#### Transcript EL 675 UHF Propagation for Wireless Applications (4)

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 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY 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 r1 s1 s2 r2 q Specular reflection ~ 1/ (r1 + r2)2 Diffuse reflection ~ A/ (s1 s2) For all construction, | (q )| 1 for q 90° © 2000 by H. L. Bertoni 5 Polytechnic University, Brooklyn, NY 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 Ai exp jkLi 2 Ai Aj exp jk Li Lj Ai 2 • Can be used to predict statistical parameters © 2000 by H. L. Bertoni 6 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY Two Dimensional Ray Tracing Technique Rx Rx Rx Rx Tx Rays are traced to corners, which act as a secondary sources for subsequent trace. © 2000 by H. L. Bertoni No Diffraction Single Diffraction Double Diffraction 8 Polytechnic University, Brooklyn, NY Image vs Pin Cushion Method for 2D Rays Image Method Pin Cushion Method Reflected ray paths found from multiple imaging of the source in the building walls Rays traced outward from the source at angular separation, Dq << 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. © 2000 by H. L. Bertoni must use capture circle to find rays that illuminate the receiver (or equivalent procedure). Dia = LDq 9 Polytechnic University, Brooklyn, NY Footprints of Buildings in the High-Rise Section of Rosslyn, Virginia © 2000 by H. L. Bertoni 10 Polytechnic University, Brooklyn, NY Comparison of Measured and, 2D computed Path Gain for Low Base Station at TX4b f = 1900MHz © 2000 by H. L. Bertoni 11 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY High Rise Buildings in Upper Manhattan, NY © 2000 by H. L. Bertoni 13 Polytechnic University, Brooklyn, NY Propagation Down the Urban Canyons of High Rise Buildings y Building x Building MAIN STREET A TX Building B RX0 4 Building Building 1 RX2 Wy Ly 2 Building Building Building 3 RX1 Wy Building Lx © 2000 by H. L. Bertoni 14 Polytechnic University, Brooklyn, NY Reflection and Diffraction Around Corners Building Building Building 1 2 3 TX Building Building Building RX © 2000 by H. L. Bertoni 15 Polytechnic University, Brooklyn, NY Ray Path for High Rise Model • All Path Include Direct Path + Path from Image Source to Account for Ground Reflections • Main Street – Rm: m reflections at building on main street • Perpendicular Streets - one turn paths – Rmn: m reflections at building on main street, n reflections on perpendicular street + ground – RmDRn: building reflections separated by corner diffractions • Parallel Streets - two turn paths – Rmnp: m, n, p, building reflections on main, perpendicular, parallel street – RmDRnp, RmnDRp,: building reflections + diffraction at a single corner – RmDRn DRp: building reflections + diffraction at two corners © 2000 by H. L. Bertoni 16 Polytechnic University, Brooklyn, NY Predictions in LOS and Perpendicular Streets LOS Received Power (dB) TX XXX XX Distance (m) © 2000 by H. L. Bertoni 17 Polytechnic University, Brooklyn, NY Turning Corners in Manhattan © 2000 by H. L. Bertoni 18 Polytechnic University, Brooklyn, NY Cell shape in a High Rise Environment © 2000 by H. L. Bertoni 19 Polytechnic University, Brooklyn, NY Vertical Plane/Slant Plane Method Building Height Rx c b c d Tx b d Rx 0 Range Left propagation channel Tx Rays are traced in the slant plane containing TX and RX to account for propagation around buildings. Rays are traced in the vertical plane containing TX and RX to account for propagation over buildings. © 2000 by H. L. Bertoni Right propagation channel 20 Polytechnic University, Brooklyn, NY 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. 