Capacity Analysis in Hybrid Wireless Networks2

Capacity Analysis ofHybrid Wireless

NetworksBy: Hakimeh Purmehdi

Advisor: Dr. Farshad Lahouti

Wireless Multimedia Communications Laboratory

Department of Electrical and Computer Engineering

University of Tehran

1

Outlines:

Conventional Cellular Network and its Challenges

Probability of Blocking in Hybrid CDMA Networks

◦ System Model

◦ Probability of Blocking for Hybrid Network with

Complete Coverage and Coverage-limited Relays

◦ Numerical Analysis

Probability of Outage in Hybrid CDMA Networks

◦ System Model

◦ Probability of outage for Conventional Cellular and

Hybrid CDMA Networks.

◦ Simulation & Analytical Results

Conclusions2

Conventional Cellular

and Hybrid Networks:

Challenges and Overview

3

Conventional Cellular Network and

its Challenges

Congested cells

Load over on the MSC

Poor coverage on the

edge of cells

Hybrid Network

Advantages:

Extend the coverage area

Reduce the interference

level by decrease in the

range of transmissions

Distribute the traffic

homogenously

throughout the network

4

Ad Hoc Elements in Hybrid Net.

5

Users of the Network.

Relays as dedicated

elements of the Network.

In-Band Frequency.

Out-of-Band Frequency

Probability of Blocking

in Hybrid CDMA

Networks

6

System Model

Each sector has C channels and traffic

intensity of Ak Erlang.

Each sector can transfer a maximum of XO

calls to, or accept up to XI channels from the

other sector(s).

A fraction of all available channels in each

cell are sharable.

Traffic model: M/G/C/C

Out-of-Band Frequency Relays

BS 1

BS 2

R

3BSCS

BS 3

7

BS 1

BS 2

R

2BSCS

Pb for Hybrid Network with with

Coverage-limited Relays

Regarding to the relay coverage ratio, p, if :

◦ New call is located in the coverage area of a relay.

◦ One of the ongoing calls within the coverage area

of the relay which is connected to the base station

is connected to the neighboring base station via the

relay and its channel is allocated to this new call.

active calls in neighboring sectors:

◦ No. of ongoing calls within the coverage area of

the relay:

8

),( 21 ii

),( 21 jj

Pb with Coverage-limited in

2BSCS◦ This call is blocked with probability of 1 if:

or

◦ This call is blocked with probability of if:

and

XCi 1Cii 221

Cij 11Ci 1

21

21

,,,

,,21 Υ),,,1(

AAXC

AXCAXC

bS

AAXCCP

p1

1

1

,12

1

,2,

1

1

,2,

!)!(

)1(

YY),,,(

N

Mu

buC

CCuua

N

Mt

atCbt

N

Ms

bsCas

CCu

ppae

baNM

XC

Ct

AtCAtAtCAtACACAAXCS1

,2,,2,,,,,, 12212121YY

9

,...2,1,0 , !0

0

,,

rdxr

xe

rx

r

s

asar

0,1,2,...r , !

,

r

ae ra

ar

r

Crs

srsra

arsrs

ppae

)!(!

)1(Y ,

321

321321

,,,,

,,,,2,,,2 'Y

AAAXC

AAAXCXCAXCAXCAXC

bS

P

p1

Using the same approach as previous case

with a six-dimensional Markov chain, the

call is blocked with probability of 1 if:

or or

This call is blocked with probability of

if: and

Probability of Blocking:

Pb with Coverage-limited in

3BSCS

XCi 21 XCii

XCii

2

2

31

21 Ciii 3321

Cij 11Ci 1

321321321 ,,,1,,2,,,,,,, AAAXCXCXCAXCAXCAXCAAAXCS

cbaNNMM

bacPNMNacbPNMNcbaPNMN

bacNMcabNMcbaNMcbaPNM

,,,1,,

,,,,,,,,,,,,,,,

,,,,,,,,,,,,,,,,,

K

csbsarcbasr ,,,,,,, T

r

Cs

as

C

XCs

asar

1

,

1

,, YT

]Y[12

1

,,,,,,,,,,,

XC

XCs

sM

XCt

btasbaNMcrcbaNMr

N

Cs

bsMas

C

XCs

bsMasbaNM

1

,,

1

,,,,, TYT

23

1 1

,,,,,,,, fffX

r

rN

XCs

srM

Pt

ctbsarcbaPMNK

Cr

Cr

ar

ar

ar

,

,

,Y

f

cbaMNcbasrNMNMMbcaMNMcbaMNMcbaNM ,,,,,,,,,1,,,,,,,,,,,, K'K'''

]YYYY['1

,,

1

1

,,,,,,,,,

N

XCr

brMar

XC

Cr

brMar

C

XCr

brMarcrcbaNM

1 1 13

,,1,,,,11,0,,,1

1

,,,, ]ff[)!(!

