Chapter 5 The Cellular Concepthscc.cs.nthu.edu.tw/~sheujp/lecture_note/11wn/Chapter 05.pdf · Cell...

Copyright © 2011, Dr. Dharma P. Agrawal and Dr. Qing-An Zeng. All rights reserved. 1

Chapter 5

The Cellular Concept


Outline

Cell Area

Actual cell/Ideal cell

Signal Strength

Handoff Region

Capacity of a Cell

Traffic theory

Erlang B and Erlang C

Frequency Reuse

How to form a cluster

Cochannel Interference

Cell Splitting

Cell Sectoring


Cell Shape

Cell

R

(a) Ideal cell

R

R

R

R

(c) Different cell models (b) Actual cell


Impact of Cell Shape and Radius on Service Characteristics

3R

Triangular cell (side=R)

2pR

p R2

Circular cell (radius=R)

6R

Hexagonal cell (side=R)

4R

R2

Square cell (side =R)

Channels/Unit Area as Size of Cell Reduced by a Factor M

Channels/Unit Area as #of Channels Increased by a Factor K

Channels/ Unit Area with N Channels/ Cell

Boundary Length/ Unit Area

Boundary

Area

Shape of the Cell

R3

4

R

4

R

2

R

34

2

N

R

235.1

N

R

2

N

Rp

23

N34

R

2

KN

R

235.1

KN

R

2

KN

Rp

23

KN34

R

2

2 NM

R

2

2

35.1

NM

R

2

2 NM

Rp

2

2

3

NM34

R

2

2

33R

2

4

3R


Signal Strength

Select cell i on left of boundary

Ideal boundary

Signal strength

(in dB)

Select cell j on right of boundary

Cell j

-60

-70

-80 -90

-100

Cell i

-60

-70

-80

-90

-100


Actual Signal Strength

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 Cell j


Universal Cell Phone Coverage

Maintaining the telephone number across

geographical areas in a wireless and mobile system

Microwave Tower

Cell

Cincinnati

Washington, DC


Rec

eived

pow

er P

(x)

Distance x of MS from BS

Variation of Received Power


Handoff Region

BSi

Signal strength due to BSj

E

X1

Signal strength due to BSi

BSj X3 X4 X2 X5 Xth

MS

Pmin

Pi(x) Pj(x)

BSj X4 X2 Xth

E

X4 X2 Xth

By looking at the variation of signal strength from either base station it is

possible to decide on the optimum area where handoff can take place

10

Handoff Strategies Used to

Determine Instant of Handoff

Relative signal strength

Relative signal strength with threshold

Relative signal strength with hysteresis

Relative signal strength with hysteresis and

threshold

Prediction techniques


Cell Capacity

Average number of MSs requesting service (Average

arrival rate):

Average length of time MS requires service (Average

holding time): T

Offered load: a = T

e.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.,

Erlangs

call

Sec

Sec

Callsa 3

360

3600

30


Cell Capacity

Average arrival rate during a short interval t is given by t

Average service (departure) rate is

The system can be analyzed by a M/M/S/S queuing model, where S is the number of channels

The steady state probability P(i) for this system in the form (for i =0, 1, …, S)

)0(!

)( Pi

aiP

i

Where and

S

i

i

i

aP

0 !)0(

-1

a


Capacity of a Cell

The probability P(S) of an arriving call being blocked is the probability that all S channels are busy

This is Erlang B formula B(S, a)

In the previous example, if S = 2 and a = 3, the blocking probability B(2, 3) is

So, the number of calls

blocked 30 x 0.529 = 15.87

S

i

i

S

i

a

S

a

SP

0 !

!)(

529.0

!

3

!2

3

)3,2(2

0

2

k

k

k

B


Capacity of a Cell

7065.02

0.529)-3(1

channels ofNumber

channel used of portions x Erlangs

Capacity

nonblocked Traffic Efficiency

]1[

),(.

!!1

!1,

1

0

aSBaS

aSBS

i

a

aSS

a

aSS

a

aSCS

i

iS

S

The probability of a call being delayed:

This is Erlang C Formula

For S = 5, a = 3, B(5,3) = 0.11

Gives C(5,3)=0.2360


Cell Structure

F2 F3 F1

(a) Line

Structure

F3

F2 F1

F3

F2 F1

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

(b) Plan Structure

F3

F2

F4

F1 F1

F2

F3

F4 F5

F6

F7

(b) Plan Structure

F3

F2

F4

F1 F1

F2

F3

F4 F5

F6

F7


Frequency Reuse

Fx: Set of frequency

7 cell reuse cluster

F1

F2

F3

F4 F5

F6

F7 F1

F2

F3

F4 F5

F6

F7

F1

F2

F3

F4 F5

F6

F7 F1

F2

F3

F4 F5

F6

F7

F1

F1

F1

F1


Reuse Distance

• For hexagonal cells, the

reuse distance is given by

RND 3

where R is cell radius and N is the

reuse pattern (the cluster size or

the number of cells per cluster).