1993 © 2000 by H. L. Bertoni 21 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY Transmitter and Receiver Locations for Core Rosslyn Propagation Predictions © 2000 by H. L. Bertoni 23 Polytechnic University, Brooklyn, NY Slant/Vertical Plane Prediction for Rooftop Antenna at 900MHz © 2000 by H. L. Bertoni 24 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY 3D Predictions of Path Gain for Elevated Base Station at TX6 and f=908MHz © 2000 by H. L. Bertoni 26 Polytechnic University, Brooklyn, NY Limitation of Regular 3D Ray Tracing Method Each segment of each edge is a source of a cone of diffracted rays b b a a g © 2000 by H. L. Bertoni 27 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY 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 Vertical plane Vertical plane containing containing back reflected diffracted rays and back diffracted rays Cone of diffracted rays © 2000 by H. L. Bertoni 29 Polytechnic University, Brooklyn, NY VPL Method for Approximate 3D Ray Tracing © 2000 by H. L. Bertoni 30 Polytechnic University, Brooklyn, NY Reflections and Rooftop Diffractions for VPL Method Form a Binary Tree 8 9 4 5 7 Diffraction Edge Reflection 10 6 3 1 2 © 2000 by H. L. Bertoni 31 Polytechnic University, Brooklyn, NY Transmitter and Receiver Locations for Core Rosslyn Propagation Predictions © 2000 by H. L. Bertoni 32 Polytechnic University, Brooklyn, NY Measurements and VPL Predictions for Rooftop Antenna (TX6 and f=908MHz) -70 -75 Path Gain (dB) -80 -85 -90 -95 -100 -105 Measurements Predictions Diffuse -110 -115 -120 1001 1051 1101 1151 1201 1251 1301 1351 Receiver Number Without diffuse: h = -0.75 dB s = 5.43 dB With diffuse: h = -0.74 dB s = 5.44 dB © 2000 by H. L. Bertoni 33 Polytechnic University, Brooklyn, NY Measurements and VPL Predictions for Street Level Antenna (TX1a and f=908MHz) -50 -60 Path Gain (dB) -70 -80 -90 -100 -110 Measurements -120 No Diffuse With Diffuse -130 1001 1051 1101 1151 1201 1251 1301 1351 Receiver Number Without diffuse: h = -0.42 dB s = 8.92 dB With diffuse: h = 0.49 dB s = 8.34 dB © 2000 by H. L. Bertoni 34 Polytechnic University, Brooklyn, NY Tx and RX Locations in Munich © 2000 by H. L. Bertoni 35 Polytechnic University, Brooklyn, NY Measurements and VPL Predictions in Munich Route 1, f=900MHz, = 0.40 dB, s = 8.67 dB -70 Measurements -80 Predictions Path Gain (dB) -90 -100 -110 -120 -130 -140 -150 1 26 51 76 101 126 151 176 201 226 251 276 301 326 351 Receiver Number © 2000 by H. L. Bertoni 36 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY Reflection Away From Glancing Is Influenced by Wall Properties For low base station (BS) antenna, reflection from glass doors at Corner A influences received signal on street L-M. © 2000 by H. L. Bertoni 38 Polytechnic University, Brooklyn, NY Measurements Along Street L-M Show Influence of Corner A on Ray Results © 2000 by H. L. Bertoni 39 Polytechnic University, Brooklyn, NY Some Examples of Building Corner Construction and Diffracted Rays Walls with windows © 2000 by H. L. Bertoni 40 Polytechnic University, Brooklyn, NY Comparison of Diffraction Coefficients (900 MHz) © 2000 by H. L. Bertoni 41 Polytechnic University, Brooklyn, NY Comparison of Power Predictions With Helsinki Measurements at 2.25 GHz © 2000 by H. L. Bertoni 42 Polytechnic University, Brooklyn, NY Comparison of DS Predictions With Helsinki Measurements at 2.25 GHz © 2000 by H. L. Bertoni 43 