)1(K'

M

Cr

rNM

Ns

srC

Nt

ctbsrNMNbcNrNMcbN

CCrr

cbaMNCrC

ppa

s

ru

buaKsrbaK ,,,,,, f

10

The stationary channel state probability:

Cii

XCii

Csr

s

A

r

A

i

A

i

A

PXC

r

XC

s

sr

ii

ii2

,0

2

!!

!!

21

21

0 0

21,

21

21

Pb with Complete Coverage in

2BSCS

C+X

C-X C+X

i2

i1

BS1

BS2

Ci1,i2

Ci1,i2+1

Ci1+1,i2Ci1,i2

λδλδ

(i2+1)μδ

(i1+1)μδC-X

11

),,(

),,( ,1,

,2

1

0

,

AXCXC

AXCXC

PPP

AXCAXC

XC

XCr

rrC

XC

r

rXCb

M

Ni

AiNMAiANAMANM ,,,1,2),,(

M

Ni

AiNMAiANAMANM ,,,1,),,(

Following similar approach, the stationary

channel state probability :

The Probability of Blocking:

Pb with Complete Coverage in

3BSCS

),,( ..

),,( ..

!!!

!!!321

0 0 0

321

),,(

321

321

iiiLts

tsrLts

t

A

s

A

r

A

i

A

i

A

i

A

XC

r

XC

s

XC

t

tsr

iii

iiiP

Ciii

XXCiiiiii

XXCiii

iiiL OI

OI

3

),2min(2,,

)2,min(,,

:),,(

321

313221

321

321

12

u

m

d

u

dm

u

m

u

C

r

ddmmmuAr

C

Cr

C

rCCs

AsrCAsAr

C

Cr

dmuArdmAC

b

ACrCrCrCCC

ACrCCACC

P

0

,

1

,3,,

1

,,

,,,minmax,,max

,,,,

mu CCii 32

mu CCii 31mu CCii 21

uC

uCuCmC

mC

mC

dC

dCdC

Ciii 3321

1BS

2BS 3BS

)2,min(

)2,min()2,min(

)2,min(

IOd

OIIOm

OIu

XXCC

XXXXCC

XXCC

13

Call Service Time Distribution

Function

For call service time:

◦ Conventional cellular networks (usually voice

calls): Exponential distribution

◦ Multimedia traffic in new wireless networks:

heavy-tail distribution functions such as Pareto

distribution.

For voice and non-voice calls the arrival rate

follows the Poisson distribution function.

m

mm

X

xx

xxx

x

xF

0

)(1)(

is the positive minimum of mx X21

14

Cc=300 channel.

No. of shared

channels, X=15.

Two scenarios:

◦ Ac1=Ac2=Ac3=240

Erlangs

◦ Ac1=300, Ac2=180,

Ac3=240 Erlangs

Numerical Analysis for Coverage-

limited

0 0.2 0.4 0.6 0.8 110

-5

10-4

10-3

10-2

10-1

100

Coverage Ratio (p)

Pro

babil

ity o

f B

lockin

g (

P b)

X=15

2BSCS: C=50, A1=50, A

2=30

2BSCS: C=50, A1=40, A

2=40

3BSCS: C=100, A1=100, A

2=60, A

2=80

3BSCS: C=100, A1=80, A

2=80, A

2=80

3BSCS: C=50, A1=50, A

2=30, A

2=40

15

45

15

0 0.2 0.4 0.6 0.8 110

-4

10-3

10-2

10-1

100

Coverage Ratio (p)

Pro

bab

ilit

y o

f B

lock

ing

(P

b)

2BSCS: C=50, A1=50, A

2=30, X=10

3BSCS: C=100, A1=100, A

2=60, A

3=80, X=10

3BSCS: C=100, A1=100, A

2=60, A

3=80, X=20

Cc=420 channel

A=390 Erlangs

Erlang B:

16

Numerical Analysis for Complete

Coverage

C

r

r

k

C

kb

rA

CAP

0

!/

!/

0 5 10 15 200

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

0.055

Number of shared channels

Pro

bab

ilit

y o

f B

lock

ing

2BSCS, C = 70 , A = 65

3BSCS, C=140 , A =130

3BSCS, C = 70 , A = 65

Probability of blocking for

traditional cellular network

Asymptotic value for probability of

blocking follows:

0282.0)6/2,6/2( ccb CABP

Asymptotic value for probability of

blocking follows:

0067.0)3/3,3/3( ccb CABP

3BSCS obtains a smaller probability of blockingin comparison with 2BSCS.

for covering a large cellular network in 2BSCS or3BSCS scenarios, the number of relays isrespectively, three times or equal to the number ofcells. Therefore, the latter scheme is moreeconomical and also yields less Pb than the formerscheme.

