Cellular

CMBUkTI

5

mUldæanRKwHé n Cellular Communications 1

cMnucsMxan; eKalkarN_rbs; Cellular ktþaEdleRbIR)as; Frequency Reuse Co-channel nigkarqøgKñarvag Channel EdlenACitKña   

2



Trunking

nigkMriténesva

eKalkarN_rbs; 

(Grade of Service)

Cellular

enAkñúgRbB½n§

Cellular

cMnYntMbn;esvasrubRtUv)anEbgEckeTACatMbn;tUc² CaeRcIn EdlEpñktUc²nimYy²kMnt;faCa {Cell{. 

BhuekaNesµIGaceRbIsMrab;tMNageGayTMhMrbs;

cell

.

Cells

Edlmanrag 6 RCugRtUv)aneKniymeRbIBIeRBaH ³

> rUbragrbs;vaRsedogeTAnwgrgVg; 3

>

eFVIeGaymankarerobcM

cellular

EdlmanlkçN³jwk

nigEpñkEdll¥\tex©aHéntMbn;esva enAkñúgRbB½n§



cellular

“frequency

re-use”

eFVIeGaymansmtßPaBeRbIR)as;nUv frequency spectrum

EdlxVHxateLIgvij.



Cells

EdleRbIR)as;

frequency

dUcKñaRtUv)aneKehAfa

“co-channel cells” (

]TahrN_

cells

tMNageGayGkSr

A)

.

Frequency

reuse

RtUv)ankMNt;eday co-channel interference

.

eKalkarN_rbs;

Cellular (t)

4

N (

:

cMnYnrbs;

RtUv)aneKsÁal;faCa

EdlmanenARKb;

cells “cluster size”

rW

“frequency re-use factor” )

J:

cMnYnrbs;

channels

EdlmanenARKb;

K:

cMnYnrbs;

channels

EdlmanenAkñúg

(=

cMnYnsrubrbs;

frequency carriers

“cluster”

cell cluster

mYy

pþl;eGayedayRbB½n§

)

 K=JXN M:

cMnYnrbs;

cell clusters

C :

cMnYnrbs;

channels

EdlmanenAkñúgRbB½n§

enAkñúgRbB½n§ (RtUv)aneKsÁal;faCa

“system capacity” )  C=MXK

5



enAeBlEdlktþaén

frequency

kareFVIeLIgvijnUv

reuse

fycuH

(

]TahrN_

EdldUcKñakan;Etjwk)

frequency

enaHRbB½n§smtßPaB

nwgekIneLIg.

eTaHbICay:agNak¾edaytMéltUcbMputrbs; KWGaRs½yeTAelIkMritén

co-channel interference

ktþaEdleRbIR)as; BinitüeTAelI

cells

EdlmanRCug

.

Frequency

eLIgvij

6

RCugmYyEdlmancMgayesµI²KñacMnYn 6 Kt;

 Cell 6 channel

N

“nearest” co-

EdlenACit

6



ExSRbsBVRtg;cMnuckNþalén

cell

NamYy

ehIycMnucEdlCitvanimYy²man KMlatBIKñacMgay 60 dWeRk 

edIm,Irk

co-channel

neighbors

EdlenACitCageKbMputRtUveFVItam 2

CMhanEdlmandUcxageRkam -

rMkilelI i cells tamry³ExSén 6 RCug bgVil

ehIyrMkilelI Edl

:

dWeRktamTisedARsbRTnicnaLikar

60

j cells i

nig

KWCaGBaØatrbs;RbB½n§sMrab;kMnt;nUvTMhMrbs;

j cluster

7

N = i2+ij+j2

ktþaEdleRbIR)as; (t)

Frequency

eLIgvij

8

ktþaEdleRbIR)as; (t)

Frequency

eLIgvij

R:

kaMrbs;

D1:

cMgayrvagcMnuckNþalén cells BIrEdlenACitKña D1

D:

=

cab;BIcMnuckNþaleTAdl;kMBUl)

cell (

3

2Rcos30 = 2R 2 =

3

R

cMgayrvagcMnuckNþalén

2 “co-channel” cells

EdlenACitKña

D 2 = ( jD1 cos θ ) 2 + (iD1 + jD1 sin θ ) 2

= (i 2 + ij + j 2 ) D1

2

D1 = 3R N = i 2 + ij + j 2

= 3NR 2 ⇒ D = 3 NR

q:

Gnu)atén

frequency reuse

9

def

q=

D = 3N R

ktþaEdleRbIR)as; (t) q

Channels



Frequency

eLIgvij

dUcKñaRtUv)aneRbIR)as;Cajwkjab;

.

smtßPaBrbs;RbB½n§fycuH . 

tMéltUcbMputrbs; kMNt; S/I = S

q

GaRs½yelIkMritén

“signal-to-co-channel interference ratio”

co-channel

interference

.

eday

NI

∑I k =1

k

10



eyIgRtUvkarkMNt;famBlsMrab;RKb;RKgelIkarrMxan interference

. cat;TukfaRKan;EtCa

 d L(d ) = L(d 0 ) d  0

   

scale path-loss effect

−n

d 0 : Reference distance

n : Path loss exponent 

BinitüeTAelI downlink (]TahrN_ forward link) ehIynµtfakMlaMgbBa ¢ÚnBIRKb; BS TaMgGs;KWdUcKña bnÞab;mk S

I k ∝ Dk−n

Dk :

cMgayBI

kth co-channel cell BSS

ktþaEdleRbIR)as; (t)

eTAkan;

MS

Frequency

.

eLIgvij

11



snµtfa

MS

manTItaMgsßitenA

]TahrN_ the worst case scenario)

cell boundary (

ehIyeRbIR)as;nUvPaBRbhak;RbEhl ]TahrN_fa S = I

S

=

NI

∑I k =1

k

Dk >> R

R −n ( D / R) n q n ( 3 N ) = = = NI NI NI N I .D − n

]TahrN_ : snµtfa path-loss model

Dk ≈ D

interference

CamYynwg

⇒

1

S n  q = N I .  I  

ekIteLIgBI

path loss exponent n=4

first-tier co-channel cells

. cat;Tukfa

ehIyKNna

frequency reuse factor

edIm,IbMeBjnUvkMritGb,brmaEdlGacTTYlyk)anén

S/I=19dB

.

enAkñúgbBaðaenHeyIgminKitdl;karrMxancab;BIlMdab; TI 2 rhUtdl;lMdab;fñak;Edlx<s;bMput , dUecñH q = (6.100)

1

4

= 4.9492

N1=6

.

N = q 2 3 = 8.165 → 9

12

epÞógpÞat;CMerIsrbs;Gñk

S = I

(

3N NI

ktþaEdleRbIR)as; (t)

)

n

= 20 .84 dB N =9

Frequency

eLIgvij

eyIgsikSareTAelIkarBitmYy val¥CaCagkarEdlsnñidæanTaMgRsugeTAe lI

Dk ≈ D

S R −n ≈ I 2( D − R ) −n + 2 D −n + 2( D + R ) −n

=

2(q −1)

−n

1 + 2q −n + 2(q +1) −n

13

. n = 4, N = 7

q = 3 N = 4.6 ⇒S / I =17 .3dB

. n = 4, N = 9

q = 3 N = 5.2 ⇒S / I =19 .8dB

karqøg 

Channel EdlenACitKña

karqøg

channel

EdlenACitKñaenH

vaCalT§plmkBIsBaØaEdlenACitKñaenAkñúg

frequency

eTACasBaØaEdleyIgcg;)an. edIm,Ikat;bnßynUvplb:HBal;enH eyIgRtUv³ 

eRbIcenøaH

channel

eGay)anCak;lak;edaykMnt;

channels

14

EdlenACitKñakñúg

cell

epSgKña. ]TahrN_

RbsinebIeyIgkMnt; frequency carrier f 1

enAkñúg

cell A

enaH

carrier frequency

bnÞab;EdlTMenr (vasßitenAEk,r KYrEtkMnt;eGayenAepSgeRkABI eRbI

 (

modulation schemes

]TahrN_ begáIt



sidelobes

Edlman

f1 )

cell A

out-of-band radiation

EdltUcCag). ]TahrN_

Receiver front end filter

tUc MSK

KWl¥Cag

QPSK

.

edayRbugRby½tñ.

