Capacity Expansion of Cellular Networks Part 1: Reuse Partitioning

1
Capacity Expansion of Cellular NetworksPart 1
Reuse Partitioning

• Chih-Wei Yi
• Department of Computer Science
• National Chiao Tung University

2
The SIR in a Cell

• In conventional cellular systems, the spatial
  reuse of channels is to ensure an adequate SIR
  even at the perimeter of the cell.
• The SIR is not constant over a cell.
• The worst SIR occurs at the perimeter of the
  cell.
• The SIR becomes better as a mobile moves toward
  the base station.
• Can we utilize the high SIR near base stations?
  YES! The technique is called reuse
  partitioning.
• Divide cells into concentric zones, each with a
  different spatial reuse pattern. Each zone is
  assigned a set of channels.

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Cell Reuse Partitioning

• Let rr1gtr2gtgt rmgt0.
• For each 1?i?m,
• Let Hi be the hexagon of radius ri, Zi Hi\Hi1,
  and ZmHm.
• Then, Z1,Z1,,Zm form a partition of the cell,
  and Zi is the referred to the ith zone of its
  cell.
• Let ni be the number of channels assigned to Zi.
• Each cell receives channels.

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Some Geometry Calculation
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Conventional Reuse Patten

• Let d be the channel reuse distance (which is a
  square-root of a rhombic number), and r be the
  cell radius.
• The worst-case SIR occurs at the cell perimeter
  and is approximately
• Let . Then, r?d.
• Let n be the number of channels allocated to each
  cell. The total number of channels is nd2.

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Reuse Partitioning

• Let dd1gtd2gtgtdm be an arbitrary strictly
  decreasing sequence of m numbers where each di is
  the square root of some rhombic number and
  corresponding to the cochannel separation
  distance.
• To ensure the SIR, let ri?di and partition each
  cell as shown in Figure 1.
• The total number of channels used in the system
  is .

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Capacity of Reuse Partitioning

• To compare the radio capacity between
  conventional systems and reuse partitioning
  systems, assume .
• Each cell receives channels, and
• Therefore, the radio capacity of each cell is
  increased.

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Uniform User Distribution Assumption

• If users are uniformly distributed, the number of
  users in the i-th zone is proportional to the
  area of the i-th zone.
• Let nicZi for a constant c and any 1?i?m.
• Then,
• This implies that
• Therefore,

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Gain of Radio Capacity
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Maximum of Gain

• Not that
  .
• The equality holds if and only if
• In other words,
• This means that all zones have equal areas, and
  the gain is at most
  and this maximum is achieved
  if and only if all zones have the same area.

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Conclusion

• Without acquiring more radio spectrum and
  sacrificing the SIR, reuse partitioning can
  increase the radio capacity, i.e. the number of
  subscribers per unit area that can be supported
  at some minimum SIR level.
• We claim that the above gain is at most
  , and this maximum is achieved if and only if
  all zones have equal areas.
• However, there is always a price to be paid for
  capacity improvement. In general, capacity
  improvement is at the expense of degradation of
  other performance parameters, such as the number
  of required intracell handoffs.

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Part 2 Sectorized Cellular Systems

• Chih-Wei Yi
• Department of Computer Science
• National Chiao Tung University

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Channel Reuse Factors

• The ratio of the number of channels assigned to
  each base station to the total number of channels
  is referred to as the channel reuse factor.
• The channel reuse factor of a conventional
  cellular system with N-cell clustering is 1/N.
• High reuse factor can be achieved by reducing the
  cluster size.
• However, the cluster size cannot be too small in
  order to maintain the SIR above an acceptable
  level.
• For examples, 18 dB, 14 dB, and 9 dB are required
  as the minimum acceptable SIR thresholds in
  Advanced Mobile Phone System (AMPS), digital Time
  Division Multiple Access (TDMA) such as the
  IS-136 system, and Global System for Mobile
  Communication (GSM), respectively.

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Radiation Patterns of Directional Antennas
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Trisection Cellular Systems

• Wide-beam trisector cellular (WBTC) systems one
  cell is composed of three 100 to 120
  directional antennas.
• Narrow-beam trisector cellular (NBTC) systems
  one cell is composed of three 60 to 70
  directional antennas.

