that TD is approximately the heuristic diffraction coefficient for a dielectric edge. Effective height of the edge may be less than the tree height at low frequencies. 00 by H.L. Bertoni 6

27 Rows of Trees Next to Buildings Attenuating phase screen Absorbing phase screen s d Modify numerical integration to account for Partial transmission through trees 00 by H.L. Bertoni 7

28 Effect of Trees on Rooftop Fields for a 900MHz Plane Wave Incident at α = 0, 0.5 o Propagation Loss Relative to Free Space Loss (db) Degrees, No Tree 90 Degrees, Elliptical Tree a=m b=4m 90 Dgerees, Elliptical Tree a=4m b=4m 89.5 Degrees, No Tree 89.5 Degrees, Elliptical Tree a=m b=4m 89.5 Degrees, Elliptical Tree a=4m b=4m Number of Screens N 00 by H.L. Bertoni 8