Wireless Networks Ch4

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Ali BAZZI

Chapter 4

The cellular concept


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2

Cell Shape Actual cell/Ideal cell

Signal Strength Handoff Region Cell Capacity

Traffic theory Erlang B and Erlang C

Cell Structure Frequency Reuse Reuse Distance Cochannel Interference Cell Splitting Cell Sectoring


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Cell

R

(a) Ideal cell (b) Actual cell

R

R R

R

(c) Different cell models


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Select cell i on left of boundary Select cell j on right of boundary

Ideal boundary

Cell iCell j

-60

-70

-80

-90

-100

-60-70

-80-90

-100

Signal strength

(in dB)


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Signal strength contours indicating actual cell tiling.

This happens because of terrain, presence of obstacles

and signal attenuation in the atmosphere.

-100

-90

-80

-70

-60

-60-70

-80

-90

-100

Signal strength

(in dB)

Cell i Cellj


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BSi

Signal strength

due to BSj

E

X1

Signal strength

due to BSi

BSjX3 X4 X2X5 Xth

MS

Pmin

Pi(x) Pj(x)

By looking at the variation of signal strength from either base station it ispossible to decide on the optimum area where handoff can take place.


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( ) ( ) cossinsincos212211

XXRXXRH

+++=

sincos

cossin

21

212

1 XX

XXAR

+

+

=

cossin

sincos

21

212

2

XX

XXAR

+

+

=

X2

X1

Since handoff can occur at sides R1

and R2

of a cell

whereA=R1R

2is the area and assuming it constant,

differentiate with respect to R1(or R

2) gives

Total handoff rate is

( )( ) cossinsincos22121

XXXXAH

++=

His minimized when =0, giving

2

1

2

1

212

X

X

R

RandXAX

H==

side

side


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Average number of MSs requesting service (Average arrivalrate):

Average length of time MS requires service (Averageholding time): T

Offered load: a = Te.g., in a cell with 100 MSs, on an average 30 requests are

generated during an hour, with average holding time T=360

seconds.

Then, arrival rate =30/3600 requests/sec.

A channel kept busy for one hour is defined as one Erlang (a),i.e.,

Erlangscall

Sec

Sec

Callsa 3

360

3600

30==


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Average arrival rate Average arrival requests during a short interval tis given by

t

Assuming Poisson distribution of service requests, theprobabilityP(n, t) for n calls to arrive in an interval of

length tis given by( ) t

n

en

ttnP

=

!),(


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Probability of an arriving call being blocked is( ) ,

!

1

!,

0

=

=S

k

k

S

k

aS

aaSB

where Sis the number of channels in a group.

Erlang B formula

( )( ) ( )

( ) ( )

,

!!1

!1,

1

0

=

+

=

S

i

iS

S

i

a

aSS

a

aSS

a

aSC Erlang C formula

where C(S, a) is the probability of an arriving call being delayed with a

load and Schannels.

n Probability of an arriving call being delayed is


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Example: for previous example, if S=2,then

B(S, a) = 0.6, ------ Blocking probability,

i.e., 60% calls are blocked.Total number of rerouted calls = 30 x 0.6 = 18

Efficiency = 3(1-0.6)/2 = 0.6

)(channelstrunksofNumber

trafficnonroutedofportionsErlangs

CapacitynonblockedTrafficEfficiency

=

=


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F2 F3F1

F3

F2F1

F3

F2

F4

F1F1

F2

F3

F4F5

F6

F7

(a) Line Structure (b) Plan Structure

Note: Fx is set of frequency, i.e., frequency group.


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F1

F2

F3

F4F5

F6

F7 F1

F2

F3

F4F5

F6

F7

F1

F2

F3

F4F5

F6

F7 F1

F2

F3

F4F5

F6

F7

F1

F1

F1

F1

Fx: Set of frequency

7 cell reuse cluster


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F1

F2

F3

F4F5

F6

F7

F1

F2

F3

F4F5

F6

F7

F1

F1

For hexagonal cells, the reuse distance isgiven by

RND 3=

R

whereR is cell radius andNis thereuse pattern (the cluster size or the

number of cells per cluster).

NR

D

q 3==

Reuse factor is

Cluster


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The cluster size or the number of cells per cluster is given by22

jijiN ++=

where i andj are integers.

