1. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni1 IX. Modeling Propagation in Residential Areas Characteristics of City Construction Propagation Over Rows of Buildings Outside the Core Macrocell Model for High Base Station Antennas Microcell Model for Low Base Station Antennas

2. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni2 Characteristics of City Construction High rise core surrounded by large areas of low buildings Street grid organizes the buildings into rows

3. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni3 High Core & Low Buildings in New York

4. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni4 High Core & Low Buildings in Chicago, IL

5. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni5 Rows of Houses in Levittown, LI - 1951

6. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni6 Rows of Houses in Boca Raton, FL - 1980’s

7. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni7 Rows in Highlands Ranch, CO - 1999

8. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni8 The EM City - Ashington, England

9. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni9 Rows of Houses in Queens, NY

10. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni10 Rectangular Street Geometry in Los Angeles, CA

11. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni11 Uniform Height Roofs in Copenhagen

12. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni12 Predicting Signal Characteristic for Different Building Environments Small area average signal strength –Low building environment: Replace rows of buildings by long, uniform radio absorbers –High rise environment: Site specific predictions accounting for the shape and location of individual buildings Time delay and angle of arrival statistics –Site specific predictions using statistical distribution of building shapes and locations

13. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni13 Summary of Characteristics of the Urban Environment High rise core surrounded by large area having low buildings Outside of core, buildings are of more nearly equal height with occasional high rise building –Near core; 4 - 6 story buildings, farther out; 1 - 4 story buildings Street grid organizes building into rows –Side-to-side spacing is small –Front-to-front and back-to-back spacing are nearly equal (~50 m) Taylor prediction methods to environment, channel characteristic –Small area average power among low buildings found from simplified geometry –High rise environments and higher order channel statistics needs ray tracing

14. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni14 Propagation Past Rows of Low Buildings of Uniform Height Propagation takes place over rooftops Separation of path loss into three factors Free space loss to rooftops near mobile Reduction of the rooftop fields due to diffraction past previous rows Diffraction of rooftop fields down to street level Find the reduction in the rooftop fields using: –Incident Plane wave for high base station antennas –Incident cylindrical wave for low base station antennas

15. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni15 Three Factors Give Path Gain for Propagation Over Buildings     d R y HBHB hShS

16. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni16 Roof Top Fields Diffract Down to Mobile (First proposed by Ikegami) hBhB Because       and  2 ~ 0.1, rays  and  have nearly equal amplitudes. Adding power is approximately the same as doubling the power of .   

17. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni17 Comparison of Theory for Mobile Antenna Height Gain with Measurements Median value of measurements made at many locations for 200MHz signals in Reading, England, whose nearly uniform height  H B  =12.5 m.

18. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni18 Summary of Propagation Over Low Buildings A heuristic argument has been made for separating the path gain into three factors –Free space path gain to the building before the mobile –Reduction Q of the roof top fields due to diffraction past previous rows of buildings –Diffraction of the rooftop fields down to the mobile Diffraction of the rooftop gives the observed height gain for the mobile antenna.

19. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni19 Computing Q for High Base Station Antennas Approximating the rows of buildings by a series of diffracting screens Finding the reduction factor using an incident plane wave Settling behavior of the plane wave solution and its interpretation in terms of Fresnel zones Comparison with measurements

20. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni20 Approximations for Computing Q Effect of previous rows on the field at top of last row of building before mobile External and internal walls of buildings reflect and scatter incident waves - waves propagate over the tops of buildings not through the buildings. Gaps between buildings are usually not aligned with path from base station to mobile - replace individual buildings by connected row of of buildings. Variations in building height effect the shadow loss, but not the range dependence - take all buildings to be the same height. Forward diffraction through small angles is approximately independent of object cross section - replace rows of buildings by absorbing screens. For high base station antenna and distances greater than 1 km, the effect of the buildings on spherical wave field is the same as for a plane wave - Q(  ) found for incident plane wave. For short ranges and low antennas, the effect of buildings on spherical wave field is the same as for a cylindrical wave - find Q M for line source.

21. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni21 Method of Solution Physical Optical Approximations –Walfisch and Bertoni - IEEE/AP, 1988 Repeated numerical integration, Incident plane wave for  –Xia & Bertoni - IEEE/AP, 1992 Series expansion in Borsma functions, screens of uniform height, spacing. –Vogler - Radio Science, 1982 Long computation time limits method to 8 screens –Saunders & Bonar - Elect. Letters, 1991 Modified Vogler Method Parabolic Method –Levy, Elect. Letters, 1992 Ray Optics Approximations –Anderson - IEE-  wave, Ant., Prop., 1994; Slope Diffraction –Neve & Rowe - IEE  wave, Ant., Prop., 1994; UTD

22. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni22 Plane Wave Solution for High Base Station Antennas –Reduction of rooftop fields for a spherical wave incident on the rows of buildings is the is the same as the reduction for an incident plane wave after many rows. –Reduction is found from multiple forward diffraction past an array of absorbing screens for a plane wave with unit amplitude that is incident at glancing the angle 

23. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni23 Physical Optics Approximations for Reduction of the Rooftop Fields I.Replace rows of buildings by parallel absorbing screens II.For parallel screens, the reduction factor is found by repeated application of the Kirchhoff integral. Going from screen n to screen n+1, the integration is  nn nn ynyn x n=1n=2n=3nn+1 Incident wave y n+1

24. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni24 Paraxial Approximation for Repeated Kirchhoff Integration

25. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni25 Paraxial Approximation for Repeated Kirchhoff Integration - cont.

26. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni26 Rooftop Field for Incident Plane Wave

27. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni27 Borsma Functions for  = 1

28. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni28 Field Incident on the N + 1 Edge for  = 0  3 N+1  x y

29. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni29 Field Incident on the N + 1 Edge for  ≠ 0 After initial variation, field settles to a constant value Q(g p ) for N > N 0 N0N0 Settled Field Q(g p ) Angles indicated are for d =200    1 2 …. n n+1 …

30. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni30 Explanation of the Settling Behavior in Terms of the Fresnel Zone About the Ray Reaching the N+1 Edge Only those edges that penetrate the Fresnel zone affect the field at the N +1 edge  d n=1 n=3 n=5 n=N n=N +1 n=2n=4 N0N0 n=N -1

31. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni31 Settled Field Q(g p ) and Analytic Approximations 0.010.020.050.10.20.51.0 0.03 0.05 0.1 0.2 0.5 1.0 1.5 Q gpgp

32. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni32 Path Gain/Loss for High Base Station Antenna Comparison with measurements made in Philadelphia by AT&T

33. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni33 Comparison Between Hata Measurement Model and the Walfisch-Ikegami Theoretical Model

34. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni34 Comparison of Theory for Excess Path Loss with Measurements of Okumura, et al. f = 922 MHz

35. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni35 Walk About From Rooftop to Street Level R

36. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni36 Summary of Q for High Base Station Antennas Rows of buildings act as a series of diffracting screens Forward diffraction reduces the rooftop field by a factor that approaches a constant past many rows The settling behavior can be understood in terms of Fresnel zones, and leads to the reduction factor Q, which depends on a single parameter g p Good comparison with measurements is obtained using a simple power expansion for Q

37. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni37 Cylindrical Wave Solution for Low Base Station Antennas Finding the reduction factor Q using an incident cylindrical wave Q is shown to depend on parameter g c and the number of rows of buildings Comparison with measurements Mobile-to-mobile communications

38. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni38 Cylindrical Wave Solutions for Microcells Using Low Base Station Antennas Microcell coverage out to about 1 km involves propagation over a limited number of rows. Must account for the number of rows covered, and hence for the field variation in the plane perpendicular to the rows of buildings. Therefore use a cylindrical incident wave with axis parallel to the array of absorbing screens to find the field reduction due to propagation past rows of buildings.

39. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni39 Physical Optics Approximations for Reduction of the Rooftop Fields I.Replace rows of buildings by parallel absorbing screens II.For parallel screens, the reduction factor will apply for a spherical wave and for a cylindrical wave. For 2D fields, Kirchhoff integration gives  nn nn ynyn x n=1n=2n=3nn+1 Incident wave y n+1

40. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni40 Paraxial Approximation for Repeated Kirchhoff Integration and Screens of Uniform Height

41. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni41 Approximation for Cylindrical Wave of a Line Source 1 y x y0y0 d 234NN+1 d

42. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni42 Integral Representation for Field at the N+1 Edge

43. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni43 Borsma Functions for Line Source Field

44. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni44 Rooftop Field Reduction Factor for Low Base Station Antenna

45. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni45 Field Reduction Past Rows of Buildings Field after multiple diffraction over absorbing screens. Values of y 0 are for a frequency of 900MHz and d=50 m. Number of Screens M = N+1 110100 10 1 0.1 0.01 0.001 0.0001 QMQM y 0 = +11.25m y 0 = –11.25m y 0 = 0m 1/M

46. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni46 Slope of field H(M) vs. Number of Screens for different Tx heights at 1800MHz 0102030405060708090100 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 Number of Screens M Slope of Field, s y 0 < 0 y 0 > 0

47. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni47 Modifications for Propagation Oblique to the Street Grid Base Station  x R x=0 mobile Radio propagation with oblique incidence x = Md + d/2

48. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni48 Comparison of Base Station Height Gain with Har/Xia Measurement Model -8-6-4-202468 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 Q in dB y0y0 Q 10 Q 20 Q exp

49. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni49 Experimentally Based Expression for Q exp

50. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni50 Comparison of Range Index n with Har/Xia Measurement Model n=2+2s -8-6-4-202468 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 n y0y0 theory exp

51. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni51 Q for Mobile to Mobile Communications     h0h0 h1h1 R n=12M HBHB Peak of first building acts as line source of strength Propagation past remaining peaks gives factor 1/(M-1) Effective reduction factor

52. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni52 Comparison of Q Factors for Plane Waves, Cylindrical Waves and Mobile-to-Mobile -15-10-5051015 -60 -50 -40 -30 -20 -10 0 Q (dB) y0y0 Q 20 (g c ) Q (gp)Q (gp) QeQe

53. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni53 Path Loss for Mobile-to-Mobile Communication

54. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni54     h0h0 h1h1 R n=12M HBHB Walk About Range for Low Buildings

55. Polytechnic University, Brooklyn, NY ©2002 by H.L. Bertoni55 Summary of Solution for Low Base Station Antennas Reduction factor found using an incident cylindrical wave Q M depends on parameter g c and the number of rows of buildings M over which the signal passes Theory gives the correct trends for base station height gain and slope index, but is pessimistic for antennas below the rooftops Theory give simple expressions for path gain in the case of Mobile-to-mobile communications