XII. Site Specific Predictions Using Ray Methods

Transcription

1 XII. Site Specific Predictions Using Ray Methods General considerations Ray tracing using 2D building database Ray tracing from a 3D building database Slant plane / vertical plane method Full 3D method Vertical lane Launch (VPL) method Ray tracing for indoor predictions Using ray methods to predict statistics of delay and angle spread 2000 by H. L. Bertoni 1

2 Goals and Motivation Goal Make propagation predictions based on the actual shape of the buildings in some region Motivation Achieve a desired quality of service in high traffic density areas Install systems without adjustment System simulations and studies Predict higher order channel statistics 2000 by H. L. Bertoni 2

3 Ray Techniques for Site Specific Predictions Numerical solvers (finite difference, finite element and moment methods) not practical for urban dimension Ray techniques are the only viable approach Predictions using 2D building data base Pin/cushion vs. image method Prediction using 3D building data base Vertical plane/slant plane - enhanced 2D methods Full 3D method Vertical plane launch - approximates full 3D method 2000 by H. L. Bertoni 3

4 Physical Phenomena and Database Requirements Physical phenomena that can be accounted for Ground reflection and blockage Specular reflection at building walls Diffraction at building corners, roofs Diffuse scattering from building walls (for last path segment) Database requirements for predictions Terrain Buildings decomposed into groups of polyhedrons that are : Stacked (wedding cake buildings) or side-by-side Polygonal base with vertical sides Some codes assume flat roofs Vector vs pixel (area element) data base Reflection coefficients at walls, diffuse scattering coefficient 2000 by H. L. Bertoni 4

5 Specular vs Diffuse Reflection from Walls Complex construction leads to scattering Mixture of construction materials Architectural details Windows - glass, frame Simplifying approximations for large distances r 1 r 2 θ s 1 s 2 Specular reflection ~ 1/ (r 1 + r 2 ) 2 Diffuse reflection ~ A/ (s 1 s 2 ) For all construction, Γ (θ ) 1 for θ by H. L. Bertoni 5

6 Modeling Limitations Cannot accurately predict phase of ray fields Position accuracy of building data base ~ 0.5 m Do not know wall construction - uncertainty in magnitude and phase of reflection coefficient Local scattering contributions not computed Do not consider vehicles, street lights, signs, people, etc. Most codes do not include diffuse scattering Cannot predict fast fading pattern in space Predict small area average by summing ray powers [ ] = A exp jkl A A exp jk L L A Can be used to predict statistical parameters ( ) [ ] 2 2 i i i j i j i 2000 by H. L. Bertoni 6

7 Ray Tracing Using a 2D Building Database Building are assumed to be infinitely high Almost all models neglect transmission through the building 2D ray tracing around building in the horizontal plane Rays that are considered Multiple specular reflections from the building walls Single or double diffraction at the vertical edge of a building Ground reflection Diffuse scattering from the building walls Advantages: Account for low base station antennas among high rise buildings Computationally efficient Limitations: Less accurate in an area of mixed building heights Fails for rooftop base stations 2000 by H. L. Bertoni 7

8 Two Dimensional Ray Tracing Technique Rx Rx Rx Rx Tx Rays are traced to corners, which act as a secondary sources for subsequent trace. No Diffraction Single Diffraction Double Diffraction 2000 by H. L. Bertoni 8

9 Image vs Pin Cushion Method for 2D Rays Image Method Pin Cushion Method Reflected ray paths found from multiple Rays traced outward from the source imaging of the source in the building walls at angular separation, θ << w/r, Rx Rx Rx Tx Tx must determine if the ray from an image passes through the actual wall, or through the analytic extension of the wall. must use capture circle to find rays that illuminate the receiver (or equivalent procedure). Dia = L θ 2000 by H. L. Bertoni 9

10 Footprints of Buildings in the High-Rise Section of Rosslyn, Virginia 2000 by H. L. Bertoni 10

11 Comparison of Measured and, 2D computed Path Gain for Low Base Station at TX4b f = 1900MHz 2000 by H. L. Bertoni 11

12 Predictions for a Generic High Rise Environment Rectangular Street Grid Propagation Down Streets, Around Corners - Specular Reflection at Building Walls Diffraction at Building Corners 2000 by H. L. Bertoni 12

