Uplink User Capacity in a CDMA Macrocell with a Hotspot Microcell: Effects of Transmit Power Constraints and Finite Dispersion

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Uplink User Capacity in a CDMA Macrocell with a
Hotspot Microcell Effects of Transmit Power
Constraints and Finite Dispersion

• Shalinee Kishore (Lehigh University)
• skishore_at_lehigh.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

• Macrocell and microcell use CDMA over same set
  of
• frequencies ? cross-tier interference.
• Users select their base stations according to
  (slowly-
• changing) local mean path gains.
• Ideal power control by each base is assumed.

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• Previous Work Uplink user capacity quanitifed
  assuming
• 1) No constraint on transmit power
• 2) Infinitely dispersive channels
• (S. Kishore, et al., IEEE Trans. On Wireless
  Communications, March 2003.)
• Goal Determine uplink user capacity for this
  system for
• 1) Finite power constraint
• 2) Finitely dispersive channels
• Infinitely dispersive channel infinitude of
  strong
• multipaths ? received signal has constant
  output power
• after RAKE processing.
• Finitely dispersive channel finite multipaths
  ? output
• power has variable fading.

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Effect of Transmit Power Constraint
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Problem Statement
Given

• N total users, NM macrocell and Nm microcell.
• Distribution of user locations.
• Random codes of length W/R, where W is system
• bandwidth and R is user data rate.
• Minimum SINR requirement, G.
• Transmit power constraint, Pmax.
• dmax, max. distance over which users are
  distributed.

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Problem Statement (Contd)

• Path gain between a user and a base is modeled
  as
• Users choose base station for which its path
  gain is higher.
• Determine
• Uplink user capacity such that POutage does not
  exceed
• some specified value, as a function of Pmax and
  dmax.

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Outage
Previously for no transmit power constraint,
SINR requirement can be met if and only if (K
- NM)(K - Nm) gt IM Im where K W/RG 1
(single-cell pole capacity), IM and Im are
normalized cross-tier interferences (random
variables). We computed the probability of not
meeting this condition, given either 1) NM and
Nm ? Pinf(NM,Nm) 2) N NM Nm ? Pinf(N)
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Outage (Contd)

• System unable to support N users if infeasible
  and/or if
• transmit power (P) of any one user exceeds
  Pmax.
• PrOutageN Pinf(N) (1 - Pinf(N))PrP gt
  PmaxN,
• We determined how to exactly compute and
  reliably
• approximate PrP gt PmaxN.
• Result PrOutageN can be solved as a
  function of
• dimensionless parameter F

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Uplink User Capacity versus Max Power Constraint
N, Total Number of Users, 5 Outage
F
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Effect of Finitely Dispersive Channels
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Motivation

• Thus far considered infinitely-dispersive
  uplink channel.
• Actual channels have finite number of paths,
  each with
• variable fading ? user output signal has
  variable fading.
• Can model fading with modified path gain Tij
  rTij,
• where r is a unit-mean random variable.
• We examine performance for four channel types
• Rural Area (RA)
• Typical Urban (TU)
• Hilly Terrain (HT)
• Uniform multipath

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Uniform Multipath Channel
Channel Delay Profile
power
Height of each line is mean- square gain of a
Rayleigh fading path.
delay
Lp Number of Paths

• Diversity Factor (DF) measures the amount of
  multipath
• diversity in channel. Computable for any delay
  profile.
• Uniform channel has DF Lp.
• Non-uniform channels with Lp paths have DF lt Lp.
  
• For example, DFRA 1.6, DFHT 3.3, and DFTU
  4.0.

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• Finite Dispersion Problem Statement
• Given
• Single-macrocell/single-microcell system
• Propagation model with variable fading
• Pmax Max transmit power level
• dmax Max distance over which users are
  distributed
• hW Noise power
• Determine
• Uplink user capacity so that PrOutage does not
  exceed
• some given value (e.g., 5).
• for the three standard environments, i.e., RA,
  TU, and HT, as
• functions of F.
• for any environment when F gt F.

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Variable Power Fading Key Results

• Uplink capacity for RA, HT, and TU terrains
  constant over
• F gt 0.1 and decreases sharply in F when F lt
  0.1.
• Capacity reduction relative to infinitely
  dispersive channel as much as 15 for the RA
  environment.
• When F gt F, user capacity in uniform multipath
  channel
• can be approximated as

, for Lp gt 1.

• Showed uplink capacity is the same for channels
  with same DF.

Replace Lp in with DF
DF
Napprox
Non-Uniform Delay Profile
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Uplink User Capacity under Finite Dispersion
N, Total Number of Users, 5 Outage
Lp, Number of Paths
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Conclusion

• Studied impact of transmit power constraints and
  finite
• dispersion on uplink user capacity of two-tier
  cellular
• CDMA system.
• Developed exact analytical methods and reliable
• approximation schemes.
• Quantified effect of maximum power constraints
  on
• coverage area and capacity.
• Used uniform multipath channel to approximate
  uplink
• user capacity for finitely-dispersive channels.
• Excellent agreements between analytical
  approximations
• and simulation results.