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
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• 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

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• 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

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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

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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
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product of the transmit and receive antenna field
radiation patterns corresponding to x and x,
respectively
R Ground reflection coefficient
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Delay spread delay between the LOS ray and the
reflected ray
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If the transmitted signal is narrowband wrt the
delay spread
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phase difference between the two received signal
components
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d Antenna separation h t Transmitter height h
r Receiver height
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When d is large compared to h t h r
Expand into a Taylor series
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The ground reflection coefficient is given by
vertical polarization
horizontal polarization
for ground, pavement, etc...
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For very large d
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• As d increases, the received power
• Varies inversely with d 4
• Independent of ?

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f 900 MHz R - 1 h t 50 m h r 2 m
G l 1 G r 1 P t 0 dBm
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• The path can be divided into three segments
• d lt h t
• The two rays add constructively
• Path loss is slowly increasing

• Path loss

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• h t lt 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 lt d
• Signal power falls off by d 4
• Signal components only combine destructively

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To find d c , set

• In segment 1, d lt h t power falls off by
• In segment 2, h t lt d lt d c power falls off by
  20 db/decade
• In segment 3, d c lt d, power falls off by 40
  db/decade
• Cell sizes are typically much less than d c and
  power falls off by

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Problem 2 5
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
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Ten Ray Model (Dielectric Canyon)

• 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)

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Overhead view of 10 ray model
x i path length of the i th reflected ray
Product of the transmit and receive antenna gains
of the i th ray
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Assume a narrowband model such that
for all i

• Power falloff is proportional to d - 2
• Multipath rays dominate over the ground reflected
  rays that decay proportional to d - 4

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General Ray Tracing

• 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

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Shadowing Diffraction and Spreading
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

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For h small wrt d and d', the signal must travel
an additional distance ? d
The phase shift is
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is called the Fresnel Kirchhoff diffraction
parameter
Approximations for the path loss relative to LOS
are
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Scattering
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• Okumura model
• 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

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Simplified Path Loss Model
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
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Generally valid where d gt d 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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