Sectorization allows for independent sharing ofthe channels of each sector without affecting theneighboring sectors of the same cell. This in turnallowed for extending the analysis to the wholenetwork.

Numerical Analysis for Complete

Coverage

17

Comparison of Sim. & Analitics for

call service time.

Cc=210.

Ac=195 Erlangs.

Mean time of each call=2min.

0 5 10 15 200.01

0.02

0.03

0.04

0.05

0.06

Number of shared channels

Pro

babil

ity o

f B

lockin

g

3BSCS - Analytic

Exponential Dist. - Simulation

Pareto Dist. - Simulation

18

Probability of Outage

in Hybrid CDMA

Networks

19

System Model

Relay Sub-Cell

Main Cell

Base Station

Relay

Base Station Sub-Cell

Target Sub-Cell

)1,2(),( hh ji

1hj

2hi

60

)0,0(

1j

1i

60

)1,1(),( ji

No. of available codes

in each cell: n

Traffic modell:

M/G/n/n

Traffic intensity/Cell: A

Traffic intensity/Sub-

Cell: A/4

Threshold on BS:

Perfect Power Control

20

System Model

Hard blocking / Code Availability call admission (CA)

The probability of outage together with the probability of hard blocking, constitute the grade of service (GoS) in a CDMA cellular network.

Signal to interference ratio call admission (SIR-CA)

Probability of outage for three scenarios will be investigated:

◦ 1st Scenario: A traditional cellular network with CA call admission,

◦ 2nd Scenario: A Hybrid network with SIR call admission, probability of outage for target BS,

◦ 3rd Scenario: A Hybrid network with SIR call admission, probability of outage for other BS,

CA

OP

SIR

OP

COP

21

Interference

The received signal power at the target base

station from the mth user in the cell (i, j):

Total interference: summation of all

interferer located inside and outside the cell.

→

A call request is accepted if a free code is

available.

10

)0,0,(

),,(

)0,0,(

)0,0(,),(,

10)(mjim

m

jim

mD

DX

Euclidian distance from the mth

user to the center of the cell (i, j)path loss exponent

shadowing loss factor for the link

between the user m and the base

station of the cell (i, j) with

normal N(0,σψ2)

0 1

),(

1

)0,0,()0,0()0,0(

i j

jiu

g

gXuI

The number of active users within

the six symmetric cells identified

by (i, j) The number of active users

connected to the target base

station

)0,0()0,0( uIIout

}Pr{}Pr{ )0,0(

O

out

CA

O IIP

)0,0(uO

22

The mean & variance of the individual interferer is:

According Fenton’s method, it is assumed that Iout has the log-normal where Iout=10-φ/10:

and

Then, the probability of outage is derived as:

This Probability should be averaged over the u(0,0).

x

x

O

O

OO

out

CA

O

dxexQQ

IP

2/10

10

10/

2

2

1)( ,

log10log10Pr

10PrPr

zQzuPCA

O

10

)0,0(

log10Pr

2

2

2

2

1

a

Ln

out

out

I

I

a

aLnoutI

225.0

A traditional cellular network with CA call admission

(Our proposed method)

nz

rA

zAzu

n

r

r

z

0 ,

!/

!/Pr

0

)0,0(

23

22

)0,0,(

),,(

),(

a

m

jim

ji eD

DE 2

),(

4

2

)0,0,(

),,(2

),(

22

ji

a

m

jim

ji eD

DE

0 1

2

),(

0 1

2

),(),(

2 6i j

ji

i j

jijiI Auout

0 1

),(

0 1

),(),( 6i j

ji

i j

jijiI Auout

Assume:

Chernoff Bound achieves the upper bound

for the

),(~ 10 210/

)0,0,(

NXm

)1()var(

)(

2222

22

222

)0,0,(

2

),(

5.0

)0,0,(),(

aaa

mji

aa

mji

eeX

eXE

)(log10)0,0,(

),,(

10

m

jim

D

D222 2 a

A traditional cellular network with CA call admission0.1×Ln(10)

CA

OP

24

Relays with CA call admission:

: the number of active users inside the BS sub-cells.

: the number of active users inside the BS sub-cells.

