Ray Tracing
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Ray Tracing. A radio signal will typically encounter multiple objects and will be reflected, diffracted, or scattered These are called multipath signal components. Represent wavefronts as simple particle Geometry determines received signal from each signal component

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Ray Tracing

A radio signal will typically encounter multiple objects and will be reflected, diffracted, or scattered

These are called multipath signal components


  • Represent wavefronts as simple particle

  • Geometry determines received signal from each signal component

  • Typically includes reflected rays, can also include scattered and diffracted rays

  • Requires site parameters

    • Geometry

    • Dielectric properties

  • Error is smallest when the receiver is many wavelengths from the nearest scatterer and when all the scatterers are large relative to a wavelength


  • Accurate model under these conditions

    • Rural areas

    • City streets when the TX and RX are close to the ground

    • Indoor environments with adjusted diffraction coefficients

  • If the TX, RX, and reflectors are all immobile, characteristics are fixed

  • Otherwise, statistical models must be used


Two – Ray Model

Used when a single ground reflection dominates the multipath effects.

  • Approach:

  • Use the free – space propagation model on each ray

  • Apply superposition to find the result


time delay of the ground reflection relative to the LOS ray

product of the transmit and receive antenna field radiation patterns in the LOS direction


product of the transmit and receive antenna field radiation patterns corresponding to x and x’, respectively

R = Ground reflection coefficient


Delay spread = patterns corresponding to x and x’, respectivelydelay between the LOS ray and the reflected ray


If the transmitted signal is narrowband wrt patterns corresponding to x and x’, respectivelythe delay spread


phase difference between the two received signal components patterns corresponding to x and x’, respectively


d = Antenna separation patterns corresponding to x and x’, respectively

h t = Transmitter height

h r = Receiver height


When d is large compared to h patterns corresponding to x and x’, respectivelyt + h r :

Expand into a Taylor series


The ground reflection coefficient is given by patterns corresponding to x and x’, respectively

vertical polarization

horizontal polarization

for ground, pavement, etc...


For very large d: patterns corresponding to x and x’, respectively


  • As patterns corresponding to x and x’, respectivelyd increases, the received power

    • Varies inversely with d 4

    • Independent of 


f = 900 MHz patterns corresponding to x and x’, respectively

R = - 1

h t = 50 m

h r = 2 m

Gl = 1

G r = 1

P t = 0 dBm


  • Path loss


  • h patterns corresponding to x and x’, respectivelyt < d c

  • Wave experiences constructive and destructive interference

  • Small – scale (Multipath) fading

  • If power is averaged in this area, the result is a piecewise linear approximation

  • d c < d

  • Signal power falls off by d – 4

  • Signal components only combine destructively


To find d patterns corresponding to x and x’, respectivelyc , set

  • In segment 1, d < h t power falls off by

  • In segment 2, h t < d < d c power falls off by – 20 db/decade

  • In segment 3, d c < d, power falls off by – 40 db/decade

  • Cell sizes are typically much less than d c and power falls off by


Problem 2 – 5 patterns corresponding to x and x’, respectively

Find the critical distance, d c , under the two – ray model for a large macrocell in a suburban area with the base station mounted on a tower or building (h t = 20 m), the receivers at height h r = 3 m, and f c = 2 GHz. Is this a good size for cell radius in a suburban macrocell? Why or why not?

Solution


Ten – Ray Model (Dielectric Canyon) patterns corresponding to x and x’, respectively

  • Assumptions:

    • Rectilinear streets

    • Buildings along both sides of the street

    • Transmitter and receiver heights close to street level

    • 10 rays incorporate all paths with 1, 2, or 3 reflections

      • LOS (line of sight)

      • GR (ground reflected)

      • SW (single wall reflected)

      • DW (double wall reflected

      • TW (triple wall reflected)

      • WG (wall – ground reflected)

      • GW (ground – wall reflected)


Overhead view of 10 – ray model patterns corresponding to x and x’, respectively

x i = path length of the i th reflected ray

Product of the transmit and receive antenna gains of the i th ray


Assume a narrowband model such that patterns corresponding to x and x’, respectively

for all i

  • Power falloff is proportional to d - 2

  • Multipath rays dominate over the ground reflected rays that decay proportional to d - 4


General Ray Tracing patterns corresponding to x and x’, respectively

  • Models all signal components

    • Reflections

    • Scattering

    • Diffraction

  • Requires detailed geometry and dielectric

  • properties of site

    • Site specific

  • Similar to Maxwell, but easier math

  • Computer packages often used

  • The GRT method uses geometrical optics to trace the propagation of the LOS and reflected signal components


Shadowing: Diffraction and Spreading patterns corresponding to x and x’, respectively

Diffraction

  • Diffraction occurs when the transmitted signal "bends around" an object in its path

  • Most common model uses a wedge which is asymptotically thin

  • Fresnel knife – edge diffraction model


For h small wrt d and d', the signal must travel an additional distance  d

The phase shift is


is called the Fresnel – Kirchhoff diffraction parameter additional distance

Approximations for the path loss relative to LOS are


Scattering additional distance


  • Okumura model additional distance

    • Empirically based (site/freq specific)

    • Awkward (uses graphs)

  • Hata model

    • Analytical approximation to Okumura model

  • Cost 136 Model:

    • Extends Hata model to higher frequency (2 GHz)

  • Walfish/Bertoni:

    • Cost 136 extension to include diffraction from rooftops


Simplified Path – Loss Model additional distance

K = dimensionless constant that depends on the antenna characteristics and the average channel attenuation

d 0 = reference distance for the antenna far field

 = path – loss exponent

LOS, 2 – ray model, Hata model, and the COST extension all have this basic form


Generally valid where d > d additional distance 0

d 0 = 1 – 10 m indoors

= 10 – 100 m outdoors

  • General approach:

  • Take data at three values of d

  • Solve for K, d o , and 


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