Polytechnic University, Brooklyn, NY Summary of Prediction Errors on Different Routes in Helsinki for Low Antennas © 2000 by H. L. Bertoni 44 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY 2-D codes for Propagation Over One Floor • Transmission through walls • Specular reflection from walls • Diffraction at corners © 2000 by H. L. Bertoni 47 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY 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. © 2000 by H. L. Bertoni 49 Polytechnic University, Brooklyn, NY Modeling Effect of Fixtures - cont. y w/2 Line Source -w/2 d 2d 3d nd w/2 (n+1)d Nd x jk r jke H(x n 1 ,y n 1 ) cosa n cosn H (x n ,y n ) dyn dzn 4 r w / 2 2 where z r n2 z2n n + n 2 n with n x n1 x n y n1 y n 2 2 For small angles cos a n cosn 2. T hen for int egrat ion over zn becoms jke jk r jke jkn (cosa n cosn )H (x n, yn ) 4 r dzn 2 H (x n ,y n ) exp( jkz2n 2n )dzn - n © 2000 by H. L. Bertoni 50 Polytechnic University, Brooklyn, NY Modeling Effect of Fixtures - cont. Since exp( jkzn2 2n )dzn e j / 4 T herefore H (xn 1 ,y n 1 ) e j / 4 2 n k w/2 H (x , y ) n w/2 n e jkn n dyn At t he first apet ure t he field of the incident cylindirical wave is H(d,y1 ) exp( jk 0 ) where 0 d 2 y12 0 T he excess path gainE(R) at a distanceR Nd is the defined as the ratio of t he average ofH (Nd,y N ) 2 over t he apert ure to the 1( Nd ), or t he magnitude squared of t he line source field T hus © 2000 by H. L. Bertoni 1 w/2 2 H (Nd,y N ) dyN E (R) Nd w w/2 51 Polytechnic University, Brooklyn, NY Excess Path Gain E(R) Excess Path Gain in dB Propagation Through Clear Space of 1.5 - 2 m Distance in m © 2000 by H. L. Bertoni 52 Polytechnic University, Brooklyn, NY Rays Experiencing Only Reflection and Transmission P ath Gain: PG PRe c PTrans For free space: PGO 4 R 2 For rays experiencing reflect ion and transmission : 2 2 2 PG E (R) p (q p ) Tn (qn ) 4 R p n where R is the unfolded pat h length of t he ray © 2000 by H. L. Bertoni 53 Polytechnic University, Brooklyn, NY 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. © 2000 by H. L. Bertoni 54 Polytechnic University, Brooklyn, NY Propagation Between Floors Can Involve Paths That Go Outside of the Building 2.62 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. 9.20 m TX 1.3 m Direct propagation between floors has losses: ~ 5 - 8 dB for wooden floors 1.3 m ~ 10 dB for reinforce concrete RX 2.1 m © 2000 by H. L. Bertoni > 20 dB for concrete over metal pans 7.50 m 55 Polytechnic University, Brooklyn, NY Path Gain (dB) Predicted vs Measured Path Gain in Hotel Number of floors between Tx and Rx © 2000 by H. L. Bertoni 56 Polytechnic University, Brooklyn, NY 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 (s < 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 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY Space-Time Ray Arrivals From a Mobile as Measured at an Elevated Base Station 1800MHz in Aalborg, Denmark © 2000 by H. L. Bertoni 59 Polytechnic University, Brooklyn, NY Delay Spread (DS) and Angular Spread (AS) Obtained from the Ray Simulation From mth ray from the jth mobile Am j amplitude m j arrival time delay j angle of arrival at base station (measured from direction to mobile) m Delay Spread 2 ( j) DS Am(j ) m(j ) (mj ) m 2 ( j) 2 m A Am( j) (mj) 2 where (mj ) m m Am (j ) 2 m Angle Spread (approximate expression for small spread) A ( j) 2 m ( j) AS m ( j) m A ( j) 2 m ( j) m 2 2 where (mj ) m © 2000 by H. L. Bertoni Am(j ) (mj ) m Am (j ) 2 m 60 Polytechnic University, Brooklyn, NY Standard and Coordinate Invariant