N= 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 28, , etc.The popular value ofNbeing 4 and 7.

i

j

60o


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(b) Formation of a cluster for N = 7

with i=2 and j=1

60

1 2 3 i

j direction

i direction

(a) Finding the center of an adjacent cluster

using integers i and j (direction of i and j can

be interchanged).

i=2i=2j=1

j=1

j=1

j=1

j=1

j=1

i=2

i=2

i=2i=2


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(c) A cluster with N =12 with i=2 and j=2

i=3

j=2

i=3 j=2 i=3

j=2

i=3

j=2

i=3j=2i=3

j=2

(d) A Cluster with N = 19 cells with i=3

and j=2

j=2

j=2

j=2

j=2j=2

j=2

i=2

i=2

i=2

i=2

i=2

i=2


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In general:N=i2 +ij +j

where i andj are integers. For computing conve- nience, we

assume i j

In reality j must be equal to 1, so:

N=i2 +ij +j

19


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First we select a cell, make the center of the cell as theorigin, and form the coordinate plane as shown in next

Figure.

The positive half of the u-axis and the positive half of thev-axis intersect at a 60-degree angle.

Define the unit distance as the distance of centers of twoadjacent cells.

Then for each cell center, we can get an ordered pair (u, v)to mark the position.

20


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We hadN= i2+ i + 1

Letsdefinethe labelL for the cell whose center is at (u, v )

as:

L = [(i + 1) u + v]mod N

For the origin cell whose center is (0, 0), u = 0, v = 0,using last equation we obtainL = 0 and label this cell as 0.

22


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Example if N=7,7= i2 + i + 1 so i= 2

And L = (3u + v) mod 7

And we can compute labelL for any cell using its centers

position (u, v) :

23


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Using the same method, we also have the results forN=13, with i=3andj=1,giving L=(4u+v) mod 13

25


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Common reuse pattern of hexagonal cells:

26


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As indicated earlier, there are many cells using the samefrequency band.

All the cells using the same channel are physically locatedapart by at least reuse distance.

Even though the power level is controlled carefully so thatsuch co-channels do not create a problem for each other,there is still some degree of interference due to nonzero

signal strength of such cells.

In a cellular system, with a cluster of seven cells, therewill be six cells using co-channels at the reuse distance.

The second-tier co-channels, are at two times the reusedistance apart, and their effect on the serving BS is

negligible.27


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Mobile Station

Serving Base Station

First tier cochannel

Base StationSecond tier cochannelBase Station

R

D1

D2

D3

D4

D5

D6


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Cochannel interference ratio is given by

=

==M

k

kI

C

ceInterferen

Carrier

I

C

1

whereIis co-channel interference andMis the maximum

number of co-channel interfering cells.

For M = 6, C/I is given by

=

=

M

k

k

R

D

C

I

C

1

- where is the propagation path loss slope = 2~5.


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Mobile Station

Serving Base Station Co-channel Base Station

R

D1

D2

D3

D4

D5

D6

D1 =D2 =DR D3 =D6 =D D4 =D5 =D+R

q=D/R is frequency

reuse factor


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We saw the BSs of all cells transmit information atthe same power level so that the net coverage area

for each cell is the same.

In reality we would like to service users in a cost-effective way, and resource demand may depend on

the concentration of users in a given area.

This implies that additional BSs need to beestablished at the center of each new cell that has

been added so that the higher density of calls can be

handled effectively. As the coverage area of newsplit cells is smaller, the transmitting power levels

are lower, and this helps in reducing co-channel

interference.


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Large cell

(low density)

Small cell(high density)

Smaller cell

(higher density)

Depending on traffic patterns the smallercells may be activated/deactivated in

order to efficiently use cell resources.


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For GSM an antenna is not omnidirectional

It covers an area of 60 degrees or 120 degrees; theseare called directional antennas, and cells served by

them are called sectored cells.

Antennas are mounted on a single microwave towerlocated at the center of the cell, and an adequatenumber of antennas is placed to cover the whole 360

degrees of the cell

In practice, the effect of an omnidirectional antennacan be achieved by employing several directionalantennas to cover the whole 360 degrees.


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The advantages of sectoring are : it requires coverage of a smaller area by each

antenna and hence lower power is required in

transmitting radio signals

It also helps in decreasing interference betweenco-channels


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60o

120o

(a). Omni (b). 120o sector

(e). 60o sector

120o

(c). 120o sector (alternate)

a

b

c

ab

c

(d). 90o sector

90oa

b

c

d

a

b

c

d

e

f


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Placing directional transmitters at corners where threeadjacent cells meet

A

C

B

X


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BS

MS

R

D + 0.7R

D

BS

BS

BS

( ) ++=

7.0qqC

IC

RDq /=


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( ) ++=

7.0qq

C

I

C

BS

MS

R

D

D

BS

BS

BS

D

RDq /=


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D +0.7R

MS

BS

BSR

( )RDq

q

C

I

C

/

7.0

=

+

=

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Wireless Networks Ch4