wireless communication network lab. chapter 5 cellular concept chih-cheng tseng1ee of niu prof....

Wireless Communication Network Lab.

Chapter 5Cellular Concept

Chih-Cheng Tseng 1EE of NIU

Prof. Chih-Cheng Tseng

[email protected]

http://wcnlab.niu.edu.tw

mailto:[email protected]

http://wcnlab.niu.edu.tw/




Cell Shape

EE of NIU Chih-Cheng Tseng 2

Cell

R

(a) Ideal cell

R

R

R

(c) Different cell models(b) Actual cell

R

A cell is the radio coverage by a transmitting station or a BS. Why hexagon?

• closer to a circle

• can be arranged next to each other without having any overlap and uncovered space in between


Impact of Cell Shape and Radius on Service Characteristics


Shape of the Cell Area Boundary

Boundary Length/ Unit

Area

Channels/Unit Area with N

Channels/Cells

Channels/Unit Area when Number of

Channels Increased by a Factor K

Channels/Unit Area when Size of Cell

Reduced by a Factor M

Square cell (side =R) R2 4R

Hexagonal cell

(side=R)6R

Circular cell (radius=R) pR2 2pR

Triangular cell

(side=R)3R

23 3

2R

23

4R

4

R

4

3R

2

R

4 3

R

2

N

R

2

4 3

3

N

R

2

1.5 3

N

R

2

N

R2

KN

R

2

1.5 3

KN

R

2

KN

R

2

4 3

3

KN

R

2

2

M N

R

2

2

1.5 3

M N

R

2

2

M N

R2

2

4 3

3

M N

R


Signal Strength


Select cell i on left of boundary

Ideal boundary

Signal strength (in dBm)

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 dBm)

Cell i Cell j


Variation of Received Power


Rec

eive

d p

ower

P(x

)

Distance x of MS from BS


Handoff Region


BSi

Signal strength due to BSj

E

X1

Signal strength due to BSi

X3 X5

MS

Pmin

Pi(x) Pj(x)

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.

X4Xth X2

BSj


1 1 2

2 1 2

cos sin

sin cos

H R N N

R N N

N1 is the number of MSs having handoff per unit length in horizontal direction

N2 is the number of MSs having handoff per unit length in vertical direction

Since handoff can occur at sides R1 and R2 of a cell


N2

N1

R 2

R 1

sin1N

cos1N

cos2N

sin2N

N1cosq + N2sinq-A/R12 (N1sinq +N2cosq)=0

Assuming area A=R1R2 is fixed, substitute R2= A/R1, differentiating lH with respect to R1 and equating to 0 gives

Handoff Rate in a Rectangular Area

Wireless Communication Network Lab. Thus, we have:

Simplifying through few steps gives

H is minimized when = 0, giving


Handoff Rate in a Rectangular

2 1 22

1 2

cos sin

sin cos

N NR A

N N

2 1 2

11 2

sin cos

cos sin

N NR A

N N

1 2 1 22 cos sin sin cosH A N N N N

1 11 2

2 2

2 and H

R NAN N

R N


The Offered Traffic Load of A Cell


30 calls 360 sec3 Erlangs

3600 sec calla

Average number of MSs requesting service (Average arrival rate):

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

Offered load: a = T Example:

• 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 an hour is defined as one Erlang


Analyses of The Call Blocking Probability (1)

Average arrival rate is 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)

where and


)0(!

)( Pi

aiP

i

a

1

0

(0)!

iS

i

aP

i


Analyses of The Call Blocking Probability (2)

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) Example: If S=2 and a=3, the blocking probability B(2, 3) is

So, the number of blocked calls is about 300.529=15.87


0

( )! !

S iS

i

a aP S

S i

2 2

0

3 3(2,3) 0.529

2! !

k

k

Bk


The Probability of A Call Being Delayed

The efficiency of a system can be given by

The probability of a call being delayed

This is Erlang C Formula• For S=5, a=3, B(5,3)=0.11, we have C(5,3)=0.2360


Traffic nonblocked Erlangs portions of used channelEfficiency

Capacity Number of channels

3(1-0.529)0.7065

2

1 !

1

1 !0

( , ),

[1 ]!

S

S

aS S a

iSa

S S ai

SB S aC S a

a S a B S ai


Erlang B and Erlang C

Probability of an arriving call being blocked is

where S is the number of channels in a group. Probability of an arriving call being delayed is

where a is the traffic load in Erlang and S is the number of channels.