Methods of Computing AS Standard met hod: ray arrival angle n measured from direct ion t o mobile AS ( 2 n A 2 2 n ) An n (n )An 2 where n n A 2 n n Coordinate invarient met hod : ray arrival anglen measured from any -xaxis D efine t he vector : un (cos n , sin n ) AS 180 u A 2 n U An2 2 n n n where U (u n )An 2 n © 2000 by H. L. Bertoni 180 2 1 U A 2 n n 61 Polytechnic University, Brooklyn, NY Summary of DS/AS Measurements © 2000 by H. L. Bertoni 62 Polytechnic University, Brooklyn, NY Greenstein Model of Measured DS in Urban and Suburban Areas DS T1km Rkm where T1km is 0.3-1.0 s and 10log is a Gaussian random variable wit h standard deviation 2- 6 Greenstein, et al., “A New Path Gain/Delay Spread Propagation Model for Digital Cellular Channels,” IEEE Trans. VT 46, May 1997. © 2000 by H. L. Bertoni 63 Polytechnic University, Brooklyn, NY Direction of Arrival and Time Delay Computed for a Mobile Location in Seoul, Korea © 2000 by H. L. Bertoni 64 Polytechnic University, Brooklyn, NY Distribution of Building Heights in Three Cities © 2000 by H. L. Bertoni 65 Polytechnic University, Brooklyn, NY Comparison of the CDF’s of Delay Spread for Mobiles in Three Cities ( hBS is 5m above the tallest building) © 2000 by H. L. Bertoni 66 Polytechnic University, Brooklyn, NY Comparison of the CDF’s of Angular Spread for Mobiles in Three Cities ( hBS is 5m above the tallest building ) © 2000 by H. L. Bertoni 67 Polytechnic University, Brooklyn, NY Scatter Plots of DS/AS vs Distance for Munich © 2000 by H. L. Bertoni 68 Polytechnic University, Brooklyn, NY Scatter Plot of DS versus Distance for Seoul Delay Spread ) c e s ( -6 Seoul x 10 d a 1.5 DS of a mobile e r Linear Fitting p 1 Greensteins's median DS S Angle Spread y a) 0.5 le ee Dr 0 g 50 e d ( d 60 a e r p 40 S e 20 l g n A 0 50 © 2000 by H. L. Bertoni 100 150 200 250 300 Distance(m) AS of a mobile Linear Fitting 100 150 0.61 usec/km 350 400 450 10.67 degree/km 200 250 300 Distance(m) 69 350 400 450 Polytechnic University, Brooklyn, NY Log Normal CDF of Delay Spreads Seoul and Munich Normal Probability Plot: HBS = Hmax + 2m Seoul Std. = 3.37 dB Munich Std. = 3.73 dB 0.997 0.99 0.98 0.95 0.90 0.75 0.50 0.25 0.10 0.05 0.02 0.01 -14 © 2000 by H. L. Bertoni -12 -10 -8 -6 Delay Spread (dB usec) 70 -4 -2 0 Polytechnic University, Brooklyn, NY Effect of Building Height Distribution on DS/AS for Modified Seoul Database BS Height Medain DS(usec) Median AS(degree) Original H=+5m 0.13 10.7 H=+2m 0.14 10.9 H=95% 0.18 20.7 H=80% 0.19 24 4-7 Story Building H=+5m 0.17 16.1 H=+0m 0.18 23.3 H=95% 0.15 35.5 H=80% 0.17 37.2 12 Story Flat Bd. H=+5m 0.14 17.7 H=-5.2m 0.12 47.6 5 Story Flat Bd. H=+5m 0.15 13.9 H=-5.2m 0.12 47.3 4-7 Story Bd. H=+5.2m 0.17 15.4 (Rayleigh Dist.) 2-3 Story © 2000 by H. L. Bertoni H=2m 0.23 71 64.4 Polytechnic University, Brooklyn, NY Correlation Coefficients of DS and AS vs Distance Range and Antenna Heights Seoul Munich H=+5m H=+2m H=95% H=+5m H=+2m H=95% © 2000 by H. L. Bertoni r1 0.32 0.23 0.38 0.59 0.57 0.53 r2 0.45 0.44 0.46 0.47 0.45 0.46 72 r3 0.66 0.63 0.47 0.63 0.63 0.54 r4 0.66 0.71 0.61 0.72 0.72 0.48 All rx 0.53 0.52 0.49 0.6 0.59 0.5 Polytechnic University, Brooklyn, NY Footprint of Buildings and Locations of Base Stations ( ) and Mobiles ( ) © 2000 by H. L. Bertoni 73 Polytechnic University, Brooklyn, NY DS/AS of LOS and Cross Roads for Modified Seoul at 8m/2m Height © 2000 by H. L. Bertoni 74 Polytechnic University, Brooklyn, NY 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 Polytechnic University, Brooklyn, NY