13 High Rise Buildings in Upper Manhattan, NY 2000 by H. L. Bertoni 13

14 Propagation Down the Urban Canyons of High Rise Buildings y Building Building Building x MAIN STREET A TX B RX Building Building Building Wy RX 2 RX 1 Ly Building Building Wy Building Lx 2000 by H. L. Bertoni 14

15 Reflection and Diffraction Around Corners Building Building Building 2 TX Building Building Building 1 3 RX 2000 by H. L. Bertoni 15

16 Ray Path for High Rise Model All Path Include Direct Path + Path from Image Source to Account for Ground Reflections Main Street R m : m reflections at building on main street Perpendicular Streets - one turn paths R mn : m reflections at building on main street, n reflections on perpendicular street + ground R m DR n : building reflections separated by corner diffractions Parallel Streets - two turn paths R mnp : m, n, p, building reflections on main, perpendicular, parallel street R m DR np, R mn DR p, : building reflections + diffraction at a single corner R m DR n DR p : building reflections + diffraction at two corners 2000 by H. L. Bertoni 16

17 Predictions in LOS and Perpendicular Streets Received Power (db) TX X X X LOS X X Distance (m) 2000 by H. L. Bertoni 17

18 Turning Corners in Manhattan 2000 by H. L. Bertoni 18

19 Cell shape in a High Rise Environment 2000 by H. L. Bertoni 19

20 Vertical Plane/Slant Plane Method Rx Building Height Tx c b d c b d Rx 0 Range Rays are traced in the vertical plane containing TX and RX to account for propagation over buildings. Left propagation channel Tx Right propagation channel Rays are traced in the slant plane containing TX and RX to account for propagation around buildings by H. L. Bertoni 20

21 Slant/Vertical Plane Prediction for Aalborg, Denmark at 955MHz T. Kurner, D.J. Cichon and W. Wiesbeck, Concepts and Results for 3D Digital Terrain-basedWave Propagation Models: An Overview, IEEE Jnl. JASC 11, Sept by H. L. Bertoni 21

22 Missing Rays in Slant Approximation Unless the building faces are perpendicular to the vertical plane, reflected rays lie outside of the vertical plane Multiply reflected rays will not lie in the slant plane Neglects rays that go over and around building Missing rays cause significant errors for high base station antenna 2000 by H. L. Bertoni 22

23 Transmitter and Receiver Locations for Core Rosslyn Propagation Predictions 2000 by H. L. Bertoni 23

24 Slant/Vertical Plane Prediction for Rooftop Antenna at 900MHz 2000 by H. L. Bertoni 24

25 Ray Tracing Using a 3D Building Database Rays that are considered: Can account for all rays in 3D space Some programs consider diffuse scattering Some simplification is made, i.e. flat roofs and/or vertical walls Rays that are not considered: Often unable to include rays that undergo more than one diffraction Usually does not include transmission into the buildings Advantages: Very robust model, works for many building environments Limitations: Limited to a maximum of 2 diffractions (unable to account for multiple rooftop diffraction) Computationally very inefficient 2000 by H. L. Bertoni 25

26 3D Predictions of Path Gain for Elevated Base Station at TX6 and f=908mhz 2000 by H. L. Bertoni 26

27 Limitation of Regular 3D Ray Tracing Method Each segment of each edge is a source of a cone of diffracted rays α β β α γ 2000 by H. L. Bertoni 27

28 Vertical Plane Launch (VPL) Method Finds rays in 3D that are multiply reflected and diffracted by buildings Assumes building walls are vertical to separate the trace into horizontal and vertical components Pin cushion method gives the ray paths in the horizontal plane Analytic methods give the ray paths in the vertical direction Makes approximation: rays diffracted at a horizontal edge lie in the vertical plane of the incident ray, or the vertical plane of the reflected rays 2000 by H. L. Bertoni 28

29 Physical Approximation of the VPL Method Treats rays diffracted at horizontal edges as being in the vertical planes defined by the incident or reflected rays (replaces diffraction cone by tangent planes) Vertical plane containing forward diffracted rays Cone of diffracted rays Vertical plane containing Vertical back plane containing diffracted reflected rays and back diffracted rays 2000 by H. L. Bertoni 29

30 VPL Method for Approximate 3D Ray Tracing 2000 by H. L. Bertoni 30

31 Reflections and Rooftop Diffractions for VPL Method Form a Binary Tree Diffraction Edge Reflection by H. L. Bertoni 31

