CS547: Wireless Networking

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CS547 Wireless Networking

• Lecture 1 Signal-to-Interference Ratio

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Path-Loss in Free-Space Propagation

• Reversed-square law the received power is
  proportional to r-2.

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Path-Loss in Ground-Wave Propagation

• Complicated by reflection, diffraction etc.
• Modified path-loss function r-? where 2 ? ? ? 5
  is a constant dependent on the wireless
  environment.
• ? is referred to as path-loss exponent.

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Transmission Power vs. Distance
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Energy-Conserving Via Relaying
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Service Regions

• In many wireless networks such as broadcast
  ratio/TV networks and cellular networks, a
  receiver communicates with the transmitter whose
  signal at its location is the strongest.
• For these wireless networks, the service region
  of a transmitter, known as a cell, is the region
  in which the signal from this transmitter is the
  strongest.

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Equal Transmission Power Voronoi Cell

• If all transmitters have equal transmission
  power, the cell of a transmitter is the set of
  points closer to that transmitter than any other.
  Such cell is called a Voronoi cell.

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Voronoi Cell and Delaunay Triangulation
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More Examples
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Lattice

• A lattice with minimal base ?1 and ?2.

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Voronoi Cells of Lattice Points

• Voronoi cells of lattice points are typically
  hexagons. The area of each cell is exactly ?1??2

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Disparate Transmission Power
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Signal-to-Interference Ratio

• S the residue power of the wanted signal
• Ij the residue power of the j-th unwanted signal
• ?j the absolute value of the frequency
  difference between the wanted signal and the j-th
  unwanted signal
• ? filtering exponent

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Typical SIR Threshold Values

• Advanced Mobile Phone System (AMPS) 18 dB
• Time Division Multiple Access (TDMA) such as
  IS-136 14 dB
• Global System for Mobile Communication (GSM) 9
  dB

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A Monotonic Property of SIR

• two transmitters p1 and p2
• an arbitrary ray l emanating from p1
• a receiver q lies in the ray l and the signal
  from p1 is its wanted signal
• ? as q moves away from p1 along l but to the
  left of p2, the SIR decreases.

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Implications of The Monotonic Property

• Generalization more than one transmitters of
  unwanted signals in a 2-dimensional plane or a
  3-dimensional space
• If the service region of a transmitter is
  bounded, then SIR with respect to this
  transmitter achieves the minimum only on the
  boundary of this region.
• The complexity of calculating the minimum SIR in
  any specific instance is reduced by an order of
  magnitude.

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Extremes of SIR in Regular Hexagon Configuration

• I(?) the total interference at the point in the
  r-circle whose counterclockwise angle separation
  from p0p1 is ?.

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Extremes of SIR in Regular Hexagon Configuration

• Symmetry I(?)I(??/3) if ??0, ?/6,
  I(?)I(?/3- ?).
• Thus, we only need to consider ??0, ?/6.
• I(?) strictly decreases on 0, ?/6.