Mean & variance of interference Iout :

Preposition 1: The average number of active users on the BS sub-

cell, , in a hybrid CDMA network with SIR-CA control for the

BSs is:

0 1

2

)2,2(

2

),(

2

0 1

)2,2(),(

6

6

h h

hhhhout

h h

hhhhout

i j

jirbjirI

i j

jirbjirI

uuu

uuu

A Hybrid network with SIR call

admission for target BS

4/Aur

bu

0

0

!/4/

!/4/1

4dx

rA

xAf

Au

x

r

r

x

Ib out

STEP 1

Given the value of , and

are obtained

buoutI

2

outI

STEP 2

is recomputed in terms of the

mean and variance of bu

outI

STEP 3

Assuming an initial value for

, the iterative method

is executed until it converges.bu

25

bu

ru

can be described by two distribution functions:

◦ Normal → CLT → ANL-CLT

◦ Log-Normal → Fenton’s method → ANL-FM

Probability of Outage:

Relays with SIR-CA:

Rescaling of conventional cellular network

A Hybrid network with SIR call

admission, Pb for target BS

outIf

0 4/

1Pr)(A

udxxIoutagexfP b

outI

SIR

O out

ε-x

r

r

ε-x

x

rA/

ε-xA/ε-xtP

0

!/4

!/4)(

26

rb uu

0 1

),(6h h

hhout

i j

jibI u

0 1

2

),(

2 6h h

hhout

i j

jibI u

Preposition 2: In the hybrid CDMA system with

SIR-CA over the BSs and CA over the relays, in

the steady state with no outage over any of the

BSs, a newly admitted call in the target BS, the

probability of outage in BSs except the target BS

using Union bound is

where

QoS in Hybrid Networks

0 1

)2,2(~

6h h

hh

i j

jiCO PP

0

0

0

)2,2( Pr

!/4/

!/4/)( dxxkx

rA

kAxfP

x

k

newx

r

r

k

Iji outhh

dssfskxxkxx Snewnew

0

)(Pr1Pr

sRxx nnew )(

27

28

Simulation & Analytical Results

Simulation:

◦ 91 cells

◦ Target cell is

in the center

of the area

◦ Monte Carlo

σ=3.5dB, ε= 14dB

ANL-FM is accurate approximation in comparison

with Chernoff bound

10 12 14 16 18 2010

-2

10-1

100

Traffic Intensity per Cell (Erlangs)

Pro

bab

ilit

y o

f O

uta

ge -

POC

A

Cellular Sys. Chernoff Bound

Cellular Sys. ANL-FLT

Cellular Sys. Sim.

Traditional cellular network with CA call admission

29


Simulation

Also:

◦ LG-CLT

◦ LG-FM

σ=3.5dB, ε= 15.5dB

ANL-FM is accurate approximation in comparison

with other three methods.

Traditional cellular network with SIR call admission,

Pb for target BS

10 15 20 25 30 35 40 45 50 55

10-4

10-3

10-2

10-1

Traffic Intensity per Cell (Erlang)

Pro

bab

ilit

y o

f O

uta

ge

- P

OSIR

Cellular Sys. Sim. =2.5dB

Cellular Sys. ANL-CLT =2.5dB

Cellular Sys. LG-CLT =2.5dB

Cellular Sys. ANL-FM =2.5dB

Cellular Sys. LG-FM =2.5dB

30


A hybrid network with SIR-CA relays and BSs

achieves better performance.

Comparison of relays in both CA call admission and

SIR-CA

15 20 25 30 35 40 45 50 5510

-2

10-1

Traffic Intesity per Cell (Erlang)

Pro

bab

ilit

y o

f O

uta

ge

PO

SIR-Hybrid Sys. w CA Relays, =4dB

PO

SIR-Hybrid Sys. w SIR-CAC Relays, =4dB

PCO

-Hybrid Sys. w CA Relays, =4dB

PCO

-Hybrid Sys. w SIR-CAC Relays, =4dB

31

Simulation & Analytical ResultsCapacity Analysis of Conventional Cellular & Hybrid

CDMA Networks

5 10 15 20 25

10-3

10-2

10-1

100

Traffic Intensity per Cell (Erlangs)

Pro

bab

ilit

y o

f O

uta

ge (

PO

)

PO

SIR

Cell. Sim.

PO

SIR

Cell. ANL-FM

PO

SIR

Hyb. Sim.

PO

SIR

Hyb. ANL-FM

PCO

Cell. Sim.

PCO

Cell. ANL-FM

PCO

Hyb. Sim.

