Downlink User Capacity in a CDMA

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Downlink User Capacity in a CDMA Macrocell with a
Hotspot Microcell
Shalinee Kishore (Lehigh University) skishore_at_lehi
gh.edu Larry J. Greenstein (WINLAB Rutgers
University) H. Vincent Poor (Princeton
University) Stuart C. Schwartz (Princeton
University)
IEEE Globecom 2003
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Two-Tier Cellular CDMA System
Macrocell with embedded Microcell

• Both macrocell and microcell use CDMA over same
• set of frequencies ? cross-tier interference.

• Goal Derive analytical methods that compute
  downlink
• user capacity and account for
• Finitely dispersive channels
• Various methods of downlink power control

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Downlink Capacity Background

• CDMA downlink Base stations transmit
  orthogonal
• signals to users.
• Channel dispersion causes loss of orthogonality
  at user
• terminals.
• Orthogonality factor, b, captures
  loss-of-orthogonality
• of user signals in a channel.
• b ? 0,1, where b 0 when no dispersion in
  channel
• and b 1 when infinite dispersion.
• b can be computed from channel delay profile.

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Orthogonality Factor
Assuming all Rayleigh fading paths, it has been
shown that
where rn is instantaneous gain on n-th path s.t.
b is time-varying but earlier simulation results
show little difference in replacing time
variation by its average.
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• Downlink Capacity Problem Statement
• Given
• Single-macrocell/single-microcell system with N
  NMNm
• users, processing gain W/R and minimum SIR
  requirement G.
• Channel delay profile ? orthogonality factor,
  b.
• Conventional RAKE receivers at user terminals
• Base station k transmits total power PTk, k ?
  M,m
• Macrocell user i assigned fraction xi of PTM
• Microcell user j assigned fraction yj of PTm
• Downlink power control scheme for allocating xi
  and yj

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Overview of Analysis
Instantaneous interference power to macrocell
user k from macrocell base is


where TMk is instantaneous path gain between user
k and macrocell base. (Similar interference at
microcell user.)

• We denote
• TMk as the fast-varying path gain and
• TMk as the slow-varying (locally-averaged) path
  gain.

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Digression Slow-varying Path Gain Model
Fast-varying Path Gain Model

where,
Tjk r Tjk
rn depends on the channel delay profile.
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Overview of Analysis (Contd)
Using SINR requirement for macrocell user i and
microcell user j, we show that PTM 0 and PTm
0 iff


Downlink feasibility condition


where K W/RG .

• Feasibility condition must be met some given
  percentage of
• time by all
• i ? UM (set of macrocell users) and
• j ? Um (set of microcell users)
• Feasibility conditions depend on allocations xi
  yj.

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3 Power Control Schemes

• Uniform power control xi 1/NM and yj
  1/Nm.
• Slow power control power allocation determined
  from
• slow-varying path gains.
• Fast power control power allocation
  determined from
• fast-varying path gains.
• Under fast power control, there exists a single
  feasibility
• condition

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Approximating Capacity for Fast Power Control

• We can approximate feasibility under fast power
  control
• by substituting LHS of feasibility condition by
  its average.

• We find this average for the uniform multipath
  channel.
• Recall uniform multipath delay profile

power
Height of each line is mean- square gain of a
Rayleigh fading path.
delay
Lp Number of Paths
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Digression Treating Non-Uniform Delay Profiles

• For uniform channels, we can compute LHS of
• feasibility condition as a simple function of
  Lp.
• What about non-uniform channels?
• In uplink study, we showed approximate
  equivalence
• between uniform and non-uniform channels using
  the
• channel diversity factor.
• Diversity factor (DF) can be computed for any
  profile.
• Substituting DF for Lp, we can approximate
  average of
• LHS for non-uniform channels.

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Approximating Capacity for Fast PC (Contd)

• Using mean approximation, feasibility condition
• depends on b (RHS) and DF (LHS).
• We found that for DF gt 1,

• Therefore, feasibility condition can be written
  in
• terms of b.
• For maximum total user capacity, NM Nm.
• Combining these results, we obtain

Closed-form solution for downlink user capacity
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Uplink User Capacity as a Function of b
We can recast uplink user capacity in terms of b
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Comparing Uplink and Downlink User Capacities

• We have uplink user capacity in terms of b.
• We have downlink user capacity for fast PC in
  terms of b.
• We can also obtain downlink user capacity in
  terms of
• b for uniform and slow PC.

Major Findings

• Uplink dominates downlink for uniform and slow
  PC.
• Downlink dominates uplink for fast PC.

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Comparing Uplink and Downlink User Capacities for
Fast Power Control
Rural Area Hilly Terrain Typical Urban
Downlink User Capacity
Total Number of Users
Uplink User Capacity
b, Orthgonality Factor
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Conclusion

• Derived downlink feasibility condition for
  single-frequency
• two-tier CDMA system in finitely-dispersive
  channels.
• Used uniform multipath channel to approximate
• downlink user capacity under fast power
  control.
• Found excellent agreements between analytical
• approximations and simulation results.
• Showed that, for uniform and slow power control,
• downlink dominated by uplink.
• Showed that, for fast power control, uplink
  dominated
• by downlink, underscoring importance of fast
  power
• control on two-tier CDMA downlinks.