Impact of Interference Model on Impact of Interference Model on Capacity in CDMA Cellular Capacity in CDMA Cellular

NetworksNetworks

Robert Akl, D.Sc.Robert Akl, D.Sc.

Asad ParvezAsad Parvez

University of North TexasUniversity of North Texas

OutlineOutline

• Introduction to CDMA networksIntroduction to CDMA networks• Average interference modelAverage interference model• Actual interference modelActual interference model• Optimized capacityOptimized capacity• 2D Gaussian user model2D Gaussian user model• ConclusionsConclusions

Code Division Multiple Access Code Division Multiple Access (CDMA) Overview(CDMA) Overview

• Multiple access schemesMultiple access schemes

Call 1

Call 3

Call 2

Call 4

Freq

uenc

y

Time

FDMAFr

eque

ncy

Time

Call 1 Call 2 Call 3

Call 4 Call 5 Call 6

Call 7 Call 8 Call 9

Call 10Call 11Call 12

TDMA CDMA

Frequency

Time

Code

Call 1Call 2

Call 3Call 4

1 bit period

1 chip period

Data Signal

PN-code

Coded Data Signal

PN-code

Decoded data Signal

Spr ea di ng

De- sp re ad in g

f

f

f

f

Data Signal

Interference

Recovered Data

Signal

Spread Spectrum: Direct Spreading

Factors Affecting CapacityFactors Affecting Capacity

d1

d2

Base Station

c1

c2

Distance

Pr2

Pr1

• Power ControlPt1: Power transmitted from c1Pt2: Power transmitted from c2Pr1: Power received at base station from c1Pr2: Power received at base station from c2

Pr1 = Pr2

Pt1

Pt2

Time

• Soft handover of calls

Factors Affecting Capacity (cont.)

• Universal frequency useUniversal frequency use

• Reverse link vs forward linkReverse link vs forward link

• Voice activity factorVoice activity factor

AC

F

GB

ED

AA AA

A

AA

AA

AA

TDMA or FDMA CDMA

Reverse link

Forward link

Factors Affecting Capacity (cont.)

Relative Average Inter-cell Relative Average Inter-cell Interference ModelInterference Model

dA

Cell j

Cell i

jr

ir

yxdAA

n

yxr

yxrji

j

j

Cji

mi

jmjI ,

/,

10,E

2

10

),( ),(

),(2

yxdAyxr

yxrI Cj m

i

mj

A

neji

j

js

jiI Relative average interference at cell i caused by nj users in cell j

A

B

Back

1111 1212 1313 …… …… 1M1M

2121 2222

3131 3232

…… ……

…… ……

M1M1 M2M2 MMMM

ijF ,

Interference Matrix

jn

MjinIijF

j

jji

cellin users ofnumber theis and

,,...,1,for /],[ where

Hence, the total relative average inter-cell interference experienced by cell i is

ijFnIM

j

ji ,1

1111 1212 1313 …… …… 1M1M

2121 2222

3131 3232

…… ……

…… ……

M1M1 M2M2 MMMM

12I

C

]2,1[12 FI

Relative Actual Inter-cell Relative Actual Inter-cell Interference ModelInterference Model

• Interference matrix F cannot be calculated in advance• Instead, a new interference matrix U is computed as follows• For a user k in cell j, the relative actual interference offered by this user to cell i is

m

i

jsk r

rejiU

2

jiUikji

jn

k

M

j

I

for ,11

• Hence, the total relative actual inter-cell interference at cell i caused by every user in the network is

D

E

k users in cell j

Actual Interference Matrix Actual Interference Matrix UU

•Example: for a new call in cell 2, compute row matrix U[2,i] for i = 1,…,M using equation D

]2M ...... 23 22 21[2 iU

• Update 2nd row of interference matrix U by adding the above row matrix to it.