Trunking 

enAkñúg

cellular system

cMnYnmYyén

radio channels

EdlTak;TgKña 15

RtUv)aneRbIsMrab;bMerIeGayGñkeRbIR)as;d¾eRcIn mYy EdlRtUv)an begáIteLIgedaykar frequency reuse)

nig

trunking

]TahrN_

design cellular (

. eyIg)ansikSarYcmkehIyGMBI

frequency

. \LÚvenH eyIgnwgsegçbBIKMnitmUldæanrbs;

reuse

 Trunking

GaceGay

mobile users

eRbIrYmKñanUv

radio channels

cell

nimYy²eTAtamtMrUvkarCaeKal



GaRs½ynwgbNþúMén

cell

nimYy²KYrEtRtUv)ankMnt;tammeFüa)ay³ > RKb; >

channels

traffic

cMnYnén

radio channels

trunking

³

enAkñúg

enAkñúg

TaMgGs;RtUv)aneRbIR)as;RKb;RKan;

Call blocking rate

KWTabCagkarkMnt;cMnuccab;epþImdMbUg

16



rgVas;én

traffic efficiency

³

1 Erlang

RtUv)ankMnt;edayGaMgtg;sIuetén ¢Úneday channel

channel

traffic

EdldwkCBa

mYy²EdleRbIR)as;eBjEtmþg. ]TahrN_

mYyEdlRtUv)aneRbIGs;ry³eBl

kñúgkMLúgeBlbBa¢Ún

0.5 Erlang

én

radio

30 minutes

traffic

kñúgeBl 1 em:ag.

Grade of Service (GoS)  Grade of Service (GoS)

KWCargVas;lT§PaBrbs;

EdlGacdMeNIrkareTAkan;

trunked system

kMLúgeBlEdlCab;rvl;bMput.

user

mYy

GoS

CaFmµtaRtUv)anpþl;Ca³

17

> »kasEdlkar

call

> »kasEdlkar

call

mYyRtUv)an

block (

sMrab;RbB½n§

Erlang B)

mYyRtUv)anBnüaeBlyUrCaRbB½n§rgcaM (

sMrab;RbB½n§

Erlang C)

niymn½yTUeTA  Blocked call (lost call)

³ KWCakar

call

ecjEdlmin)ansMercenAeBlEdlmankarCab;rvl;eRcIn  Average holding time (H)  Traffic intensity (A)

³ KWCary³eBlmFüménkar

³ rgVas;eBlEdl

CamFümEdlvas;KitCa

channel

call

mYy

eRbI EdlkareRbI

channel

Erlang

18

 Load

³ Ca

traffic intensity

Edlqøgkat;

trunked radio system

Edlvas;enAkñúg

1

Erlang  Request rate ( λ )

³ CacMnYnmFüménkar

call

kñúgeBlmYyrbs;

user

mñak;

Grade of Service (GoS)  Traffic intensity

Edlpþl;eday

user

mñak;² (KitCa

Erlang)

KW³

Au = λ.H



sMrab;RbB½n§mYyCamYy

load)

u users enaH offered traffic intensity (traffic

KW³

A = u. Au = u.λ.H

19



enAkñúgRbB½n§

C-channel trucked

mYy snñidæanfa

RtUv)anEckcayesµIKñakñúgcMeNam enaHnaMeGay

traffic intensity

kñúg

1 channel

channels

traffic

TaMgGs;

KW³

Ac = u. Au C = u.λ.H C



PaBxusKñarvag }offered }

RbePTén 

RbsinebIKµan

channels

traffic

nig }carried }

traffic

Trunked System

EdlTMenr enaH³

20

> karesñIrbs; ehIykar call

call

user

RtUv)an

block

edayKµandMeNIrkar

RtUv)anlubecj RBmTaMgeGay

user

TMenrkñúgkar

mþgeTot → Blocked Calls Cleared

> kar

call

RtUv)anBnüaeBlrhUtdl;

channel

mYyTMenr

→ Blocked

Calls Delayed

snñidæanfakar P ( X = i ) = e −λ

λi i!

call

mkdl;

, i = 0,1,2...

