Capacity and Coverage in Two-Tier CDMA Cellular Networks

Shalinee Kishore

Department of Electrical Engineering

Princeton University

Supported by: AT&T Labs Fellowship

Advisors: H. V. Poor, S. Schwartz,

L. J. Greenstein (WINLAB)

November 25, 2002

Two-Tier System: Macrocells and Microcells

Macrocells - cells in the traditional cellular system

• Cell radii are 1 to 10 km.

• Base stations are costly, antenna tower heights 30 m.

Microcells - smaller cells embedded within macrocells

• Cell radii are less than 1 km.

• Base stations are compact, low-cost, at heights of ~10 m.

MacrocellMicrocell

Desired Coverage

Why Microcells? An Example

High Density of Users

Actual Coverage

Due to high-user-density regions, actual performance of macrocell falls short of desired performance.

Other Reasons: Users can be separated based on

• mobility

• desired data rates

Fast moving users Macrocell

Slow moving users Microcell

Voice users Macrocell

Data users Microcell

Why Microcells? (Cont’d)

Microcells in Single-Frequency Code Division Multiple Access (CDMA) Systems

• CDMA is employed in current cellular phones in US and is standard for third generation systems worldwide.

• CDMA uplink (user-to-base): users assigned random codes.

• Every user’s signal interferes with signals from every other user.

• In single-tier systems (macrocells only), there is in-cell and out-of-cell interference.

• CDMA downlink (base-to-user): base station uses orthogonal codes to transmit to all in-cell users.

• In single-tier systems, there is ideally only out-of-cell interference.

• Dispersive wireless channels cause loss-of-orthogonality, leading to in-cell interference.

• In both the uplink and downlink of two-tier systems, there is additionally cross-tier interference.

Two Classes of CDMA Microcells

Hotspots:* Small cells Clusters/Overlay: Small embedded inside a larger cells that tesselate and spanmacrocell to provide almost all of macrocellcoverage in small region coverage area. No handoffwith high user/traffic between tiers.density or poor coverage. Handoff between tiers. - Single-frequency (near-far problem)

- Dual-frequency (spectral efficiency issues)

* Focus of our research

Previous Work on CDMA Microcells

Hotspots

• Shapira, “Microcell Engineering in CDMA Cellular Networks,” IEEE Transactions on Vehicular Technology, 1994.

• Gaytan and Rodriguez, “Analysis of Capacity Gain and BER Performance for CDMA Systems with Desensitized Embedded Microcells,” ICUPC, 1998.

• Wu, et al., “Performance Study for a Microcell Hot Spot Embedded in CDMA Macrocell Systems,” IEEE Transactions on Vehicular Technology, 1999.

Overlays

• I, et al., “A Microcell/Macrocell Cellular Architecture for Low- and High-Mobility WirelessUsers,” IEEE Journal on Selected Areas in Communications, Vol. 11, Issue 6, Aug. 1993.

• Hamalainen, et al., “Performance of CDMA Based Hierarchical Cell Structure Network,”IEEE TENCON, 1999.

• Ghaleb, et al. “Tiered Services/Private System Support for CDMA Systems,” VTC, 1999.

Expand understanding of Macrocell/Microcell architectures in CDMA networks.

• Develop new methods of analysis for evaluating such systems.

• Evaluate impact of propagation, user distribution, channel fading, maximum transmit power constraints, and dispersion on uplink and downlink capacity and coverage area.

• Devise techniques, tradeoffs, and engineering rules for performance improvement and system deployment.

Research Goals

Summary of Thesis

• Ideal Conditions:

No variable fading of user signal powersUplink: no transmit power constraintDownlink: no in-cell interference

- Single-Macrocell/Single-Microcell (Two-Cell) System

- Multiple-Macrocell/Multiple-Microcell (Multi-Cell) System

- Other Issues in Two-Cell Systems

1) Effect of soft-handoff 2) Effect of voice activity detection3) Effect of propagation parameters4) Microcells as Data Access Points (DAP’s)

• Non-Ideal Conditions:

- Uplink Capacity and Coverage

1) Effect of transmit power constraints

2) Effect of received power fading

- Downlink Capacity: No Multiuser Detectors

1) Effect of Channel Dispersion

2) Alternative methods of power control

Summary of Thesis (Cont’d)

Two-Cell System:Uplink and Downlink in Ideal Conditions

Uplink Capacity of Two-Cell System: Problem Statement

Given:• CDMA system with single macrocell and single microcell• Matched filter receiver and SINR-based power control• Probability density of user location over coverage region• Processing gain (W/R) and desired SINR () • Propagation characteristics, including shadow fading• Criterion for base station selection (e.g., strongest path gain, minimum required transmit power)• Hard-handoff: each user communicates with only one base