1111 1212 1313 …… …… 1M1M

2121 2222

3131 3232

…… ……

…… ……

M1M1 M2M2 MMMM

iUijU 2],[

CapacityCapacity

• The capacity of a CDMA network is determined by maintaining a lower bound on the bit energy to interference density ratio, given by

Mi

NWInRE

E

I

E

iib

b

i

b

,...,1for

/1 00

W = Spread signal bandwidth

R = bits/sec (information rate)

α = voice activity factor

ni = users in cell i

N0 = background noise spectral

density

F

,...,1for

1/

11/

0

Mi

cNE

RWIn eff

bii

• Let τ be that threshold above which the bit error rate must be maintained, then by rewriting Eq. F

G

Back

Capacity CasesCapacity Cases

• Equal capacity:Equal capacity: all cells have an equal number of users all cells have an equal number of users

ini allfor n

• Optimized Capacity:Optimized Capacity: A set of users in each cell obtained A set of users in each cell obtained by solving following optimization problemby solving following optimization problem

.,...,1for

, subject to

, max1

n

Mi

cIn

n

effii

M

ii

H

SimulationsSimulations• Network configurationNetwork configuration

• COST-231 propagation modelCOST-231 propagation model• Carrier frequency = 1800 MHzCarrier frequency = 1800 MHz• Average base station height = 30 metersAverage base station height = 30 meters• Average mobile height = 1.5 metersAverage mobile height = 1.5 meters• Path loss coefficient, m = 4Path loss coefficient, m = 4• Shadow fading standard deviation, Shadow fading standard deviation, σσss = 6 dB = 6 dB• Processing gain, W/R = 21.1 dBProcessing gain, W/R = 21.1 dB• Bit energy to interference ratio threshold, τ = 9.2 dBBit energy to interference ratio threshold, τ = 9.2 dB• Interference to background noise ratio, IInterference to background noise ratio, I00/N/N00 = 10 dB = 10 dB• Voice activity factor, α = 0.375Voice activity factor, α = 0.375

• These values in Eq. G give upper bound on the relative These values in Eq. G give upper bound on the relative interference in every cell, c_eff = 38.25.interference in every cell, c_eff = 38.25.

Simulations – Equal CapacitySimulations – Equal Capacity

• Average interferenceAverage interference• Users in each cell: 18Users in each cell: 18

• Actual interferenceActual interference• Users in each cell: 17Users in each cell: 17

Simulations – Optimized Capacity Vs Actual Simulations – Optimized Capacity Vs Actual Interference CapacityInterference Capacity

• Optimized Capacity using average interference = 559

• Simulated Capacity using actual interference = 554

More Simulations – Actual InterferenceMore Simulations – Actual Interference

• Simulated Capacity = 568• Simulated Capacity = 564

Individual Cell Capacity ComparisonIndividual Cell Capacity Comparison

• Comparison of cell capacity for 3 simulation trials.

• Comparison of average cell capacity for 50 simulation trials.

Extreme Cases Using Actual Interference – Extreme Cases Using Actual Interference – Non-Uniform DistributionNon-Uniform Distribution

• Maximum network capacity of 1026 with best case non-uniform user distribution

• Maximum network capacity of 108 with worst case non-uniform user distribution

Model User Distribution by 2D GaussianModel User Distribution by 2D Gaussian

• Mean = 0 and standard deviation = 200 • Mean = 0 and standard deviation = 500

Model User Distribution by 2D GaussianModel User Distribution by 2D Gaussian

• Mean = 0 and standard deviation = 900 • Non-zero mean, standard deviation between 100-300

ConclusionsConclusions

• Actual interference model is computationally Actual interference model is computationally intensive.intensive.

• Capacity obtained using average interference is Capacity obtained using average interference is close to the capacity obtained using actual close to the capacity obtained using actual interference for uniform user distribution.interference for uniform user distribution.

• Average interference model cannot predict Average interference model cannot predict extreme variations in network capacity under non-extreme variations in network capacity under non-uniform user distribution.uniform user distribution.

• Can use 2D Gaussian distribution to model Can use 2D Gaussian distribution to model uniform and non-uniform user distribution.uniform and non-uniform user distribution.