FREQUENCY REUSE

Cellular Concepts

Frequency Reuse (I)

Frequency Reuse (II)

Frequency Reuse How many cells must intervene

between two cells using the same frequency?D: Minimum distance between centers of cells that use

the same band (co-channels)R: Radius of a celld: distance between adjacent cells (d=3 R)N: Number of cells in a repetitious pattern (reuse factor)

D/R = √(3N)or D/d = √N

Frequency Reuse is the core concept of cellular mobile radio

Users in different geographical areas (in different cells) may simultaneously use the same frequency

Frequency reuse drastically increases user capacity and spectrum efficiency

Frequence reuse causes mutual interference (trade off link quality versus subscriber capacity)

Channel Reuse The total number of channels are

divided into K groups.› K is called reuse factor or cluster size.

Each cell is assigned one of the groups. The same group can be reused by two

different cells provided that they are sufficiently far apart.

Example: K = 7

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Frequency Reuse

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

Reuse distance D

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Reuse Distance

F1

F2

F3

F4F5

F6

F7

F1

F2

F3

F4F5

F6

F7

F1

F1

Reuse distance D

• For hexagonal cells, the reuse distance is given by

RND 3

R

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

NRDq 3

• Reuse factor is

Cluster

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Reuse Distance (Cont’d)

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

22 jijiN

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.

i

j

60o

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Reuse Distance (Cont’d)

(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=2i=2

i=2i=2

Frequency Reuse (III)

Co-Channel Cells

Finding the Nearest Co-Channel

(1) Move i cells along any chain of hexagons

(2) Turn 600 counter-clockwise and move j cells, to reach the next cell using same frequency sets this distance D is required for a given frequency reuse

to provide enough reduced same channel interference ie, after every distance D we could reuse a set of

frequencies in a new cell

Co-Channel Cells

Cellular Frequency Reuse Concept

Prof. Sridhar Iyer Session: 22.21

Coordinate System

Use (i,j) to denote a particular cell.

Example:

Cell A is represented by (2,1).

A

Prof. Sridhar Iyer Session: 22.22

R D

Distance Formula

RK

RjijiD

3

)(3 22

22 jijiK

Note: i and j are integers

where

Reuse factor

Relations between Cluster Size and i, j

Relations between Cluster Size and i, j

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D

L * iL * j

r

In this case: j=2, i=1

Compute D based on “law of cosine”

NijjirD

ijjiLD

jiLjLiLD

jLiLjLiLD

3)(3/

)(

)5.0(2

)3/2cos())((2)()(

22

2222

222222

222

rL 3

How frequency Reuse Increases Capacity

Example:A GSM communication system uses a frequency reuse

factor of 1/7 and 416 channels available. If 21 channels are allocated as control channels, compute its system capacity. Assume a channel supports 20 users

Channels available for allocation = 416 - 21 = 395Number of cells = 395 / 7 = 57Number of simultaneous users per cell = 20 x 57 = 1140

Number of simultaneous users in system = 7 x 1140 = 7980

Cell Planning Example Suppose you have 33 MHz bandwidth

available, an FM system using 25 kHz channels, how many channels per cell for 4,7,12 cell re-use?

total channels = 33,000/25 = 1320 N=4 channels per cell = 1320/4 = 330 N=7 channels per cell = 1320/7 = 188 N=12 channels per cell = 1320/12 = 110

Smaller clusters can carry more traffic However, smaller clusters result in larger

co-channel interference

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Practical deployment issues Location to setup antenna

› Antenna towers are expensive› Local people do not like BSs

Antenna/BS does not look like antenna/BS Antenna

› Omni-directional› Directional antenna

Remarks on Reuse Ratio

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Cochannel Interference

Mobile Station

Serving Base Station

First tier cochannel Base StationSecond tier cochannel

Base Station

R

D1

D2

D3

D4

D5

D6

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Cochannel Interference

Cochannel interference ratio is given by

M

kkI

CceInterferen

CarrierIC

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

÷ø

öçè

æ

M

k

kR

D

C

I

C

1

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

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Worst Case of Cochannel Interference

Mobile Station

Serving Base Station Co-channel Base Station

R

D1

D2

D3

D4

D5

D6

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