Determine:Uplink user capacity (number of simultaneous voice users)

In order to meet SINR requirements for macrocell and microcell users,

where

IINKNK MM ))((

MNN

1

1

Mj

j

Mj Mj

j

j

Mj

j j

MjM

T

TMj

T

TI

T

Tj

T

TI

RWK

Cross-TierInterference

Terms

Feasibility

(single-cell pole capacity)

(Feasibility)

Tij = Transmission gain from base i to user j, = desensitivity

Transmission Gain (Path Gain) Model

bd

dbH

bddbH

T

,

,

4

2

T = Transmission Gain

d = Distance Between User and Base

b = Breakpoint Distance of Median Path Gain

H = Proportionality Constant, Accounts for Antenna Gains and Wavelength

= Lognormal Shadow Fading

),( locations over Users ofDensity ),(where

),(41,

2

),(41,

2),(),(

where

),(],|[

222

222

)),min(,max(

)),max(,min(

1

maxmax2

2

max

2max

yxyxf

wzDgD

hhwDzf

wzDgD

hhwDzf

wzgwzf

dwdzwzfRvvP

XY

MXY

MXY

ZW

wvzb

b

w

vzbw

ZWM

M

M

Finding the CDF for one term of IM: Let TMj/Tj = vM

Exact analysis is doable but extremely complicated.

Simpler Analysis: Mean Approximation

• Instead of computing distribution of and , we compute their mean values

•

• Obtain the following requirement on NM and N:

MI I

vNvENIEvNvENIE MMMMM ][][ and ][][

)1()(

vvNK

NKKN

MM

M

• Since IM and I are sums, they converge fairly tightly to their means.

Capacity Contours for Single-Macrocell/Single-Microcell System

Number of Macrocell Users

Nu

mb

er o

f M

icro

cell

Use

rs

Exact Analysis

Simulation

Approximation

Multicell System:Under Ideal Conditions

Multicell Systems: Key Results

• Showed total user capacity is maximum when there are an equal number of users served by each cell.

• Showed total user capacity is approximately linear in L and M (number of macrocell bases) for L small. Specifically,

LKNMKNKMLN TTM )()(),(

TMN and can be calculated using two-cell techniques.TN

• Derived a simple and reliable approximation for NT:

vv

KN

M

T

1

2

Mutlicell Systems: Key Results (Cont’d)

• Similar analysis yields reliable approximation for NTM.

Single-Macrocell/Multiple-Microcell System

To

tal

Ave

rag

e N

um

ber

of

Use

rs,

95%

Fea

sib

ilit

y

L, Number of Microcells

Simulation Results, error bar

Linear Approximation

Simulation Results, error bar

Linear Approximation

9-Macrocell/Multiple-Microcell System

To

tal

Ave

rag

e N

um

ber

of

Use

rs,

95%

Fea

sib

ilit

y

L, Number of Microcells

Other Issues in Ideal Two-Cell Systems:

Soft-Handoff,Voice Activity Detection,

Propagation Parameter Sensitivity,and Microcells as DAPs

• Effect of Soft-Handoff: Both base stations receive each user’s signal; two signals added

using maximal ratio combining.

- Developed analytical methods to approximate user capacity under soft-handoff.

- Showed user capacity increases by at most 20% over hard-handoff.

Other Issues in Two-Cell Systems: Key Results

• Effect of Voice Activity Factor: Let be the fraction of time voice users speak. Under voice activity detection, mean approximation contour is modified as:

)1(~ˆ

)~ˆ(ˆ~

vvNK

NKKN

MM

M

.~

and ,~

,1ˆ where,

NN

NNKK M

M

• Sensitivity to Propagation Parameters: Fairly insensitive

Other Issues in Two-Cell Systems: Key Results (Cont’d)

Microcells as Data Access Points

DAP: Base station with limited coverage that provides high-speed data access to users one-at-a-time.

Downloading a map to a passing car

Email, voice mail,and fax to thepedestrian

High bit-rateDAP coverage

Low bit-ratecellular coverage

Examples of DAP’s: Infostations, Dedicated Short-Range Communications (DSRC), and Intelligent Transportation Systems (ITS)

Problem Statement

Recall: Microcell coverage shrinks as desensitivity () reduces.

Question: What happens when and microcell coverage area shrinks to that of a DAP?

0

Determine: Per-user throughput, u , and total DAP throughput, , as functions of .