PCO

Hyb. ANL-FM PCO

PCO

Hybrid

Cellular

σ= 3dB, ε=15.5dB

32


The average number of active users in hybrid CDMA

network is much more than the amount which is presented

by the conventional CDMA cellular network.

Effect of Shadowing on the Average Number of

Active Users

10 15 20 25 30 35 40 45 50 55

10

15

20

25

30

35

40

45

50

55

60


Ave

rage

Num

ber

of A

ctiv

e U

sers

Cell. Simul. = 0

Cell. Simul. = 2.5dB

Cell. Simul. = 4dB

Cell. ANL-FM = 0

Cell. ANL-FM =2.5dB

Cell. ANL-FM = 4dB

Hyb. ANL-FM =0

Hyb. ANL-FM = 2.5dB

Hyb. ANL-FM = 4dB

Cellular

Hybrid

33


Effect of Shadowing on the POSIR & PCO

10 15 20 25 30 35 40 45 50 5510

-4

10-3

10-2

10-1

100


Pro

babi

lity

of O

utag

e -

P OSIR

Cell. Sim. = 0

Cell. Sim. = 2.5dB

Cell. Sim. = 4dB

Cell. ANL-FM = 0

Cell. ANL-FM = 2.5dB

Cell. ANL-FM = 4dB

Hyb. ANL-FM = 0

Hyb. ANL-FM = 2.5dB

Hyb. ANL-FM = 4dB

10 15 20 25 30 35 40 45 50 5510

-6

10-5

10-4

10-3

10-2

10-1

100


Prob

abili

ty o

f O

utag

e -

P CO

Cell. Sim. = 0

Cell. Sim. = 2.5dB

Cell. Sim. = 4dB

Cell. ANL-FM = 0

Cell. ANL-FM = 2.5dB

Cell. ANL-FM = 4dB

Hyb. ANL-FM = 0

Hyb. ANL-FM = 2.5dB

Hyb. ANL-FM = 4dB

34

Conclusions: Challenges in Cellular Network.

Advantages of Hybrid Network as a solution.

Hybrid Network overview.

Two hybrid model was introduced.

◦ In load balancing: 2BSCS & 3BSCS

◦ In interference reduction: A hybrid network model

Pb in hybrid networks for 2BSCS & 3BSCS in two scenarios:

◦ Complete coverage of relays.

◦ Coverage limited relays.

Result: Load balancing improves the Capacity of hybrid network

in comparison with conventional cellular networks as:

◦ Both introduced schemes are effective for improving the

grade of service compared to conventional cellular networks.

35

◦ The 3BSCS scheme provides a better performance even

with a smaller number of relays per cell.

◦ 15% of available codes in each sector to dedicate for

channel sharing in complete coverage scheme, or 50%

of a sector area for coverage-limited scheme achieves

the performance improvement.

◦ The presented analysis for the sectorized configurations

is applicable to the whole network.

◦ According to comparisons of simulation vs. analytical

results, the Pb in our analysis is independent of the

distribution function of call service time.

Conclusions:

36

Two call admission policies are introduced as CA call admission

& SIR-CA.

Probability of outage according to different call admission

policies in both conventional cellular and hybrid CDMA

networks is investigated.

Results:

◦ A new approximation method named as ANL-FM in addition

to an iterative method for computing the probability of outage

is introduced.

◦ The accuracy of this method compared to Chernoff bound and

other three proposed approximation methods by simulation vs.

analytics.

◦ Hybrid network achieves better performance in terms of

probability of outage & the average No. of active users

compared to the conventional cellular network.

Conclusions:

37

◦ Total probability of blocking is the function of hard

blocking and soft blocking.

Future work: Relays in our system model are Out-of-

Band frequency. It can be assumed that relays work

in In-band frequency. Hence, the issue changes to

Cooperative problem in cellular network. The

Probability of outage according to SIR-CA in this

cooperative network can be investigated.

Conclusions & Future Work:

38

Publications: H. Purmehdi and F. Lahouti, “Channel Sharing in

Hybrid Sectorized Cellular Networks with Coverage-

limited Relays”, IEEE European Modeling

Symposium, EMS’09, Greece, Athens, Nov. 2009.

(Accepted)

H. Purmehdi, A. Behnad and F. Lahouti,

“Performance Analysis of Hybrid CDMA Systems”,

IEEE European Modeling Symposium, EMS’09,

Greece, Athens, Nov. 2009. (Accepted)

H. Purmehdi, A. Behnad and F. Lahouti,“Hybrid

CDMA System with SIR based Call Admission

Control”, (Under Preparation)

39

Thanks for your

attention!

Any Question?!

40

Documents

Capacity Analysis in Hybrid Wireless Networks2