NR

Dq 3

• Reuse factor is

F1

F2

F3

F4 F5

F6

F7

F1

F2

F3

F4 F5

F6

F7

F1

F1

R Cluster


Reuse Distance (Cont’d)

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

where i and j are integers

N = 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 28, …, etc.

The popular value of N being 4 and 7

22 jijiN

j direction

60°

1 2 3 … i

j direction

60°

1 2 3 … i i direction


Reuse Distance (Cont’d)

(4, -3)

(-3, 3)

u and v coordinate representation of cells with (0, 0) center

22 jijiN with i and j as integers

u (v =0)

0 1

2

-1

-2

-1 -2

1

2

3 4

-3 -4

3

-3

v (u =0)


We can obtain label L for the cell whose center is at (u, v).

Reuse Distance and Channel Set to Use

NvuiL mod])1[(

7mod)3( vuL

For j = 1, the cluster size is given by 12 iiNThen defining

u v

0 3

6

6

5

4 1

1

2 2

5 2

3

4

4

3

2

1

0

6

4

5

6

0

1

5

4

3

2

1

2

5

6

0

1

3

2

1

2

3

4

5

6

0

6

5

5 1

4 3

4 6

0

6 3

4

3

2

1

0

6

5

4

1

0

6

0

6

5

4

3

2

2 5

3

2

1

0

6

5

4

6

0

4

3

1

2

3

3

4

5

6

0

1

0

1

2

3

4

5

5 2

4

5

6

0

1

2

3

0

1

Labeling

cells with

L values

for N=7

u 0 1 -1 0 0 1 -1

v 0 0 0 1 -1 -1 1

L 0 3 4 1 6 2 5

For N = 7, with i = 2, j = 1:

Gives assignment of

channels to use in

different cells

An alternative choice for 7-cell cluster


Reuse Distance and Channel set to use

For N = 13, i = 3, j = 1; 13mod)4( vuL

Cell

labeled

with L

values

for N = 13;

0 to 12

u

v

0 4

8

12

11

9 5

1

2 12

1 10

3

10

3 7

11

6 2

9

4

10

11

12

0

8

7

6

6

7

8

9

10

4

3

2

2

3

4

5

6

0

12

11

12

0

1

2

3

9

8 5

7

8

9

10

1

3

4

5

6

7

8

5

9

11

12

6

7

3

2

1

0

9

10

11

7

6

5

4

3

0

1

11

10

9

8

7

4

5

2

1

0

12

11

10

6

5

4

3

2

1

8

10

9

8

7

6

5

4

12



Mobile Station

(MS)

Serving Base Station (BS)

Second tier cochannel

Base Station

First tier cochannel

Base Station

R

D1

D2

D3

D4

D5

D6


Worst Case of Cochannel Interference

Mobile Station

Serving Base Station Co-channel Base Station

R

D1

D2

D3

D4

D5

D6



Cochannel interference ratio is given by

M

k

kI

C

ceInterferen

Carrier

I

C

1

where I is co-channel interference and M is 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

g where g is the propagation path loss

slope and g = 2 ~ 5


Cell Splitting

Large cell (low

density)

Small cell (high

density)

Depending on traffic patterns

the smaller cells may be

activated/deactivated in order

to efficiently use cell resources.

Smaller cell (higher

density)


Cell Sectoring by Antenna Design

(a). Omni

120o

(b). 120o sector

a

b

c

120o

(c). 120o sector (alternate)

a b

c

(d). 90o sector

90o a

b

c

d

60o

(e). 60o sector

a

b

c

d

e

f


Cell Sectoring by Antenna Design

Placing directional transmitters at corners where three

adjacent cells meet

A

C

B

X


Worst Case for Forward Channel Interference in Three-sectors

BS

MS

R

D + 0.7R

D

BS

BS

gg

7.0qq

C

I

C

RDq /

D + 0.7R

D

BS

where g is the propagation path loss slope and g = 2 ~ 5


Worst Case for Forward Channel Interference in Three-sectors

gg

7.0qq

C

I

C

BS

MS

R

D’

D

BS

BS

BS

D

RDq /



Worst Case for Forward Channel Interference in Six-sectors

D +0.7R

MS

BS

BS R

RDq

q

C

I

C

/

7.0

g


Chapter 5 The Cellular Concepthscc.cs.nthu.edu.tw/~sheujp/lecture_note/11wn/Chapter 05.pdf · Cell...

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Transcript of Chapter 5 The Cellular Concepthscc.cs.nthu.edu.tw/~sheujp/lecture_note/11wn/Chapter 05.pdf · Cell...