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Six-Sector Cellular Systems

• Each cell is composed of six 60 directional
  antennas.
• The interlocking layout the boresight direction
  of each 2 antennae points to the right middle of
  a pair of adjacent base stations. Each sector in
  this layout is a quadrilateral.
• The triangular layout the boresight directions
  of the antennae point to the six adjacent base
  stations. Each sector is a regular triangle.

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The N?k Reuse Plan

• Consider an N-cell tiling in a k-sector cellular
  system.
• To each cochannel sublattice, exactly k channels,
  instead of one, are assigned, with one channel
  per sector.
• The allocation of the k channels to the sectors
  are the same for all base stations in this
  sublattice.
• The reuse factor is still 1/N but enjoys higher
  SIR.

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Example 7?3 Reuse Plan in an NBTC System

• The worst-case interference scenario in 7?3 reuse
  plane two from the main lobes, and the other
  four from the minor lobes.
• In an omni-directional system, the worst SIR is
  from 17.8 dB.
• Here the worst SIR increase to 20.5 dB.

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Base Diversity

• A mobile user near cell/sector boundaries can be
  potentially served by multiple sectors and/or
  cells.
• At a given location, the SIR with base diversity
  is defined as the best SIR that can be offered by
  all possible potential serving sectors.

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Channel Alternation and Rotation (CAR) N?(kx)
Scheme

• Consider an N-cell tiling in a k-sector cellular
  system.
• Each cochannel sublattice receives exactly kx
  channels. However, each base station only uses k
  channels.
• To avoid the nearest main-lobe interference,
  different base stations in the same sublattice
  may use different sets of k channels.
• The reuse factor is , that is at most
  1/N. But the CAR reuse plane provide better SIR.

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CAR Reuse Plan for WBTC (a) 2?(31) (b)
3?(31). (Figure 6)
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CAR Reuse Plan for WBTC (c) 4?(31) (d)
5?(31). (Figure 6)
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CAR Reuse Plan for NBTC (a) 1?(31) (b)
2?(31). (Figure 7)
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CAR Reuse Plan for Six-Sector Cellular with
Interlocking Layout (a) 1?(64) (b) 2?(60).
(Figure 8)
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CAR Reuse Plan for Six-Sector Cellular with
Interlocking Layout (c) 3?(60). (Figure 8)
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CAR Reuse Plan for Six-Sector Cellular with
Triangular Layout (a) 1?(62). (Figure 9)
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CAR Reuse Plan for Six-Sector Cellular with
Triangular Layout (b) 2?(60) (c) 2?(60).
(Figure 9)
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Worst SIR of Various CAR Reuse Plans
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Reuse Factor Analysis

• For the same or comparable targeted SIR level,
  CAR often allows for smaller cluster size than
  the conventional reuse plan.
• Suppose that a CAR N?(kx) plan and a
  conventional N?k plan both meet the required SIR
  level. Then as long as , CAR
  provides tighter channel reuse.
• In IS-136 systems, the minimum SIR level is 14dB.
• NBTC The tightest conventional reuse plan is the
  3?3 reuse plan, The tightest CAR reuse plan is
  the 2?(31) reuse plan.
• These two plans have the reuse factor of 3/9 and
  3/8 respectively.
• WBTC The tightest conventional reuse plan is the
  4?3 reuse plan. The tightest CAR reuse plan is
  the 3?(31) reuse plan.
• Both reuse plans have the same reuse factor of
  3/12.
• But the CAR reuse plan achieves a better worst
  SIR both with and without base diversity.

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Conclusion

• The CAR reuse plan improves the radio capacity
  and/or signal quality without introducing
  additional costs. The implementation of the CAR
  reuse plans merely requires a different channel
  allocation to the directional antennae.
• CAR can also be combined with other capacity
  expansion techniques.
• For example, the combination of CAR and reuse
  partitioning, called Channel Alternation and
  Rotation for Tiered Network (CART), was proposed
  to further increases frequency reuse efficiency.
• V.A. Nguyen, Channel Alternation And Rotation for
  Sectorized and Tiered Cellular Systems, Ph.D.
  dissertation, Department of Computer Science,
  Illinois Institute of Technology, May 2003.