,

!!1

!1,

1

0

S

i

iS

S

i

a

aSS

a

aSS

a

aSC Erlang C formula

Erlang B formula 0

, ,! !

S kS

k

a aB S a

S k


Frequency Reuse: 7 Cell Reuse Cluster


Fx: A set of frequency bands

F1

F2

F3

F4F5

F6

F7

F2

F3

F4F5

F6

F7

F2

F3

F4F5

F6

F7

F2

F3

F4F5

F6

F7

F1

F1

F1

F1


Reuse Distance (1)

For hexagonal cells, the reuse distance is given by

where R is cell radius and N is the reuse pattern (the cluster size or the number of cells per cluster).

Reuse factor is


RND 3

/ 3q D R N

Reuse distance D

F2

F3

F4F5

F6

F7

F2

F3

F4F5

F6

F7

F1

F1

R Cluster


Reuse Distance (2)

The cluster size or the number of cells per cluster is given by where i and j are integers and N = 1, 3, 4, 7, 9, 12, 13, 16, 19, 21, 28, …, etc.

The popular values of N are 4 and 7. Finding the center of an adjacent cluster using integers i and j


22 jijiN

j direction

60°

1 2 3 … i

i direction


Select a cell and make the center of the cell as the origin.

u-axis and v-axis intersects at 60-degree angle.

Define the unit distance as the distance of centers of two adjacent cells.

Each cell can then get an ordered pair (u,v) to mark the position.

How to Form a Cluster?


(4, -3)

(-3, 3)

u (v =0)

01

2

-1

-2

-1-2

1

2

34

-3-4

3

-3

v (u =0)


Labeling Cells with L Values for N=7 (i.e. i=2, j=1)

For j=1, the cluster size is given by N=i2+i+1.

Define L=[(i+1)u+v)] mod N, we can obtain cell labels L for the cell whose center is at (u,v).

For N=7, i=2 and j=1


u 0 1 -1 0 0 1 -1

v 0 0 0 1 -1 1 1

L 0 3 4 1 6 4 5

u

v

03

6

6

5

41

1

22

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

51

43

46

0

63

4

3

2

1

0

6

5

4

1

0

6

0

6

5

4

3

2

25

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

52

4

5

6

0

1

2

3

0

1

An alternative choice for 7-cell cluster


Labeling Cells with L Values for N=13 (i.e. i=3, j=1)


(4 ) mod 13L u v

u

v

04

8

12

11

95

1

212

1 10

3

10

37

11

62

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

85

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


Common Reuse Pattern of Hex Cell Clusters



Worst Case of Cochannel Interference (Omnidirectional Antenna)


Mobile Station

Serving Base Station Co-channel Base Station

R

D1

D2

D3

D4

D5

D6


Cochannel Interference Ratio (CCIR)

Cochannel interference ratio is given by

• Ik is co-channel interference from the kth co-channel interfering cell.

• M is the maximum number of co-channel interfering cells Techniques to reduce CCIR

• Cell splitting• Cell sectoring


1

Carrier

Interference M

kk

C C

I I


Cell Splitting

Depending on traffic patterns, the smaller cells may be activated/deactivated in order to efficiently use cell resources.

Smaller cell size, smaller transmitting power, and reduces cochannel interference


Large cell (low traffic density)

Small cell (high traffic density)

Smaller cell (higher traffic density)


Cell Sectoring by Antenna Design


(a). Omni

120o

(b). 120o sector

a

b

c120o

(c). 120o sector (alternate)

ab

c

(d). 90o sector

90oa

b

c

d

60o

(e). 60o sector

a

bc

d

e

f


The CCIR in the worst case for 3-sectors

is the propagation path loss slope and = 2 ~ 5


7.0qq

C

I

CBS

MS

R

D’

D

BS

BS

BS

D

RDq /

Worst Case for Forward Channel Interference in Three-sectors


The CCIR in the worst case for 6-sectors

is the propagation path loss slope and = 2 ~ 5


D+0.7R

MS

BS

BSR

RDq

q

C

I

C

/

7.0

Worst Case for Forward Channel Interference in Six-sectors



A

C

B

X

Cell Sectoring by Placing Directional Antennas at Three Common Corners


Homework

P5.5 P5.7 P5.11 P5.14 P5.15


wireless communication network lab. chapter 5 cellular concept chih-cheng tseng1ee of niu prof....

Documents

cell shapeee of niuchih

rr24rhexagonal cell

rpr22prtriangular cell

size of cell

cheng tseng4select cell

cheng tseng3shape

cheng tseng9handoff

actual cell tiling