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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) [email protected] Larry J. Greenstein (WINLAB-Rutgers University) H. Vincent Poor (Princeton University)

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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)

[email protected]

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 Microcell: Effects of Transmit Power Constraints and Finite Dispersion

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: Microcell: Effects of Transmit Power Constraints and Finite Dispersion 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 Microcell: Effects of Transmit Power Constraints and Finite Dispersion


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Problem Statement Microcell: Effects of Transmit Power Constraints and Finite Dispersion

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 (Cont’d) Microcell: Effects of Transmit Power Constraints and Finite Dispersion

  • 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 P[Outage] does not exceed

  • some specified value, as a function of Pmax and dmax.


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Outage Microcell: Effects of Transmit Power Constraints and Finite Dispersion

Previously: for no transmit power constraint, SINR

requirement can be met if and only if

(K - NM)(K - Nm) > IMIm

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 (Cont’d) Microcell: Effects of Transmit Power Constraints and Finite Dispersion

  • System unable to support N users if infeasible and/or if

  • transmit power (P) of any one user exceeds Pmax.

  • Pr[Outage|N] = Pinf(N) + (1 - Pinf(N))·Pr[P > Pmax|N],

  • We determined how to exactly compute and reliably

  • approximate Pr[P > Pmax|N].

  • Result: Pr[Outage|N] can be solved as a function of

  • dimensionless parameter F:


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Uplink User Capacity versus Max Power Constraint Microcell: Effects of Transmit Power Constraints and Finite Dispersion

N, Total Number of Users, 5% Outage

F*


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Effect of Finitely Dispersive Channels Microcell: Effects of Transmit Power Constraints and Finite Dispersion


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Motivation Microcell: Effects of Transmit Power Constraints and Finite Dispersion

  • 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,

  • wherer 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 Microcell: Effects of Transmit Power Constraints and Finite Dispersion

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 < Lp.

    • For example, DFRA= 1.6, DFHT= 3.3, and DFTU = 4.0.


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  • Finite Dispersion: Problem Statement Microcell: Effects of Transmit Power Constraints and Finite Dispersion

  • 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 Pr[Outage] 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 > F*.


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Variable Power Fading: Key Results Microcell: Effects of Transmit Power Constraints and Finite Dispersion

  • Uplink capacity for RA, HT, and TU terrains: constant over

  • F > 0.1 and decreases sharply in F when F < 0.1.

  • Capacity reduction relative to infinitely dispersive channel: as much as 15% for the RA environment.

  • When F > F*, user capacity in uniform multipath channel

  • can be approximated as:

, for Lp > 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 Microcell: Effects of Transmit Power Constraints and Finite Dispersion

N, Total Number of Users, 5% Outage

Lp, Number of Paths


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Conclusion Microcell: Effects of Transmit Power Constraints and Finite Dispersion

  • 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.


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