Propagation

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Propagation
A modulated signal can be transmitted through a
medium
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Received Signal
noise
Attenuation
Time delay
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Modulation and Demodulation one receiver
MOD
DEM
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Recall FT of Modulated Signal
Usually
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Multiple Receivers and a Planar Wave
We have a number of receivers
If the wave comes from direction we have
with
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See the FT of each received signal
Let with B the Bandwidth of the
transmitted signal
This implies
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See a bit further
Call
Then
where
Finally
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Beamforming
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Beamforming
If the waveform comes from a direction
then
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Condition for no ambiguity
Since is periodic with period , in
order to guarantee one to one correspondence
between angle and gain we need to
satisfy
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Overall demodulated signal
Recall
With all phase shifts due to carrier
propagation and synchronization errors. Then,
for a wavefront coming from direction
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Choice of the Gains
To maximize the return from a direction
then choose the gains as
where, again,
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Examples
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Example gain pattern of the array
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Example
You receive a signal from a direction There are
receivers Carrier Frequency

• Then
• Wavelength
• Distance between receivers
• Spatial Frequency
• Gains