MASSIMO FRANCESCHETTI

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Stochastic rays propagation
MASSIMO FRANCESCHETTI University of California at
Berkeley
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Maxwell Equations
in complex environments

• No closed form solution
• Use approximated numerical solvers

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We need to characterize the channel

• Power loss
• Bandwidth
• Correlations

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The true logic of this world is in the calculus
of probabilities. James Clerk Maxwell
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Simplified theoretical model
solved analytically
2 parameters h density g absorption
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The photons stream
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The wandering photon
Walks straight for a random length Stops with
probability g Turns in a random direction with
probability (1-g)
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The wandering photon
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The wandering photon
After a random length, with probability g stop
with probability (1-g ) pick a random direction
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The wandering photon
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The wandering photon
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The wandering photon
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The wandering photon
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The wandering photon
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The wandering photon
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The wandering photon
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The wandering photon
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The wandering photon
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The wandering photon
r
P(absorbed at r) g(r,g,h)
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Derivation
Stop first step
Stop second step
Stop third step
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Relating g(r,g,h) to the received power
Density model
Flux model
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Validation
Random walks
Model with losses
analytic solution
Experiments
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(No Transcript)
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Fitting the data
Power Flux
Power Density
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Fitting the data
dashed blue line wandering photon model red
line power law model, 4.7 exponent staircase
green line best monotone fit
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The wandering photon
can do more
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Random walks with echoes
impulse response of a urban wireless channel
Channel
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Impulse response
r3
R is total path length in n steps
r
r2
r is the final position after n steps
o
r1
r0
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Results
Varying absorption
Varying pulse width
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Results
Time delay and time spread evaluation
Varying transmitter to receiver distance
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Papers
A random walk model of wave propagation M.
Franceschetti J. Bruck and L. Shulman IEEE
Transactions on Antennas and Propagation to
appear in 2004
Stochastic rays pulse propagation M.
Franceschetti Submitted to IEEE Trans. Ant. Prop.
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