Normalized Average Throughput (E[ / W ]) Versus N

orm

aliz

ed A

vera

ge

Th

rou

gh

pu

t

Desensitivity

Uplink Capacity and Coverage:

Max Power Constraintsand Variable Power Fading

Maximum Power Constraints: Problem Statement

Given:

• A Single-Macrocell/Single-Microcell System

• User distribution

• Propagation model

• Pmax = Maximum transmit power level for any user

• dmax = Maximum distance over which users are distributed

• W = Noise power

Determine:

Uplink user capacity as a function of Pmax and dmax

Maximum Power Constraints: Key Results

• Defined P [Outage] as

• Presented uplink user capacity for given level of outage as a function of a single, dimensionless parameter F, where

.4

max

max

d

b

W

PF

P [Outage] = (1-P [Feasibility]) + P [Feasibility] ·P [Transmit Power > Pmax].

N,

To

tal

Nu

mb

er o

f U

sers

, 5%

Ou

tag

e

4

max

max

db

WP

F

Capacity in System with Max Power Constraints

• Thus far: considered infinitely-dispersive uplink channel user signal has constant output power after RAKE processing.

• Actual channels have finite number of paths with variation about mean path power user signal has variable fading.

• Can model fading with modified transmission gain: Tij’ = Tij, is a unit-mean random variable.

• Examine performance for four scenarios:

• Rural Area (RA) environment• Typical Urban (TU) environment• Hilly Terrain (HT) environment• Uniform multipath channel

Variable Power Fading: Background

Uniform Multipath Channel

Channel Delay Profile

delay

power

Lp

Number of Paths

Height of each path is mean square value of a Rayleigh random-variable.

• 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.

Variable Power Fading: Problem Statement

Given:

• Single-macrocell/single-microcell system• Propagation model with variable fading• Pmax = Maximum transmit power level• dmax = Maximum distance over which users are distributed• W = Noise power

Determine:

Uplink user capacity so that P[Outage] does not exceed .

• for the three standard environments, i.e., RA, TU, and HT, as functions of F.

• for any environment when F >> F* (unlimited terminal power).

• Uplink capacity constant for RA, HT, and TU environments whenF < 0.1 and decreases sharply in F when F < 0.1.

• Capacity reduces by as much as 15% for the RA environment.

• When F >> F*, user capacity in uniform multipath channel can be approximated as:

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

DF Replace Lp in with DF

Napprox

Non-UniformDelay Profile

vvL

LK

N

Mp

p

11

2

, for Lp > 1.

Variable Power Fading: Key Results

RA HT TU

Uplink Capacityusing Simulation

Uplink Capacityusing Approximation

(via Uniform Channel)

33 36 37

32.5 35.86 37.1429

Obtaining NT for RA, HT, and TU Channels via the Uniform Channel

Downlink Capacity:

Channel Dispersionand Effect of Alternate Power Control

Downlink Capacity: Background

• CDMA downlink: Base stations transmit orthogonal signals to users.

• Channel dispersion causes loss of orthogonality at userterminals.

• Orthogonality factor, , captures loss-of-orthogonality of user signals in a channel. [0,1], where = 0 when no dispersion in channel and = 1 when infinite dispersion.

• can be computed from channel delay profile.

• Thus far: assumed = 1 (infinite dispersion) but ideal multiuser detectors removed all in-cell interference.

Downlink Capacity: Problem Statement

Given:

• Single-macrocell/single-microcell system• Channel delay profile, i.e., orthogonality factor, .• Conventional receivers at user terminals• Base station k transmits total power PTk, k { M,}• Macrocell user i assigned fraction xi of PTM

• Microcell user j assigned fraction yj of PT

• Downlink power control scheme for allocating xi and yj

Determine:

Downlink user capacity, number of simultaneous voiceusers

Downlink Capacity: Key Results

• Recast uplink capacity, NT, as a function of .

• Capacity of any channel ( ) approximated using capacity of uniform channel.

• For two of three power control strategies studied (uniform and slow), overall capacity dominated by uplink for all .

• Under fast power control, user capacity can be approximated (by relating to u) as:

• Fast power control leads to downlink capacity that is higher than uplink.

.0 for ,

21

1

2

vv

KN

M

Conclusion

• Analytical methods developed for estimating attainable uplink user capacity in two-tier CDMA systems.

• Analysis done in progression from single-macrocell/single- microcell, to single-macrocell/multiple-microcells, to multiple-macrocells/multiple-microcells.

• Results general with respect to system and propagation parameters and accurate, as confirmed via simulation.

• Analysis extended to DAP, showing how microcells can be modified to support high speed data.

• Computed effect of soft-handoff and voice activity detection on uplink user capacity.

• Quantified effect of maximum power constraints on coverage area and capacity.

• Used the uniform multipath channel to approximate the uplink user capacity and downlink user capacity under fast power control for finitely-dispersive channels.

• Demonstrated the importance of fast downlink power control in two-tier CDMA systems.