32 Transmitter and Receiver Locations for Core Rosslyn Propagation Predictions 2000 by H. L. Bertoni 32

33 Measurements and VPL Predictions for Rooftop Antenna (TX6 and f=908mhz) Path Gain (db) Measurements Predictions -115 Diffuse Receiver Number Without diffuse: η = db σ = 5.43 db With diffuse: η = db σ = 5.44 db 2000 by H. L. Bertoni 33

34 Measurements and VPL Predictions for Street Level Antenna (TX1a and f=908mhz) Path Gain (db) Measurements -120 No Diffuse -130 With Diffuse Receiver Number Without diffuse: η = db σ = 8.92 db With diffuse: η = 0.49 db σ = 8.34 db 2000 by H. L. Bertoni 34

35 Tx and RX Locations in Munich 2000 by H. L. Bertoni 35

36 Measurements and VPL Predictions in Munich Route 1, f=900mhz, h = 0.40 db, s = 8.67 db Measurements Predictions Path Gain (db) Receiver Number 2000 by H. L. Bertoni 36

37 Diffraction at Building Corners Important to correctly model shape of building corners Luebbers diffraction coefficient used by many to model diffraction at building corners Heuristic coefficient for lossy dielectric wedges Developed for forward diffraction over hills Exhibits nulls in the back diffraction direction that are not physical Building corners are not dielectric wedges, e.g., fitted with windows, metal framing Need a single diffraction coefficient to use for all corners 2000 by H. L. Bertoni 37

38 Reflection Away From Glancing Is Influenced by Wall Properties x L F G D E P Q Corner A M I H C BS J x 10 5 For low base station (BS) antenna, reflection from glass doors at Corner A influences received signal on street L-M by H. L. Bertoni 38

39 Measurements Along Street L-M Show Influence of Corner A on Ray Results 100 Mean Received Power, dbm Corner A Measurements Exact shape of corner A with epsilon = 2 Exact shape of corner A with epsilon = 6 Right angle shape of corner A Mean rms delay spread, ns Measurements Exact shape with epsilon = 2 Exact shape with epsilon = 6 Right angle shape Crossing Street Distance, m Crossing Street Distance, m 2000 by H. L. Bertoni 39

40 Some Examples of Building Corner Construction and Diffracted Rays Walls with windows 2000 by H. L. Bertoni 40

41 Comparison of Diffraction Coefficients (900 MHz) 0 10 Excess Loss, db Absorbing (Felsen) Dielectric (New) Dielectric (Luebbers) FDTD simulation Angle φ, degrees 2000 by H. L. Bertoni 41

42 Comparison of Power Predictions With Helsinki Measurements at 2.25 GHz 30 Mean Received Power, dbm Measurements VPL with LHDC VPL with NHDC Crossing Street Distance, m 2000 by H. L. Bertoni 42

43 Comparison of DS Predictions With Helsinki Measurements at 2.25 GHz 110 Mean rms delay spread, ns Measurements VPL with LHDC VPL with NHDC Crossing Street Distance, m 2000 by H. L. Bertoni 43

44 Summary of Prediction Errors on Different Routes in Helsinki for Low Antennas 2000 by H. L. Bertoni 44

45 Conclusions Site specific predictions are possible with accuracy Average error ~ 1 db RMS error ~ 6-10 db Requires multiple interactions for accurate predictions Six or more reflections required for best accuracy Double diffraction at vertical edges is sometimes needed Lubbers diffraction coefficient needs modification 2000 by H. L. Bertoni 45

46 Ray Tracing Inside Buildings Ray tracing over one floor Propagation through the clear space between furnishings and ceiling structure Propagation between floors 2000 by H. L. Bertoni 46

47 2-D codes for Propagation Over One Floor Transmission through walls Specular reflection from walls Diffraction at corners 2000 by H. L. Bertoni 47

48 Effects of Floors & Ceilings Drop ceilings taken up with beams, ducts, light fixtures, etc. Floors covered by furniture Propagation takes place in clear space between irregularities W 2000 by H. L. Bertoni 48