X

 a − eα y , y ≥ 0 fY ( y ) =   0, y < 0

holding time Y

Poisson distribution

mYy³

λ : Request rate E[ X ] = λ

snñídæanfa

tamrUbmnþ Var [ X ] = λ

tamrUbmnþ

exponential distribution

mYy³

α : exponent parameter

21

1 α Var[Y]= α 2

E[Y]=H= 1

karlub

Blocked Calls (

rUbmnþ

Erlang-B)

xageRkamkarsnñídæan³ > mancMnYn user d¾c,as;las;mYy > man }memoryless} énkar call vaGacniyay)anfaRKb; users rYmTaMg blocked user Gacnwgcg;eRbI channel EtmYyenAeBlNamYy > mancMnYn channel c,as;las;EdlTMenrenAkñúg trunked channels’ 

pool 

kMritlT§PaB

call blocking

RtUv)anpþl;eGayedayrUbmnþ

Erlang-

B PB =

AC C! C

∑A

K

K!

A:

cMnYnGaMgtg;sIuetsrubén

offered traffic

k =0

C:

cMnYn

channels

srubenAkñúg

system

22



karsnñidæanfamancMnYn

user

c,as;las;enAkñúg

CalT§plviC¢manénkar)a:n;sµanelI kMritlT§PaBénkar

block

GoS

system

.

CamYynwgcMnYnBitR)akdrbs;

KWticCagkarEdlGaceFVI)anedayrUbmnþ

karBnüarrbs;

Erlang-B

users

.

Blocked Calls ( rUbmnþ

Erlangl-C) 

kñúgkarsnñidæandUcKñaenAkñúgKMrUBImun

eyIgeRbIrUbmnþ call

Erlang-C

edIm,IEsVgrkkMritlT§PaBénkar

mYyEdlminmandMeNIrkarPøam²eTAkan;

channel

mYy

23

P ( Delay > 0) =



AC A C −1  AC + C!1 − ∑ AK K ! C k = 0 

(

RbsinebIKµan

)

channel

NaTMenrPøam²enaHeT enaHkar

nwgRtUvBnüar ehIykMritlT§PaBEdlBnüarkar nwgRtUvCMrujeGayrgcaMeRcIn Cag P ( Delay

>t ) =P (delay

>0) P ( Delay

>t Delay

t seconds

call

call

.

>0)

= P ( Delay > 0) exp[ −(C − A)t H ]

]TahrN_³ sikSaelI cMnYn

21

én

channels

cellular system

mYyEdlman

416 radio channels

TaMgenHRtUv)ankMnt;eRbICa

eGaykareRbIR)as;eBlén

channels

CamFüménkar

call

. ]bmafa

control channels

mYy KW

. 3 minutes

24

naMeGaykMriténkar

block

kMnt;BIcMnYnénkar

calls

KW

2%

enAkñúg

cMnYnén

voice channels

KW

cMnYnén

voice channels

kñúgmYy

395 N

ehIyktþaén cell

frequency reuse

esµInwg 9.

mYykñúgry³eBl 1 em:ag.

416 – 21 = 395 cell

KW

≈ 44 N =9

CamYynwg

44 channels

man

esµInwg

Erlang-B

traffic intensity

enAkñúg

34 .683 ≈12 calls 3

EdlTMenr nig 34.683 Erlangs

PB = 0.02 ,

. emIltarag

.

Appendix F

kñúg

34 .683 × 60 ≈ 693 calls 3

1 cell

kñúg

ry³eBl 1 cell

1 minute

ry³eBl

1 minute

25