Smart antenna arrays - a geometrical explanation of how they work

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Smart antenna arrays - a geometrical explanation
ofhow they work

• Peter F. Driessen
• Electrical and Computer Engineering University of
  Victoria
• Victoria B.C. Canada
• www.driessen.ca

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Outline

• Introduction
• Capacity expressions
• Ricean channels
• Line-of-sight channels
• Specified environments
• System design
• Summary

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Introduction

• With multiple antennas at both ends of a radio
  link,
• Channel capacity grows linearly with number of
  antennas by
• sending different messages on each antenna on
  the same carrier frequency, and
• Separating the messages using the multiple
  antennas at the receiver
• 8 antennas yield 8 times the capacity
• Generalized polarity

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Introduction (2)

• If send same message on each antenna
• Then we get only the power gain of the antenna
  array, and
• Capacity grows only logarithmically with the
  number of antennas
• 8 antennas yield 3 times the capacity

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Outline

• Introduction
• Capacity expressions
• Ricean channels
• Line-of-sight channels
• Specified environments
• System design
• Summary

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Channel capacity
nT transmit antennas, nR receive antennas
Channel transfer function is a matrix nT x nR of
complex scalars
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Channel capacity
Generalized Shannon capacity for matrix channel
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Outline

• Introduction
• Capacity expressions
• Ricean channels
• Line-of-sight channels
• Specified environments
• System design
• Summary

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Ricean channels
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Outline

• Introduction
• Capacity expressions
• Ricean channels
• Line-of-sight channels
• Specified environments
• System design
• Summary

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Line of sight

• Close antenna spacing
• Wide antenna spacing
• 3 examples
• Narrow-wide spacing
• Narrow spacing (constrained to practical size) at
  one end,
• wide spacing at the other end

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LOS - close antenna spacing (1)
All elements have same amplitude and phase (e.g.
all equal to 1)
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LOS - close antenna spacing (2)
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LOS - wide antenna spacing
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T1
R1
R2
T2
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T1
R2
T2
R1
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Example 3
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Narrow-wide spacing
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For large number of array elements , arc 126
degrees
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Outline

• Introduction
• Capacity expressions
• Ricean channels
• Line-of-sight channels
• Specified environments
• System design
• Summary

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Street canyon
View from above
buildings
street
buildings
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Capacity in street canyon
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Ricean channels
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Capacity calculation
H is a combination of LOS matrix of rank
depending on geometry plus Rayleigh matrix
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Minimum capacity, high correlation
Large k, and close-spaced antennas
Small k, independent Rayleigh, antennas spaced
sufficiently for small correlation
Maximum capacity, no correlation
Large k, and wide-spaced antennas to a specific
calculated spacing
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Outline

• Introduction
• Capacity expressions
• Ricean channels
• Line-of-sight channels
• Specified environments
• System design
• Summary

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System design options
Mobile cellular
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System design options

• Fixed wireless
• Antennas spaced equally at both ends of link

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Outline

• Introduction
• Capacity expressions
• Ricean channels
• Line-of-sight channels
• Specified environments
• System design
• Summary

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Summary

• Geometric interpretation of multiple antenna
  systems
• Transmitter antenna pattern has nulls on all but
  one receiver antenna
• Thus can have independent channels on the same
  carrier frequency