49 Modeling Effect of Fixtures y w/2 Line Source -w/2 d 2d 3d nd (n+1)d Nd x Assume the excess path loss for a point source is the same as that of a line source perpendicular to the direction of propagation. Represent the effects of the furnishings and fixtures by apertures of width w in a series of absorbing screens separated by the distance d. Use Kirchhoff-Hyugens method to find the field in the aperture of the n + 1 screen do to the field in the aperture of the n screen. The field in the aperture of the first screen is the line source field by H. L. Bertoni 49

50 Modeling Effect of Fixtures - cont. y w/2 Line Source -w/2 d 2d 3d nd (n+1)d Nd x ρ n where + z n 2 r= ρn + zn ρn with ρn = ( xn+ 1 xn) + ( yn+ 1 yn) 2ρn For small angles cosα + cosδ 2. Then for integration over z becoms - (cos H( x, y ) = cosα + cos δ H( x, y ) α n n+ 1 n+ 1 n n n n w / 2 n w / 2 ( ) n jke 4πr jkr dy dz jkr jkρ jke + cos δn) H( xn, yn) n (, ) exp( ρ ) πr dz n jke 2 H x y jkz 2 dz 4 2πρ n n n n n n n n n by H. L. Bertoni 50

51 Modeling Effect of Fixtures - cont. 2 jπ / 4 2πρn Since exp( jkzn 2ρn) dzn e k jπ / 4 w / 2 jkρn e e Therefore H( xn+ 1, yn+ 1) = H( xn, yn) dyn λ w / 2 ρn At the first apeture the field of the incident cylindirical wave is 2 Hdy (, ) = exp( jkρ ) ρ where ρ = d + y The excess path gain ER ( ) at a distance R = Nd ratio of the average of HNdy (, N ) over the aperture to the the magnitude squared of the line source field ( = 1 Nd ), or w / Thus ER ( ) = Nd HNdy (, N) dyn w w / is the defined as the 2000 by H. L. Bertoni 51

52 Excess Path Gain E(R) Propagation Through Clear Space of m Excess Path Gain in db Distance in m 2000 by H. L. Bertoni 52

53 Rays Experiencing Only Reflection and Transmission Path Gain : For free space : PG P P PG = λ 4πR For rays experiencing reflection and transmission: PG Re c O Trans = 2 λ R ER ( ) Γ ( θ ) T ( θ ) 4π where R is the unfolded path length of the ray p p p n n n 2000 by H. L. Bertoni 53

54 Predictions at 900 MHz in a University Building Diffraction at far corners of hallway is responsible for the received signal when the direct rays go through many walls by H. L. Bertoni 54

55 Propagation Between Floors Can Involve Paths That Go Outside of the Building 2.62 m 9.20 m TX 1.3 m Propagation can take place via paths that go outside the building via diffraction or reflection from adjacent buildings. Stair wells, pipe shafts, etc. are also paths for propagation between floors. Direct propagation between floors has losses: ~ 5-8 db for wooden floors 1.3 m ~ 10 db for reinforce concrete RX 2.1 m 7.50 m > 20 db for concrete over metal pans 2000 by H. L. Bertoni 55

56 Predicted vs Measured Path Gain in Hotel Path Gain (db) Number of floors between Tx and Rx 2000 by H. L. Bertoni 56

57 Summary of Propagation in Buildings Ray codes for coverage over on floor Need to account for 2 or 3 reflections and 1 diffraction event Can achieve low errors (σ < 6 db) Propagation through clear space can give excess loss at lower frequencies Propagation between floors can involve paths that lie outside of buildings 2000 by H. L. Bertoni 57

58 Predicting Statistics of Channel Parameters Need high order channel statistics (e.g. delay spread DS and angle spread AS) for advanced system design Measurements are expensive and time consuming Not sure if measurements for one link geometry, city, apply elsewhere Monte Carlo simulation using site specific predictions allow different link geometry, cities to be examined Simulations allow modifications of building database Relate statistics of channel parameters to the statistical properties of the building distribution 2000 by H. L. Bertoni 58

59 Space-Time Ray Arrivals From a Mobile as Measured at an Elevated Base Station 1800MHz in Aalborg, Denmark 2000 by H. L. Bertoni 59

60 Delay Spread (DS) and Angular Spread (AS) Obtained from the Ray Simulation From mth ray from the jth mobile A m τ φ m m () j = amplitude () j = arrival time delay () j = angle of arrival at base station (measured from direction to mobile) Delay Spread DS ( j) = m A ( j) 2 2 ( j) ( j) m τm τm m ( ) A ( j) 2 m where τ ( j) m = m m A ( j) 2 ( j) m τ m A ( j) 2 m Angle Spread (approximate expression for small spread) AS ( j) = m A ( j) 2 2 ( j) ( j) m φm φm m ( ) A ( j) 2 m where φ ( j) m = m m A ( j) 2 ( j) m φm A ( j) 2 m 2000 by H. L. Bertoni 60

61 Standard and Coordinate Invariant Methods of Computing AS Standard method : ray arrival angle φ measured from direction to mobile n n n n n n n n n AS = ( φ Φ) A A where Φ= ( φ ) A A n 2 n Coordinate invarient method : ray arrival angle φ measured from any x - axis Define the vector : u = (cos φ, sin φ ) n n n n 2 2 AS = un U An An = π π U n n ( 2 ) where 2 = ( n) n U u A A n n 2 n 2000 by H. L. Bertoni 61

62 Summary of DS/AS Measurements 2000 by H. L. Bertoni 62

63 Greenstein Model of Measured DS in Urban and Suburban Areas = 1 km DS T R km where T is µ s and 1km 10logξ is a Gaussian random variable with standard deviation 2-6 ξ Greenstein, et al., A New Path Gain/Delay Spread Propagation Model for Digital Cellular Channels, IEEE Trans. VT 46, May by H. L. Bertoni 63

64 Direction of Arrival and Time Delay Computed for a Mobile Location in Seoul, Korea 2000 by H. L. Bertoni 64

65 Distribution of Building Heights in Three Cities 2000 by H. L. Bertoni 65

66 Comparison of the CDF s of Delay Spread for Mobiles in Three Cities ( h BS is 5m above the tallest building) 2000 by H. L. Bertoni 66

67 Comparison of the CDF s of Angular Spread for Mobiles in Three Cities ( h BS is 5m above the tallest building ) 2000 by H. L. Bertoni 67

68 Scatter Plots of DS/AS vs Distance for Munich 2000 by H. L. Bertoni 68

69 Scatter Plot of DS versus Distance for Seoul s ( d a e r p S Angle Spread Delay Spread y a) le e Dr g e d ( d a e r p S e l g n A 1.5 x Distance(m) DS of a mobile Linear Fitting Greensteins's median DS AS of a mobile Linear Fitting Seoul 0.61 usec/km degree/km Distance(m) 2000 by H. L. Bertoni 69

70 Log Normal CDF of Delay Spreads Seoul and Munich Normal Probability Plot: H BS = H max + 2m Seoul Std. = 3.37 db Munich Std. = 3.73 db Delay Spread (db usec) 2000 by H. L. Bertoni 70

71 Effect of Building Height Distribution on DS/AS for Modified Seoul Database BS Height Medain DS(usec) Median AS(degree) Original H=+5m H=+2m H=95% H=80% Story Building H=+5m H=+0m H=95% H=80% Story Flat Bd. H=+5m H=-5.2m Story Flat Bd. H=+5m H=-5.2m Story Bd. H=+5.2m (Rayleigh Dist.) 2-3 Story H=2m by H. L. Bertoni 71

72 Correlation Coefficients of DS and AS vs Distance Range and Antenna Heights r1 r2 r3 r4 All rx Seoul H=+5m H=+2m H=95% Munich H=+5m H=+2m H=95% by H. L. Bertoni 72

73 Footprint of Buildings and Locations of Base Stations ( ) and Mobiles ( ) 2000 by H. L. Bertoni 73

74 DS/AS of LOS and Cross Roads for Modified Seoul at 8m/2m Height 2000 by H. L. Bertoni 74

75 Conclusions Site specific predictions are possible with accuracy Average error ~ 1 db, RMS error ~ 6-10 db Requires multiple interactions for accurate predictions6 or more reflections, double diffraction at vertical edges Site specific prediction can be used for Monte Carlo simulation of statistical channel characteristics Delay Spread is not strongly dependent on path geometry or building statistic Angular Spread at base station depends strongly on antenna height and building height distribution Weak correlation between Delay Spread and Angular Spread Further work needed on reflection and diffuse scattering at the building walls 2000 by H. L. Bertoni 75